THE JOURNAL OF THE ALABAMA ACADEMY OF SCIENCE VOLUME 77 JANUARY 2006 NO. 1 Platanthera ciliaris Photo courtesy of Pete Conroy This rare orchid is found in the wettest portion of the bog, often growing out of the perennially wet Sphagnum layer. Because of its rarity and sensitivity to slight wetland disturbances, this orchid is a candidate for listing on the federal endangered species list.” THE JOURNAL OF THE ALABAMA ACADEMY OF SCIENCE AFFILIATED WITH THE AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE VOLUME 77 JANUARY 2006 NO. 1 EDITOR: Safaa Al-Hamdani, 700 Pelham Rd North, Jacksonville State University, Jacksonville, AL 36265-1602 ASSISTANT TO THE EDITOR: Sue C. Bradley, 2073 Evergreen Drive, Auburn, AL 36830 ARCHIVIST: Troy Best, Department of Zoology and Wildlife Science, Auburn University, AL 36849 EDITORIAL BOARD: Thane Wibbels, Chair, Department of Biology, University of Alabama at Birmingham, Birmingham, AL 35294 David H. Myer, English Department, Jacksonville State University, Jacksonville, AL Prakash Sharma, Department of Physics, Tuskegee University, Tuskegee, AL 36088 Publication and Subscription Policies Submission of manuscripts: Submit all manuscripts and pertinent correspondence to the EDITOR. Each manuscript will receive two simultaneous reviews. For style details, follow instructions to Authors (see inside back cover). Reprints. Requests for reprints must be addressed to Authors. Subscriptions and Journal Exchanges: Address all Correspondence to the CHAIRMAN OF THE EDITORIAL BOARD ISSN 002-4112 BENEFACTORS OF THE JOURNAL OF THE ALABAMA ACADEMY OF SCIENCE The following have provided financial support to partially defray publication costs of the journal. AUBURN UNIVERSITY BIRMINGHAM-SOUTHERN COLLEGE UNIVERSITY OF MONTEVALLO AUBURN UNIVERSITY AT MONTGOMERY UNIVERSITY OF SOUTH ALABAMA TROY STATE UNIVERSITY UNIVERSITY OF ALABAMA AT BIRMINGHAM JACKSONVILLE STATE UNIVERSITY SAMFORD UNIVERSITY UNIVERSITY OF ALABAMA TUSKEGEE UNIVERSITY UNIVERSITY OF NORTH ALABAMA Journal of the Alabama Academy of Science, Vol. 77, No. 1, January 2006. CONTENTS ARTICLES Examining the Relationship Between Sprawl and Neighborhood Social Conflicts in Alabama James O. Bukenya, Ericka Branch and Constance Wilson . 1 Fibrinogen Levels in Polycythemia Vera Patients and Hematocrit Target For Performing a Therapeutic Phlebotomy in Southwest Alabama Virginia C. Hughes, Alice L Anderson and Doris C. Davidson . 13 A Novel Approach to Model Turbulence Part I: Theoretical Formulation . 18 Abdel K. Mazher BOOK REVIEW The Search for Human Immortality: The Biology and the Ethics . 32 Jaime Bres and James T. Bradley BIOGRAPHY W. Peter Conroy, Director of Jacksonville State University’s Environmental Policy and Information . 36 MINUTES of Executive Committee Meeting . 38 Journal of the Alabama Academy of Science, Vol. 77, No. 1, January 2006. EXAMINING THE RELATIONSHIP BETWEEN SPRAWL AND NEIGHBORHOOD SOCIAL CONFLICTS IN ALABAMA James O. Bukenya* Ericka Branch Constance Wilson Department of Agribusiness and Community and Urban Planning Alabama A&M University Normal, AL ABSTRACT The paper examines the relationship between sprawl and neighborhood social conflicts between non-farm residents and farmers in north Alabama. The analysis is based on 2000 census data and 2004 data from a multi-county survey of farmers in areas where sprawl has been identified as a problem. Sprawl is measured through residential density and new development within five miles of a farm while neighborhood social conflicts are measured using two different measures. The findings have policy implications and shed some light on the ongoing social conflict between non-farm residents and farmers in Alabama. INTRODUCTION As the United States has become increasingly urban, with approximately 79 percent of the population currently residing in urban areas, residential and commercial development has spread further from city centers, consuming more agricultural land in traditionally rural areas (Barnard, 2000; Plantinga and Miller, 2001, p. 56). The unplanned, relatively low density growth (known as sprawl) is often characterized by discontiguous residential development (often interspersed with idle land, and often connected by commercial corridors along busy roads) that relies on automobiles for transportation. The level terrain that makes farmland advantageous for agricultural production also makes these lands attractive for housing and commercial uses (Barnard, 2000). Over time, this conversion process could have implications on quality of life, preservation of small and family farms and sustainable agricultural production, as well as on public interests of open space, farming tradition, and landscape preservation standards (Hailu, 2002; Carver and Yahner, 1996). Of interest in this paper is the relationship between sprawl (measured through residential density and new development within five miles of a farm) and neighborhood social conflicts between non-farm residents and *Contact author 1 Bukenya, et al. farmers in northern Alabama. At the present time, farmers in northern Alabama, like many others across the country, are fighting to retain land for agricultural purposes. Sprawl in Alabama Sprawl is dispersed development outside of compact urban and village centers along highways and in rural countryside. In Alabama, sprawl has taken two main forms: urban sprawl in the form of expanding urban areas that have pushed outward into the countryside at densities of 1500 or more people per square mile, and scattered residential sprawl outside established settlements at densities of 500 to 1500 people per square mile. Even though the state and local governments have devised efforts to reduce the opportunity costs of farming in areas where cities have encroached, the problem is proving to be overwhelming, especially at the periphery of the state’s largest metropolitan areas (Table 1 ). The seriousness of the issue is highlighted by recent statistics showing that over the last 20 years, sprawling development patterns have resulted in the conversion of more than four million acres of farmland in Alabama (Crew and Runge, 2000). According to the National Resources Inventory, a project of the Department of Agriculture, Alabama ranked 13th among states in the amount of rural land that was converted to urban uses between 1992 and 1997. During that 5 year span (92-97) 445,300 acres were converted at an average annual rate of 89,060 acres per year (NRI, 2000). Additionally, agricultural land was converted at five times the rate of population growth over this period (Figure 1), an indication of increased competition for incompatible uses of agricultural land in Alabama. Table 1. Index of sprawling metros by population in Alabama Metro area Sprawl index score Population in 1999 Pop. % in urbanized areas in 1999 Rank Change 1990 - 1999 Rank Index for metros with population of 250,000 to 1 million Mobile 433 536,301 58.60% 178 -7.10% 255 Huntsville 381 343,820 59.10% 175 -3.90% 206 Birmingham 323 913,565 71.10% 114 -4.00% 209 Montgomery 322 323,675 69.20% 124 -3.70% 198 Index for metro areas with populations of fewer than 250,000 Anniston 320 117,136 57.40% 186 -2.30% 134 Dothan 255 134,980 46.50% 247 3.30% 8 Florence 220 137,612 53.90% 207 2.40% 13 Gadsden 170 104,326 71.60% 112 -0.30% 58 Auburn- 157 101,903 66.10% 142 2.00% 15 Opelika Tuscaloosa 129 161.726 71.80% 111 1.50% 18 Source : USA Today. 2001 2 Sprawl and Neighborhood Conflicts 25% 20% 15% 10% 5% 0% Change in Population Change in Developed Land Data Source : National Resource Inventory, US Census Bureau Figure 1. Comparison of population growth to increase in developed land in Alabama, 1992-97 According to a report issued by the Sierra Club on sprawl (Sierra Club Sprawl Report, 1999), Alabama lags far behind neighboring states in planning for land-use and transportation (Table 2). Additionally, urban sprawl is quickly becoming a major environmental issue throughout Alabama as statistics show the rapid conversion of forests and farmland into built up areas. For example, in a report by the Mobile Register (as quoted in the Bama Environmental news, BEN, 1999, October 6), Mobile County's rural to urban land conversion has outpaced population by a margin of four to one since 1975. While the county's population grew by 25% from 320,000 to 400,000 in two decades the amount of urbanized land in the county has grown from 82,000 acres to more than 170,000 acres (BEN, 1999). In another report by an organization which promotes "Green Plans", the Resource Renewal Institute, Alabama ranks poorly in "Green Planning". In the report, Alabama ranked 50th, according to the group's Green Plan Capacity (GPC) Index1. Additionally, in a published index of sprawling metros by state, Mobile and Huntsville metros’ sprawl index scores are among the highest in the nation for metros with population of 250,000 to one million (USA Today, Feb. 21,2001). Consequences of Sprawl in North Alabama In northern Alabama, the increasing demand for these non-agricultural land uses has fragmented the agricultural land base and has driven up land values, as the “market value” for such non-agricultural land-use is normally significantly higher than the value of the land for agricultural production. The new land-use patterns in the region feature (1) Single-family houses on large lots— anywhere from 1/4 acre to 10 acres; (2) Elaborate road networks to serve 3 Bukenya, et al. Table 2. How Alabama ranked and fared with its neighbors in planning for land-use and transportation. State Rankings State Land Use Planning Transportation Planning Open Space Protection Community Revitalization Alabama 42nd 47th 37th 22nd Georgia 4th 24th 24th 6th Tennessee 6th 46th 34th 39th Florida 11th 29th 14th 13th Mississippi 31st 49th 36th 14th Source : The Sierra Club national report, 1999. auto and truck travel; and (3) Huge shopping malls and office parks. The negative impacts of the new land-use patterns are most readily felt on the farm in terms of a reduction in the number and size of farms, an increase in the average age of farmers (with fewer young people venturing into fanning), a general weakening of resource-based rural economies, and a variety of other economic and social problems (NASS, 2001; Workman and Allen. 2002). such as neighborhood social conflicts. Neighborhood social conflicts can arise between urban neighbors using secondary roads as commuter routes and farmers traveling to and from distant fields with farm equipment. Other problems for farmers can include increased incidence of vandalism and theft, including damage to crops from urban neighbors driving through fields. Nuisance complaints may also increase as more neighbors voice opposition to the sounds and smells of t\pical agricultural operations (Barnard. 2003). Land Use Conflicts Land use conflicts (usually defined by a use that is incompatible with or acts as a nuisance to other property owners) result when one person interferes with the way that another person wants to use land. These conflicts are, of course, two-sided (Table 3). Agricultural operations can interfere with residential uses while non-farming rural dwellers can hinder the use of land for agricultural purposes. These conflicts increase as more and more rural non¬ farmland use activities take place and additional people move into agricultural areas. Any one of a number of land use conflicts can arise, and the problem is compounded by the fact that these conflicts tend to occur simultaneously (Green County Farmland Preservation Plan, 2000; Roakes, 1996; Dowling, 2000). Land use conflicts, or nuisances, may include the following: residents' complaints (that may become law suits) or zoning related complaints over farm odors, flies, noise, dust, chemicals and pesticide spraying; predation of livestock by domestic pets, especially dogs; indiscriminate refuse disposal and littering; trespassing, theft and vandalism; traffic congestion; and significantly altered traffic patterns. Highway improvements necessitated by increased traffic can also result in farmland being taken out of production for road widening. Additionally, farmers can be held financially responsible for any damage caused to residential 4 Sprawl and Neighborhood Conflicts areas by wandering farm animals. Coping with these nuisances has proven highly annoying as well as financially burdensome for farmers (Green County Farmland Preservation Plan. 2000; Raad and Kenworthy. 1998; Jakle and Wilson. 1992). Table 3. Positive and negative impacts of proximity of farms to urban areas Positive Impacts of Urbanization on Farming Negative Impacts of Urbanization on Farming Proximity to urban centers may provide a larger pool of seasonal or part-time labor that is especially important to harvest high- value crops. o One reason metro farms can adopt high- value crops is that local sources of labor are available at peak periods (Jordon. 1989). Greater off-farm employment opportunities for the farmer or his/her family may help support the farming operation (Stallman and Alwang, 1991). o Opportunities from urban employment run in both directions. People in urbanizing areas may work part time on the farm or start recreational farms that eventually develop into full-time, part- time, or retirement businesses. Suburban neighbors' complaints about farm odors and chemical spray ing may force farmers to turn to enterprises that produce fewer negative side effects. o Some of the alternative enterprises w ill be more profitable and some will be less profitable (Revnnells, 1987; Van Driesche et al., 1987). ' Markets for traditional dairy products or field crops may be reduced, as milk-collection routes are curtailed and grain elevators go out of business. o In some areas, farm input suppliers, machinery dealers, and other forms of agricultural support may decline. • Nationally, 90 percent of average farm household income was from off-farm sources in 1999, including part-time employment, spousal income, and other business income. o The percentage in recent years has varied from 83 to 90 percent. • Expanding populations provide opportunities for farmers to grow new crops and to market them in new ways, such as through farmers’ markets (Price and Harris, 2000). o High-value crops, such as fresh fruits and vegetables, can be sold through restaurants and gourmet grocery outlets or directly to consumers in roadside stands or U-pick operations. Conflicts can arise between growers and new suburban neighbors over early morning noise, and increased traffic can hinder farmers’ ability to move their equipment along overcrowded rural roads being used as commuter routes. Real estate taxes may rise as land prices rise to reflect the potential for non-farm development. Growers may face increased pressure from water- and land-use restrictions. Farms may face deteriorating crop yields from urban smog, theft, and vandalism 5 Bukenya, et al. METHODOLOGY Data To accomplish the study objective, we analyzed 2000 Census data and 2004 data from the multi-county survey of farmers and land owners of agricultural lands in areas of north Alabama where sprawl has been identified as a problem. The survey collected information on issues encountered by farmers, which can serve as proxies for neighborhood social conflicts, and the census block group of each respondent (Table 4). The questionnaire was mailed to a non-random sample (convenience sampling) of about 400 farmers and owners of agricultural lands in north Alabama in Spring 2005. The sample was drawn from a list of farmers and 'j owners of agricultural land in 20 counties in north Alabama (Figure 2). The list of the farmers and land owners was obtained from the data base of the Small Farms Research Center3, Alabama A&M University. The initial response rate was 30 percent. A follow-up reminder with a replacement questionnaire was mailed out to 273 of the non respondents. The response rate was 17 percent from the follow-up. Thus, the analysis is based on the overall response rate of 41.5 percent. The descriptive statistics indicate that the majority of the respondents (58.3 percent) in the sample are white, while 33 percent are black and 8.7 percent are Native Americans. Looking at the age distribution, 35 percent of the respondents are between 60-70 years old while 25 percent, 30 percent and 10 percent are between the ages of 50-59, 30-39, and below 30 years, respectively. In reference to education, 45 percent of the respondents have a high school diploma or less, 25 percent have some college education while 30 percent have a bachelors degree and above. As for off farm employment, 47 percent of the respondents indicated holding employment outside of farming. The mode category for acres of land owned/operated by the respondents is 21-40 acres. Overall, the data represent individuals who are mostly white, educated and fairly old farmers/agricultural land owners. Table 4. Descriptive statistics — MSA’s in North Alabama Variable Minimum Maximum Mean Stand. Dev. Density 28.10 857.80 307.75 214.76 Poverty rate 0.34% 48.72% 12.03% 8.41 Drove to work alone 63.28 96.82 84.05 7.62 Farm size Less than 20 acres 250 acres 77.5 acres 123.8 Number of conflicts 0 13 5 4 Econometric Approach Using survey responses, two dependent variables measuring neighborhood social conflicts were developed: 1) Whether or not the survey respondent had encountered any neighborhood social conflict (based on responses to questions asking respondents whether they have encountered complaints from non-farm residents about “nuisances” that come with living in an agricultural area or had encountered any problem resulting from urban growth); and 2) the number of such conflicts, ranging from zero to thirteen. 6 Sprawl and Neighborhood Conflicts Figure 2. Map of Alabama showing the surveyed counties The first group of independent variables is drawn from the 2000 census block group data and consists of census block group density, the proportion of individuals in the neighborhood who drive to work alone, and census block group poverty rate. The second group, which consists of presence of new development within five miles of a farm along with respondents’ age, gender, race/ethnicity, educational attainment, household incomes, farm size, tenure type, family structure, and length of time at present residence, is drawn from the questionnaire. Because of the small sample size, however, and the need to increase the statistical power of the model, only five variables (2000 census block group density, the 7 Bukenya, et al. proportion of individuals who drive to work alone, 2000 census block group poverty rate, presence of new development within five miles or less from a farm, and farm size) are included in the analysis. Model 1: Binomial Probit Model Model 1 is a binomial probit equation which assumes that while we observe only the values of 0 and 1 for whether or not the survey respondent had encountered any neighborhood social conflict (CONF), there is a latent, unobserved continuous variable CONF that determines the value of CONF. We assume that CONF can be specified as follows: CONF, = /?„ + P\XXi + p2x2i + ... + pkxkl + u, (1) and that: CONF ; = 1 if CONF* > 0 CONFl = 0 otherwise where xg x2, ... X|< represent vectors of random variables, and u represents a random disturbance term. Now from equation 1 , Pr {CONFj = 1) = Pr(/?0 + /?,*„ + p2x2, + ... + Pkxh + u, > 0) (2) Rearranging terms, Pr (CONF, = 1) = Pr(w, > -(/?0 + + P2x 2, +... + fikxkl)) = 1 - Pr(w; <-(/?0 +P[xu+P2x2l + ...+ /VJ) (3) = 1-F(-(A) + P] *1, + P2X 2/ + — +PkXkl)) where F is the cumulative density function of the variable u. By asserting the usual assumption that u is normally distributed, then: Pr(CCWF, = 1) = 1 - O(-(/?0 + Pxxu + p2x2i + ...+ pkxkl)) = 1 -(S>(-X,p) (4) = ®(XIP) where d> represents the cumulative normal distribution function. Using maximum likelihood technique, the estimates of the coefficients ((5s) and their corresponding standard errors that are asymptotically efficient are computed. The probabilities of an individual for each response category are given by: Prob [CONF, = 0] = - aX] (5) Prob [CONFt = 1 ] = Q>\jd | -aX] - o[/i0 - aX ] (6) with a = (3/a and 0 j I E c a> O) o c •c £ 123456789 10 Patients — HCT Fibrinogen] Fig 1. Fibrinogen concentration versus hematocrit in polycythemia vera patients. HCT = hematocrit DISCUSSION The Polycythemia Vera Study Group (PVSG) was organized in 1 967 to identify the optimal approach to the diagnosis and treatment of PV (Streiff et al., 2002). In a survey conducted in 2000 by PVSG, investigators found that of the physicians who treat PV with TP, most respondents of the survey used a target hematocrit of 44% or less for phlebotomy therapy. Approximately 24% of physicians used a hematocrit target of 42%, 61 % used a target of 44% , 1 5% used a target of 50%, and only 2% used a target of 55% (Streiff et al., 2002). Although an initial target hematocrit of 52% for TP was originally set by the PVSG (Berk et al., 1981 ), recent literature suggests the PVSG has discontinued using the target hematocrit number and has instead focused on a hematocrit value post-treatment: maintain the hematocrit at less than 45% (Stuart et al., 2004). This is due in large part to an increased risk of thromboses with high hematocrits (Solberg et al., 2002). It was clear from the patients enrolled in this study that symptoms such as excessive itching and abdominal discomfort occurred at much lower hematocrits than 52%, prompting a physician’s order for a TP. Other therapies for treating PV patients include myelosuppressive agents such as chlorambucil, radioactive phosphorus (32P), hydroxyurea, and interferon-gamma. Plateletpheresis may also be used to reduce a markedly elevated platelet count. The only cure for PV is a bone marrow transplant. In this study, nine out of ten patients exhibited adequate levels of fibrinogen in their plasma. The patient with the low fibrinogen level had a hematocrit above 55% with a concomitant lower plasma concentration of fibrinogen. With the majority of physicians ordering TP’s at hematocrits 16 Therapeutic Phlebotomy less than 55%, it seems unlikely that the anticoagulant volume is corrected on a routine basis. Plasma from a TP is routinely discarded and could be used in a clinical laboratory setting as controls in coagulation testing or in proficiency testing, or further processed to make buffy coats (concentrated white blood cells and platelets) or a variety of plasma products (i.e. cryoprecipitate) to be used in research. Unlike the scenario with HH patients, this blood could not be used for in vivo use or transfusion to other patients as PV is a form of cancer and can transform into leukemia With a PV incidence of 2.3 per 1 00 000 in the general population and TP as the most common treatment, blood that is discarded from this procedure could be used in many other facets of medicine. LITERATURE CITED Berk, P.D., J.D. Goldberg, M.N. Silverstein, A. Weinfeld, P.B. Donovan, J.T. Ellis, S.A. Landaw, J. Laszlo, Y. Najean, A. V. Pisciotta, and L.R. Wasserman. 1981. Increased incidence of acute leukemia in polycythemia vera associated with chlorambucil therapy. New England Journal of Medicine 304: 44 1 -447. Brittenham, G.M., H.G. Klein, J.P. Kushner, and R.S. Ajioka. 2001 . Preserving the national blood supply. Hematology 1 : 422-430. Solberg, L.A. 2002. Therapeutic options for essential thrombocythemia and polycythemia vera. Seminars in Oncology 29(3 Suppl 10): 10-15. Spivak J.L., G. Baroki, G. Tognoni, T. Barbui, G. Finazzi, R. Marchioli, and M. Marchetti. 2003. Chronic myeloproliferative disorders. Hematology (American Society of Hematology Education Program) 200-24. Streiff, M.B., B. Smith, J.L. Spivak. 2002. The diagnosis and management of polycythemia vera in the era since the polycythemia vera study group: a survey of American Society of Hematology members’ practice pattern. Blood 99: 1 144-1 149. Stuart, B.J., and Viera, A.J. 2004. Polycythemia vera. American Family Physician 69: 2 1 39-44. Vaquez, J.M. 1892. Sur une forme speciale de cyanose s’accompagnant d’ hyperglobulie excessive ET peristante. Social Biology (Paris) 44: 384-388. 17 Journal of the Alabama Academy of Science, Vol. 77, No. 1, January 2006. A NOVEL APPROACH TO MODEL TURBULENCE PART I: THEORETICAL FORMULATION Abdel K. Mazher Aerospace Science Engineering Department Tuskegee University Tuskegee, AL 36088, ABSTRACT This paper describes a novel unifying formulation of turbulence modeling via the optimal control theory. In this formulation, Reynolds stresses are considered control variables while the averaged velocities are considered state variables. The Reynolds stresses are selected to optimize a performance index with the averaged Navier-Stokes (N-S) equations as constraints. The main problem of the new approach is the selection of the performance index to model diverse turbulence problems. The key feature in this approach is the selection of a performance index to represent the information about flow field and geometry implicitly. This stands in contrast to the classical turbulence modeling that proposes explicit models, which differ according to the flow problem and the geometry. The entropy concept is utilized to formulate the performance index. Entropy is related to the turbulence data, as described by probability density function of the velocity field. Entropy is taken as a measure of the information losses that result from averaging. Turbulence model is calculated to optimize the entropy and to satisfy the averaged N-S equations. The paper describes the mathematical formulation of turbulence modeling and the idea of information content of differential equations. Also, it outlines the new research problems related to this novel approach. BACKGROUND It is postulated that N-S equations, the geometry of the flow field, boundary and initial conditions describe the turbulent flow field completely. Turbulent flow field is computed numerically either by integrating the full N-S equations or by integrating an averaged N-S equations. The averaged N-S equations contain unknown terms called Reynolds stresses. Reynolds stresses are described in advance, in specific mathematical forms called turbulence models, to solve the closure problem of turbulence. Models range from an algebraic and differential equation models to the sub-grid models of Large Eddy Simulation (LES) technique (Brachet et al., 1986; Durbin and Reif, 2001; Dwoyer et al., 1985; Ferziger, 1987; George and Arndt, 1989; Godeferd et al., 2001; Hunt et al. 2001; Leonard and Hill, 1988). Selecting a turbulence model depends on the problem and differs from application to application. It is a heuristic procedure that combines physical insight, engineering sense and experience. There is no rigorous procedure to select a model for a given fluid flow problem. 18 Mazher The closure problem of turbulence is the result of averaging the convective nonlinear terms of N-S equations. Reynolds stresses appear as new source terms in the averaged equations. To integrate these equations, models of Reynolds stresses are selected empirically. The assumed terms add information to the equations from sources other than N-S equations. Successful models must be consistent with the information contents of N-S equations. This means that, to solve the averaged N-S equations properly the turbulence models must be consistent with information content of the full N-S equations. In an attempt to establish a systematic and unified modeling approach for turbulent model selection, the optimal control methodology is proposed. In this approach, a performance index must be specified in advance to complete the problem formulation. It is suggested that a performance index, which measures the information loss caused by averaging, is a good candidate. When averaging the flow field equations, certain information disappears and other terms appear. The additional terms (Reynolds stresses) must somehow include part or all of the information that disappeared by averaging. To have a consistent model of turbulence, an information measure of N-S equations should be defined. This information measure may explain where information goes when N-S equations are averaged and how to retrieve it through proper selection of Reynolds stresses. The Probability Density Function (PDF) of the velocity field is suggested as the information measure as it is used in the entropy definition of information theory. The maximum entropy method is employed by many investigators of spectrum analysis ( Childers, 1978) to generate more data points from a limited record of data in such a way that keeps the information content of the limited record of data unchanged. The novel approach presented in this paper outlines the possibility of modeling turbulence by utilizing the maximum entropy concept to justify the turbulence models. The turbulence-modeling problem is formulated using the optimal control theory. The averaged N-S equations are considered the dynamical constraints, the Reynolds stresses are considered control variables, and the information measure is considered as the performance index. Since the averaging of N-S equations does not conserve information, a more general formulation of a measure of the information content of N-S equations is required. In this case, the information measure of N-S equations may represent the losses of information due to averaging. If the information measure is expressed as a functional of Reynolds stresses, the averaged velocity, and the gradient of the averaged velocity, then the turbulence model is computed to minimize information losses subject to the averaged N-S equation. Formulating turbulence modeling using optimal control techniques will help to unify the turbulence¬ modeling problem and suggests a scheme that can be used to understand the turbulent models used in literature. But the main issue here is the quantitative formulation of information measure. TURBULENCE AND CLOSURE PROBLEM It is postulated that for homogeneous and isotropic fluids (Newtonian fluid), N-S equations describe completely the turbulence. This means that given the geometry, the flow conditions, and the proper initial and boundary condition, the solution of the N-S equations gives the full picture of turbulence. Solving full N-S equations for 3D turbulence is a very difficult problem. This difficulty is the result of the lack of a general theory of nonlinear phenomena and the difficulty of resolving the different scales of turbulence computationally. For Eulerian formulation, let the spatial coordinates be Xj, i=l, 2, 3. Also, let the velocity components, the density and the pressure be V; , p and P respectively. For incompressible, unsteady 3D flow, the equations of fluid motion are given as follows: 19 Turbulence Modeling Mass conservation: dx i (1) Momentum conservation: dVi TdV i dP d2V i A. + Vj — — b — — - v — — — — = 0, z = 1,2,3 cbc; p dx, dxjdxi (2) Let the velocity components and the pressure be separated into mean (Uj and PP) and fluctuating quantities (u; & p): Vj = Uj + u; P = PP + p Where the mean quantity is defined as follows: Ui = — - — f wVtdt ti-t\ J (3) In the above equation, w is a weighting function. From the definition of averaging, the average of any fluctuating quantities is zero. The averaging time is long compared with the time scale of the turbulent motion. In transition problems, t2-tj has to be small compared with the time scale of the mean flow. Using the above decomposition, with w =1, the averaged N-S equations can be written as follows: dU, dx, = 0 (4) dU, TT dU, 1 dPP d2Ui - + Uj - + - - v - 5t dx i P dx, dxjdx, - — (uni/) = 0 ,i = 1,2,3 dXj (5) Averaging nonlinear terms leads to the appearance of additional Reynolds stresses terms UjUj. Since equations (1) & (2) contain more variables, more equations are required to describe the additional terms and to close the system of equations. Closing the problem by selecting Reynolds stresses is called turbulence modeling. Researchers use empirical, semi- empirical, or analytical formulae for different models. These models include algebraic models, one-equation models, one and half-models, k-e or two-equation models, and LES sub-grid models (Mathiew, and Scott, J. 2000; Braza and Dussauge, 1998; Monin, and Yaglom, 1971; Orszag and Kells, 1980; Piquet, 1999; Pope, 2000; Rodi, 1980; Wilcox, 1994). Selection of the model depends on the experience, the flow conditions, and the geometry. Turbulence models add information from outside sources other than N-S equations. This addition, 20 Mazher consistent or inconsistent with the full N-S equations, may explain the difficulties of selecting the proper model. TURBULENCE MODELING VIA OPTIMAL CONTROLS THEORY The variational approach will be proposed here as a tool to unify turbulence modeling problems. Define the mean values Uj & PP as the state variables, and x, y, z & t as the independent variables. Let the control variables be y] = U]\ y2 = UiU2, y3 = U]U3, y4=u22, y5= u2u3 & y6=u32. Let T be a control vector with six elements, and U is the velocity vector with three elements: r= [yi y2 yj Y4 ys y6lr u= [U, U2 U3]t The turbulence modeling problem is formulated as follows. Find the six control variables (YrY6) to optimize the functional: I = \ \ \\ <£> dx dy dz dt Subject to the constraints: dUx dUi dU 3 n - + - + - = 0 dx dy dz (6) (7) dU, „ dU i „ dU i „ dUx i dPP -Jt72„ d , . d , . d dt = U x dx + U 2- dy U 3 - + _ „ « -vv U'+—(rx)+— (r2) +—(ri) w dz P dx dx dy dz dUi TT dUi rr dU 2 TT dU 2 i dPP xj2t j d d f . d a/ av ay az ay ac 2 ay dz 5 at/s ,, ai/3 rr at/3 rr at/3 i apa n2n a . . a, . a, , _ - = - + f/2 - + f/3 - + a - vV2t/3 + — (v,)+ — (y.) + — (/,) (10) dt dx dy dz P dz dx 3 ay 5 az /6 The LaGrange multiplier method is used to formulate the augmented functional, and the maximum principle (cf. appendix) is employed to derive the equations for the Reynolds stresses. The resulting equations for the Reynolds stresses are generally nonlinear. To complete the modeling problem, a well-defined O of the performance index (6) must be specified. The closure problem is mainly due to nonlinearity of the original equations. Hence, the nonlinear terms, convective terms of the N-S equations, will affect the turbulence model. Formulating the turbulence-modeling problem using the optimal control methodology reveals that the general mathematical structure of the model should be nonlinear. The general nonlinear structure of the turbulence model can be seen from the mathematical formulation of equations and constraints. This can be demonstrated by the following observations. The 21 Turbulence Modeling optimal control problem, which is described by a linear system of differential equations and quadratic performance index, leads to the nonlinear Riccati equation as solution for the control. The Reynolds stresses appear as a result of averaging the nonlinear convective terms of the N-S equations; therefore, the most suitable and general form of the model may be nonlinear to be consistent with the N-S equations. A COMPUTATIONAL ALGORITHM OF THE TURBULENCE MODEL In the direct methods, the solution of the averaged N-S equations is advanced in steps, from time tk to time tk+i , with integration time step At(k) = tk+i - tk. At every time step, initial and boundary conditions (IC/BC) are supplied and a turbulence model UjUj is required to integrate the system of equations (7)-(10). At each time step At(k), the following procedure is repeated from r=0 to a fixed value R: 1 . Assume any form for U;Uj (tk)rto advance the solution from Uj (tk) to U, (tk+i) r. 2. Calculate Ir = I (u^ (tk)r , Uj (tk+i)r ) 3. Select another form for UjUj (4)^' to advance the solution from U, (tk) to U* (tk+i) r+l 4. Calculate I r+1 = I ( (uiUj (tk)rfl , Uj (tk+i) ^ ) 5. Calculate 5Ir = I r+1 - Ir 6. Update uiiij(tk)r+2 = (1-0) UjUj(tk)r + 0 UjUjCtfc)^1 + y Sr, O<0 < 1 Sr, in step 6, is the direction of search for the optimum value of I, and y is the value of travel in S- direction to reduce 5Ir to zero. Let AUi(tk+1)r = Ui(tk+1)rf,-U,(tk+i)r A UjUj (tk)r= UjUj (tk+i) r+I - UjUj (tk+i)r Repeat steps 1 -6 for many values of r, the best solution is obtained when Limit AUj (tk+i) — > o(8), r — > R Limit AujUj (tk) r — > o(e), r-> R and 8Ir o(s) The behavior of AuiUj(tk)r can be investigated during the iterations using the following formula: A^Uj (tk) r = - A Up + ^ Up + °(£ )> P = 1»2,3 cllu dVUp 22 Mazher The initial selection of UjUj (tk)° can use a simple algebraic model. If a converged solution occurs, the same procedure is repeated for tk+2 , tk+3 , tk+N. A good starting guess for UjUj (tk+1)° for the next time step is UjUj (tk)R. In this dynamic modeling, a heuristic relation between UjUj (tk+]) and UjUj (tk) may speed up the convergence. SEARCHING FOR A POSSIBLE must be specified in advance. The argument of d> may contain the mean velocity, the mean velocity gradient, mean convected terms in addition to Reynolds stresses. From the literature it appears that there is no unique model for turbulence but there are different models depending on the application. The existence of a unique model depends of the definition of averaging and the existence and uniqueness solution of the N-S equations. Since the N-S equations are nonlinear there is no guarantee that there exists only one solution. On the other side it can be shown that for a large category of flow problems governed by incompressible assumption there is a unique solution, Ladyzhenskaya, 1969, Temam, 1981. In this case let us assume that there exists a unique solution of the N-S equations and hence an optimum turbulence model. Let the best selection of Reynolds stress be as follows: UjUj = UiUj0pl If we substitute u,Uj0p* into equation (5) the right hand side will be zero. For other selections the right hand side will not be zero. And the solution of (4) and (5) will not give the correct solution of the averaged values. Assume that for any selection other than UjUj0pt, the residuals of the momentum and continuity equations will be e„ e y, ez and e. Here, ex, e y, ez and e are the right hand side of equations (4) and (5). The Reynolds stresses can be computed to minimize the total squared residual errors as expressed by O = e2x + e2y + e2z + e2, i.e. i= mi < £ dU, dxi /=3 V = 1,2, 3, 4, 5,6. OZ Ufep 23 Turbulence Modeling Also, the Euler-LaGrange equations for Ui are: ao 0,5© a ao a , a© x a a© x - — (— ) - t-(ttt-) - t-Ctttt) - — (-tttt) + at/, a2 a/ at/, ax: at/// av at/// a? at//- , a© x a2 , a© x a2 a© x A . , „ „ , ( - ) h - ^ ( - ) 4 - t" ( - ) — 0,1 — 1,2,3 . abc2 dUiJ dy2 dlJUy dz 2 dlh-.. Turbulence Generation and Dissipation Model One of the goals of the present study is to find a quantitative formulation for ©. Since no specific performance index exists at present, the turbulent energy production (P) and dissipation (e) terms are considered for investigation. The turbulence budget is a good start for this search. Some results from the literature (Pope, 2000; Durbin and Reif, 2001; Mathiew and Scott, 2000) suggest that the dissipation and production distribution are similar in shape and have symmetrical distributions. Therefore, a suitable integrand of equation (6) should have the form: © =/(e,P) To account for the published results of turbulence budgets, a possible function can be written as a difference between two functions X & ( P) A suggested simple form is © = / (c, P) = a e2 - p P2 where a and p are suitable positive constants. More studies are needed to find the suitable function /. At present, the author is conducting pilot studies to check this form of © . Results of the pilot study focus on investigating the behavior of the dissipation term (e) and production term (P) for different turbulent models of different geometries. Information Losses Model In the optimal control formulation of turbulence modeling, a reasonable selection of a performance index ‘I* is required. Hence, the focus is changed from selecting a proper mathematical representation of Reynolds stresses to selecting a proper . In information losses model, ‘I’ is selected to represent information losses produced by averaging. Part of the losses appears as new terms ‘Reynolds stresses.’ Minimizing ‘I’ will produce appropriate Reynolds stresses that minimize information losses. Here © represents information losses of the averaged N-S equations. Then the problem of turbulence closure becomes the problem of the choice of © as information measure, which leads to the new concept of information content of differential equations. To use this model, a definition of the information measure of the N-S equations is necessary. In this case, the following questions must be answered: What is the information measure of the N-S equations? Does it exist? Can we find it? 24 Mazher Information Measure: Does It Exist? A mathematical model represented by the equations, boundary conditions, initial conditions, and geometry describe a physical phenomenon. It is postulated that an information measure of the system of differential equations exists that conveys basic features of the physics. Since the information about the field conveys physical characteristics, the information measure must be invariant under mathematical transformation of equations describing the physics. Averaging is a special type of transformation of equations. If the averaging is an invariant transformation with respect to the information, then we should be able to select Reynolds stresses to satisfy the invariance properties. If the average is not an invariant operation, we can select the Reynolds stress to minimize the amount of information lost by averaging. In the first case, finding a measure of information content requires finding the invariant quantities of differential equations and proving that information does not change by transformation. From the mathematical definition of averaging, it appears that, for non-linear equations, part of the information is lost by averaging. Since averaging does not conserve information, another measure of information losses needs to be defined. Finding O depends on answering the following: What are the invariants of nonlinear differential equations? And if the invariants do not exist, then how to define the information losses? Information Measure and the Invariants of Differential Equation In turbulence modeling, the nonlinearity of the N-S equations necessitates looking for invariant properties of nonlinear differential equations. Since invariants of a nonlinear equation is an unsolved mathematical problem, extending concepts from linear analysis may shed some light on finding the information measure of nonlinear differential equations. Then, as a first trial to find the invariants, the concepts of the eigen value and the trace of a matrix, as invariants of linear systems, can be extended to nonlinear systems. This issue requires more theoretical research. Averaging and Information Losses To study the information losses mechanism, an investigation of the process of averaging is required. In addition to that, investigating the different ways of representing a function using different mean values is essential. Averaging operation includes selection of time interval trt2 and weighting function (w in equation 3). It can be assumed that there is an optimum selection of the time interval and weighting function that lead to minimum information losses. On the other side, higher order averages or moments will represent more closely the real function and reduce the information losses. These averages may be included in the performance index that represents the information content of differential equations. Flere again, since the deterministic set of the N-S equations becomes indeterminate by averaging, the additional Reynolds stresses terms can be seen as a source of information losses. In this respect, an invariant property may be expressed as a function of different mean values of the flow field variables. This expresses information as an additive property by using more moments. Elements of Information Measure The assumed information measure is composed mainly of three terms. One term represents the geometry; the second term represents the initial and boundary conditions; the third term represents some invariant properties of the N-S equations. Since Reynolds stresses 25 Turbulence Modeling appear as a result of the nonlinear terms, some mathematical form derived from the convective term must be included in this term. Maximum Entropy Concept There is no single correct technique to calculate UjUj in absence of knowledge or information about the type of process that generates the turbulence. Information about a flow field and the probability density function of velocities are connected through the concept of entropy, Childers, 1978; Katz, 1967. This is because the probability of occurrence of an event is related to information about the event. Therefore, entropy, as a measure of the uncertainty described by a set of probabilities, will be taken as a guide to formulate the performance index in turbulence modeling. If UjUj is perfectly determined, i.e. no uncertainty exists, the entropy is zero and in all other cases the entropy is positive. Hence, entropy is taken as a measure of uncertainty in selecting the Reynolds stresses as it appears in the averaged N-S equations. By this selection, minimization of the entropy increases the possibility of selecting the right UjUj. A mathematical form of entropy that describes the turbulent field is required. Taking the definition of the entropy from information theory, Childers, 1978, we can demonstrate the similarities between the data representing the turbulence in fluids and the data representing the signal in information theory. The entropy as an information measure of a random signal is defined by the equation, S = ~ Xpi log pi (11) Entropy, as a measure of the uncertainty described by a set of probabilities pi, is a nonlinear function. Since it is hypothesized that the full N-S equations, geometry, initial and boundary conditions determine turbulence, then the entropy should be based on these equations as a source of generating flow field data. A heuristic definition of the S may be formulated if we consider the discrete form of the N-S equations as a source of generating velocity and pressure signals Vi and Pi with sampling intervals Ax, Ay, Az for each At. Given the PDF of the flow field, S in the above equation represents an information measure of the N- S equations. Some information will be lost as a result of averaging the nonlinear convective terms. Minimization means that we select the UjUj terms in such a way as to reduce the uncertainties or information not related to the N-S equations. That is, we minimize the losses in information due to averaging or due to inappropriate selection of Reynolds stresses. The use of the logarithm in equation (11) indicates that the information is an additive quantity. The entropy is zero for a deterministic system; i.e., all the probabilities p; are zero except, one which is unity. In that case, the system is perfectly determined and no uncertainty exists. This corresponds to the case of direct solution of the N-S equations. In all other cases, the entropy is positive. Entropy is then a measure of disorder in the averaged N-S system, and hence it suggests our ignorance about the mathematical structure of the turbulence stresses. In this sense, optimizing entropy is a procedure to select the turbulence model without adding any other information other than that given by the N-S equations. TURBULENCE MODELING ALGORITHM USING INFORMATION THEORY Maximum entropy concept (Childers, 1978) will be utilized to formulate the proper performance index. It is known that the probability of occurrence of an event (pfi is related to information. If P(V) is the probability density function of velocity distribution ( Monin and Yaglom, 1971; Pope, 2000) then 26 Mazher 1 = \ P(V ) dV Ui = / Vi />(V) dV UiUj + UjUj = l Vi Vj P(V) dV The last equation can be written as u^j = \ Vi Vj P(V) dV - J Vi P(V) dV \ Vj />(V) dV It can be shown that a formula of P(X) that satisfies the above equations is given by i-3 =3 j — 3 r(r)=exp(X«,r, + XlA/,r,)/zz ;=1 i=l 7= 1 zz = vyyv.dv^v 3 /=! /=1 y=/ =3 7=3 where or, and ptj are arbitrary functions. From the above equations, the averaged velocities and the Reynolds stresses are given by: U. = da, log(ZZ) u.u, = ' J % -k>g(ZZ)-U,U. ,i>j The turbulence modeling problem can be stated as finding the nine coefficients at and j at each point (x, y, z; t), to optimize the entropy S locally, where S(P) = -J/>(V) log P(V) dV subject to equations (7)-( 1 0) as constraints. The function S is a function of nine coefficients. s= S (a, , pu) The function S will be used in an iterative procedure to compute the Reynolds stress at each point. 27 Turbulence Modeling NEW AREAS OF RESEARCH In addition to the unifying mathematical formulation, the new approach has demonstrative capabilities that can be used to explain multitudes of turbulence models existing in the literatures. Despite the fact that the optimal control formulation of turbulence modeling is rational, logical, and consistent with basics of mathematics and physics, it needs proof. Additional measures must be proposed to prove the variational approach of turbulence modeling. To investigate the validity of the above idea, the following studies are new research topics: 1) Since no specific entropy function exists at present to represent the information content of the N-S equations, the following plan is taken. A kernel of the integral is formulated to measure the loss of the value of the velocity and the loss of the value of the direction cosines of the velocity vector due to averaging at specific space-time point (x, y, z, t). Assuming the validity of Boussinesq assumption, a selected number of problems from the literature using this assumption should be solved by a CFD code. For each specific problem, different models are used and the assumed entropy functional is computed. The pilot studies will be focused on investigating the behavior of the entropy functional for different turbulent models of the same problem. The same study will be repeated for other problems. 2) Another study will use analogy to form similar to the entropy and define the probability using the discrete velocities. In this formulation, turbulence is considered a random phenomenon and the entropy is taken as a measure of turbulence randomness. 3) A third study will focus on the probabilistic formulation as a formal mathematical approach and solve for the PDF using the maximum entropy formulation. 4) A fourth study will focus on discovering the ways by which the information disappears by averaging. Simple turbulence problems will be selected and numerical integration of the full and the averaged N-S equations will be employed to solve the problem. Repeating the procedure using different models will help answering the following question: where does the information go when we average the N-S equations, and how can it be recovered through the controlled selection of the model to minimize the losses of information during averaging process? 5) The ultimate mathematical proof focuses on the selection of to produce the familiar algebraic and differential equation models. Another problem is the derivation of Boussinesq hypothesis using quadratic form of the Reynolds stresses. 6) A computational algorithm and CFD code to solve the turbulence modeling based on equations (6)-( 10) will be developed. CONCLUSION This paper presents a general mathematical formulation of the problem of turbulence modeling using optimal control theory and entropy as a measure of information. It is postulated that turbulence can be described fully by the N-S equations with the proper initial and boundary conditions. Assuming that there is information measure of the N-S equations, and assuming that averaging is a transformation, then the information measure should not be changed by averaging N-S equations. Through averaging, certain amounts of information disappear and other sources of information, Reynolds stresses, appear. The Reynolds stresses must contain part or all of the information that disappeared by averaging. The key concept is the calculation of turbulent stresses to minimize the information losses resulted from averaging N-S equations. Most of the existing turbulence models could be viewed from the 28 Mazher above formulation. The new concept of information measure may be used to select the turbulence model in such a way as to make the information measure of the averaged N-S equations as close as possible to the information measure of the original N-S equations. The main problem in this formulation is the selection of information measure of the N-S equations. In the next paper, a heuristic approach will be used to study different measures computationally. APPENDIX Maximum principle for distributed parameter systems Suppose a dynamical system is described by the partial vector differential equation, Schwarz 1971; dU{X't) = f(x,u(x,t), ,r(x,0), dt dXk where X is the vector of independent spatial coordinates (x, y, z) , t is the time, U(X, t)eQ is the vector of n-dimensional state vector, T(X, t) is r-dimensional control vector, and f is a vector-valued function of its arguments. The notation UxA dkU(X,t ) dXk takes care of all possible partial derivatives where k is the highest partial derivatives of U w. r. t. X. The solution of the above equation needs specification of initial and boundary conditions: U(t0,X)=U0 (X) , and dk-'U(X,t) dXk~' ' i— 1,2,3,.. ,A-1 at to and on the boundary dQ. We desire to find a control vector T(X, t) from among the admissible controls that minimizes the performance index I for fixed initial and final times t0 and tf : *f /= J jF(U,X,Vxk,r(X,t))dQdt t0 o The solution of this problem, if it exists, can be obtained from the following equations: dU__dH__ dt ~ cU ~ * 29 Turbulence Modeling ^ = ( n* dk ( dH , dt dXk ^^rdkU* d[ ; J 8Xk where the Hamiltonian H is defined as H=F+X\X, t )/ The optimal controls T* are determined by minimizing H w. r. t. choice of T (X, t) such that //*>//, where the asterisk denotes that the optimal admissible control vector T(X, t) is used. Under certain condition this reduces to: er ACKNOWLEDGMENTS This research was supported by NASA Stennis Space Center (SSC) grant NAG 1 3 - 03009. LITERATURE CITED Brachet, M. E., M. Meneguzzi, Politano, H. and Sulem, P. L. 1986. Computer Simulation of Decaying Two-Dimensional Turbulence, In G. Comte-Bellot and J. Mathieu [eds.], Advances in Turbulence, pp. 245-254. Springer- Verlag, New York, USA. Braza, M. and Dussauge, J.-P. 1998. Computation and Comparison of Efficient Turbulent Models for Aeronautics, European Research Project ETMA. Verlag- Vieweg, Wiesbaden, Germany. Childers, D. G. 1978, Modem Spectrum Analysis. IEEE Press, The Institute of Electrical and Electronics Engineers, Inc., New York, USA. Durbin, P. A. and Reif, B. A. P. 2001. Statistical Theory and Modeling for Turbulent Flows. John Wiley & Sons, Ltd., USA. Dwoyer, D. L., Hussaini, M. Y., and Voigt, R. G. 1985. Theoretical Approaches to Turbulence. Springer-Verlag, New York, USA. Ferziger, J. H. 1987. Simulation of Incompressible Turbulent Flows: A Review. Journal of Computational Physics 69, 1-48, USA. George, W. K., and Amdt, R. 1989. Advances in Turbulence, Hemisphere Publishing Corporation, New York, USA. Godeferd, F. S., Cambon, C., and Scott, J. F. 2001. Two-Point Closures and their Applications: report on a workshop. JFM, Vol. 436, pp. 393-407, UK. Hunt, J. C. R. et al. 2001. Development in Turbulence Research: a review based on the 1999 Programme of the Isaac Newton Institute, Cambridge. JFM, Vol. 436, pp.353-391. UK Katz, A. 1967. Principles of Statistical Mechanics: The Information Theory Approach, W. H. Freeman and company, San Francisco and London, USA. 30 Mazher Ladyzhenskaya, O. A. 1969. Incompressible Navier-Stokes Equations. Pergamon Press, New York, USA. Leonard, A. D. and Hill, J. C. 1988. Direct Numerical Simulation of Homogeneous Turbulent Reacting Flow. AIAA-88-3624 paper, USA. Mathiew, J., and Scott, J. 2000. An Introduction to Turbulent Flow. Cambridge University Press, New York, USA. Monin, A. S., and Yaglom, A. M. 1971. Statistical Fluid Mechanics, Vol. I. MIT Press, USA. Orszag, S. A., and Kells, L. C. 1980. Transition to Turbulence in Plane Poiseuille and Plane Couette Flow. JFM, Vol. 96, Part 1, pp. 159-205, UK. Piquet, J. 1999. Turbulent Flows- Models and Physics. Springer- Verlag, New York, USA. Pope, S. B. 2000. Turbulent Flows. Cambridge University Press, New York, USA. Rodi, W. 1980. Turbulence Models and Their Application in Hydraulics- A State of the Art Review. Karlsruhe University, Germany. Schwarz, H. 1971. Multivariable Technical Control Systems. North-Holland & American Elsevier publishing company, USA. Temam, R., 1981. Navier-Stokes Equations. North Holland Company, Netherlands. Wilcox, D. C. 1994. The Turbulence Modeling for CFD. DCW Industries, Inc., CA, USA, November 1994. 31 Journal of the Alabama Academy of Science, Vol. 77, No. 1, January 2006. BOOK REVIEW THE SEARCH FOR HUMAN IMMORTALITY: THE BIOLOGY AND THE ETHICS *Jaime Bres James T. Bradley Department of Biological Sciences Auburn University Auburn, AL 36849 Merchants of Immortality: Chasing the Dream of Human Life Extension . Stephen S. Hall. 360 pp. plus Notes, Bibliography. Acknowledgements, and Index. Houghton Mifflin Company. New York. New York. 2003. Scientific discovery has often kindled intense philosophical, theological, and ethical debate. Well known examples include Copernicus' and Galileo's advocacy of a heliocentric planetary system in the 16th and 17th centuries. Darwin's 19th century insights, and 20th century revelations about the origin and fate of our universe. The science of aging is poised to provoke similar controversy and debate in the 21st century. For millennia humankind has been fascmated by the idea of finding a "fountain of youth " able to confer perpetual health and life. But only during the past two decades or so has scientific discover} led to suggestions that virtual immortality for humans may become a 21st century possibility. Stephen Hall is a contributing writer for the New York Times and an author of many critically acclaimed books on contemporary science, including Invisible Frontiers (1987) and A Commotion in the Blood (1997). In his latest book. Merchants of Immortality (2003), Hall explores the science and ethics of life span extension The President's Council on Bioethics distinguishes between three terms that are sometimes confused (httpV/wwu bioethics.gov/background/age retardation.html) - "age retardation." "life span extension" and "life span prolongation ' The last term refers to the prolongation of life through heroic medical measures like dialysis or artificial respiration without special regard for the quality of life. Hall's book is not about life prolongation; rather, it is about life span extension - increasing the period of active, productive, health}-, enjoyable living dramatically beyond the 75-80 years common for persons born in developed countries today. Age retardation . the slowing down of processes that normally occur during biological aging, is one approach for achieving life span extension Other approaches include tissue regeneration in agmg organs and organ replacement. In Merchants of Immortality Hall recounts key discoveries in cell biology, molecular biolog}, and developmental biology that have relevance for age retardation and tissue regeneration Personalities behmd the discoveries and the impact of those discoveries on the worlds of business, politics, and religion are described in riveting detail with insight gained by frequently being at the scene of action. Scientists and politicians have shaped the landscape of age retardation research in the United States. Hall gives special attention to biologist Leonard Ha}flick. biologist-entrepreneur Michael West, and Presidents Bill Clinton and George W. Bush. 32 Bres and Bradley Leonard Hayflick discovered that cells growing in laboratory cultures possess a species-specific limit to the number of times they will reproduce by cell division. The limit became known as the Hayflick Limit. Hayflick’s work is indirectly responsible for igniting bioethical debate over the legitimacy of pursuing research aimed at dramatically increasing human lifespan by age retardation. Several cell biologists set out to discover why the Hayflick limit, about 50 for human cells, exists at all. Their research led to discovery of an enzyme, telomerase, responsible for repairing the ends of chromosomes called telomeres. With every cell division, telomeres become slightly shorter. A cell can tolerate only so much chromosomal shortening before vital genes become damaged and the cell dies. Interestingly, cancer cells, which are virtually immortal, escape cumulative telomere shortening because they have an active telomerase gene. That telomere shortening is directly responsible for the Hayflick Limit is doubtful, but the discovery of telomerase led some entrepreneurs, scientists, and media persons to believe that it was the key to curing cancer and also a Holy Grail for extending human lifespan. These expectations proved overly optimistic and naive, but they were also responsible for the founding of Geron, a private company that has developed into one of the key players in biotechnology research in the United States today. Geron was founded by Michael West, once a practicing biologist but now a biotechnology entrepreneur. The company’s initial objective was to isolate and characterize the gene for telomerase and patent resulting applications aimed at age retardation. Two Geron scientists, Carol Greider and Kathleen Collins, isolated the protein portion of this unusual enzyme whose structure also includes an RNA component. High expectations for creating long- lived individuals by reactivating the quiescent telomerase gene in normal tissues turned out to be unrealistic. But West was on the lookout for other approaches to age retardation. Work on embryonic stem cells (ESCs) in non-human primates at the University of Wisconsin and on similar cells from aborted fetuses at Johns Hopkins University attracted West’s attention because of these cells’ potential to rejuvenate injured, worn out and diseased tissues. Soon researchers at both institutions had received grants from Geron, and by 1998 Wisconsin’s James Thomson had created the first line of human ESCs. Unfortunately, Hall never clearly defines “ESC line” and devotes only two sentences (p. 161) to explaining the biological origin of ESCs. As biologists, the authors of this review believe this is important information and worthy of a brief digression. Contrary to common misperceptions, ESCs are not derived from aborted fetuses or from umbilical cord blood. Rather, they are obtained from 5-day-old human embryos called blastocysts that are produced in surplus at in vitro fertilization (IVF) clinics. A blastocyst is a hollow ball of cells smaller than the head of a pin and containing a mass of about 1 00 cells inside of it. When removed from the blastocyst and cultured in a glass dish in the laboratory, the inner cell mass gives rise to ESCs. The ESCs will continue to divide indefinitely in the laboratory as unspecialized cells. ESCs derived from one particular blastocyst are collectively referred to as an ESC line. Surplus blastocysts, embryos left over after a woman has successfully become pregnant by IVF, are stored frozen in liquid nitrogen and eventually discarded. Surplus blastocysts contain no specialized cell types, have never been inside a woman’s womb, and presently number about 400,000 in the United States. With permission from the egg and sperm-donating couple, blastocysts not used for implantation may be donated for research. Results from both mouse and human ESC research indicate that the cells can be used to develop new therapies for diseases and injuries that cause tissue and organ degeneration or destruction. 33 Book Review Returning now to Hall’s book, consider a portion of the fascinating description of how politics have affected ESC research in the United States. George W. Bush’s August 9, 2001 pronouncement on human ESC research has become legendary or infamous, depending on which side of the fence one sits on this controversial issue. Citing religion-based valuation of human life, Bush disallowed spending any federal funds to support the creation of new ESC lines. The proclamation prohibits government-funded scientists from using any of the nearly 400,000 surplus, blastocyst-stage embryos stored frozen at IVF clinics around the United States, even though these are designated to be destroyed at the end of their contractual period of storage. Since that time, cutting-edge ESC research has moved toward state or privately funded institutions and overseas to countries with less restrictive policies regulating human embryo research like England, Israel, and South Korea. How did the United States, the world’s longtime leader in biomedical science and technology, come to opt out of one of the 21st century’s most promising and exciting areas of research? Political uncertainties for the Democrats leading up to the mid-term elections of 1994 may have spelled doom for human embryo research in the United States for decades to come. Moreover, election politics apparently moved President Clinton to back-pedal at a time when his support of a controversial government commissioned report on embryo research might have assured United States leadership in ESC research a decade later. Recommendations of the Embryo Research Panel were released on September 27, 1994, just weeks before what would be a devastating election for Democrats. Until then Clinton had shown every sign of being one of the strongest advocates for biomedical research ever in the White House. But one of the Panel’s recommendations - to allow, under very limited circumstances, federal support for the creation of human embryos for research purposes - attracted vehement public criticism and apparently made the President lose his political nerve. Fearing Republican victories in November, Clinton quickly and explicitly distanced himself from the report and its controversial recommendation. Nevertheless, the President's fears were realized on November 4, and his failure to support the Panel’s report contributed to an atmosphere that ultimately resulted in passage of the Dickey-Wicker amendment in January 1996. This legislation, which has been renewed each year since its passage, prohibits the Department of Health and Human Services (including the National Institutes of Health) from funding research that would create human embryos or “in which a human embryo or embryos are destroyed, discarded, or knowingly subjected to risk of injury or death greater than that allowed for research on fetuses in utero.” The Dickey-Wicker amendment goes much further in restricting embryo research than simply countering the single controversial recommendation in the 1994 Embryo Research Panel Report. Although the legislation came at a time when it was unknown whether human ESCs could ever be produced, a part of its legacy is the present restriction on using surplus embryos to create new ESC lines in this country So Hayflick, West, Clinton and Bush, acting on their personal scientific, entrepreneurial, ethical or religious values, have played critical roles in shaping the course of human longevity research in the United States. But Hall’s book is about more than just people and their personal endeavors. It is also about ethical issues arising from new biotechnologies. A central one of these is the question of when human life begins. What is the meaning of the term “human life?” Hall presumes that the reader will view this term unambiguously as referring to a living entity to which special legal and moral status has been conferred - an individual possessing personhood. It is worth noting though, that for a biologist studying human cells growing in laboratory cell or tissue culture, the term simply refers to the genetic make-up of living cells; that is, the biologist is studying human life rather than bacterial, fish, or insect life. 34 Bres and Bradley The moral acceptability of destroying an embryo in order to obtain ESCs is controversial due to disagreement on when personhood begins. If the blastocyst is not a person, then using it for biomedical research is morally acceptable. But if the 5-day old blastocyst is recognized as a person, then destroying it for the purpose of research is the equivalent of murder. Persons belonging to The Nightlight group take the latter position. Hall reports that the group has found couples in need of assisted reproduction that are willing to “adopt” up to 10,000 embryos in frozen storage at IVF clinics. Economic issues also arise in connection with age retardation research. If federal funds and policies are approved to support various aspects of age retardation research, how will the benefits of the research be justly distributed? Is it ethical to spend large sums of money to retard the normal aging process when hundreds of millions of children around the world die early deaths from malaria or lack of effective vaccination programs against childhood diseases? Yet another ethical issue involves patenting human genes and genetically engineered human cells. For example, when Geron Corporation obtained a patent on the telomerase gene, it obtained a material transfer agreement. This means that another laboratory wishing to use the telomerase gene must agree to give commercial rights of any discovery that comes from its use of the gene to Geron. Some people feel that the commercialization of human genes is wrong and might ultimately lead to a devaluation of humans themselves. Although Hall does a commendable job explaining the scientific and ethical debates surrounding anti-aging research, he does not give the reader much information about the social implications of the research. For example, if research were to yield an anti-aging drug, how available would it be to the general public? Who would decide who is eligible to receive the benefits of the research? What effects would increased life spans have on the world’s population? Would the birth rate decrease, or would the population increase beyond what the earth can sustain? If people lived longer, would they retire later? If so, what would that do to the job market for younger persons? What about the innovation and creativity that normally come from new generations of persons? If reproduction were curtailed to insure room for the long-lived, would societal stagnation be the outcome? Finally, Hall does not discuss how an age-retarded person might eventually age. Would problems of old age like arthritis and osteoporosis simply be delayed, only to manifest themselves later? These are important questions to consider before spending billions of dollars on age-retardation technologies. We would like to have seen Hall’s discussion of these issues. Despite these omissions. Merchants of Immortality is a good read for both scientists and non-scientists - especially for those interested in a cross disciplinary understanding of the emerging biotechnology of age retardation and its intersections with politics and business. *Jaime Bres is a recent graduate in Biomedical Sciences at Auburn University. This review was written for a senior level Bioethics Research course with mentoring and editing by James T. Bradley, Department of Biological Sciences, 331 Funchess Hall, Auburn, AL 36849. 35 Journal of the Alabama Academy of Science. Vol. 77. No. 1. January 2006. BIOGRAPHY of W PETER CONROY Pete Conroy atop the Mountain Longleaf National Wildlife Refuge Pete Conroy is the Director of Jacksonville State University's Environmental Policy and Information Center (EPIC). Trained as a biologist. Mr. Conroy moved to Alabama m 1985 to work as the curator of the Anniston Museum of Natural History. Through his work with the museum he began leading efforts to popularize science and create enthusiasm for natural history. In 1986 he led over a thousand amateur astronomers into the darkness looking for Halley's Comet "It was just a little fuzzy spot in mght sky. but the reaction was huge" Conroy said. "Not being able to see them, it was a strange way to meet people" he continued. One of the voices he became friends with was that of Doug Ghee, who later because a State Senator and one of Pete's early advocates, encouraging his involvement in Alabama's political process. Working together with Senator Ghee and others, they helped to create the Forever Wild program that has now protected over 100.000 acres of habitat throughout the State. Conroy is more directly credited for the protection of other areas. Through his leadership, the Little River Canyon National Preserve was created in 1992. the Dugger Mountain Wilderness in 1999 and the Mountain Longleaf National Wildlife Refuge in 2002. "The plan is to connect these protected areas with attractions and educational facilities that increase our interest in science and appreciation for biological diversity" Conroy says. "We continue to prove that environmental protection and economic development can be a symbiotic relationship" he says. Also serving as the Director of JSU's Field Schools. Conroy points to several of his construction projects as examples. The Little River Canyon Center has been funded over $6 36 million to JSU. through NASA, for use by the National Park Service near Fort Pa\me. The JSU Longleaf Center has been funded nearly $1 million for use as a natural resource center near the Longleaf National Wildlife Refuge and adjoining the Talladega National Forest in Heflin. "From the deepest canyon to the highest mountain, these terrific partnerships will promote conservation, science education, cultural appreciation, and tourism' Conroy says. Since his early days in Alabama. Conroy has received appointments from Governors Guy Hunt (R). Jim Folsom (D). Fob James (R). and Don Siegelman (D). In 2000 he was selected by Governor Siegelman to Chair the Alabama Commission on Environmental Initiatives and in 2002. he was appointed to Chair the Alabama Geographic Information Council. Pete received White House appointments by President Bill Clinton in early 1999 to serve as the Alternate U S Federal Commissioner of the Tri-State (ACT/ACF) Water Compacts. In his capacity as Commissioner, he remained as an outspoken advocate for natural flow regimes, science based decision making and for the agencies tasked to collect river data. The reuse of the former Fort McClellan is another example of Conroy's impact. At McClellan. Conroy has created "Music at McClellan” (an outdoor concert series featuring the Alabama Symphony Orchestra), the Mountam Longleaf Festival (an Earthday celebration of arts and environment), and currently he is working on the creation of an environmental research park "Starting with McClellan's vast acreage and a $200,000 RFP. we are working with both the private and pubic sectors to look at the feasibility of a center that will combine technology, science and some amazingly synergistic partnerships ' Conroy continues. "We continue to make progress. Who knows, it might just work! " Among the awards and recognition for his efforts, Conroy has received: • The Golden Leaf Award, from the Nature Conservancy of Alabama 1992. • Malcolm Stewart Award, Alabama Environmental Council, 1993 and 2000. • Beta Beta Beta Biological Honor Society, Membership Award, JSU, 1994. • Alabama Wildlife Rehabilitation Center, Outstanding Board Member Award, 1999. • W. Kelly Mosley Environmental Award for Achievements in Forestry, Wildlife, and Related Resources, 2000. • Patriotic Service Award, US Department of the Army, 2003 • Citizen of the Year Award, the Anniston Star, 2006 Born in Pennsylvania, Pete moved to Asheville, North Carolina with his family in 1970. He later received his Bachelor's degree in biology from Furman University in South Carolina and his Master's degree in zoology from the University of Georgia. With his wife Roxana and daughter Haley, Pete lives in Jacksonville, Alabama. He is the son of Mr. and Mrs. David Conroy of Asheville, NC. His web site is http://epic.jsu.edu and he encourages its use! The Alabama Academy of Sciences expresses its deepest gratitude and admiration for the contributions of Pete Conroy. We wish Mr. Conroy continuous success in all his future endeavors. 37 AAS Fall 2005 Executive Committee Meeting Biology Department Samford University Birmingham, AL, 35229 October 29, 2005 Call to Order and Approval of Minutes (AC Officer Reports (B) 1. Board of Trustees, Eugene Omasta Trustee members are very active in the affairs of the Academy with their presence at the Friday night committee meeting preceding the Fall Executive Committee meeting, at the Fall and Spring Executive Committee meetings, and at the annual spring meeting. As in previous years there will be a Thursday luncheon meeting with the Trustees and the elected officers of the Academy. I apologize for my absence at this meeting as I had a previous commitment that I could not change. 2. President, Larry Davenport No written report available. 3 President Elect, David Nelson No written report available. 4 Second Vice-President, George Cline No written report available. 5 Secretary, Peggy Hayes Resigned position. 6 Treasurer, Mijitaba Hamissou Second quarter April - October 2005 1 . Compass Bank, checking account Balance as of 3-28-2005 $3,374.15 A. Income May $11,509.01 June $6,694.00 July $50.00 August $4,977.00 September $3,780.00 38 Minutes October $9,430.92 Journal subscriptions $2,200.00 Total income $39,815.08 B. Expenses JASS expenses $7,978.08 Honoraria $2,865 Conference expenses $11,891.63 Go r gas $850.00 Student Awards $1,445.00 Mason Scholarship $1,400.00 Intel $8,868.81 Total expenses $35,298.52 Checking account balance Compass $4,516.56 2. Compass Saving account balance $1,258.00 Total assess Compass $5,774.56 3. Colonial Bank Balance as of May, 2005 $6,064.63 Transfer to Compass $4,000.00 Interest accrued $5.04 Total assess Colonial Bank checking Balance $2,069.67 4. cd(l) + cd(2) +cd(3) as of 10 26-2005 $56,051.17 7 Journal Editor, Safaa Al-Hamdani I assumed the responsibility of the editorial ship of Alabama Academy of Science Journal in May 2005. We were successful in releasing the April issue of the journal and we are in the process of completing and editing the October issue. I suggested to the executive committee to add David Meyer out of Jacksonville State University to the editorial board. David’s responsibility will be exclusively reviewing the English part of each manuscript and submitting it to the journal. A guideline to the Authors was established to attempt to unify the style of the journal. In addition, a Guideline for the Reviewer was established to clarify the major points needed to be covered by the author in the manuscript. 8 Counselor to AJAS, B.J. Bateman No written report available. 39 9 Science Fair Coordinator, Virginia Valardi No written report available. 10 Science Olympiad Coordinator, Jane Nall No written report available. 1 1 Counselor to AAAS, Steve Watts No written report available. 12 Section Officers No written reports available. 13. Executive Officer, Larry Krannich Since March, 2005, 1 have been involved in the following activities associated with the Executive Director of the Alabama Academy of Science position: 1 . Worked with Anne Cusic to update and revise the Local Arrangements Committee manual for distribution to the annual meeting local arrangements committee and posting on the Academy web site. 2. Distributed materials to Ken Sundberg concerning arrangements, program booklet needs, and deadlines associated with the annual meeting of the Academy to be held on the Troy University campus, Marcy 15-18, 2006. 3. Mailed letters to Alabama colleges and universities to solicit financial support for the Journal and forwarded all received checks to the Treasurer. 4. Prepared the Call for Papers for the 83rd meeting of the Academy that will be distributed to all Section Chairs in hard and electronic copy after November 15th. 5. Designed bookmarks advertising the Academy and participation in the annual meeting. These will be distributed statewide in mid-November. 6. Updated the fliers and letters being sent to all Alabama chemistry faculty to solicit the participation of undergraduates and Alabama college and university Chemistry faculty in the 2nd annual Undergraduate Chemistry Research symposium to be held in conjunction with the annual meeting of the Academy. The four local sections of the American Chemical Society in the State are being contacted to assess their willingness to again co-sponsor this state-wide undergraduate research symposium with the Academy 7. Have worked with Dr. Heather Sutton, President of the Southeastern Region Society for Environmental Toxicology and Chemistry, to hold their annual meeting jointly with the Academy in March. 40 Minutes 8. Met with the Gorgas Scholarship Committee and participated in the ASTA meeting. Committee Reports (C) 1 . Local Arrangements, Ken Sundberg No written report available. 2. Finance, Eugene Omasta The Alabama Academy of Science continues to be in excellent financial condition with total assets of $63,895, although the decrease in assets of $ 1 0,370 over last years assets at this time is a concern. The assets for the past five years as reported at the Fall Executive Committee meetings and Annual Spring meetings of the Academy are listed below: Period Assets Change Period Assets Change (End of (End of Period) Period) 1/1 - 10/12/2001 $71,763 1/1 - 12/31/2001 $75,813 1/1 - 10/12/2002 $72,197 $434 1/1 - 12/31/2002 $72,813 -$ 3,000 1/1 - 10/12/2003 $71,403 -$794 1/1 - 12/31/2003 $74,800 $ 1,987 1/1 - 10/26/ 2004 $74,265 $2,862 1/1 - 12/31/2004 $74,610* -$ 190 1/1 - 10/26/2005 $63,895 -$10, 370 The $10,370 decrease in assets is a result of declining dues revenue and an increase in Journal expenses due printing back issues of the Journal this year. As reported at the last annual meeting, there has been a steady decline in dues revenue over the past several years. Again, I recommend the Academy explore ways of increasing revenues and in particular increasing membership. I did not have access to proposed budget for next year, but recommend the same budget as this year. * estimated 3. Membership, Mark Meade No written report available. 4. Research, Steve Watts No written report available. 5 Long-Range Planning, Ken Marion No written report available. 6 Auditing, Senior Academy, David Schedler 41 No written report available. 7 Auditing, Junior Academy, Govind Menon No written report available. 8. Editorial Board & Associate Journal Editors, Thane Wibbels No written report available. 9. Place and Date of meeting, Tom Bilbo No written report available. 10. Public Relations, Richard Buckner No written report available. 1 1 Archives, Troy Best No written report available. 12 Science and Public Policy, Dail Mullins No written report available. 13. Gardner Award, Prakash Sharma No written report available. 14 Carmichael Award, Richard Hudiburg No written report available. 15 Resolutions, — No written report available. 16 Nominating committee, George Cline No written report available. 17 Mason Scholarship, Mike Moeller Last spring we had six completed applications for the William H. Mason Scholarship. After reviewing all application materials and with approval of the Executive Committee to award two scholarships for 2005-2006, the Scholarship Committee offered the $1000 scholarships to Ms. Mary Busbee and Ms. Bethany Knox. Both applicants accepted the award. The previous recipients of the William H. Mason Scholarship are: 1990- 1991 1991- 1992 1992- 1993 1993- 1994 1994 -1995 Amy Livengood Sumner Leella Shook Holt Joni Justice Shankles Jeffrey Baumbach (Not awarded) 42 Minutes 1995- 1996 Laura W. Cochran 1 996- 1 997 Tina Anne Beams 1997- 1998 Carole Collins Clegg 1 998- 1 999 Cynthia Ann Phillips 1 999- 2000 Ruth Borden 2000- 2001 Karen Celestine, Amy Murphy 200 1 -2002 Jeannine Ott 2002- 2003 (Not awarded) 2003- 2004 Kanessa Miller 2004- 2005 (Not awarded) 2005- 2006 Mary Busbee, Bethany Knox Attached to this report is a copy of an announcement that the committee plans to be sending soon to deans in schools of science and education within Alabama. Members of the AAS Executive Committee are encouraged to copy and disseminate this information. 18. Gorgas Scholarship Program, Ellen Buckner No written report available. 19. Electronic Media, Richard Hudiburg No written report available. 43 Alabama Academy of Science Journal Scope of the Journal The Alabama Academy of Science publishes significant, innovative research of interest to a wide audience of scientists in all areas. Papers should have a broad appeal, and particularly welcome will be studies that break new ground or advance our scientific understanding. Information for the Authors • Manuscript layout should follow the specific guidelines of the journal. • The authors are encouraged to contact the editor (E-mail: sahfgiisu.edu) prior to paper submission to obtain detailed guidelines for the author • At least one author must be a member of the Alabama Academy of Science (except for Special Papers). • The correspondent author should provide the names and addresses of at least two potential reviewers. • Assemble the manuscript in the following order: Title Page, Abstract Page, Text, Brief Acknowledgments (if needed). Literature Cited, Figure Legends, Tables, Figures. What and Where to Submit The original and two copies of the manuscript and a cover letter should be submitted to the following. Dr. Safaa Al-Hamdani Editor- Alabama Academy of Science Journal Biology Department Jacksonville State University 700 Pelham Road North Jacksonville, AL 36265-1602 Review Procedure and Policy Manuscripts will be reviewed by experts in the research area. Manuscripts receiving favorable reviews will be tentatively accepted. Copies of the reviewers’ comments (and reviewer-annotated files of the manuscript, if any) will be returned to the correspondent author for any necessary revisions. The final revision and electronic copies are then submitted to the /Alabama Academy of Science Journal/ Editor. The author is required to pay $100 for partial coverage of printing costs of the article. The Journal of the Alabama Academy of Science. American Museum of Natural History Received on; 05-lb_0b AMNH LIBRARY 100232737 o3 g ’cs P p o £ £ I— -O p £ U £ o . > >r ; ■ r\ ^r r*3 liiillllil,lllliiiillll"llilil!il,'lii!iilil