Small Sample Sizes Yield Biased Allometric Equations in Temperate Forests
Duncanson, L.; Rourke, O.; Dubayah, R.
2015-01-01
Accurate quantification of forest carbon stocks is required for constraining the global carbon cycle and its impacts on climate. The accuracies of forest biomass maps are inherently dependent on the accuracy of the field biomass estimates used to calibrate models, which are generated with allometric equations. Here, we provide a quantitative assessment of the sensitivity of allometric parameters to sample size in temperate forests, focusing on the allometric relationship between tree height and crown radius. We use LiDAR remote sensing to isolate between 10,000 to more than 1,000,000 tree height and crown radius measurements per site in six U.S. forests. We find that fitted allometric parameters are highly sensitive to sample size, producing systematic overestimates of height. We extend our analysis to biomass through the application of empirical relationships from the literature, and show that given the small sample sizes used in common allometric equations for biomass, the average site-level biomass bias is ~+70% with a standard deviation of 71%, ranging from −4% to +193%. These findings underscore the importance of increasing the sample sizes used for allometric equation generation. PMID:26598233
NASA Astrophysics Data System (ADS)
Duncanson, L.; Dubayah, R.
2015-12-01
Lidar remote sensing is widely applied for mapping forest carbon stocks, and technological advances have improved our ability to capture structural details from forests, even resolving individual trees. Despite these advancements, the accuracy of forest aboveground biomass models remains limited by the quality of field estimates of biomass. The accuracies of field estimates are inherently dependent on the accuracy of the allometric equations used to relate measurable attributes to biomass. These equations are calibrated with relatively small samples of often spatially clustered trees. This research focuses on one of many issues involving allometric equations - understanding how sensitive allometric parameters are to the sample sizes used to fit them. We capitalize on recent advances in lidar remote sensing to extract individual tree structural information from six high-resolution airborne lidar datasets in the United States. We remotely measure millions of tree heights and crown radii, and fit allometric equations to the relationship between tree height and radius at a 'population' level, in each site. We then extract samples from our tree database, and build allometries on these smaller samples of trees, with varying sample sizes. We show that for the allometric relationship between tree height and crown radius, small sample sizes produce biased allometric equations that overestimate height for a given crown radius. We extend this analysis using translations from the literature to address potential implications for biomass, showing that site-level biomass may be greatly overestimated when applying allometric equations developed with the typically small sample sizes used in popular allometric equations for biomass.
Developing a generalized allometric equation for aboveground biomass estimation
NASA Astrophysics Data System (ADS)
Xu, Q.; Balamuta, J. J.; Greenberg, J. A.; Li, B.; Man, A.; Xu, Z.
2015-12-01
A key potential uncertainty in estimating carbon stocks across multiple scales stems from the use of empirically calibrated allometric equations, which estimate aboveground biomass (AGB) from plant characteristics such as diameter at breast height (DBH) and/or height (H). The equations themselves contain significant and, at times, poorly characterized errors. Species-specific equations may be missing. Plant responses to their local biophysical environment may lead to spatially varying allometric relationships. The structural predictor may be difficult or impossible to measure accurately, particularly when derived from remote sensing data. All of these issues may lead to significant and spatially varying uncertainties in the estimation of AGB that are unexplored in the literature. We sought to quantify the errors in predicting AGB at the tree and plot level for vegetation plots in California. To accomplish this, we derived a generalized allometric equation (GAE) which we used to model the AGB on a full set of tree information such as DBH, H, taxonomy, and biophysical environment. The GAE was derived using published allometric equations in the GlobAllomeTree database. The equations were sparse in details about the error since authors provide the coefficient of determination (R2) and the sample size. A more realistic simulation of tree AGB should also contain the noise that was not captured by the allometric equation. We derived an empirically corrected variance estimate for the amount of noise to represent the errors in the real biomass. Also, we accounted for the hierarchical relationship between different species by treating each taxonomic level as a covariate nested within a higher taxonomic level (e.g. species < genus). This approach provides estimation under incomplete tree information (e.g. missing species) or blurred information (e.g. conjecture of species), plus the biophysical environment. The GAE allowed us to quantify contribution of each different
NASA Astrophysics Data System (ADS)
Mahmood, H.; Siddique, M. R. H.; Akhter, M.
2016-08-01
Estimations of biomass, volume and carbon stock are important in the decision making process for the sustainable management of a forest. These estimations can be conducted by using available allometric equations of biomass and volume. Present study aims to: i. develop a compilation with verified allometric equations of biomass, volume, and carbon for trees and shrubs of Bangladesh, ii. find out the gaps and scope for further development of allometric equations for different trees and shrubs of Bangladesh. Key stakeholders (government departments, research organizations, academic institutions, and potential individual researchers) were identified considering their involvement in use and development of allometric equations. A list of documents containing allometric equations was prepared from secondary sources. The documents were collected, examined, and sorted to avoid repetition, yielding 50 documents. These equations were tested through a quality control scheme involving operational verification, conceptual verification, applicability, and statistical credibility. A total of 517 allometric equations for 80 species of trees, shrubs, palm, and bamboo were recorded. In addition, 222 allometric equations for 39 species were validated through the quality control scheme. Among the verified equations, 20%, 12% and 62% of equations were for green-biomass, oven-dried biomass, and volume respectively and 4 tree species contributed 37% of the total verified equations. Five gaps have been pinpointed for the existing allometric equations of Bangladesh: a. little work on allometric equation of common tree and shrub species, b. most of the works were concentrated on certain species, c. very little proportion of allometric equations for biomass estimation, d. no allometric equation for belowground biomass and carbon estimation, and d. lower proportion of valid allometric equations. It is recommended that site and species specific allometric equations should be developed and
Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests.
Ishihara, Masae I; Utsugi, Hajime; Tanouchi, Hiroyuki; Aiba, Masahiro; Kurokawa, Hiroko; Onoda, Yusuke; Nagano, Masahiro; Umehara, Toru; Ando, Makoto; Miyata, Rie; Hiura, Tsutom
2015-07-01
Accurate estimation of tree and forest biomass is key to evaluating forest ecosystem functions and the global carbon cycle. Allometric equations that estimate tree biomass from a set of predictors, such as stem diameter and tree height, are commonly used. Most allometric equations are site specific, usually developed from a small number of trees harvested in a small area, and are either species specific or ignore interspecific differences in allometry. Due to lack of site-specific allometries, local equations are often applied to sites for which they were not originally developed (foreign sites), sometimes leading to large errors in biomass estimates. In this study, we developed generic allometric equations for aboveground biomass and component (stem, branch, leaf, and root) biomass using large, compiled data sets of 1203 harvested trees belonging to 102 species (60 deciduous angiosperm, 32 evergreen angiosperm, and 10 evergreen gymnosperm species) from 70 boreal, temperate, and subtropical natural forests in Japan. The best generic equations provided better biomass estimates than did local equations that were applied to foreign sites. The best generic equations included explanatory variables that represent interspecific differences in allometry in addition to stem diameter, reducing error by 4-12% compared to the generic equations that did not include the interspecific difference. Different explanatory variables were selected for different components. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable. For branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area), suggesting importance of other traits in addition to these traits, such as canopy and root architecture. Inclusion of tree height in addition to stem diameter improved
Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests.
Ishihara, Masae I; Utsugi, Hajime; Tanouchi, Hiroyuki; Aiba, Masahiro; Kurokawa, Hiroko; Onoda, Yusuke; Nagano, Masahiro; Umehara, Toru; Ando, Makoto; Miyata, Rie; Hiura, Tsutom
2015-07-01
Accurate estimation of tree and forest biomass is key to evaluating forest ecosystem functions and the global carbon cycle. Allometric equations that estimate tree biomass from a set of predictors, such as stem diameter and tree height, are commonly used. Most allometric equations are site specific, usually developed from a small number of trees harvested in a small area, and are either species specific or ignore interspecific differences in allometry. Due to lack of site-specific allometries, local equations are often applied to sites for which they were not originally developed (foreign sites), sometimes leading to large errors in biomass estimates. In this study, we developed generic allometric equations for aboveground biomass and component (stem, branch, leaf, and root) biomass using large, compiled data sets of 1203 harvested trees belonging to 102 species (60 deciduous angiosperm, 32 evergreen angiosperm, and 10 evergreen gymnosperm species) from 70 boreal, temperate, and subtropical natural forests in Japan. The best generic equations provided better biomass estimates than did local equations that were applied to foreign sites. The best generic equations included explanatory variables that represent interspecific differences in allometry in addition to stem diameter, reducing error by 4-12% compared to the generic equations that did not include the interspecific difference. Different explanatory variables were selected for different components. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable. For branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area), suggesting importance of other traits in addition to these traits, such as canopy and root architecture. Inclusion of tree height in addition to stem diameter improved
Nam, Vu Thanh; van Kuijk, Marijke; Anten, Niels P. R.
2016-01-01
Allometric regression models are widely used to estimate tropical forest biomass, but balancing model accuracy with efficiency of implementation remains a major challenge. In addition, while numerous models exist for aboveground mass, very few exist for roots. We developed allometric equations for aboveground biomass (AGB) and root biomass (RB) based on 300 (of 45 species) and 40 (of 25 species) sample trees respectively, in an evergreen forest in Vietnam. The biomass estimations from these local models were compared to regional and pan-tropical models. For AGB we also compared local models that distinguish functional types to an aggregated model, to assess the degree of specificity needed in local models. Besides diameter at breast height (DBH) and tree height (H), wood density (WD) was found to be an important parameter in AGB models. Existing pan-tropical models resulted in up to 27% higher estimates of AGB, and overestimated RB by nearly 150%, indicating the greater accuracy of local models at the plot level. Our functional group aggregated local model which combined data for all species, was as accurate in estimating AGB as functional type specific models, indicating that a local aggregated model is the best choice for predicting plot level AGB in tropical forests. Finally our study presents the first allometric biomass models for aboveground and root biomass in forests in Vietnam. PMID:27309718
Nam, Vu Thanh; van Kuijk, Marijke; Anten, Niels P R
2016-01-01
Allometric regression models are widely used to estimate tropical forest biomass, but balancing model accuracy with efficiency of implementation remains a major challenge. In addition, while numerous models exist for aboveground mass, very few exist for roots. We developed allometric equations for aboveground biomass (AGB) and root biomass (RB) based on 300 (of 45 species) and 40 (of 25 species) sample trees respectively, in an evergreen forest in Vietnam. The biomass estimations from these local models were compared to regional and pan-tropical models. For AGB we also compared local models that distinguish functional types to an aggregated model, to assess the degree of specificity needed in local models. Besides diameter at breast height (DBH) and tree height (H), wood density (WD) was found to be an important parameter in AGB models. Existing pan-tropical models resulted in up to 27% higher estimates of AGB, and overestimated RB by nearly 150%, indicating the greater accuracy of local models at the plot level. Our functional group aggregated local model which combined data for all species, was as accurate in estimating AGB as functional type specific models, indicating that a local aggregated model is the best choice for predicting plot level AGB in tropical forests. Finally our study presents the first allometric biomass models for aboveground and root biomass in forests in Vietnam. PMID:27309718
Smith, T. J.; Whelan, K.R.T.
2006-01-01
Mathematical relations that use easily measured variables to predict difficult-to-measure variables are important to resource managers. In this paper we develop allometric relations to predict total aboveground biomass and individual components of biomass (e.g., leaves, stems, branches) for three species of mangroves for Everglades National Park, Florida, USA. The Greater Everglades Ecosystem is currently the subject of a 7.8-billion-dollar restoration program sponsored by federal, state, and local agencies. Biomass and production of mangroves are being used as a measure of restoration success. A technique for rapid determination of biomass over large areas is required. We felled 32 mangrove trees and separated each plant into leaves, stems, branches, and for Rhizophora mangle L., prop roots. Wet weights were measured in the field and subsamples returned to the laboratory for determination of wet-to-dry weight conversion factors. The diameter at breast height (DBH) and stem height were also measured. Allometric equations were developed for each species for total biomass and components of biomass. We compared our equations with those from the same, or similar, species from elsewhere in the world. Our equations explained ???93% of the variance in total dry weight using DBH. DBH is a better predictor of dry weight than is stem height and DBH is much easier to measure. Furthermore, our results indicate that there are biogeographic differences in allometric relations between regions. For a given DBH, stems of all three species have less mass in Florida than stems from elsewhere in the world. ?? Springer 2006.
Predicting trophic relations in ecological networks: a test of the Allometric Diet Breadth Model.
Allesina, Stefano
2011-06-21
Few food web theory hypotheses/predictions can be readily tested using likelihoods of reproducing the data. Simple probabilistic models for food web structure, however, are an exception as their likelihoods were recently derived. Here I test the performance of a more complex model for food web structure that is grounded in the allometric scaling of interactions with body size and the theory of optimal foraging (Allometric Diet Breadth Model-ADBM). This deterministic model has been evaluated by measuring the fraction of trophic relations it correctly predicts. I contrasted this value with that produced by simpler models based on body sizes and found that the quantitative information on allometric scaling and optimal foraging does not significantly increase model fit. Also, I present a method to compute the p-value for the fraction of trophic interactions correctly predicted by the ADBM, or any other model, with respect to three probabilistic models. I find that the ADBM predicts significantly more links than random graphs, but other models can outperform it. Although optimal foraging and allometric scaling may improve our understanding of food webs, the ADBM needs to be modified or replaced to find support in the data.
Zuo, Shu-di; Ren, Yin; Weng, Xian; Ding, Hong-feng; Luo, Yun-jian
2015-02-01
Biomass allometric equation (BAE) considered as a simple and reliable method in the estimation of forest biomass and carbon was used widely. In China, numerous studies focused on the BAEs for coniferous forest and pure broadleaved forest, and generalized BAEs were frequently used to estimate the biomass and carbon of mixed broadleaved forest, although they could induce large uncertainty in the estimates. In this study, we developed the species-specific and generalized BAEs using biomass measurement for 9 common broadleaved trees (Castanopsis fargesii, C. lamontii, C. tibetana, Lithocarpus glaber, Sloanea sinensis, Daphniphyllum oldhami, Alniphyllum fortunei, Manglietia yuyuanensis, and Engelhardtia fenzlii) of subtropical evergreen broadleaved forest, and compared differences in species-specific and generalized BAEs. The results showed that D (diameter at breast height) was a better independent variable in estimating the biomass of branch, leaf, root, aboveground section and total tree than a combined variable (D2 H) of D and H (tree height) , but D2H was better than D in estimating stem biomass. R2 (coefficient of determination) values of BAEs for 6 species decreased when adding H as the second independent variable into D- only BAEs, where R2 value for S. sinensis decreased by 5.6%. Compared with generalized D- and D2H-based BAEs, standard errors of estimate (SEE) of BAEs for 8 tree species decreased, and similar decreasing trend was observed for different components, where SEEs of the branch decreased by 13.0% and 20.3%. Therefore, the biomass carbon storage and its dynamic estimates were influenced largely by tree species and model types. In order to improve the accuracy of the estimates of biomass and carbon, we should consider the differences in tree species and model types.
Allometric comparison of skulls from two closely related weasels, Mustela itatsi and M. sibirica.
Suzuki, Satoshi; Abe, Mikiko; Motokawa, Masaharu
2011-09-01
We conducted an interspecific comparison of skulls from two closely related but differently sized mustelid species, Mustela itatsi and M. sibirica (Mammalia, Carnivora, Mustelidae); a sexual comparison within the latter species showed remarkable size dimorphism. We clarified several differences in skull proportion related to size using allometric analyses and qualitative comparisons. Allometric analysis revealed that the skulls of male M. itatsi (the smaller species) have a relatively long palate; a slender viscerocranium and postorbital constriction; a broad, short, and low neurocranium; small carnassials; and a short mandible with a thin body and small ramus compared to the skulls of male M. sibirica (the larger species). Similar results were obtained when male M. itatsi were compared to female M. sibirica, although the male M. itatsi had a broader viscerocranium than female M. sibirica. A sexual comparison in M. sibirica revealed a larger skull size among the males with a relatively wide viscerocranium; wide postorbital constriction; a slender, long, and high neurocranium; short and wide auditory bullae; short carnassials; and a long and high mandible compared to females. Qualitative comparisons revealed changes in a few characters depending on skull size or with respect to some cranial components in each species. The interspecific differences observed were clearly larger than the intraspecific differences for three qualitative characters. The allometric and qualitative differences detected between these species suggest that each species is not simply the dwarf and/or giant morph of the other, and complicated differences were clarified. PMID:21882957
Osland, Michael J.; Day, Richard H.; Larriviere, Jack C.; From, Andrew S.
2014-01-01
Across the globe, species distributions are changing in response to climate change and land use change. In parts of the southeastern United States, climate change is expected to result in the poleward range expansion of black mangroves (Avicennia germinans) at the expense of some salt marsh vegetation. The morphology of A. germinans at its northern range limit is more shrub-like than in tropical climes in part due to the aboveground structural damage and vigorous multi-stem regrowth triggered by extreme winter temperatures. In this study, we developed aboveground allometric equations for freeze-affected black mangroves which can be used to quantify: (1) total aboveground biomass; (2) leaf biomass; (3) stem plus branch biomass; and (4) leaf area. Plant volume (i.e., a combination of crown area and plant height) was selected as the optimal predictor of the four response variables. We expect that our simple measurements and equations can be adapted for use in other mangrove ecosystems located in abiotic settings that result in mangrove individuals with dwarf or shrub-like morphologies including oligotrophic and arid environments. Many important ecological functions and services are affected by changes in coastal wetland plant community structure and productivity including carbon storage, nutrient cycling, coastal protection, recreation, fish and avian habitat, and ecosystem response to sea level rise and extreme climatic events. Coastal scientists in the southeastern United States can use the identified allometric equations, in combination with easily obtained and non-destructive plant volume measurements, to better quantify and monitor ecological change within the dynamic, climate sensitive, and highly-productive mangrove-marsh ecotone.
Osland, Michael J.; Day, Richard H.; Larriviere, Jack C.; From, Andrew S.
2014-01-01
Across the globe, species distributions are changing in response to climate change and land use change. In parts of the southeastern United States, climate change is expected to result in the poleward range expansion of black mangroves (Avicennia germinans) at the expense of some salt marsh vegetation. The morphology of A. germinans at its northern range limit is more shrub-like than in tropical climes in part due to the aboveground structural damage and vigorous multi-stem regrowth triggered by extreme winter temperatures. In this study, we developed aboveground allometric equations for freeze-affected black mangroves which can be used to quantify: (1) total aboveground biomass; (2) leaf biomass; (3) stem plus branch biomass; and (4) leaf area. Plant volume (i.e., a combination of crown area and plant height) was selected as the optimal predictor of the four response variables. We expect that our simple measurements and equations can be adapted for use in other mangrove ecosystems located in abiotic settings that result in mangrove individuals with dwarf or shrub-like morphologies including oligotrophic and arid environments. Many important ecological functions and services are affected by changes in coastal wetland plant community structure and productivity including carbon storage, nutrient cycling, coastal protection, recreation, fish and avian habitat, and ecosystem response to sea level rise and extreme climatic events. Coastal scientists in the southeastern United States can use the identified allometric equations, in combination with easily obtained and non-destructive plant volume measurements, to better quantify and monitor ecological change within the dynamic, climate sensitive, and highly-productive mangrove-marsh ecotone. PMID:24971938
Allometric scaling of countries
NASA Astrophysics Data System (ADS)
Zhang, Jiang; Yu, Tongkui
2010-11-01
As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, and urban systems. We systematically investigated the allometric scaling relationships between a large number of macroscopic properties and geographic (area), demographic (population) and economic (GDP, gross domestic production) sizes of countries respectively. We found that most of the economic, trade, energy consumption, communication related properties have significant super-linear (the exponent is larger than 1) or nearly linear allometric scaling relations with the GDP. Meanwhile, the geographic (arable area, natural resources, etc.), demographic (labor force, military age population, etc.) and transportation-related properties (road length, airports) have significant and sub-linear (the exponent is smaller than 1) allometric scaling relations with area. Several differences of power law relations with respect to the population between countries and cities were pointed out. First, population increases sub-linearly with area in countries. Second, the GDP increases linearly in countries but not super-linearly as in cities. Finally, electricity or oil consumption per capita increases with population faster than cities.
Mayhew, Terry M
2006-06-01
Correlations between placental size and fetal mass during gestation fail to account for changes in composition that accompany placental growth and maturation. This study uses stereological data on the sizes of different tissue compartments in human placentas from 10 weeks of gestation to term and relates them to placental volume and to fetal mass by means of allometric analysis. In addition, tissue dimensions are used to calculate a physiological transport measure (diffusive conductance) for the villous membrane. Histological sections randomly sampled from placentas and analysed stereologically provided estimates of structural quantities (volumes, exchange surface areas, lengths, numbers of nuclei, diffusion distances). These data were combined with a physicochemical quantity (Krogh's diffusion coefficient) in order to estimate oxygen diffusive conductances for the villous membrane and its two components (trophoblast and stroma). Allometric relationships between these quantities and placental volume or fetal mass were obtained by linear regression analyses after log-transformation. Placental tissues had different growth trajectories: most grew more rapidly than placental volume and all grew more slowly than fetal mass. Diffusion distances were inversely related to placental and fetal size. Differential growth impacted on diffusive conductances, which, again, did not improve commensurately with placental volume but did match exactly growth of the fetus. Findings show that successful integration between supply and demand can be achieved by differential tissue growth. Allometric analysis of results from recent studies on the murine placenta suggest further that diffusive conductances may also be matched to fetal mass during gestation and to fetal mass at term across species.
A kinetic-allometric approach to predicting tissue radionuclide concentrations for biota
Higley, K. A.; Domotor, S. L.; Antonio, E. J.
2003-01-01
Allometry, or the biology of scaling, is the study of size and its consequences. It has become a useful tool for comparative phsiology. There are several allometric equations that relate body size to many parameters, including ingestion rate, lifespan, inhalation rate, home range and more. While these equations were originally derived from empirical observations, there is a growing body of evidence that these relationships have their origins in the dynamics of energy transport mechanisms. As part of an ongoing effort to assist the Department of Energy in developing generic methods for evaluating radiation dose to biota, we have examined the utility of applyig allometric techniques to predicting radionuclide tissue concentration across a large range of terrestrial and riparian species of animals. This particular study examined twenty-three elements. Initial investigations suggest that the allometric approach can provide a useful tool to derive limiting values of uptake and elimination factors for biota.
Allometric scaling laws of metabolism
NASA Astrophysics Data System (ADS)
da Silva, Jafferson Kamphorst Leal; Garcia, Guilherme J. M.; Barbosa, Lauro A.
2006-12-01
One of the most pervasive laws in biology is the allometric scaling, whereby a biological variable Y is related to the mass M of the organism by a power law, Y=YM, where b is the so-called allometric exponent. The origin of these power laws is still a matter of dispute mainly because biological laws, in general, do not follow from physical ones in a simple manner. In this work, we review the interspecific allometry of metabolic rates, where recent progress in the understanding of the interplay between geometrical, physical and biological constraints has been achieved. For many years, it was a universal belief that the basal metabolic rate (BMR) of all organisms is described by Kleiber's law (allometric exponent b=3/4). A few years ago, a theoretical basis for this law was proposed, based on a resource distribution network common to all organisms. Nevertheless, the 3/4-law has been questioned recently. First, there is an ongoing debate as to whether the empirical value of b is 3/4 or 2/3, or even nonuniversal. Second, some mathematical and conceptual errors were found these network models, weakening the proposed theoretical arguments. Another pertinent observation is that the maximal aerobically sustained metabolic rate of endotherms scales with an exponent larger than that of BMR. Here we present a critical discussion of the theoretical models proposed to explain the scaling of metabolic rates, and compare the predicted exponents with a review of the experimental literature. Our main conclusion is that although there is not a universal exponent, it should be possible to develop a unified theory for the common origin of the allometric scaling laws of metabolism.
Allometric scaling of marbofloxacin pharmacokinetics: a retrospective analysis.
Yohannes, S; Hossain, Md Akil; Kim, J Y; Lee, S J; Kwak, D M; Suh, J W; Park, S C
2014-01-01
The association between physiologically dependent pharmacokinetic parameters (CL(B), T1/2beta, Vd(ss)) of marbofloxacin and body weight was studied in eight animal species based on allometric equation Y = aWb, where 'Y' is the pharmacokinetic parameter, 'W' is body weight, 'a' is allometric coefficient (intercept) and 'b' is the exponent that describes relation between pharmacokinetic parameter and body weight. The body clearance of marbofloxacin has shown significant (P < 0.0001) relation with size (Bwt) in various animal species. However, half-life and volume of distribution were not in association with body weight. Although half-life and volume of distribution were not in a good correlation with body weight, statistically significant association between the body clearance and body weight suggests validity of allometric scaling for predicting pharmacokinetic parameters of marbofloxacin in animal species that have not been studied yet. However further study considering large sample size and other parameters influencing pharmacokinetics of marbofloxacin is recommended.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
ERIC Educational Resources Information Center
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
Allometric scaling of intraspecific space use
Gozlan, Rodolphe E.
2016-01-01
Allometric scaling relationships enable exploration of animal space-use patterns, yet interspecific studies cannot address many of the underlying mechanisms. We present the first intraspecific study of home range (HR) allometry relative to energetic requirements over several orders of magnitude of body mass, using as a model the predatory fish, pike Esox lucius. Analogous with interspecific studies, we show that space use increases more rapidly with mass (exponent = 1.08) than metabolic scaling theories predict. Our results support a theory that suggests increasing HR overlap with body mass explains many of these differences in allometric scaling of HR size. We conclude that, on a population scale, HR size and energetic requirement scale allometrically, but with different exponents. PMID:26979558
Allometric scaling of intraspecific space use.
Rosten, Carolyn M; Gozlan, Rodolphe E; Lucas, Martyn C
2016-03-01
Allometric scaling relationships enable exploration of animal space-use patterns, yet interspecific studies cannot address many of the underlying mechanisms. We present the first intraspecific study of home range (HR) allometry relative to energetic requirements over several orders of magnitude of body mass, using as a model the predatory fish, pike Esox lucius. Analogous with interspecific studies, we show that space use increases more rapidly with mass (exponent = 1.08) than metabolic scaling theories predict. Our results support a theory that suggests increasing HR overlap with body mass explains many of these differences in allometric scaling of HR size. We conclude that, on a population scale, HR size and energetic requirement scale allometrically, but with different exponents. PMID:26979558
Allometric disparity in rodent evolution
Wilson, Laura A B
2013-01-01
In this study, allometric trajectories for 51 rodent species, comprising equal representatives from each of the major clades (Ctenohystrica, Muroidea, Sciuridae), are compared in a multivariate morphospace (=allometric space) to quantify magnitudes of disparity in cranial growth. Variability in allometric trajectory patterns was compared to measures of adult disparity in each clade, and dietary habit among the examined species, which together encapsulated an ecomorphological breadth. Results indicate that the evolution of allometric trajectories in rodents is characterized by different features in sciurids compared with muroids and Ctenohystrica. Sciuridae was found to have a reduced magnitude of inter-trajectory change and growth patterns with less variation in allometric coefficient values among members. In contrast, a greater magnitude of difference between trajectories and an increased variation in allometric coefficient values was evident for both Ctenohystrica and muroids. Ctenohystrica and muroids achieved considerably higher adult disparities than sciurids, suggesting that conservatism in allometric trajectory modification may constrain morphological diversity in rodents. The results provide support for a role of ecology (dietary habit) in the evolution of allometric trajectories in rodents. PMID:23610638
NASA Astrophysics Data System (ADS)
Hirao, Shoji; Asaeda, Takashi; Sakamoto, Kentaro
A dynamic model of the growth of riparian trees, based on the energy budget of the plant and widely used empirical allometiric relations, is developed, as to be capable for multi-purpose in river management. The model was applied to Salix gilgiana and Robinia pseudoacacia, common riparian species in Japanese rivers. The model successfully reproduced the morphological characteristics of these species observed on the sand bar of Arakawa river. The observation also indicated that Salix gilgiana colonized only less than 3m high from the normal water surface, while Robinia pseudoacacia did at higher than 3m, and the colonization of both species was peaked with tree biomass of approximately 100ind/ha. The mode provides the maximum biomass, thus, was approximately 20,000kg/ha.
Connecting Related Rates and Differential Equations
ERIC Educational Resources Information Center
Brandt, Keith
2012-01-01
This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.
Gagnat, Maren Ranheim; Wold, Per-Arvid; Bardal, Tora; Øie, Gunvor; Kjørsvik, Elin
2016-01-01
Small fish larvae grow allometrically, but little is known about how this growth pattern may be affected by different growth rates and early diet quality. The present study investigates how different growth rates, caused by start-feeding with copepods or rotifers the first 30 days post-hatch (dph), affect allometric growth and development of nine major organs in ballan wrasse (Labrus bergylta) larvae up to experimental end at 60 dph. Feeding with cultivated copepod nauplii led to both increased larval somatic growth and faster development and growth of organ systems than feeding with rotifers. Of the organs studied, the digestive and respiratory organs increased the most in size between 4 and 8 dph, having a daily specific growth rate (SGR) between 30 and 40% in larvae fed copepods compared with 20% or less for rotifer-fed larvae. Muscle growth was prioritised from flexion stage and onwards, with a daily SGR close to 30% between 21 and 33 dph regardless of treatment. All larvae demonstrated a positive linear correlation between larval standard length (SL) and increase in total tissue volume, and no difference in allometric growth pattern was found between the larval treatments. A change from positive allometric to isometric growth was observed at a SL close to 6.0 mm, a sign associated with the start of metamorphosis. This was also where the larvae reached postflexion stage, and was accompanied by a change in growth pattern for most of the major organ systems. The first sign of a developing hepatopancreas was, however, first observed in the largest larva (17.4 mm SL, 55 dph), indicating that the metamorphosis in ballan wrasse is a gradual process lasting from 6.0 to at least 15-17 mm SL. PMID:27422903
Wold, Per-Arvid; Bardal, Tora; Øie, Gunvor; Kjørsvik, Elin
2016-01-01
ABSTRACT Small fish larvae grow allometrically, but little is known about how this growth pattern may be affected by different growth rates and early diet quality. The present study investigates how different growth rates, caused by start-feeding with copepods or rotifers the first 30 days post-hatch (dph), affect allometric growth and development of nine major organs in ballan wrasse (Labrus bergylta) larvae up to experimental end at 60 dph. Feeding with cultivated copepod nauplii led to both increased larval somatic growth and faster development and growth of organ systems than feeding with rotifers. Of the organs studied, the digestive and respiratory organs increased the most in size between 4 and 8 dph, having a daily specific growth rate (SGR) between 30 and 40% in larvae fed copepods compared with 20% or less for rotifer-fed larvae. Muscle growth was prioritised from flexion stage and onwards, with a daily SGR close to 30% between 21 and 33 dph regardless of treatment. All larvae demonstrated a positive linear correlation between larval standard length (SL) and increase in total tissue volume, and no difference in allometric growth pattern was found between the larval treatments. A change from positive allometric to isometric growth was observed at a SL close to 6.0 mm, a sign associated with the start of metamorphosis. This was also where the larvae reached postflexion stage, and was accompanied by a change in growth pattern for most of the major organ systems. The first sign of a developing hepatopancreas was, however, first observed in the largest larva (17.4 mm SL, 55 dph), indicating that the metamorphosis in ballan wrasse is a gradual process lasting from 6.0 to at least 15-17 mm SL. PMID:27422903
Gagnat, Maren Ranheim; Wold, Per-Arvid; Bardal, Tora; Øie, Gunvor; Kjørsvik, Elin
2016-09-15
Small fish larvae grow allometrically, but little is known about how this growth pattern may be affected by different growth rates and early diet quality. The present study investigates how different growth rates, caused by start-feeding with copepods or rotifers the first 30 days post-hatch (dph), affect allometric growth and development of nine major organs in ballan wrasse (Labrus bergylta) larvae up to experimental end at 60 dph. Feeding with cultivated copepod nauplii led to both increased larval somatic growth and faster development and growth of organ systems than feeding with rotifers. Of the organs studied, the digestive and respiratory organs increased the most in size between 4 and 8 dph, having a daily specific growth rate (SGR) between 30 and 40% in larvae fed copepods compared with 20% or less for rotifer-fed larvae. Muscle growth was prioritised from flexion stage and onwards, with a daily SGR close to 30% between 21 and 33 dph regardless of treatment. All larvae demonstrated a positive linear correlation between larval standard length (SL) and increase in total tissue volume, and no difference in allometric growth pattern was found between the larval treatments. A change from positive allometric to isometric growth was observed at a SL close to 6.0 mm, a sign associated with the start of metamorphosis. This was also where the larvae reached postflexion stage, and was accompanied by a change in growth pattern for most of the major organ systems. The first sign of a developing hepatopancreas was, however, first observed in the largest larva (17.4 mm SL, 55 dph), indicating that the metamorphosis in ballan wrasse is a gradual process lasting from 6.0 to at least 15-17 mm SL.
Ibáñez, Inés; Zak, Donald R; Burton, Andrew J; Pregitzer, Kurt S
2016-04-01
As increasing levels of nitrogen (N) deposition impact many terrestrial ecosystems, understanding the potential effects of higher N availability is critical for forecasting tree carbon allocation patterns and thus future forest productivity. Most regional estimates of forest biomass apply allometric equations, with parameters estimated from a limited number of studies, to forest inventory data (i.e., tree diameter). However most of these allometric equations cannot account for potential effects of increased N availability on biomass allocation patterns. Using 18 yr of tree diameter, height, and mortality data collected for a dominant tree species (Acer saccharum) in an atmospheric N deposition experiment, we evaluated how greater N availability affects allometric relationships in this species. After taking into account site and individual variability, our results reveal significant differences in allometric parameters between ambient and experimental N deposition treatments. Large trees under experimental N deposition reached greater heights at a given diameter; moreover, their estimated maximum height (mean ± standard deviation: 33.7 ± 0.38 m) was significantly higher than that estimated under the ambient condition (31.3 ± 0.31 m). Within small tree sizes (5-10 cm diameter) there was greater mortality under experimental N deposition, whereas the relative growth rates of small trees were greater under experimental N deposition. Calculations of stemwood biomass using our parameter estimates for the diameter-height relationship indicated the potential for significant biases in these estimates (~2.5%), with under predictions of stemwood biomass averaging 4 Mg/ha lower if ambient parameters were to be used to estimate stem biomass of trees in the experimental N deposition treatment. As atmospheric N deposition continues to increase into the future, ignoring changes in tree allometry will contribute to the uncertainty associated with aboveground carbon storage
Ibáñez, Inés; Zak, Donald R; Burton, Andrew J; Pregitzer, Kurt S
2016-04-01
As increasing levels of nitrogen (N) deposition impact many terrestrial ecosystems, understanding the potential effects of higher N availability is critical for forecasting tree carbon allocation patterns and thus future forest productivity. Most regional estimates of forest biomass apply allometric equations, with parameters estimated from a limited number of studies, to forest inventory data (i.e., tree diameter). However most of these allometric equations cannot account for potential effects of increased N availability on biomass allocation patterns. Using 18 yr of tree diameter, height, and mortality data collected for a dominant tree species (Acer saccharum) in an atmospheric N deposition experiment, we evaluated how greater N availability affects allometric relationships in this species. After taking into account site and individual variability, our results reveal significant differences in allometric parameters between ambient and experimental N deposition treatments. Large trees under experimental N deposition reached greater heights at a given diameter; moreover, their estimated maximum height (mean ± standard deviation: 33.7 ± 0.38 m) was significantly higher than that estimated under the ambient condition (31.3 ± 0.31 m). Within small tree sizes (5-10 cm diameter) there was greater mortality under experimental N deposition, whereas the relative growth rates of small trees were greater under experimental N deposition. Calculations of stemwood biomass using our parameter estimates for the diameter-height relationship indicated the potential for significant biases in these estimates (~2.5%), with under predictions of stemwood biomass averaging 4 Mg/ha lower if ambient parameters were to be used to estimate stem biomass of trees in the experimental N deposition treatment. As atmospheric N deposition continues to increase into the future, ignoring changes in tree allometry will contribute to the uncertainty associated with aboveground carbon storage
Cox, S K
2007-10-01
The purpose of this study was to examine the allometric analyses of marbofloxacin, moxifloxacin, danofloxacin and difloxacin using pharmacokinetic data from the literature. The parameters of interest (half-life, clearance and volume of distribution) were correlated across species as a function of body weight using an allometric approach (Y = aWb). Results of the allometric analysis indicated similarity between clearance and volume of distribution as they relate to body weight for all drugs. The elimination half-life was independent of body mass for all fluoroquinolones except moxifloxacin. Results of the analysis suggest that allometric scaling can be used as a tool for predicting pharmacokinetic parameters for fluoroquinolones.
Relations Among Systems of Electromagnetic Equations
ERIC Educational Resources Information Center
page, Chester H.
1970-01-01
Contends that the equations of electromagnetism, whether in rationalized or non-rationalized form, express an invariant set of physical relationships. The relationships among corresponding symbols are given and applied to precise statements about the relation between the oersted and the amphere per meter, the abampere and the ampere, etc.…
An allometric analysis of the giraffe cardiovascular system.
Mitchell, G; Skinner, J D
2009-12-01
There has been co-evolution of a long neck and high blood pressure in giraffes. How the cardiovascular system (CVS) has adapted to produce a high blood pressure, and how it compares with other similar sized mammals largely is unknown. We have measured body mass and heart structure in 56 giraffes of both genders ranging in body mass from 18 kg to 1500 kg, and developed allometric equations that relate changes in heart dimensions to growth and to cardiovascular function. Predictions made from these equations match measurements made in giraffes. We have found that heart mass increases as body mass increases but it has a relative mass of 0.51+/-0.7% of body mass which is the same as that in other mammals. The left ventricular and interventricular walls are hypertrophied and their thicknesses are linearly related to neck length. Systemic blood pressure increases as body mass and neck length increase and is twice that of mammals of the same body mass. Cardiac output is the same as, but peripheral resistance double that predicted for similar sized mammals. We have concluded that increasing hydrostatic pressure of the column of blood during neck elongation results in cardiac hypertrophy and concurrent hypertrophy of arteriole walls raising peripheral resistance, with an increase in blood pressure following.
NASA Astrophysics Data System (ADS)
Banavar, Jayanth
2009-03-01
The unity of life is expressed not only in the universal basis of inheritance and energetics at the molecular level, but also in the pervasive scaling of traits with body size at the whole-organism level. More than 75 years ago, Kleiber and Brody and Proctor independently showed that the metabolic rates, B, of mammals and birds scale as the three-quarter power of their mass, M. Subsequent studies showed that most biological rates and times scale as M-1/4 and M^1/4 respectively, and that these so called quarter-power scaling relations hold for a variety of organisms, from unicellular prokaryotes and eukaryotes to trees and mammals. The wide applicability of Kleiber's law, across the 22 orders of magnitude of body mass from minute bacteria to giant whales and sequoias, raises the hope that there is some simple general explanation that underlies the incredible diversity of form and function. We will present a general theoretical framework for understanding the relationship between metabolic rate, B, and body mass, M. We show how the pervasive quarter-power biological scaling relations arise naturally from optimal directed resource supply systems. This framework robustly predicts that: 1) whole organism power and resource supply rate, B, scale as M^3/4; 2) most other rates, such as heart rate and maximal population growth rate scale as M-1/4; 3) most biological times, such as blood circulation time and lifespan, scale as M^1/4; and 4) the average velocity of flow through the network, v, such as the speed of blood and oxygen delivery, scales as M^1/12. Our framework is valid even when there is no underlying network. Our theory is applicable to unicellular organisms as well as to large animals and plants. This work was carried out in collaboration with Amos Maritan along with Jim Brown, John Damuth, Melanie Moses, Andrea Rinaldo, and Geoff West.
Control of metabolic rate is a hidden variable in the allometric scaling of homeotherms.
Chaui-Berlinck, José Guilherme; Navas, Carlos Arturo; Monteiro, Luiz Henrique Alves; Bicudo, José Eduardo Pereira Wilken
2005-05-01
The allometric scaling exponent of the relationship between standard metabolic rate (SMR) and body mass for homeotherms has a long history and has been subject to much debate. Provided the external and internal conditions required to measure SMR are met, it is tacitly assumed that the metabolic rate (B) converges to SMR. If SMR does indeed represent a local minimum, then short-term regulatory control mechanisms should not operate to sustain it. This is a hidden assumption in many published articles aiming to explain the scaling exponent in terms of physical and morphological constraints. This paper discusses the findings of a minimalist body temperature (Tb) control model in which short-term controlling operations, related to the difference between Tb and the set-point temperatures by specific gains and time delays in the control loops, are described by a system of differential equations of Tb, B and thermal conductance. We found that because the gains in the control loops tend to increase as body size decreases (i.e. changes in B and thermal conductance are speeded-up in small homeotherms), the equilibrium point of the system potentially changes from asymptotically stable to a centre, transforming B and Tb in oscillating variables. Under these specific circumstances the very concept of SMR no longer makes sense. A series of empirical reports of metabolic rate in very small homeotherms supports this theoretical prediction, because in these animals B seems not to converge to a SMR value. We conclude that the unrestricted use of allometric equations to relate metabolic rate to body size might be misleading because metabolic control itself experiences size effects that are overlooked in ordinary allometric analysis.
Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents.
Wilson, Laura A B; Sánchez-Villagra, Marcelo R
2010-04-22
It has been hypothesized that most morphological evolution occurs by allometric differentiation. Because rodents encapsulate a phenomenal amount of taxonomic diversity and, among several clades, contrasting levels of morphological diversity, they represent an excellent subject to address the question: how variable are allometric patterns during evolution? We investigated the influence of phylogenetic relations and ecological factors on the results of the first quantification of allometric disparity among rodents by exploring allometric space, a multivariate morphospace here derived from, and encapsulating all, the ontogenetic trajectories of 34 rodent species from two parallel phylogenetic radiations. Disparity was quantified using angles between ontogenetic trajectories for different species and clades. We found an overlapping occupation of allometric space by muroid and hystricognath species, revealing both clades possess similar abilities to evolve in different directions of phenotypic space, and anatomical diversity does not act to constrain the labile nature of allometric patterning. Morphological features to enable efficient processing of food serve to group rodents in allometric space, reflecting the importance of convergent morphology, rather than shared evolutionary history, in the generation of allometric patterns. Our results indicate that the conserved level of morphological integration found among primates cannot simply be extended to all mammals. PMID:20018789
Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents.
Wilson, Laura A B; Sánchez-Villagra, Marcelo R
2010-04-22
It has been hypothesized that most morphological evolution occurs by allometric differentiation. Because rodents encapsulate a phenomenal amount of taxonomic diversity and, among several clades, contrasting levels of morphological diversity, they represent an excellent subject to address the question: how variable are allometric patterns during evolution? We investigated the influence of phylogenetic relations and ecological factors on the results of the first quantification of allometric disparity among rodents by exploring allometric space, a multivariate morphospace here derived from, and encapsulating all, the ontogenetic trajectories of 34 rodent species from two parallel phylogenetic radiations. Disparity was quantified using angles between ontogenetic trajectories for different species and clades. We found an overlapping occupation of allometric space by muroid and hystricognath species, revealing both clades possess similar abilities to evolve in different directions of phenotypic space, and anatomical diversity does not act to constrain the labile nature of allometric patterning. Morphological features to enable efficient processing of food serve to group rodents in allometric space, reflecting the importance of convergent morphology, rather than shared evolutionary history, in the generation of allometric patterns. Our results indicate that the conserved level of morphological integration found among primates cannot simply be extended to all mammals.
Allometric scaling and accidents at work
Cempel, Czesław; Tabaszewski, Maciej; Ordysiński, Szymon
2016-01-01
Allometry is the knowledge concerning relations between the features of some beings, like animals, or cities. For example, the daily energy rate is proportional to a mass of mammals rise of 3/4. This way of thinking has spread quickly from biology to many areas of research concerned with sociotechnical systems. It was revealed that the number of innovations, patents or heavy crimes rises as social interaction increases in a bigger city, while other urban indexes such as suicides decrease with social interaction. Enterprise is also a sociotechnical system, where social interaction and accidents at work take place. Therefore, do these interactions increase the number of accidents at work or, on the contrary, are they reduction-driving components? This article tries to catch such links and assess the allometric exponent between the number of accidents at work and the number of employees in an enterprise. PMID:26655044
Cade, B.S.; Terrell, J.W.; Neely, B.C.
2011-01-01
Increasing our understanding of how environmental factors affect fish body condition and improving its utility as a metric of aquatic system health require reliable estimates of spatial variation in condition (weight at length). We used three statistical approaches that varied in how they accounted for heterogeneity in allometric growth to estimate differences in body condition of blue suckers Cycleptus elongatus across 19 large-river locations in the central USA. Quantile regression of an expanded allometric growth model provided the most comprehensive estimates, including variation in exponents within and among locations (range = 2.88–4.24). Blue suckers from more-southerly locations had the largest exponents. Mixed-effects mean regression of a similar expanded allometric growth model allowed exponents to vary among locations (range = 3.03–3.60). Mean relative weights compared across selected intervals of total length (TL = 510–594 and 594–692 mm) in a multiplicative model involved the implicit assumption that allometric exponents within and among locations were similar to the exponent (3.46) for the standard weight equation. Proportionate differences in the quantiles of weight at length for adult blue suckers (TL = 510, 594, 644, and 692 mm) compared with their average across locations ranged from 1.08 to 1.30 for southern locations (Texas, Mississippi) and from 0.84 to 1.00 for northern locations (Montana, North Dakota); proportionate differences for mean weight ranged from 1.13 to 1.17 and from 0.87 to 0.95, respectively, and those for mean relative weight ranged from 1.10 to 1.18 and from 0.86 to 0.98, respectively. Weights for fish at longer lengths varied by 600–700 g within a location and by as much as 2,000 g among southern and northern locations. Estimates for the Wabash River, Indiana (0.96–1.07 times the average; greatest increases for lower weights at shorter TLs), and for the Missouri River from Blair, Nebraska, to Sioux City, Iowa (0.90
Analytic theories of allometric scaling.
Agutter, Paul S; Tuszynski, Jack A
2011-04-01
During the 13 years since it was first advanced, the fractal network theory (FNT), an analytic theory of allometric scaling, has been subjected to a wide range of methodological, mathematical and empirical criticisms, not all of which have been answered satisfactorily. FNT presumes a two-variable power-law relationship between metabolic rate and body mass. This assumption has been widely accepted in the past, but a growing body of evidence during the past quarter century has raised questions about its general validity. There is now a need for alternative theories of metabolic scaling that are consistent with empirical observations over a broad range of biological applications. In this article, we briefly review the limitations of FNT, examine the evidence that the two-variable power-law assumption is invalid, and outline alternative perspectives. In particular, we discuss quantum metabolism (QM), an analytic theory based on molecular-cellular processes. QM predicts the large variations in scaling exponent that are found empirically and also predicts the temperature dependence of the proportionality constant, issues that have eluded models such as FNT that are based on macroscopic and network properties of organisms.
Stochastic partial differential equations in turbulence related problems
NASA Technical Reports Server (NTRS)
Chow, P.-L.
1978-01-01
The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.
Logic programming: Functions, relations and equations
DeGroot, D.
1985-01-01
This collection of articles describes and explains the major approaches used to combine logic programming and functional programming. It examines both theory and details of implementations, emphasizing relationships, and prospects for fruitful combination in the future. It introduces functional syntax and semantics, and equational theories, using a variety of methods. It provides several actual program codes, to allow readers to begin experimenting immediately using standard Prolog-language interpreters.
Equations of motion in general relativity and quantum mechanics
NASA Astrophysics Data System (ADS)
O'Hara, Paul
2011-12-01
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves is investigated. A generalized Dirac equation is derived and shown to be related to the Lie derivative of the momentum along the curve. In addition,the equations of motion are derived from the Hamilton-Jacobi equation associated with the metric and the wave equation associated with the Hamiltonian is then shown not to commute with the Dirac operator. Finally, the Maxwell-Boltzmann distribution is shown to be a consequence of geodesic motion.
Allometric Scaling Across Environmental Gradients
NASA Astrophysics Data System (ADS)
Duncanson, L.; Dubayah, R.
2014-12-01
Developing a better understanding of the controls on biomass allocation in forested systems and the consequences for carbon stocks and fluxes is required for improved ecosystem and climate modeling. A simple model, based largely on resource distribution networks, was presented by West, Brown and Enquist (1999). Their model predicts that the exponents of allometric relationships between many forest structural and functional properties will be constants, irrespective of environment or species. In this research we assess the validity of model predictions across the United States and examine their independence with respect to environment. We focus on two relationships with particular importance to biomass: Ht ∝ DBH2/3 nDBH ∝ DBH-2 where Ht is height, DBH is Diameter at Breast Height, and nDBH is the number of trees in a given DBH size class. We obtained DBH and height data from the U.S. Forest Inventory Analysis (FIA) dataset, and fit an exponent to each relationship for every FIA plot across the US. We extracted environmental data from the FIA plots (forest maximum height, species type, age, topography) and the North American Regional Reassessment dataset (precipitation, temperature, PAR) and performed random forest regression to estimate observed exponents as a function of environment. We found that forest height, age, and forest type were the most important drivers of allometry, explaining about 40% of observed variability. We found that for both relationships, as forest height and age increase, exponents constrain to the theoretical predictions presented by WBE. This suggests that WBE predictions are valid and may be useful constraints in biomass mapping and ecosystem flux models. However, they deviate from predictions in younger, shorter stands where forests have not had time to develop a complex size structure. Additionally, there is a significant difference in both relationships between conifer and deciduous-dominated stands, suggesting that species type
Growth of the eye lens: II. Allometric studies
2014-01-01
Purpose The purpose of this study was to examine the ontogeny and phylogeny of lens growth in a variety of species using allometry. Methods Data on the accumulation of wet and/or dry lens weight as a function of bodyweight were obtained for 40 species and subjected to allometric analysis to examine ontogenic growth and compaction. Allometric analysis was also used to compare the maximum adult lens weights for 147 species with the maximum adult bodyweight and to compare lens volumes calculated from wet and dry weights with eye volumes calculated from axial length. Results Linear allometric relationships were obtained for the comparison of ontogenic lens and bodyweight accumulation. The body mass exponent (BME) decreased with increasing animal size from around 1.0 in small rodents to 0.4 in large ungulates for both wet and dry weights. Compaction constants for the ontogenic growth ranged from 1.00 in birds and reptiles up to 1.30 in mammals. Allometric comparison of maximum lens wet and dry weights with maximum bodyweights also yielded linear plots with a BME of 0.504 for all warm blooded species except primates which had a BME of 0.25. When lens volumes were compared with eye volumes, all species yielded a scaling constant of 0.75 but the proportionality constants for primates and birds were lower. Conclusions Ontogenic lens growth is fastest, relative to body growth, in small animals and slowest in large animals. Fiber cell compaction takes place throughout life in most species, but not in birds and reptiles. Maximum adult lens size scales with eye size with the same exponent in all species, but birds and primates have smaller lenses relative to eye size than other species. Optical properties of the lens are generated through the combination of variations in the rate of growth, rate of compaction, shape and size. PMID:24715759
Alternate Forms of Relative Attitude Kinematics and Dynamics Equations
NASA Technical Reports Server (NTRS)
Xing, Guang Q.; Parvez, Shabbir A.
2001-01-01
In this paper the alternate forms of the relative attitude kinematics and relative dynamics equations are presented. These developments are different from the earlier developments that have been presented in other publications. The current forms of equations have the advantage of being simpler than earlier ones. These equations are applied in developing the necessary kinematics and dynamics for relative navigation in formation flying and virtual platforms. These equations also have application in the implementation of nonlinear full state feedback and nonlinear output feedback control for large attitude angle acquisition and tracking. This paper presents simulations from such a full state feedback control application.
Ontogenetic study of allometric variation in Homo and Pan mandibles.
Singh, Nandini
2014-02-01
Investigating ontogenetic variation and allometry in the mandible can provide valuable insight and aid in addressing questions related to the ontogeny of the skull. Here, patterns of ontogenetic shape change and allometric trajectories were examined in the mandible of 187 sub-adult and adult humans, bonobos, and chimpanzees. Procrustes-based geometric morphometrics was employed to quantify and analyze mandibular form. Thirty three-dimensional landmarks were used to capture the overall morphology of the mandible, and the landmarks were analyzed as a whole and subdivided into separate anterior and posterior units. Principal component analyses in Procrustes shape-space and form-space, and multivariate regressions were used to examine patterns of ontogenetic and allometric shape change. Results suggest that humans are distinct from Pan both in their mandibular morphology, particularly in the anterior-alveolar region, and direction of allometric trajectory. Chimpanzees and bonobos have parallel ontogenetic trajectories, but also show differences in mandibular shape. Species-specific features and adult mandibular shape are established before or by the eruption of the deciduous dentition. This suggests that developmental processes prior to deciduous teeth eruption have a stronger effect establishing taxa-specific phenotypes than later postnatal effects. This additionally implies that divergent trajectories between Pan and Homo do not contribute much to the adult mandibular shape after deciduous teeth eruption. Separate analyses of the anterior-alveolar region and ascending ramus show that these regions are semi-independent in their developmental pattern of shape change and allometry. This implies that allometric variation and ontogenetic shape change in the hominoid mandible is decoupled.
Allometric relationships between the length of pregnancy and body parameters in mammals
NASA Astrophysics Data System (ADS)
Atanasov, A. T.; Todorova, M.; Valev, D. T.; Todorova, R.
2014-10-01
In this manuscript we investigated the presence of allometric relationships between the length of pregnancy and the body parameters in mammals. The relationships between the length of pregnancy T (d) and the square of body length H2 (m2), body surface S (m2), body mass to surface ratio M/S (kg/m2) and body-mass index (BMI) (M/H2) were investigated in mammals: Metatheria and Placentalia, including animals with body mass ranging from 8g in Common shrew to 15t in Killer whale. In result, the found power equations are: T = 114.3 (H2)0.352; T= 120.4 S0.38; T = 9.147 (M/S)0.757 and T = 17.6 BMI0.605. The study showed that the M/S ratio and BMI are nearly equivalent characteristics in relation to length of pregnancy.
Quantum statistics and allometric scaling of organisms
NASA Astrophysics Data System (ADS)
Demetrius, Lloyd
2003-05-01
This article proposes a mechanism to explain allometric relations between basal metabolic rate and the body size of organisms. The model postulates that energy transduction in biological organisms is constrained by two classes of dynamical processes: The first process has its origin in quantum mechanics and the constraints which the coupling of electron transport and proton translocation impose on metabolic activity. The second derives from evolutionary dynamics and the constraints which ecological and demographic forces impose on metabolic rate. These two processes are invoked to show that the scaling exponent between basal metabolic rate and body size follows a {3}/{4} rule, in the case of organisms subject to ecological constraints defined by scarce but dependable resources, and a {2}/{3} rule when constraints are defined by ample but only temporarily available resources. Our conclusions are based on general arguments incorporating the molecular mechanisms that determine metabolic activity at all levels of biological organization. Hence the model applies to uni-cellular organisms, plants and animals.
BOOK REVIEW: Equations of Motion in General Relativity Equations of Motion in General Relativity
NASA Astrophysics Data System (ADS)
Schäfer, Gerhard
2012-03-01
Devoted exclusively to the problem of motion in general relativity, this book by H. Asada, T. Futamase, and P. A. Hogan is highly welcome to close up a gap in the book sector presenting a concise account of theoretical developments and results on gravitational equations of motion achieved since the discovery of the binary neutron star system PSR 1913+16 in 1974. For the most part, the book is concerned with the development and application of the important post-Newtonian approximation (PNA) framework which allows for highly efficient approximate analytic solutions of the Einstein field equations for many-body systems in terms of a slow-motion and weak-field ordering parameter. That approximation scheme is shown to be applicable also to the external motion of strongly self-gravitating objects if their internal dynamics is frozen in (strong field point particle limit) and the external conditions fit. Relying on the expertise of the authors, the PNA framework is presented in a form which, at the 1PNA level, had become famous through the work by Einstein, Infeld and Hoffmann in 1938; therein, surface integrals over gravitational field expressions in the outside-body regime play a crucial role. Other approaches which also succeeded with the highest achieved PNA level so far are mentioned too, if not fully exhaustively with respect to the highest, the 3.5PNA level which contains the inverse power of the speed of light to the seventh order. Regarding the 3PNA, the reader gains a clear understanding of how the equations of motion for binary systems with compact components come about. Remarkably, no deviation from four-dimensional space-time is needed. Various explicit analytic expressions are derived for binary systems: the periastron advance and the orbital period at the 2PNA, the orbital decay through gravitational radiation reaction at the 2.5PNA, and effects of the gravitational spin-orbit and spin-spin couplings on the orbital motion. Also the propagation of light
A microscopic model of interface related to the Burgers equation
De Masi, A.; Ferrari, P.A.; Vares, M.E. )
1989-05-01
A microscopic model for a solid-on-solid type of interface under the influence of an external field is introduced. It is proven that in equilibrium the macroscopic profile satisfies a partial differential equation which is (up to a transformation) the stationary Burgers equation. The study is based on the structure of the invariant measures for a related asymmetric simple exclusion process.
Dispersion relation equation preserving FDTD method for nonlinear cubic Schrödinger equation
NASA Astrophysics Data System (ADS)
Sheu, Tony W. H.; Le Lin
2015-10-01
In this study we aim to solve the cubic nonlinear Schrödinger (CNLS) equation by the method of fractional steps. Over a time step from tn to tn+1, the linear part of the Schrödinger equation is solved firstly through four time integration steps. In this part of the simulation, the explicit symplectic scheme of fourth order accuracy is adopted to approximate the time derivative term. The second-order spatial derivative term in the linear Schrödinger equation is approximated by centered scheme. The resulting symplectic and space centered difference scheme renders an optimized numerical dispersion relation equation. In the second part of the simulation, the solution of the nonlinear equation is computed exactly thanks to the embedded invariant nature within each time increment. The proposed semi-discretized difference scheme underlying the modified equation analysis of second kind and the method of dispersion error minimization has been assessed in terms of the spatial modified wavenumber or the temporal angular frequency resolution. Several problems have been solved to show that application of this new finite difference scheme for the calculation of one- and two-dimensional Schrödinger equations can deemed conserve Hamiltonian quantities and preserve dispersion relation equation (DRE).
The equations of relative motion in the orbital reference frame
NASA Astrophysics Data System (ADS)
Casotto, Stefano
2016-03-01
The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill-Clohessy-Wiltshire equations. Circular motion is not, however, a solution when the Earth's flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the J_2 effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the J_2 perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a J_2-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill-Clohessy-Wiltshire equations for circular reference motion, or the de Vries/Tschauner-Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the J_2 perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession
Some mathematical questions related to the MHD equations
Sermange, M.; Temam, R.
1983-09-01
Some questions relating to the large time behavior of the solutions of MHD equations for a viscous incompressible resistive fluid are investigated. The physical system is briefly described and the functional setting of the equations, a flow in a bounded domain or in whole space with a space periodicity property in all directions. The main existence and uniqueness results for weak and strong solutions of the MHD equations are recalled. Regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular. The squeezing property of the trajectories are stated and it is shown that any functional invariant set for the MHD equations, and in particular any attractor, has a finite Haussdorf dimension. The flow is found to be totally determined for large dimensions by a finite number of parameters. 26 references.
Problems of allometric scaling analysis: examples from mammalian reproductive biology.
Martin, Robert D; Genoud, Michel; Hemelrijk, Charlotte K
2005-05-01
Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best
BOOK REVIEW: Partial Differential Equations in General Relativity
NASA Astrophysics Data System (ADS)
Halburd, Rodney G.
2008-11-01
Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed
Time-dependent closure relations for relativistic collisionless fluid equations
Bendib-Kalache, K.; Bendib, A.; El Hadj, K. Mohammed
2010-11-15
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space ({omega},k), where {omega} and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter {omega}/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc{sup 2}/T, where m is the particle rest mass and T, the plasma temperature in energy units.
Vector order parameter in general relativity: Covariant equations
Meierovich, Boris E.
2010-07-15
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are derived. The topological defects are classified in accordance with the symmetry of the covariant derivative of the vector order parameter. The abilities of the derived equations are demonstrated in application to the braneworld concept. New solutions of the Einstein equations with a transverse vector order parameter are presented. In the vicinity of phase transition, the solutions are found analytically.
Time-dependent closure relations for relativistic collisionless fluid equations.
Bendib-Kalache, K; Bendib, A; El Hadj, K Mohammed
2010-11-01
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units.
Bäcklund transformations relating different Hamilton-Jacobi equations
NASA Astrophysics Data System (ADS)
Sozonov, A. P.; Tsiganov, A. V.
2015-06-01
We discuss one of the possible finite-dimensional analogues of the general Bäcklund transformation relating different partial differential equations. We show that different Hamilton-Jacobi equations can be obtained from the same Lax matrix. We consider Hénon-Heiles systems on the plane, Neumann and Chaplygin systems on the sphere, and two integrable systems with velocity-dependent potentials as examples.
NASA Astrophysics Data System (ADS)
Hofhansl, Florian; Schnecker, Jörg; Singer, Gabriel; Wanek, Wolfgang
2014-05-01
Tropical forest ecosystems play a major role in global water and carbon cycles. However, mechanisms of C allocation in tropical forests and their response to environmental variation are largely unresolved as, due to the scarcity of data, they are underrepresented in global syntheses of forest C allocation. Allocation of gross primary production to wood production exerts a key control on forest C residence time and biomass C turnover, and therefore is of special interest for terrestrial ecosystem research and earth system science. Here, we synthesize pantropical data from 105 old-growth rainforests to investigate relationships between climate (mean annual precipitation, mean annual temperature, dry season length and cloud cover), soil nutrient relations (soil N:P) and the partitioning of aboveground net primary production (ANPP) to wood production (WPart) using structural equation modelling. Our results show a strong increase of WPart with ANPP, pointing towards allometric scaling controls on WPart, with increasing light competition in more productive forests triggering greater ANPP allocation to wood production. ANPP itself was positively affected by mean annual temperature and soil N:P. Beyond these allometric controls on WPart we found direct environmental controls. WPart increased with dry season length in tropical montane rainforests and with mean annual precipitation in lowland tropical rainforests. We discuss different trade-offs between plant traits, such as community-wide changes along the wood economics spectrum, the leaf economics spectrum and the plant resource economics spectrum, as underlying mechanisms for direct climatic controls on WPart. We thereby provide new insights into mechanisms driving carbon allocation to WPart in tropical rainforests and show that low and high productive tropical rainforests may respond differently to projected global changes.
Peng, Yunfeng; Yang, Yuanhe
2016-01-01
Allometric and optimal hypotheses have been widely used to explain biomass partitioning in response to resource changes for individual plants; however, little evidence has been reported from measurements at the community level across a broad geographic scale. This study assessed the nitrogen (N) effect on community-level root to shoot (R/S) ratios and biomass partitioning functions by synthesizing global manipulative experiments. Results showed that, in aggregate, N addition decreased the R/S ratios in various biomes. However, the scaling slopes of the allometric equations were not significantly altered by the N enrichment, possibly indicating that N-induced reduction of the R/S ratio is a consequence of allometric allocation as a function of increasing plant size rather than an optimal partitioning model. To further illustrate this point, we developed power function models to explore the relationships between aboveground and belowground biomass for various biomes; then, we generated the predicted root biomass from the observed shoot biomass and predicted R/S ratios. The comparison of predicted and observed N-induced changes of the R/S ratio revealed no significant differences between each other, supporting the allometric allocation hypothesis. These results suggest that allometry, rather than optimal allocation, explains the N-induced reduction in the R/S ratio across global biomes. PMID:27349584
NASA Astrophysics Data System (ADS)
Peng, Yunfeng; Yang, Yuanhe
2016-06-01
Allometric and optimal hypotheses have been widely used to explain biomass partitioning in response to resource changes for individual plants; however, little evidence has been reported from measurements at the community level across a broad geographic scale. This study assessed the nitrogen (N) effect on community-level root to shoot (R/S) ratios and biomass partitioning functions by synthesizing global manipulative experiments. Results showed that, in aggregate, N addition decreased the R/S ratios in various biomes. However, the scaling slopes of the allometric equations were not significantly altered by the N enrichment, possibly indicating that N-induced reduction of the R/S ratio is a consequence of allometric allocation as a function of increasing plant size rather than an optimal partitioning model. To further illustrate this point, we developed power function models to explore the relationships between aboveground and belowground biomass for various biomes; then, we generated the predicted root biomass from the observed shoot biomass and predicted R/S ratios. The comparison of predicted and observed N-induced changes of the R/S ratio revealed no significant differences between each other, supporting the allometric allocation hypothesis. These results suggest that allometry, rather than optimal allocation, explains the N-induced reduction in the R/S ratio across global biomes.
Allometric Scaling of Wingate Anaerobic Power Test Scores in Women
ERIC Educational Resources Information Center
Hetzler, Ronald K.; Stickley, Christopher D.; Kimura, Iris F.
2011-01-01
In this study, we developed allometric exponents for scaling Wingate anaerobic test (WAnT) power data that are reflective in controlling for body mass (BM) and lean body mass (LBM) and established a normative WAnT data set for college-age women. One hundred women completed a standard WAnT. Allometric exponents and percentile ranks for peak (PP)…
Complexity Increases Predictability in Allometrically Constrained Food Webs.
Iles, Alison C; Novak, Mark
2016-07-01
All ecosystems are subjected to chronic disturbances, such as harvest, pollution, and climate change. The capacity to forecast how species respond to such press perturbations is limited by our imprecise knowledge of pairwise species interaction strengths and the many direct and indirect pathways along which perturbations can propagate between species. Network complexity (size and connectance) has thereby been seen to limit the predictability of ecological systems. Here we demonstrate a counteracting mechanism in which the influence of indirect effects declines with increasing network complexity when species interactions are governed by universal allometric constraints. With these constraints, network size and connectance interact to produce a skewed distribution of interaction strengths whose skew becomes more pronounced with increasing complexity. Together, the increased prevalence of weak interactions and the increased relative strength and rarity of strong interactions in complex networks limit disturbance propagation and preserve the qualitative predictability of net effects even when pairwise interaction strengths exhibit substantial variation or uncertainty.
Peak power prediction in junior basketballers: comparing linear and allometric models.
Duncan, Michael J; Hankey, Joanne; Lyons, Mark; James, Rob S; Nevill, Alan M
2013-03-01
Equations, commonly used to predict peak power from jump height, have relied on linear additive models that are biologically unsound beyond the range of observations because of high negative intercept values. This study explored the utility of allometric multiplicative modeling to better predict peak power in adolescent basketball players. Seventy-seven elite junior basketball players (62 adolescent boys, 15 adolescent girls, age = 16.8 ± 0.8 years) performed 3 counter movement jumps (CMJs) on a force platform. Both linear and multiplicative models were then used to determine their efficacy. Four previously published linear equations were significantly associated with actual peak power (all p < 0.01), although here were significant differences between actual and estimated peak power using the SJ and CMJ equations by Sayers (both p < 0.001). Allometric modeling was used to determine an alternative biologically sound equation which was more strongly associated with (r = 0.886, p < 0.001), and not significantly different to (p > 0.05), actual peak power and predicted 77.9% of the variance in actual peak power (adjusted R = 0.779, p < 0.001). Exponents close to 1 for body mass and CMJ height indicated that peak power could also be determined from the product of body mass and CMJ height. This equation was significantly associated (r = 0.871, p < 0.001) with, and not significantly different to, actual peak power (adjusted R = 0.756, p > 0.05) and offered a more accurate estimation of peak power than previously validated linear additive models examined in this study. The allometric model determined from this study or the multiplicative model (body mass × CMJ height) provides biologically sound models to accurately estimate peak power in elite adolescent basketballers that are more accurate than equations based on linear additive models.
BOOK REVIEW: Partial Differential Equations in General Relativity
NASA Astrophysics Data System (ADS)
Choquet-Bruhat, Yvonne
2008-09-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory.
Static gravitational equations of general relativity and "the fifth force"
NASA Astrophysics Data System (ADS)
Das, A.
2015-10-01
Einstein's static field equations are investigated in various coordinate charts. After comparing Newtonian gravitational theory (in a curvilinear coordinate chart) with various charts of Einstein's static gravitational equations, the most appropriate choice of the coordinate chart for Einstein's static field equations is made. As a consequence, Einstein's equations imply the non-linear potential equation instead of the usual Poisson's equation of the Newtonian theory. Investigating the non-linear potential equation above in the spherically symmetric cases, the corresponding potentials yield scenarios comparable to "the fifth force". Next, static gravitational and electric fields generated by an incoherent charged dust are investigated. The corresponding non-linear potential equation is derived. Finally, the static Einstein-Maxwell-Klein-Gordon equations are explored and again, the corresponding non-linear potential equation is obtained. This potential resembles the static Higgs boson field.
NASA Astrophysics Data System (ADS)
Tatarskii, V. I.
1995-06-01
The steps necessary to produce the Rayleigh equation that is based on the Rayleigh hypothesis from the equation that is based on the Green's formula are shown. First a definition is given for the scattering amplitude that is true not only in the far zone of diffraction but also near the scattering surface. With this definition the Rayleigh equation coincides with the rigorous equation for the surface secondary sources that is based on Green's formula. The Rayleigh hypothesis is equivalent to substituting the far-zone expression of the scattering amplitude into this rigorous equation. In this case it turns out to be the equation not for the sources but directly for the scattering amplitude, which is the main advantage of this method. For comparing the Rayleigh equation with the initial rigorous equation, the Rayleigh equation is represented in terms of secondary sources. The kernel of this equation contains an integral that converges for positive and diverges for negative values of some parameter. It is shown that if we regularize this integral, defining it for the negative values of this parameter as an analytical continuation from the domain of positive values, this kernel becomes equal to the kernel of the initial rigorous equation. It follows that the formal perturbation series for the scattering amplitude obtained from the Rayleigh equation and from Green's equation always coincide. This means that convergence of the perturbation series is a sufficient condition
Relations between nonlinear Riccati equations and other equations in fundamental physics
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2014-10-01
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.
Allometric scaling and predicting cycling performance in (well-) trained female cyclists.
Lamberts, R P; Davidowitz, K J
2014-03-01
As female cycling attains greater professionalism, a larger emphasis is placed on the ability to predict and monitor changes in their cycling performance. The main aim of this study was to determine if peak power output (PPO) adjusted for body mass (W · kg-0.32) accurately predicts flat 40-km time trial performance (40 km TT) in female cyclists as found in men. 20 (well-) trained female cyclists completed a PPO test including maximal oxygen consumption (VO2max) and a flat 40 km TT test. Relationships between cycling performance parameters were also compared to the cycling performance of 45 male cyclists. Allometrically scaled PPW (W · kg(-0.32)) most accurately predicted 40 km TT performance in the female cyclists (r = -0.87, p<0.0001) compared to any other method, however different slopes between the parameters were found in the female and male cyclists (p=0.000115). In addition gender differences were also found between the relationship between relative PPO (W · kg-1) and relative VO2max (ml · min-1 · kg(-1))(p<0.0001), while no gender differences were found between actual and predicted cycling performance based on the Lamberts and Lambert Submaximal Cycle Test (LSCT), which was used a standardized warm-up. In conclusion, relationships between relative cycling parameters seem to differ between genders, while relationships between absolute cycling parameters seem to be similar. Therefore gender specific regression equations should be used when predicting relative cycling performance parameters.
Huang, Q; Gehring, R; Tell, L A; Li, M; Riviere, J E
2015-06-01
Allometric scaling is widely used for the determination of first dosage regimen and the interpolation or extrapolation of pharmacokinetic parameters across many animal species during drug development. In this article, 85 drugs used in veterinary medicine obtained from the Food Animal Residue Avoidance Databank database were selected for allometric scaling analysis. Outlier species were identified by statistical methods. The results showed that 77% and 88% of drugs displayed significant correlations between total systemic clearance (CL) and volume of distribution at steady status (Vss) vs. body weight (P < 0.05) on a log-log scale, respectively. The distribution of the allometric exponent b for CL and Vss displays approximate normal distribution, with means (0.87 and 0.99) and standard deviations (0.143 and 0.157) for CL and Vss, respectively. Twelve drugs were identified to have at least one outlier species for CL and ten drugs for Vss. The human CL and Vss were predicted for selected drugs by the obtained allometric equations. The predicted CL and Vss were within a threefold error compared to observed values, except the predicted CL values for antipyrine, warfarin and diazepam. The results can be used to estimate cross-species pharmacokinetic profiles for predicting drug dosages in veterinary species, and to identify those species for which interpolation or extrapolation of pharmacokinetics properties may be problematic.
Jellyfish Body Plans Provide Allometric Advantages beyond Low Carbon Content
Pitt, Kylie A.; Duarte, Carlos M.; Lucas, Cathy H.; Sutherland, Kelly R.; Condon, Robert H.; Mianzan, Hermes; Purcell, Jennifer E.; Robinson, Kelly L.; Uye, Shin-Ichi
2013-01-01
Jellyfish form spectacular blooms throughout the world’s oceans. Jellyfish body plans are characterised by high water and low carbon contents which enables them to grow much larger than non-gelatinous animals of equivalent carbon content and to deviate from non-gelatinous pelagic animals when incorporated into allometric relationships. Jellyfish have, however, been argued to conform to allometric relationships when carbon content is used as the metric for comparison. Here we test the hypothesis that differences in allometric relationships for several key functional parameters remain for jellyfish even after their body sizes are scaled to their carbon content. Data on carbon and nitrogen contents, rates of respiration, excretion, growth, longevity and swimming velocity of jellyfish and other pelagic animals were assembled. Allometric relationships between each variable and the equivalent spherical diameters of jellyfish and other pelagic animals were compared before and after sizes of jellyfish were standardised for their carbon content. Before standardisation, the slopes of the allometric relationships for respiration, excretion and growth were the same for jellyfish and other pelagic taxa but the intercepts differed. After standardisation, slopes and intercepts for respiration were similar but excretion rates of jellyfish were 10× slower, and growth rates 2× faster than those of other pelagic animals. Longevity of jellyfish was independent of size. The slope of the allometric relationship of swimming velocity of jellyfish differed from that of other pelagic animals but because they are larger jellyfish operate at Reynolds numbers approximately 10× greater than those of other pelagic animals of comparable carbon content. We conclude that low carbon and high water contents alone do not explain the differences in the intercepts or slopes of the allometric relationships of jellyfish and other pelagic animals and that the evolutionary longevity of jellyfish and
NASA Astrophysics Data System (ADS)
Gourgoulhon, Eric
2011-04-01
Numerical relativity is one of the major fields of contemporary general relativity and is developing continually. Yet three years ago, no textbook was available on this subject. The first textbook devoted to numerical relativity, by Alcubierre, appeared in 2008 [1] (cf the CQG review [2]). Now comes the second book, by Baumgarte and Shapiro, two well known players in the field. Inevitably, the two books have some common aspects (otherwise they would not deal with the same topic!). For instance the titles of the first four chapters of Baumgarte and Shapiro are very similar to those of Alcubierre. This arises from some logic inherent to the subject: chapter 1 recaps basic GR, chapter 2 introduces the 3+1 formalism, chapter 3 focuses on the initial data and chapter 4 on the choice of coordinates for the evolution. But there are also many differences between the two books, which actually make them complementary. At first glance the differences are the size (720 pages for Baumgarte and Shapiro vs 464 pages for Alcubierre) and the colour figures in Baumgarte and Shapiro. Regarding the content, Baumgarte and Shapiro address many topics which are not present in Alcubierre's book, such as magnetohydrodynamics, radiative transfer, collisionless matter, spectral methods, rotating stars and post-Newtonian approximation. The main difference regards binary systems: virtually absent from Alcubierre's book (except for binary black hole initial data), they occupy not less than five chapters in Baumgarte and Shapiro's book. In contrast, gravitational wave extraction, various hyperbolic formulations of Einstein's equations and the high-resolution shock-capturing schemes are treated in more depth by Alcubierre. In the first four chapters mentioned above, some distinctive features of Baumgarte and Shapiro's book are the beautiful treatment of Oppenheimer-Snyder collapse in chapter 1, the analogy with Maxwell's equations when discussing the constraints and the evolution equations in
Probabilistic delay differential equation modeling of event-related potentials.
Ostwald, Dirk; Starke, Ludger
2016-08-01
"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach.
QPO observations related to neutron star equations of state
NASA Astrophysics Data System (ADS)
Stuchlik, Zdenek; Urbanec, Martin; Török, Gabriel; Bakala, Pavel; Cermak, Petr
We apply a genetic algorithm method for selection of neutron star models relating them to the resonant models of the twin peak quasiperiodic oscillations observed in the X-ray neutron star binary systems. It was suggested that pairs of kilo-hertz peaks in the X-ray Fourier power density spectra of some neutron stars reflect a non-linear resonance between two modes of accretion disk oscillations. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density ρc . These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR,ρc , Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR,ρc , Ω, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have most chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR,ρ, Ω, EOS) into chromosome we used Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.
Expression of VO2peak in Children and Youth, with Special Reference to Allometric Scaling.
Loftin, Mark; Sothern, Melinda; Abe, Takashi; Bonis, Marc
2016-10-01
The aim of this review was to highlight research that has focused on examining expressions of peak oxygen uptake (VO2peak) in children and youth, with special reference to allometric scaling. VO2peak is considered the highest VO2 during an increasing workload treadmill or bicycle ergometer test until volitional termination. We have reviewed scholarly works identified from PubMed, One Search, EBSCOhost and Google Scholar that examined VO2peak in absolute units (L·min(-1)), relative units [body mass, fat-free mass (FFM)], and allometric expressions [mass, height, lean body mass (LBM) or LBM of the legs raised to a power function] through July 2015. Often, the objective of measuring VO2peak is to evaluate cardiorespiratory function and fitness level. Since body size (body mass and height) frequently vary greatly in children and youth, expressing VO2peak in dimensionless units is often inappropriate for comparative or explanatory purposes. Consequently, expressing VO2peak in allometric units has gained increased research attention over the past 2 decades. In our review, scaling mass was the most frequent variable employed, with coefficients ranging from approximately 0.30 to over 1.0. The wide variance is probably due to several factors, including mass, height, LBM, sex, age, physical training, and small sample size. In summary, we recommend that since skeletal muscle is paramount for human locomotion, an allometric expression of VO2peak relative to LBM is the best expression of VO2peak in children and youth.
A potential mechanism for allometric trabecular bone scaling in terrestrial mammals.
Christen, Patrik; Ito, Keita; van Rietbergen, Bert
2015-03-01
Trabecular bone microstructural parameters, including trabecular thickness, spacing, and number, have been reported to scale with animal size with negative allometry, whereas bone volume fraction is animal size-invariant in terrestrial mammals. As for the majority of scaling patterns described in animals, its underlying mechanism is unknown. However, it has also been found that osteocyte density is inversely related to animal size, possibly adapted to metabolic rate, which shows a negative relationship as well. In addition, the signalling reach of osteocytes is limited by the extent of the lacuno-canalicular network, depending on trabecular dimensions and thus also on animal size. Here we propose animal size-dependent variations in osteocyte density and their signalling influence distance as a potential mechanism for negative allometric trabecular bone scaling in terrestrial mammals. Using an established and tested computational model of bone modelling and remodelling, we run simulations with different osteocyte densities and influence distances mimicking six terrestrial mammals covering a large range of body masses. Simulated trabecular structures revealed negative allometric scaling for trabecular thickness, spacing, and number, constant bone volume fraction, and bone turnover rates inversely related to animal size. These results are in agreement with previous observations supporting our proposal of osteocyte density and influence distance variation as a potential mechanism for negative allometric trabecular bone scaling in terrestrial mammals. The inverse relationship between bone turnover rates and animal size further indicates that trabecular bone scaling may be linked to metabolic rather than mechanical adaptations.
FAST TRACK COMMUNICATION: Unified theory of interspecific allometric scaling
NASA Astrophysics Data System (ADS)
da Silva, Jafferson K. L.; Barbosa, Lauro A.; Silva, Paulo Roberto
2007-11-01
A general simple theory for the interspecific allometric scaling is developed in the d + 1-dimensional space (d biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the metabolic states in such a way that the mass and energy d + 1-densities are size-invariant quantities (independent of body mass). The different metabolic states (basal and maximum) are described by considering that the biological lengths and the physiological time are related by different transport processes of energy and mass. In the basal metabolism, transportation occurs by ballistic and diffusion processes. In d = 3, the 3/4 law occurs if the ballistic movement is the dominant process, while the 2/3 law appears when both transport processes are equivalent. Accelerated movement during the biological time is related to the maximum aerobic sustained metabolism, which is characterized by the scaling exponent 2d/(2d + 1) (6/7 in d = 3). The results are in good agreement with empirical data and a verifiable empirical prediction about the aorta blood velocity in maximum metabolic rate conditions is made.
Integration of exercise response and allometric scaling in endotherms.
Bishop, Charles M; Spivey, Robin J
2013-04-21
The relationship between heart beat frequency and the rate of oxygen consumption for different species of birds and mammals is influenced by body size, the type of exercise being undertaken and its intensity. Here a model is presented combining allometric scaling and exercise-induced variations in oxygen consumption and blood flow, when birds and mammals undergo their primary mode of locomotion. Novel relationships, common to the regulatory systems of all endotherms, are found to relate the rate of oxygen consumption, heart-rate, body and heart mass in 24 species of endotherms spanning 5 orders of body mass. We show that these relationships can be derived from linearity between heart-rate and the arteriovenous oxygen difference, present in data from exercise-attuned humans. We find that the metabolic rate of endotherms undergoing their primary mode of locomotion across a range of exercise intensities is quadratically related to heart-rate and that body mass is inferior to heart mass as a predictive scaling variable. The model facilitates graphical comparisons between species, and enables metabolic costs to be extrapolated from heart-rate data whenever direct measurements of oxygen consumption prove prohibitively challenging.
DE Leo, Giulio A; Dobson, Andrew P; Gatto, Marino
2016-06-01
In this paper we derive from first principles the expected body sizes of the parasite communities that can coexist in a mammal of given body size. We use a mixture of mathematical models and known allometric relationships to examine whether host and parasite life histories constrain the diversity of parasite species that can coexist in the population of any host species. The model consists of one differential equation for each parasite species and a single density-dependent nonlinear equation for the affected host under the assumption of exploitation competition. We derive threshold conditions for the coexistence and competitive exclusion of parasite species using invasion criteria and stability analysis of the resulting equilibria. These results are then used to evaluate the range of parasites species that can invade and establish in a target host and identify the 'optimal' size of a parasite species for a host of a given body size; 'optimal' is defined as the body size of a parasite species that cannot be outcompeted by any other parasite species. The expected distributions of parasites body sizes in hosts of different sizes are then compared with those observed in empirical studies. Our analysis predicts the relative abundance of parasites of different size that establish in the host and suggests that increasing the ratio of parasite body size to host body size above a minimum threshold increases the persistence of the parasite population. PMID:27001526
An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans.
Reardon, Paul Kirkpatrick; Clasen, Liv; Giedd, Jay N; Blumenthal, Jonathan; Lerch, Jason P; Chakravarty, M Mallar; Raznahan, Armin
2016-02-24
Structural neuroimaging of humans with typical and atypical sex-chromosome complements has established the marked influence of both Yand X-/Y-chromosome dosage on total brain volume (TBV) and identified potential cortical substrates for the psychiatric phenotypes associated with sex-chromosome aneuploidy (SCA). Here, in a cohort of 354 humans with varying karyotypes (XX, XY, XXX, XXY, XYY, XXYY, XXXXY), we investigate sex and SCA effects on subcortical size and shape; focusing on the striatum, pallidum and thalamus. We find large effect-size differences in the volume and shape of all three structures as a function of sex and SCA. We correct for TBV effects with a novel allometric method harnessing normative scaling rules for subcortical size and shape in humans, which we derive here for the first time. We show that all three subcortical volumes scale sublinearly with TBV among healthy humans, mirroring known relationships between subcortical volume and TBV among species. Traditional TBV correction methods assume linear scaling and can therefore invert or exaggerate sex and SCA effects on subcortical anatomy. Allometric analysis restricts sex-differences to: (1) greater pallidal volume (PV) in males, and (2) relative caudate head expansion and ventral striatum contraction in females. Allometric analysis of SCA reveals that supernumerary X- and Y-chromosomes both cause disproportionate reductions in PV, and coordinated deformations of striatopallidal shape. Our study provides a novel understanding of sex and sex-chromosome dosage effects on subcortical organization, using an allometric approach that can be generalized to other basic and clinical structural neuroimaging settings.
An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans.
Reardon, Paul Kirkpatrick; Clasen, Liv; Giedd, Jay N; Blumenthal, Jonathan; Lerch, Jason P; Chakravarty, M Mallar; Raznahan, Armin
2016-02-24
Structural neuroimaging of humans with typical and atypical sex-chromosome complements has established the marked influence of both Yand X-/Y-chromosome dosage on total brain volume (TBV) and identified potential cortical substrates for the psychiatric phenotypes associated with sex-chromosome aneuploidy (SCA). Here, in a cohort of 354 humans with varying karyotypes (XX, XY, XXX, XXY, XYY, XXYY, XXXXY), we investigate sex and SCA effects on subcortical size and shape; focusing on the striatum, pallidum and thalamus. We find large effect-size differences in the volume and shape of all three structures as a function of sex and SCA. We correct for TBV effects with a novel allometric method harnessing normative scaling rules for subcortical size and shape in humans, which we derive here for the first time. We show that all three subcortical volumes scale sublinearly with TBV among healthy humans, mirroring known relationships between subcortical volume and TBV among species. Traditional TBV correction methods assume linear scaling and can therefore invert or exaggerate sex and SCA effects on subcortical anatomy. Allometric analysis restricts sex-differences to: (1) greater pallidal volume (PV) in males, and (2) relative caudate head expansion and ventral striatum contraction in females. Allometric analysis of SCA reveals that supernumerary X- and Y-chromosomes both cause disproportionate reductions in PV, and coordinated deformations of striatopallidal shape. Our study provides a novel understanding of sex and sex-chromosome dosage effects on subcortical organization, using an allometric approach that can be generalized to other basic and clinical structural neuroimaging settings. PMID:26911691
Modeling aboveground tree woody biomass using national-scale allometric methods and airborne lidar
NASA Astrophysics Data System (ADS)
Chen, Qi
2015-08-01
Estimating tree aboveground biomass (AGB) and carbon (C) stocks using remote sensing is a critical component for understanding the global C cycle and mitigating climate change. However, the importance of allometry for remote sensing of AGB has not been recognized until recently. The overarching goals of this study are to understand the differences and relationships among three national-scale allometric methods (CRM, Jenkins, and the regional models) of the Forest Inventory and Analysis (FIA) program in the U.S. and to examine the impacts of using alternative allometry on the fitting statistics of remote sensing-based woody AGB models. Airborne lidar data from three study sites in the Pacific Northwest, USA were used to predict woody AGB estimated from the different allometric methods. It was found that the CRM and Jenkins estimates of woody AGB are related via the CRM adjustment factor. In terms of lidar-biomass modeling, CRM had the smallest model errors, while the Jenkins method had the largest ones and the regional method was between. The best model fitting from CRM is attributed to its inclusion of tree height in calculating merchantable stem volume and the strong dependence of non-merchantable stem biomass on merchantable stem biomass. This study also argues that it is important to characterize the allometric model errors for gaining a complete understanding of the remotely-sensed AGB prediction errors.
Shestopaloff, Yuri K
2016-08-15
Living organisms need energy to be 'alive'. Energy is produced by the biochemical processing of nutrients, and the rate of energy production is called the metabolic rate. Metabolism is very important from evolutionary and ecological perspectives, and for organismal development and functioning. It depends on different parameters, of which organism mass is considered to be one of the most important. Simple relationships between the mass of organisms and their metabolic rates were empirically discovered by M. Kleiber in 1932. Such dependence is described by a power function, whose exponent is referred to as the allometric scaling coefficient. With the increase of mass, the metabolic rate usually increases more slowly; if mass increases by two times, the metabolic rate increases less than two times. This fact has far-reaching implications for the organization of life. The fundamental biological and biophysical mechanisms underlying this phenomenon are still not well understood. The present study shows that one such primary mechanism relates to transportation of substances, such as nutrients and waste, at a cellular level. Variations in cell size and associated cellular transportation costs explain the known variance of the allometric exponent. The introduced model also includes heat dissipation constraints. The model agrees with experimental observations and reconciles experimental results across different taxa. It ties metabolic scaling to organismal and environmental characteristics, helps to define perspective directions of future research and allows the prediction of allometric exponents based on characteristics of organisms and the environments they live in.
Waghorn, Matthew J.; Watt, Michael S.
2013-01-01
Background and Aims Allometric relationships and the determination of critical buckling heights have been examined for Pinus radiata in the past. However, how they relate to more mature Pinus radiata exhibiting a wide range of stem diameters, slenderness and modulus of elasticity (E) at operationally used stand densities is largely unknown. The aim of this study was to examine the relationship between Pinus radiata stand structure variables and allometric scaling and critical buckling height. Methods Utilizing a Pinus radiata Nelder trial with stand density and genetic breed as variables, critical buckling height was calculated whilst reduced major axis regression was used to determine scaling exponents between critical height (Hcrit), actual height (H), ground line diameter (D), slenderness (S), density-specific stiffness (E/ρ) and modulus of elasticity (E). Key Results Critical buckling height was highly responsive to decreasing diameter and increasing slenderness. Safety factors in this study were typically considerably lower than previously reported margins in other species. As density-specific stiffness scaled negatively with diameter, the exponent of 0·55 between critical height and diameter did not meet the assumed value of 0·67 under constant density-specific stiffness. E scaled positively with stem slenderness to the power of 0·78. Conclusions The findings suggest that within species density-specific stiffness variation may influence critical height and the scaling exponent between critical height and diameter, which is considered so important in assumptions regarding allometric relationships. PMID:23388878
Shestopaloff, Yuri K
2016-08-15
Living organisms need energy to be 'alive'. Energy is produced by the biochemical processing of nutrients, and the rate of energy production is called the metabolic rate. Metabolism is very important from evolutionary and ecological perspectives, and for organismal development and functioning. It depends on different parameters, of which organism mass is considered to be one of the most important. Simple relationships between the mass of organisms and their metabolic rates were empirically discovered by M. Kleiber in 1932. Such dependence is described by a power function, whose exponent is referred to as the allometric scaling coefficient. With the increase of mass, the metabolic rate usually increases more slowly; if mass increases by two times, the metabolic rate increases less than two times. This fact has far-reaching implications for the organization of life. The fundamental biological and biophysical mechanisms underlying this phenomenon are still not well understood. The present study shows that one such primary mechanism relates to transportation of substances, such as nutrients and waste, at a cellular level. Variations in cell size and associated cellular transportation costs explain the known variance of the allometric exponent. The introduced model also includes heat dissipation constraints. The model agrees with experimental observations and reconciles experimental results across different taxa. It ties metabolic scaling to organismal and environmental characteristics, helps to define perspective directions of future research and allows the prediction of allometric exponents based on characteristics of organisms and the environments they live in. PMID:27284070
General relativity as the equation of state of spin foam
NASA Astrophysics Data System (ADS)
Smolin, Lee
2014-10-01
Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson's argument that the Einstein equations emerge as the equation of state of a quantum gravitational system. I give three criteria a quantum theory of gravity must satisfy if it is to allow Jacobson's argument to be run. I then show that the results of FGP and Bianchi provide evidence that loop quantum gravity satisfies two of these criteria, and argue that the third should also be satisfied in loop quantum gravity. I also show that the energy defined by FGP is the canonical energy associated with the boundary term of the Holst action.
Phytoplankton productivity in relation to light intensity: A simple equation
Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.
1987-01-01
A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.
An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans
Clasen, Liv; Giedd, Jay N.; Blumenthal, Jonathan; Lerch, Jason P.; Chakravarty, M. Mallar; Raznahan, Armin
2016-01-01
Structural neuroimaging of humans with typical and atypical sex-chromosome complements has established the marked influence of both Yand X-/Y-chromosome dosage on total brain volume (TBV) and identified potential cortical substrates for the psychiatric phenotypes associated with sex-chromosome aneuploidy (SCA). Here, in a cohort of 354 humans with varying karyotypes (XX, XY, XXX, XXY, XYY, XXYY, XXXXY), we investigate sex and SCA effects on subcortical size and shape; focusing on the striatum, pallidum and thalamus. We find large effect-size differences in the volume and shape of all three structures as a function of sex and SCA. We correct for TBV effects with a novel allometric method harnessing normative scaling rules for subcortical size and shape in humans, which we derive here for the first time. We show that all three subcortical volumes scale sublinearly with TBV among healthy humans, mirroring known relationships between subcortical volume and TBV among species. Traditional TBV correction methods assume linear scaling and can therefore invert or exaggerate sex and SCA effects on subcortical anatomy. Allometric analysis restricts sex-differences to: (1) greater pallidal volume (PV) in males, and (2) relative caudate head expansion and ventral striatum contraction in females. Allometric analysis of SCA reveals that supernumerary X- and Y-chromosomes both cause disproportionate reductions in PV, and coordinated deformations of striatopallidal shape. Our study provides a novel understanding of sex and sex-chromosome dosage effects on subcortical organization, using an allometric approach that can be generalized to other basic and clinical structural neuroimaging settings. SIGNIFICANCE STATEMENT Sex and sex-chromosome dosage (SCD) are known to modulate human brain size and cortical anatomy, but very little is known regarding their impact on subcortical structures that work with the cortex to subserve a range of behaviors in health and disease. Moreover
Heterogeneity of cells may explain allometric scaling of metabolic rate.
Takemoto, Kazuhiro
2015-04-01
The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only demonstrate either two important observations for the allometric scaling: the variability of scaling exponents and predominance of 3/4-power law. Thus, these models have a dispute over their validity. In this study, we propose a simple geometry model, and show that a hypothesis that total surface area of cells determines metabolic rate can reproduce these two observations by combining two concepts: the impact of cell sizes on metabolic rate and fractal-like (hierarchical) organization. The proposed model both theoretically and numerically demonstrates the approximately 3/4-power law although several different biological strategies are considered. The model validity is confirmed using empirical data. Furthermore, the model suggests the importance of heterogeneity of cell size for the emergence of the allometric scaling. The proposed model provides intuitive and unique insights into the origin of allometric scaling laws in biology, despite several limitations of the model.
Allometric scaling for predicting human clearance of bisphenol A
Collet, Séverine H. Picard-Hagen, Nicole Lacroix, Marlène Z. Puel, Sylvie Viguié, Catherine Bousquet-Melou, Alain Toutain, Pierre-Louis Gayrard, Véronique
2015-05-01
The investigation of interspecies differences in bisphenol A (BPA) pharmacokinetics (PK) may be useful for translating findings from animal studies to humans, identifying major processes involved in BPA clearance mechanisms, and predicting BPA PK parameters in man. For the first time, a large range of species in terms of body weight, from 0.02 kg (mice) to 495 kg (horses) was used to predict BPA clearance in man by an allometric approach. BPA PK was evaluated after intravenous administration of BPA in horses, sheep, pigs, dogs, rats and mice. A non-compartmental analysis was used to estimate plasma clearance and steady state volume of distribution and predict BPA PK parameters in humans from allometric scaling. In all the species investigated, BPA plasma clearance was high and of the same order of magnitude as their respective hepatic blood flow. By an allometric scaling, the human clearance was estimated to be 1.79 L/min (equivalent to 25.6 mL/kg.min) with a 95% prediction interval of 0.36 to 8.83 L/min. Our results support the hypothesis that there are highly efficient and hepatic mechanisms of BPA clearance in man. - Highlights: • Allometric scaling was used to predict BPA pharmacokinetic parameters in humans. • In all species, BPA plasma clearance approached hepatic blood flow. • Human BPA clearance was estimated to be 1.79 L/min.
A general model for the origin allometric scaling laws in biology
West, G.B. |; Brown, J.H.; Enquist, B.J. |
1997-04-04
Allometric scaling relations, including the 3/4 power law for metabolic rates, are characteristic of all organisms and are here derived from a general model that describes how essential materials are transported through space-filling fractal networks of branching tubes. The model assumes that the energy dissipated is minimized and that the terminal tubes do not vary with body size. It provides a complete analysis of scaling relations for mammalian circulatory systems that are in agreement with data. More generally, the model predicts structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks. 24 refs., 2 figs., 1 tab.
Allometric scaling of orbifloxacin disposition in nine mammal species: a retrospective analysis.
Gebru, Elias; Lee, Seung-Jin; Kim, Jong-Choon; Park, Seung-Chun
2011-06-01
The objective of this study was to analyze the relationship between pharmacokinetic parameters and body weight (W) for orbifloxacin using reported pharmacokinetic data. The parameters of interest: clearance (Cl), volume of distribution at steady state (Vss) and elimination half-life were correlated across nine mammal species, including cattle, dog, rat, rabbit, goat, camel, horse, cat and sheep as a function of W using the conventional allometric equation Y = aW(b), where Y is the pharmacokinetic parameter, W is the body weight, a is the allometric coefficient (intercept) and b is the exponent that describes the relationship between the pharmacokinetic parameter and W. Our estimates (Cl=4.40 W(1.03); Vss=1.10W(1.05)) indicated that the increase in these parameters with W approximates a linear power relationship with slopes being very close to one. Overall, the results of this study indicated that it is possible to use allometry to predict pharmacokinetic variables of orbifloxacin based on W of mammal species.
Conformally related Einstein-Langevin equations for metric fluctuations in stochastic gravity
NASA Astrophysics Data System (ADS)
Satin, Seema; Cho, H. T.; Hu, Bei Lok
2016-09-01
For a conformally coupled scalar field we obtain the conformally related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally related spacetime is known. For example, from the Minkowski solution of Martín and Verdaguer, those of the Einstein-Langevin equations in conformally flat spacetimes, especially for spatially flat Friedmann-Robertson-Walker models, can be readily obtained.
University-Industry-Government Relations. A "Complexes" Equation.
ERIC Educational Resources Information Center
Marceau, Jane
1996-01-01
The triple helix image of university-industry-government relations should be reconsidered with a focus on knowledge production systems. Public policies aimed at improving relationships should recognize the contributions made in this new mode of production and take into account users as the fourth player. (SK)
A new method to compute standard-weight equations that reduces length-related bias
Gerow, K.G.; Anderson-Sprecher, R. C.; Hubert, W.A.
2005-01-01
We propose a new method for developing standard-weight (Ws) equations for use in the computation of relative weight (Wr) because the regression line-percentile (RLP) method often leads to length-related biases in Ws equations. We studied the structural properties of W s equations developed by the RLP method through simulations, identified reasons for biases, and compared Ws equations computed by the RLP method and the new method. The new method is similar to the RLP method but is based on means of measured weights rather than on means of weights predicted from regression models. The new method also models curvilinear W s relationships not accounted for by the RLP method. For some length-classes in some species, the relative weights computed from Ws equations developed by the new method were more than 20 Wr units different from those using Ws equations developed by the RLP method. We recommend assessment of published Ws equations developed by the RLP method for length-related bias and use of the new method for computing new Ws equations when bias is identified. ?? Copyright by the American Fisheries Society 2005.
Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation
Cicogna, G.; Pegoraro, F.; Ceccherini, F.
2010-10-15
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.
Master equation solutions in the linear regime of characteristic formulation of general relativity
NASA Astrophysics Data System (ADS)
Cedeño M., C. E.; de Araujo, J. C. N.
2015-12-01
From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and Mädler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the J metric variable of the Bondi-Sachs metric. Once β , another Bondi-Sachs potential, is obtained from the field equations, and J is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, Mädler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new solutions to the master equation for any multipolar moment l , with and without matter sources in terms only of the first kind Bessel's functions for the Minkowski, and in terms of the Confluent Heun's functions (Generalised Hypergeometric) for radiative (nonradiative) case in the Schwarzschild's background. We particularize our families of solutions for the known cases for l =2 reported previously in the literature and find complete agreement, showing the robustness of our results.
Groot; Meicenheimer
2000-03-01
Two methods of analyses were used to investigate tooth development in serrate (se) mutant and wild-type Columbia-1 (Col-1) Arabidopsis thaliana leaves. There were almost twice as many teeth with deeper sinuses and two orders of toothing on the margins of serrate compared with Columbia-1 leaves. The main objective of this study was to test three hypotheses relative to the source of polymorphism in tooth development: (i) Teeth share similar growth rates and initial sizes, but the deeper teeth are initiated earlier in leaf development. (ii) Teeth share similar timing of initiation and growth rates, but the deeper teeth have a larger initial size. (iii) Teeth share similar timing of initiation and initial sizes, but the deeper teeth have a faster growth rate. Leaf plastochron index (LPI) was used as the time variable for leaf development. Results showed teeth in se were initiated at -27 LPI, 15 plastochrons earlier than those of Col-1. Serrate leaf expansion was biphasic, with the early phase expanding at half the relative plastochron rate of the later phase, which equaled the constant relative expansion rate of Col-1 leaves. Allometric analyses of tooth development obscured the interactions between time of tooth and leaf initiation and the early phase of leaf expansion characteristic of serrate leaves and teeth. Timing of developmental events that allometric analysis obscured can be readily detected with the LPI as a developmental index.
An alternative approach to detection of length-related biases in standard weight equations
Gerow, K.G.; Hubert, W.A.; Anderson-Sprecher, R. C.
2004-01-01
We propose a new method for assessing length-related biases in standard weight (Ws) equations computed by the regression-line-percentile method. We evaluated the performance of the new method relative to two previous methods for assessing length-related biases using 15 data sets from which W s equations have been computed. The new method detected potentially serious length-related biases in 10 Ws equations, whereas one of the previously used methods failed to detect any biologically significant biases and the other method detected biases in only one equation. The new method can detect curvilinear relationships between Ws and length, so it provides insight that is not available from previous methods.
NASA Astrophysics Data System (ADS)
Alonzo, M.; Bookhagen, B.; McFadden, J. P.; Sun, A.; Roberts, D. A.
2014-12-01
In urban areas leaf area index (LAI) is a key ecosystem structural attribute with implications for energy and water balance, gas exchange, and anthropogenic energy use. Typically, citywide LAI estimates are extrapolated from those made on forest inventory sample plots through intensive crown measurement and allometric scaling. This is a time- and labor-intensive process yielding coarse spatial resolution results. In this study we generate spatially explicit estimates of LAI using high-point density airborne lidar throughout our study area in downtown Santa Barbara, CA. We implement two theoretically distinct modeling approaches. First, based on hemispherical photography at our 71 field plots, we estimate effective LAI using scan-angle corrected lidar laser penetration metrics (LPM). For our second approach, we adapt existing allometric equations for use with a suite of crown structural metrics (e.g., tree height, crown base height) measured with lidar. This approach allows for estimates of LAI to be made at the individual tree crown scale (ITC). This is important for evaluating fine-scale interactions between canopy and urban surfaces. The LPM method resulted in good agreement with field estimates (r2 = 0.80) and a slope of near unity (β = 0.998) using a model that assumed a spherical leaf angle distribution. Within ITC segments that were automatically delineated using watershed segmentation, lidar estimates of crown structure closely paralleled field measurements (r2=0.87 for crown length). LAI estimates based on the lidar structural variables corresponded well with estimates from field measurements (r2 = 0.84). Agreement between the LPM and allometric lidar methods was also strong across the 71 validation plots (r2 = 0.88) and among 450 sample points (r2 = 0.72) randomly distributed throughout the citywide maps. This is notably higher than the agreement between the hemiphoto and allometric ground-based estimates (r2 = 0.56). The allometric approach generally
Development of LiDAR aware allometrics for Abies grandis: A Case Study
NASA Astrophysics Data System (ADS)
Stone, G. A.; Tinkham, W. T.; Smith, A. M.; Hudak, A. T.; Falkowski, M. J.; Keefe, R.
2012-12-01
Forest managers rely increasingly on accurate allometric relationships to inform decisions regarding stand rotations, silvilcultural treatments, timber harvesting, and biometric modeling. At the same time, advances in remote sensing techniques like LiDAR (light detection and ranging) have brought about opportunities to advance how we assess forest growth, and thus are contributing to the need for more accurate allometries. Past studies have attempted to relate LiDAR data to both plot and individual tree measures of forest biomass. However, many of these studies have been limited by the accuracy of their coincident observations. In this study, 24 Abies grandis were measured, felled, and dissected for the explicit objective of developing LiDAR aware allometrics. The analysis predicts spatial variables of competition, growth potential (e.g, trees per acre, aspect, elevation, etc.) and common statistical distributional metrics (e.g., mean, mode, percentiles, variance, skewness, kurtosis, etc.) derived from LiDAR point cloud returns to coincident in situ measures of Abies grandis stem biomass. The resulting allometries exemplify a new approach for predicting structural attributes of interest (biomass, basal area, volume, etc.) directly from LiDAR point cloud data, precluding the measurement errors that are propogated by indirectly predicting these structure attributes of interest from LiDAR data using traditional plot-based measurements.
Chirinos, Julio A; Segers, Patrick; De Buyzere, Marc L; Kronmal, Richard A; Raja, Muhammad W; De Bacquer, Dirk; Claessens, Tom; Gillebert, Thierry C; St John-Sutton, Martin; Rietzschel, Ernst R
2010-07-01
The need for left ventricular mass (LVM) normalization to body size is well recognized. Currently used allometric exponents to normalize LVM may not account for the confounding effect of sex. Because sex is a strong determinant of body size and LVM, we hypothesized that these are subject to potential bias. We analyzed data from 7528 subjects enrolled in the Asklepios Study (n=2524) and the Multiethnic Study of Atherosclerosis (limited access data set; n=5,004) to assess metric relationships between LVM and body size, generate normative data for indexed LVM, and compare the ability of normalization methods to predict cardiovascular events. The allometric exponent that adequately described the LVM-body height relationship was 1.7 in both studies and significantly different from both the unity and 2.7, whereas the LVM-body surface area relationship was approximately linear. LVM/height(2.7) consistently demonstrated important residual relationships with body height and systematically misclassified subjects regarding the presence of LVH. LVH defined by LVM/height(1.7) was more sensitive than LVM/body surface area to identify obesity-related LVH and was most consistently associated with cardiovascular events and all-cause death. In contrast to current assumptions, LVM/height(2.7) is not an adequate method to normalize LVM for body size. We provide more appropriate normalization methods, normative data by 2D echocardiography and gradient-echo cardiac MRI, and cutoffs for defining LVH, along with prognostic validation data. PMID:20458004
NASA Astrophysics Data System (ADS)
Mahabadi Mahabad, N.; Jang, J.
2013-12-01
There are several studies of numerical simulation on predicting long-term behavior of hydrate-bearing sediments during gas production. Numerical simulators explore coupled processes that require numerous equations and parameters. Important equations for the estimation of gas production from hydrate-bearing sediments are soil-water characteristic curves and relative permeability equations. These equations require empirical parameters, laboratory and in-situ experiments which are very difficult and expensive. In this research, pore-network model simulation is performed to obtain the fitting parameters for capillary pressure functions and relative permeability equations. First, several sediment packings similar to in-situ sediment are generated by discrete element method. Then, the pore-network model is extracted from the pore space of sediment packing as a system of pores connected at throats. Numerical algorithm to simulate gas hydrate dissociation and gas expansion, and calculate gas and water relative permeability at every saturation is developed for the pore-network model. The assessment of water pore connectivity and the identification of gas clusters are performed using Hoshen-Kopelman algorithm. Finally, reliable fitting parameters for capillary pressure functions and relative permeability equations during gas production will be suggested for further use.
The primer vector in linear, relative-motion equations. [spacecraft trajectory optimization
NASA Technical Reports Server (NTRS)
1980-01-01
Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.
Allometric and temporal scaling of movement characteristics in Galapagos tortoises.
Bastille-Rousseau, Guillaume; Yackulic, Charles B; Frair, Jacqueline L; Cabrera, Freddy; Blake, Stephen
2016-09-01
Understanding how individual movement scales with body size is of fundamental importance in predicting ecological relationships for diverse species. One-dimensional movement metrics scale consistently with body size yet vary over different temporal scales. Knowing how temporal scale influences the relationship between animal body size and movement would better inform hypotheses about the efficiency of foraging behaviour, the ontogeny of energy budgets, and numerous life-history trade-offs. We investigated how the temporal scaling of allometric patterns in movement varies over the course of a year, specifically during periods of motivated (directional and fast movement) and unmotivated (stationary and tortuous movement) behaviour. We focused on a recently diverged group of species that displays wide variation in movement behaviour - giant Galapagos tortoises (Chelonoidis spp.) - to test how movement metrics estimated on a monthly basis scaled with body size. We used state-space modelling to estimate seven different movement metrics of Galapagos tortoises. We used log-log regression of the power law to evaluate allometric scaling for these movement metrics and contrasted relationships by species and sex. Allometric scaling of movement was more apparent during motivated periods of movement. During this period, allometry was revealed at multiple temporal intervals (hourly, daily and monthly), with values observed at daily and monthly intervals corresponding most closely to the expected one-fourth scaling coefficient, albeit with wide credible intervals. We further detected differences in the magnitude of scaling among taxa uncoupled from observed differences in the temporal structuring of their movement rates. Our results indicate that the definition of temporal scales is fundamental to the detection of allometry of movement and should be given more attention in movement studies. Our approach not only provides new conceptual insights into temporal attributes in one
Allometric and temporal scaling of movement characteristics in Galapagos tortoises.
Bastille-Rousseau, Guillaume; Yackulic, Charles B; Frair, Jacqueline L; Cabrera, Freddy; Blake, Stephen
2016-09-01
Understanding how individual movement scales with body size is of fundamental importance in predicting ecological relationships for diverse species. One-dimensional movement metrics scale consistently with body size yet vary over different temporal scales. Knowing how temporal scale influences the relationship between animal body size and movement would better inform hypotheses about the efficiency of foraging behaviour, the ontogeny of energy budgets, and numerous life-history trade-offs. We investigated how the temporal scaling of allometric patterns in movement varies over the course of a year, specifically during periods of motivated (directional and fast movement) and unmotivated (stationary and tortuous movement) behaviour. We focused on a recently diverged group of species that displays wide variation in movement behaviour - giant Galapagos tortoises (Chelonoidis spp.) - to test how movement metrics estimated on a monthly basis scaled with body size. We used state-space modelling to estimate seven different movement metrics of Galapagos tortoises. We used log-log regression of the power law to evaluate allometric scaling for these movement metrics and contrasted relationships by species and sex. Allometric scaling of movement was more apparent during motivated periods of movement. During this period, allometry was revealed at multiple temporal intervals (hourly, daily and monthly), with values observed at daily and monthly intervals corresponding most closely to the expected one-fourth scaling coefficient, albeit with wide credible intervals. We further detected differences in the magnitude of scaling among taxa uncoupled from observed differences in the temporal structuring of their movement rates. Our results indicate that the definition of temporal scales is fundamental to the detection of allometry of movement and should be given more attention in movement studies. Our approach not only provides new conceptual insights into temporal attributes in one
Allometric and temporal scaling of movement characteristics in Galapagos tortoises
Bastille-Rousseau, Guillaume; Yackulic, Charles B.; Frair, Jacqueline L.; Cabrera, Freddy; Blake, Stephen
2016-01-01
Understanding how individual movement scales with body size is of fundamental importance in predicting ecological relationships for diverse species. One-dimensional movement metrics scale consistently with body size yet vary over different temporal scales. Knowing how temporal scale influences the relationship between animal body size and movement would better inform hypotheses about the efficiency of foraging behaviour, the ontogeny of energy budgets, and numerous life-history trade-offs.We investigated how the temporal scaling of allometric patterns in movement varies over the course of a year, specifically during periods of motivated (directional and fast movement) and unmotivated (stationary and tortuous movement) behaviour. We focused on a recently diverged group of species that displays wide variation in movement behaviour – giant Galapagos tortoises (Chelonoidis spp.) – to test how movement metrics estimated on a monthly basis scaled with body size.We used state-space modelling to estimate seven different movement metrics of Galapagos tortoises. We used log-log regression of the power law to evaluate allometric scaling for these movement metrics and contrasted relationships by species and sex.Allometric scaling of movement was more apparent during motivated periods of movement. During this period, allometry was revealed at multiple temporal intervals (hourly, daily and monthly), with values observed at daily and monthly intervals corresponding most closely to the expected one-fourth scaling coefficient, albeit with wide credible intervals. We further detected differences in the magnitude of scaling among taxa uncoupled from observed differences in the temporal structuring of their movement rates.Our results indicate that the definition of temporal scales is fundamental to the detection of allometry of movement and should be given more attention in movement studies. Our approach not only provides new conceptual insights into temporal attributes in one
Declining well yields related to depth in fractured rocks - Use of an exponential equation
Page, R.W. )
1993-03-01
In southwestern Nevada County, where most wells are drilled into granitic or metamorphic rocks, well yields were found to decrease with increasing well depth. Data from that report indicated that declining well yields in the area probably could be approximated by an exponential equation. The purpose of this report is to demonstrate that an exponential equation can be used to approximate declining well yields related to depth in hard-rock areas of granitic and metamorphic rocks in the western foothills of the Sierra Nevada. The scope includes applying this equation to data from southwestern Nevada County, California.
Dececchi, T Alexander; Larsson, Hans C E
2013-09-01
The origin of birds and powered flight is a classic major evolutionary transition. Research on their origin often focuses on the evolution of the wing with trends of forelimb elongation traced back through many nonavian maniraptoran dinosaurs. We present evidence that the relative forelimb elongation within avian antecedents is primarily due to allometry and is instead driven by a reduction in body size. Once body size is factored out, there is no trend of increasing forelimb length until the origin of birds. We report that early birds and nonavian theropods have significantly different scaling relationships within the forelimb and hindlimb skeleton. Ancestral forelimb and hindlimb allometric scaling to body size is rapidly decoupled at the origin of birds, when wings significantly elongate, by evolving a positive allometric relationship with body size from an ancestrally negative allometric pattern and legs significantly shorten by keeping a similar, near isometric relationship but with a reduced intercept. These results have implications for the evolution of powered flight and early diversification of birds. They suggest that their limb lengths first had to be dissociated from general body size scaling before expanding to the wide range of fore and hindlimb shapes and sizes present in today's birds.
Germanaud, D; Lefèvre, J; Fischer, C; Bintner, M; Curie, A; des Portes, V; Eliez, S; Elmaleh-Bergès, M; Lamblin, D; Passemard, S; Operto, G; Schaer, M; Verloes, A; Toro, R; Mangin, J F; Hertz-Pannier, L
2014-11-15
The strong positive-allometric relationship between brain size, cortical extension and gyrification complexity, recently highlighted in the general population, could be modified by brain developmental disorders. Indeed, in case of brain growth insufficiency, the pathophysiological relevance of the "simplified gyral pattern" phenotype is strongly disputed since almost no genotype-phenotype correlations have been found in primary microcephalies. Using surface scaling analysis and newly-developed spectral analysis of gyrification (Spangy), we tested whether the gyral simplification in groups of severe microcephalies related to ASPM, PQBP1 or fetal-alcohol-syndrome could be fully explained by brain size reduction according to the allometric scaling law established in typically-developing control groups, or whether an additional disease effect was to be suspected. We found the surface area reductions to be fully explained by scaling effect, leading to predictable folding intensities measured by gyrification indices. As for folding pattern assessed by spectral analysis, scaling effect also accounted for the majority of the variations, but an additional negative or positive disease effect was found in the case of ASPM and PQBP1-linked microcephalies, respectively. Our results point out the necessity of taking allometric scaling into account when studying the gyrification variability in pathological conditions. They also show that the quantitative analysis of gyrification complexity through spectral analysis can enable distinguishing between even (predictable, non-specific) and uneven (unpredictable, maybe disease-specific) gyral simplifications. PMID:25107856
On the Relation of Von Mises Equation with Acoustic Black Holes
NASA Astrophysics Data System (ADS)
Cherubini, Christian; Filippi, Simonetta
2015-01-01
In this article a discussion of Analogue Gravity is presented in relation with its recently discovered relation, valid at any perturbative order, with the nonlinear Von Mises wave equation of fluid dynamics. A discussion of the role of the acoustic metric at nonlinear level is presented.
Generalization of the Biot--Savart law to Maxwell's equations using special relativity
Neuenschwander, D.E.; Turner, B.N. )
1992-01-01
Maxwell's equations are obtained by generalizing the laws of magnetostatics, which follow from the Biot--Savart law and superposition, to be consistent with special relativity. The Lorentz force on a charged particle and its rate of energy change also follow by making Newton's second law for a particle in a magnetostatic field consistent with special relativity.
Languages cool as they expand: Allometric scaling and the decreasing need for new words
Petersen, Alexander M.; Tenenbaum, Joel N.; Havlin, Shlomo; Stanley, H. Eugene; Perc, Matjaž
2012-01-01
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This “cooling pattern” forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature. PMID:23230508
Allometric scaling predicts preferences for burned patches in a guild of East African grazers.
Sensenig, Ryan L; Demment, Montague W; Laca, Emilio A
2010-10-01
The high herbivore diversity in savanna systems has been attributed to the inherent spatial and temporal heterogeneity related to the quantity and quality of food resources. Allometric scaling predicts that smaller-bodied grazers rely on higher quality forage than larger-bodied grazers. We replicated burns at varying scales in an East African savanna and measured visitation by an entire guild of larger grazers ranging in size from hare to elephant. We found a strong negative relationship between burn preference and body mass with foregut fermenters preferring burns to a greater degree than hindgut fermenters. Burns with higher quality forage were preferred more than burns with lower quality forage by small-bodied grazers, while the opposite was true for large-bodied grazers. Our results represent some of the first experimental evidence demonstrating the importance of body size in predicting how large herbivores respond to fire-induced changes in plant quality and quantity.
The Relation among Fit Indexes, Power, and Sample Size in Structural Equation Modeling
ERIC Educational Resources Information Center
Kim, Kevin H.
2005-01-01
The relation among fit indexes, power, and sample size in structural equation modeling is examined. The noncentrality parameter is required to compute power. The 2 existing methods of computing power have estimated the noncentrality parameter by specifying an alternative hypothesis or alternative fit. These methods cannot be implemented easily and…
The general class of the vacuum spherically symmetric equations of the general relativity theory
Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
ERIC Educational Resources Information Center
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient. PMID:24741477
Input-output relations in biological systems: measurement, information and the Hill equation.
Frank, Steven A
2013-01-01
Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system's overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.
Allometric growth in the extant coelacanth lung during ontogenetic development.
Cupello, Camila; Brito, Paulo M; Herbin, Marc; Meunier, François J; Janvier, Philippe; Dutel, Hugo; Clément, Gaël
2015-09-15
Coelacanths are lobe-finned fishes known from the Devonian to Recent that were long considered extinct, until the discovery of two living species in deep marine waters of the Mozambique Channel and Sulawesi. Despite extensive studies, the pulmonary system of extant coelacanths has not been fully investigated. Here we confirm the presence of a lung and discuss its allometric growth in Latimeria chalumnae, based on a unique ontogenetic series. Our results demonstrate the presence of a potentially functional, well-developed lung in the earliest known coelacanth embryo, and its arrested growth at later ontogenetic stages, when the lung is clearly vestigial. The parallel development of a fatty organ for buoyancy control suggests a unique adaptation to deep-water environments. Furthermore, we provide the first evidence for the presence of small, hard, flexible plates around the lung in L. chalumnae, and consider them homologous to the plates of the 'calcified lung' of fossil coelacanths.
Allometric growth in the extant coelacanth lung during ontogenetic development
Cupello, Camila; Brito, Paulo M.; Herbin, Marc; Meunier, François J; Janvier, Philippe; Dutel, Hugo; Clément, Gaël
2015-01-01
Coelacanths are lobe-finned fishes known from the Devonian to Recent that were long considered extinct, until the discovery of two living species in deep marine waters of the Mozambique Channel and Sulawesi. Despite extensive studies, the pulmonary system of extant coelacanths has not been fully investigated. Here we confirm the presence of a lung and discuss its allometric growth in Latimeria chalumnae, based on a unique ontogenetic series. Our results demonstrate the presence of a potentially functional, well-developed lung in the earliest known coelacanth embryo, and its arrested growth at later ontogenetic stages, when the lung is clearly vestigial. The parallel development of a fatty organ for buoyancy control suggests a unique adaptation to deep-water environments. Furthermore, we provide the first evidence for the presence of small, hard, flexible plates around the lung in L. chalumnae, and consider them homologous to the plates of the ‘calcified lung' of fossil coelacanths. PMID:26372119
The energy balance relation for weak solutions of the density-dependent Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Leslie, T. M.; Shvydkoy, R.
2016-09-01
We consider the incompressible inhomogeneous Navier-Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the energy balance relation for this system holds for weak solutions if the velocity, density, and pressure belong to a range of Besov spaces of smoothness 1/3. A density-dependent version of the classical Kármán-Howarth-Monin relation is derived.
Lim, C. W.; Wu, B. S.; He, L. H.
2001-12-01
A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.
Maie, Takashi; Schoenfuss, Heiko L; Blob, Richard W
2013-07-01
Gobiid fishes possess a distinctive ventral sucker, formed from fusion of the pelvic fins. This sucker is used to adhere to a wide range of substrates including, in some species, the vertical cliffs of waterfalls that are climbed during upstream migrations. Previous studies of waterfall-climbing goby species have found that pressure differentials and adhesive forces generated by the sucker increase with positive allometry as fish grow in size, despite isometry or negative allometry of sucker area. To produce such scaling patterns for pressure differential and adhesive force, waterfall-climbing gobies might exhibit allometry for other muscular or skeletal components of the pelvic sucker that contribute to its adhesive function. In this study, we used anatomical dissections and modeling to evaluate the potential for allometric growth in the cross-sectional area, effective mechanical advantage (EMA), and force generating capacity of major protractor and retractor muscles of the pelvic sucker (m. protractor ischii and m. retractor ischii) that help to expand the sealed volume of the sucker to produce pressure differentials and adhesive force. We compared patterns for three Hawaiian gobiid species: a nonclimber (Stenogobius hawaiiensis), an ontogenetically limited climber (Awaous guamensis), and a proficient climber (Sicyopterus stimpsoni). Scaling patterns were relatively similar for all three species, typically exhibiting isometric or negatively allometric scaling for the muscles and lever systems examined. Although these scaling patterns do not help to explain the positive allometry of pressure differentials and adhesive force as climbing gobies grow, the best climber among the species we compared, S. stimpsoni, does exhibit the highest calculated estimates of EMA, muscular input force, and output force for pelvic sucker retraction at any body size, potentially facilitating its adhesive ability. PMID:23450656
Maie, Takashi; Schoenfuss, Heiko L; Blob, Richard W
2013-07-01
Gobiid fishes possess a distinctive ventral sucker, formed from fusion of the pelvic fins. This sucker is used to adhere to a wide range of substrates including, in some species, the vertical cliffs of waterfalls that are climbed during upstream migrations. Previous studies of waterfall-climbing goby species have found that pressure differentials and adhesive forces generated by the sucker increase with positive allometry as fish grow in size, despite isometry or negative allometry of sucker area. To produce such scaling patterns for pressure differential and adhesive force, waterfall-climbing gobies might exhibit allometry for other muscular or skeletal components of the pelvic sucker that contribute to its adhesive function. In this study, we used anatomical dissections and modeling to evaluate the potential for allometric growth in the cross-sectional area, effective mechanical advantage (EMA), and force generating capacity of major protractor and retractor muscles of the pelvic sucker (m. protractor ischii and m. retractor ischii) that help to expand the sealed volume of the sucker to produce pressure differentials and adhesive force. We compared patterns for three Hawaiian gobiid species: a nonclimber (Stenogobius hawaiiensis), an ontogenetically limited climber (Awaous guamensis), and a proficient climber (Sicyopterus stimpsoni). Scaling patterns were relatively similar for all three species, typically exhibiting isometric or negatively allometric scaling for the muscles and lever systems examined. Although these scaling patterns do not help to explain the positive allometry of pressure differentials and adhesive force as climbing gobies grow, the best climber among the species we compared, S. stimpsoni, does exhibit the highest calculated estimates of EMA, muscular input force, and output force for pelvic sucker retraction at any body size, potentially facilitating its adhesive ability.
The Einstein-Klein-Gordon Equations, Wave Dark Matter, and the Tully-Fisher Relation
NASA Astrophysics Data System (ADS)
Goetz, Andrew S.
2015-01-01
We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. These two equations together are known as the Einstein-Klein-Gordon system. In the low-field, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schrodinger system. We describe the simplest solutions of these systems in spherical symmetry, the spherically symmetric static states, and some scaling properties they obey. We also describe some approximate analytic solutions for these states. The EKG system underlies a theory of wave dark matter, also known as scalar field dark matter (SFDM), boson star dark matter, and Bose-Einstein condensate (BEC) dark matter. We discuss a possible connection between the theory of wave dark matter and the baryonic Tully-Fisher relation, which is a scaling relation observed to hold for disk galaxies in the universe across many decades in mass. We show how fixing boundary conditions at the edge of the spherically symmetric static states implies Tully-Fisher-like relations for the states. We also catalog other ``scaling conditions'' one can impose on the static states and show that they do not lead to Tully-Fisher-like relations--barring one exception which is already known and which has nothing to do with the specifics of wave dark matter.
Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion
NASA Technical Reports Server (NTRS)
Lane, Christopher; Axelrad, Penina
2004-01-01
Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.
Input-output relations in biological systems: measurement, information and the Hill equation
2013-01-01
Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system’s overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints. Reviewers This article was reviewed by Eugene Koonin, Georg Luebeck and Sergei Maslov. PMID:24308849
Exponential mapping of quantitative trait loci governing allometric relationships in organisms.
Ma, Chang-Xing; Casella, George; Littell, Ramon C; Khuri, André I; Wu, Rongling
2003-10-01
Allometric scaling relationships or quarter-power rules, as a universal biological law, can be viewed as having some genetic component, and the particular genes (or quantitative trait loci, QTL) underlying these allometric relationships can be mapped using molecular markers. We develop a mathematical and statistical model for mapping allometric QTL on the basis of nonlinear power functions using Taylor's approximation theory. Simulation studies indicate that the QTL position and effect can be estimated using our model, but the estimation precision can be improved from the higher- over lower-order approximation when the sample size used and gene effects are small. The application of our approach in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship between 3rd-year stem height and 3rd-year stem biomass. It is expected that our model will have broad implications for genetic, evolutionary, biomedical and breeding research.
The Einstein equation of state as the Clausius relation with an entropy production
NASA Astrophysics Data System (ADS)
Shimada, Kengo; Okazawa, Susumu; Iso, Satoshi
2012-11-01
We give a modified derivation of the Einstein equation of state by considering the Clausius relation TδS - δN = δQ on a null hypersurface with a non-vanishing expansion (θ ≠ 0), i.e. not in the equilibrium. The derivation corresponds to choosing a specific observer to the hypersurface, and such a generalization gives a hint how we can improve the original derivation by Jacobson. We also give an interpretation of the thermodynamic relation based on the Noether charge method.
Kaminski, R.; Pelaez, J. R.; Yndurain, F. J.
2008-03-01
We complete and improve the fits to experimental {pi}{pi} scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations belowKK threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by 1.5{sigma}. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find a{sub 0}{sup (0)}=0.223{+-}0.009M{sub {pi}}{sup -1}, a{sub 0}{sup (2)}=-0.0444{+-}0.0045M{sub {pi}}{sup -1}, and {delta}{sub 0}{sup (0)}(m{sub K}{sup 2})-{delta}{sub 0}{sup (2)}(m{sub K}{sup 2})=50.9{+-}1.2{sup o}.
NASA Astrophysics Data System (ADS)
Nordtvedt, K.
2015-11-01
A local system of bodies in General Relativity whose exterior metric field asymptotically approaches the Minkowski metric effaces any effects of the matter distribution exterior to its Minkowski boundary condition. To enforce to all orders this property of gravity which appears to hold in nature, a method using linear algebraic scaling equations is developed which generates by an iterative process an N-body Lagrangian expansion for gravity's motion-independent potentials which fulfills exterior effacement along with needed metric potential expansions. Then additional properties of gravity - interior effacement and Lorentz time dilation and spatial contraction - produce additional iterative, linear algebraic equations for obtaining the full non-linear and motion-dependent N-body gravity Lagrangian potentials as well.
Pressure-velocity relations in reservoir rocks: Modified MacBeth's equation
NASA Astrophysics Data System (ADS)
Grana, Dario
2016-09-01
The knowledge of the saturation and pressure effects on elastic properties is a key factor in reservoir monitoring. The relation between saturation changes and velocity variations is well known in rock physics and at seismic frequency it can be satisfactorily described by Gassmann's equations. The pressure effect still requires deeper investigations in order to be included in rock physics models for 4D studies. Theoretical models of velocity-pressure relations often do not match lab measurements, or contain empirical constants or theoretical parameters that are difficult to calibrate or do not have a precise physical meaning. In this work, I present a new model to describe the pressure sensitivity of elastic moduli for clastic rocks. The proposed model is an extension of MacBeth's relations. These equations are then integrated within a complete rock physics model to describe the relation between rock properties (porosity and clay content), dynamic attributes (saturation and pressure) and elastic properties. The proposed model is calibrated with laboratory measurements of dry samples over a wide range of pressure variations and then applied to well data to simulate different production scenarios. The complete rock physics model can then be used in time-lapse inversion to predict the distribution of dynamic property changes in the reservoir within an inversion workflow for reservoir monitoring.
NASA Astrophysics Data System (ADS)
Zhao, Ning; He, Nianpeng; Wang, Qiufeng; Wang, Ruili; Xu, Zhiwei; YU, Guirui
2014-05-01
Plant nutrient allocation explicitly links the plant resource capture strategy to the material and energy cycles of ecosystems. The nitrogen (N) to phosphorus (P) relationship in plant organs is of particular interest, as N and P are the major limiting elements for plant growth. Here we analyze the relations of N and P in leaves, stems and fine roots of 269 species along an altitudinal transect on the northern slope of Changbai Mountain, China, to explore the partitioning of nutrients in major plant organs and its response to environmental gradient. We find that N, P contents as well as N: P ratio are significantly higher in leaves than in stems and fine roots. Nutrient contents of major plant organs show consistent response to the altitudinal gradient. N and P contents of leaves, stems and fine roots increased while N:P ratios decreased with elevation. Moreover, general allometric scaling relations of N and P is found in leaves, stems and fine roots with slopes of 0.78, 0.72 and 0.87, respectively, and differences exist among different plant growth forms. In general, the exponent values of the allometric scaling of N and P in leaves, stems and fine roots keep as an invariant constant along the altitudinal gradient, which implies the existence of conserved nutrient allocation strategies in plant.
Propulsion-related flowfields using the preconditioned Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Venkateswaran, S.; Weiss, J. M.; Merkle, C. L.; Choi, Y.-H.
1992-01-01
A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.
Dispersion relation of the nonlinear Klein-Gordon equation through a variational method.
Amore, Paolo; Raya, Alfredo
2006-03-01
We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the linear delta expansion. All the results obtained in this article are fully analytical, never involve the use of special functions, and can be used to obtain systematic approximations to the exact results to any desired degree of accuracy. We compare our findings with similar results in the literature and show that our approach leads to better and simpler results.
NASA Astrophysics Data System (ADS)
Sourie, Aurélien; Oertel, Micaela; Novak, Jérôme
2016-04-01
We present a numerical model for uniformly rotating superfluid neutron stars in a fully general relativistic framework with, for the first time, realistic microphysics including entrainment. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a nondissipative interaction which in the case of a nonvanishing relative velocity between the fluids causes the fluid momenta to be not aligned with the respective fluid velocities. We extend the formalism put forth by Comer and Joynt in order to calculate the equation of state (EOS) and entrainment parameters for an arbitrary relative velocity as far as superfluidity is maintained. The resulting entrainment matrix fulfills all necessary sum rules, and in the limit of small relative velocity our results agree with Fermi liquid theory ones derived to lowest order in the velocity. This formalism is applied to two new nuclear equations of state which are implemented in the numerical model, which enables us to obtain precise equilibrium configurations. The resulting density profiles and moments of inertia are discussed employing both EOSs, showing the impact of entrainment and the dependence on the EOS.
NASA Astrophysics Data System (ADS)
de Boer, H. J.; Price, C. A.; Wagner-Cremer, F.; Dekker, S. C.; Veneklaas, E. J.
2013-12-01
Stomatal pores on plants leaves are an important link in the chain of processes that determine biosphere fluxes of water and carbon. Stomatal density (i.e. the number of stomata per area) and the size of the stomatal pore at maximum aperture are particularly relevant traits in this context because they determine the theoretical maximum diffusive stomatal conductance (gsmax) and thereby set an upper limit for leaf gas exchange. Observations on (sub)fossil leaves revealed that changes in stomatal densities are anti-correlated with changes in stomatal sizes at developmental and evolutionary timescales. Moreover, this anti-correlation appears consistently within single species, across multiple species in the extant plant community and at evolutionary time scales. The consistency of the relation between stomatal densities and sizes suggests that common mechanisms constrain the adaptation of these traits across the plant community. In an attempt to identify such potential generic constraints, we investigated the allometry between stomatal densities and sizes in the extant plant community and across geological time. As the size of the stomatal pore at maximum aperture is typically derived from the length of the stomatal pore, we considered the allometric scaling of pore length (lp) with stomatal density (Ds) as the power law: lp = k . Dsa in which k is a normalization constant and the exponent a is the slope of the scaling relation. Our null-hypothesis predicts that stomatal density and pore length scale along a constant slope of -1/2 based on a scale-invariant relation between pore length and the distance between neighboring pores. Our alternative hypothesis predicts a constant slope of -1 based on the idea that stomatal density and pore length scale along an invariant gsmax. To explore these scaling hypotheses in the extant plant community we compiled a dataset of combined observations of stomatal density and pore length on 111 species from published literature and new
A Structural Equation Model of HIV-related Symptoms, Depressive Symptoms, and Medication Adherence
Yoo-Jeong, Moka; Waldrop-Valverde, Drenna; McCoy, Katryna; Ownby, Raymond L
2016-01-01
Adherence to combined antiretroviral therapy (cART) remains critical in management of HIV infection. This study evaluated depression as a potential mechanism by which HIV-related symptoms affect medication adherence and explored if particular clusters of HIV symptoms are susceptible to this mechanism. Baseline data from a multi-visit intervention study were analyzed among 124 persons living with HIV (PLWH). A bifactor model showed two clusters of HIV-related symptom distress: general HIV-related symptoms and gastrointestinal (GI) symptoms. Structural equation modeling showed that both general HIV-related symptoms and GI symptoms were related to higher levels of depressive symptoms, and higher levels of depressive symptoms were related to lower levels of medication adherence. Although general HIV-related symptoms and GI symptoms were not directly related to adherence, they were indirectly associated with adherence via depression. The findings highlight the importance of early recognition and evaluation of symptoms of depression, as well as the underlying physical symptoms that might cause depression, to improve medication adherence.
Barros, Breno; Sakai, Yoichi; Pereira, Pedro H. C.; Gasset, Eric; Buchet, Vincent; Maamaatuaiahutapu, Moana; Ready, Jonathan S.; Oliveira, Yrlan; Giarrizzo, Tommaso; Vallinoto, Marcelo
2015-01-01
Mimesis is a relatively widespread phenomenon among reef fish, but the ontogenetic processes relevant for mimetic associations in fish are still poorly understood. In the present study, the allometric growth of two allopatric leaf-mimetic species of ephippid fishes, Chaetodipterus faber from the Atlantic and Platax orbicularis from the Indo-Pacific, was analyzed using ten morphological variables. The development of fins was considered owing to the importance of these structures for mimetic behaviors during early life stages. Despite the anatomical and behavioral similarities in both juvenile and adult stages, C. faber and P. orbicularis showed distinct patterns of growth. The overall shape of C. faber transforms from a rounded-shape in mimetic juveniles to a lengthened profile in adults, while in P. orbicularis, juveniles present an oblong profile including dorsal and anal fins, with relative fin size diminishing while the overall profile grows rounder in adults. Although the two species are closely-related, the present results suggest that growth patterns in C. faber and P. orbicularis are different, and are probably independent events in ephippids that have resulted from similar selective processes. PMID:26630347
Barros, Breno; Sakai, Yoichi; Pereira, Pedro H C; Gasset, Eric; Buchet, Vincent; Maamaatuaiahutapu, Moana; Ready, Jonathan S; Oliveira, Yrlan; Giarrizzo, Tommaso; Vallinoto, Marcelo
2015-01-01
Mimesis is a relatively widespread phenomenon among reef fish, but the ontogenetic processes relevant for mimetic associations in fish are still poorly understood. In the present study, the allometric growth of two allopatric leaf-mimetic species of ephippid fishes, Chaetodipterus faber from the Atlantic and Platax orbicularis from the Indo-Pacific, was analyzed using ten morphological variables. The development of fins was considered owing to the importance of these structures for mimetic behaviors during early life stages. Despite the anatomical and behavioral similarities in both juvenile and adult stages, C. faber and P. orbicularis showed distinct patterns of growth. The overall shape of C. faber transforms from a rounded-shape in mimetic juveniles to a lengthened profile in adults, while in P. orbicularis, juveniles present an oblong profile including dorsal and anal fins, with relative fin size diminishing while the overall profile grows rounder in adults. Although the two species are closely-related, the present results suggest that growth patterns in C. faber and P. orbicularis are different, and are probably independent events in ephippids that have resulted from similar selective processes.
Thermodynamics constrains allometric scaling of optimal development time in insects.
Dillon, Michael E; Frazier, Melanie R
2013-01-01
Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the "hotter is better" hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes. The
Thermodynamics Constrains Allometric Scaling of Optimal Development Time in Insects
Dillon, Michael E.; Frazier, Melanie R.
2013-01-01
Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the “hotter is better” hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes
Interspecies Allometric Scaling of Antimalarial Drugs and Potential Application to Pediatric Dosing
Senarathna, S. M. D. K. Ganga
2014-01-01
Pharmacopeial recommendations for administration of antimalarial drugs are the same weight-based (mg/kg of body weight) doses for children and adults. However, linear calculations are known to underestimate pediatric doses; therefore, interspecies allometric scaling data may have a role in predicting doses in children. We investigated the allometric scaling relationships of antimalarial drugs using data from pharmacokinetic studies in mammalian species. Simple allometry (Y = a × Wb) was utilized and compared to maximum life span potential (MLP) correction. All drugs showed a strong correlation with clearance (CL) in healthy controls. Insufficient data from malaria-infected species other than humans were available for allometric scaling. The allometric exponents (b) for CL of artesunate, dihydroartemisinin (from intravenous artesunate), artemether, artemisinin, clindamycin, piperaquine, mefloquine, and quinine were 0.71, 0.85, 0.66, 0.83, 0.62, 0.96, 0.52, and 0.40, respectively. Clearance was significantly lower in malaria infection than in healthy (adult) humans for quinine (0.07 versus 0.17 liter/h/kg; P = 0.0002) and dihydroartemisinin (0.81 versus 1.11 liters/h/kg; P = 0.04; power = 0.6). Interpolation of simple allometry provided better estimates of CL for children than MLP correction, which generally underestimated CL values. Pediatric dose calculations based on simple allometric exponents were 10 to 70% higher than pharmacopeial (mg/kg) recommendations. Interpolation of interspecies allometric scaling could provide better estimates than linear scaling of adult to pediatric doses of antimalarial drugs; however, the use of a fixed exponent for CL was not supported in the present study. The variability in allometric exponents for antimalarial drugs also has implications for scaling of fixed-dose combinations. PMID:25092696
NASA Astrophysics Data System (ADS)
Theil, Florian
We study the viscoelastically damped wave equation \\ddot u =\\pl_x \\( \\sigma(\\pl_x u) + \\beta \\pl_x \\dot u\\) - \\alpha u, \\quad \\alpha \\geq 0, \\beta > 0,; x \\in (0,1) with a nonmonotone stress-strain relation σ. This system describes the dynamics of phase transitions, which is closely related to the creation of microstructures. In order to analyze the dynamic behavior of microstructures we consider highly oscillatory initial states. Two questions are addressed in this work: How do oscillations propagate in space and time? What can be said about the long-time behavior? An appropriate tool to deal with oscillations are Young measures. They describe the local distribution or one-point statistics of a sequence of fast fluctuating functions. We demonstrate that highly oscillatory initial states generate in a unique fashion an evolution in the space of Young measures and we derive the determining equations. Further on we prove a generalized dissipation identity for Young-measure solutions. As a consequence, it is shown that every low-energy solution converges to a Young-measure equilibrium as t-->∞. This is a generalization of G. Friesecke's & J. B. McLeod's [FM96] convergence result for classical solutions to the case of Young-measure solutions.
Woesler, Richard
2007-02-21
The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future.
Caldwell, Gary W; Masucci, John A; Yan, Zhengyin; Hageman, William
2004-01-01
In a drug discovery environment, reasonable go/no-go human in-vivo pharmacokinetic (PK) decisions must be made in a timely manner with a minimum amount of animal in-vivo or in-vitro data. We have investigated the accuracy of the in-vivo correlation between rat and human for the prediction of the total systemic clearance (CL), the volume of distribution at steady state (Vss), and the half-life (t1/2) using simple allometric scaling techniques. We have shown, using a large diverse set of drugs, that a fixed exponent allometric scaling approach can be used to predict human in-vivo PK parameters CL, Vss and t(1/2) solely from rat in-vivo PK data with acceptable accuracy for making go/no-go decisions in drug discovery. Human in-vivo PK predictions can be obtained using the simple allometric scaling relationships CL(Human) approximately = 40 CL(Rat) (L/hr), Vss(Human) approximately = 200 Vss(Rat) (L), and t1/2(Human) approximately = 4 t1/2(Rat) (hr). The average fold error for human CL predictions for N = 176 drugs was 2.25 with 79% of the drugs having a fold error less than 3. The average fold error for human Vss predictions for N = 144 drugs was 1.85 with 84% of the drugs having a fold error less than 3. The average fold error for human t1/2 predictions for N = 145 drugs was 2.05 with 76% of the drugs having a fold error less than 3. Using these simple allometric relationships, the sorting of drug candidates into a low/medium/high/very high human classification scheme was also possible from rat data. Since these simple allometric relationships between rat and human CL, Vss, and t1/2 are reasonably accurate, easy to remember and simple to calculate, these equations should be useful for making early go/no-go in-vivo human PK decisions for drug discovery candidates.
Didactic derivation of the special theory of relativity from the Klein-Gordon equation
NASA Astrophysics Data System (ADS)
Arodź, H.
2014-09-01
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are ‘discovered’ as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity v of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound |{\\bf v}| is presented as a simple theorem that follows from the structure of the Lorentz group. The polar decomposition of Lorentz matrices is used to explain noncommutativity and nonassociativity of the relativistic composition (‘addition’) of velocities.
NASA Astrophysics Data System (ADS)
Park, Han-Earl; Kim, Young-Rok
2016-01-01
A relative navigation method for autonomous formation flying using the state-dependent Riccati equation filter (SDREF) is presented. In the SDREF, nonlinear relative dynamics, including J2 perturbation, are parameterized into a state-dependent coefficient (SDC) form without any loss of nonlinearity. The relative navigation algorithm is established based on the carrier-phase differential GPS (CDGPS) and single-frequency GPS data, in which the SDREF is used as a nonlinear estimator. To evaluate the SDREF performance, two different extended Kalman filters (EKFR1 and EKFR2) are introduced. The dynamic models of all the filters are based on relative motion including J2 perturbation. However, the SDREF and the EKFR1 use linear state propagation, whereas EKFR2 employs nonlinear state propagation. The navigation simulation is performed for each filter using live GPS signals simulated by a GPS signal generator, and the result is analyzed in terms of estimation accuracy and computational load. As a result, the SDREF provides a relative navigation solution with 3-D RMS accuracies of 6.0 mm and 0.153 mm/s for position and velocity, respectively, for a separation of 50 km with a computation time of approximately 34 s. The simulation results demonstrate that the SDREF estimates the relative states as rapidly as the EKFR1 and as accurately as the EKFR2, which means that the developed SDREF combines the strong points of EKFR1 and EKFR2 and overcomes their disadvantages.
Bruner, Emiliano; Manzi, Giorgio; Arsuaga, Juan Luis
2003-01-01
The term “encephalization” is commonly used to describe an enlargement in brain size, considered as either absolute endocranial volumes or relative values in relation to body size. It is widely recognized that a considerable endocranial expansion occurred throughout the evolution of the genus Homo. This article aims to evaluate whether this phenomenon was the outcome of distinct evolutionary lineages, reaching similar brain expansions but through different trajectories. Endocranial morphology was studied in a sample of fossil hominines by multivariate approaches using both traditional metrics and geometric morphometrics. The analysis was focused on the transition from a generalized archaic pattern within the genus Homo to the modern morphology and compared with changes that occurred along the Neandertal lineage. The main result was the identification of two different evolutionary trajectories, in which a similar expansion in endocranial size has been reached by different changes in shape. Along the Neandertal lineage we observed maintenance of an “archaic” endocranial model, in which a large amount of variability is based on a single allometric trend. By contrast, when modern endocasts were compared with nonmodern ones, we found important differences apparently led by a parietal expansion. In this light, the origin of our species may have represented the opportunity to surpass the constraints imposed on encephalization by the ontogenetic pattern shared by nonmodern Homo representatives. PMID:14673084
Bruner, Emiliano; Manzi, Giorgio; Arsuaga, Juan Luis
2003-12-23
The term "encephalization" is commonly used to describe an enlargement in brain size, considered as either absolute endocranial volumes or relative values in relation to body size. It is widely recognized that a considerable endocranial expansion occurred throughout the evolution of the genus Homo. This article aims to evaluate whether this phenomenon was the outcome of distinct evolutionary lineages, reaching similar brain expansions but through different trajectories. Endocranial morphology was studied in a sample of fossil hominines by multivariate approaches using both traditional metrics and geometric morphometrics. The analysis was focused on the transition from a generalized archaic pattern within the genus Homo to the modern morphology and compared with changes that occurred along the Neandertal lineage. The main result was the identification of two different evolutionary trajectories, in which a similar expansion in endocranial size has been reached by different changes in shape. Along the Neandertal lineage we observed maintenance of an "archaic" endocranial model, in which a large amount of variability is based on a single allometric trend. By contrast, when modern endocasts were compared with nonmodern ones, we found important differences apparently led by a parietal expansion. In this light, the origin of our species may have represented the opportunity to surpass the constraints imposed on encephalization by the ontogenetic pattern shared by nonmodern Homo representatives.
Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity.
Urošević, A; Ljubisavljević, K; Ivanović, A
2013-02-01
We explored the ontogenetic dynamics of the morphological and allometric disparity in the cranium shapes of twelve lacertid lizard species. The analysed species (Darevskia praticola, Dinarolacerta mosorensis, Iberolacerta horvathi, Lacerta agilis, L. trilineata, L. viridis, Podarcis erhardii, P. melisellensis, P. muralis, P. sicula, P. taurica and Zootoca vivipara) can be classified into different ecomorphs: terrestrial lizards that inhabit vegetated habitats (habitats with lush or sparse vegetation), saxicolous and shrub-climbing lizards. We observed that there was an overall increase in the morphological disparity (MD) during the ontogeny of the lacertid lizards. The ventral cranium, which is involved in the mechanics of jaw movement and feeding, showed higher levels of MD, an ontogenetic shift in the morphospace planes and more variable allometric patterns than more conserved dorsal crania. With respect to ecology, the allometric trajectories of the shrub-climbing species tended to cluster together, whereas the allometric trajectories of the saxicolous species were highly dispersed. Our results indicate that the ontogenetic patterns of morphological and allometric disparity in the lacertid lizards are modified by ecology and functional constraints and that the identical mechanisms that lead to intraspecific morphological variation also produce morphological divergence at higher taxonomic levels.
Visualising DEM-related flood-map uncertainties using a disparity-distance equation algorithm
NASA Astrophysics Data System (ADS)
Brandt, S. Anders; Lim, Nancy J.
2016-05-01
The apparent absoluteness of information presented by crisp-delineated flood boundaries can lead to misconceptions among planners about the inherent uncertainties associated in generated flood maps. Even maps based on hydraulic modelling using the highest-resolution digital elevation models (DEMs), and calibrated with the most optimal Manning's roughness (n) coefficients, are susceptible to errors when compared to actual flood boundaries, specifically in flat areas. Therefore, the inaccuracies in inundation extents, brought about by the characteristics of the slope perpendicular to the flow direction of the river, have to be accounted for. Instead of using the typical Monte Carlo simulation and probabilistic methods for uncertainty quantification, an empirical-based disparity-distance equation that considers the effects of both the DEM resolution and slope was used to create prediction-uncertainty zones around the resulting inundation extents of a one-dimensional (1-D) hydraulic model. The equation was originally derived for the Eskilstuna River where flood maps, based on DEM data of different resolutions, were evaluated for the slope-disparity relationship. To assess whether the equation is applicable to another river with different characteristics, modelled inundation extents from the Testebo River were utilised and tested with the equation. By using the cross-sectional locations, water surface elevations, and DEM, uncertainty zones around the original inundation boundary line can be produced for different confidences. The results show that (1) the proposed method is useful both for estimating and directly visualising model inaccuracies caused by the combined effects of slope and DEM resolution, and (2) the DEM-related uncertainties alone do not account for the total inaccuracy of the derived flood map. Decision-makers can apply it to already existing flood maps, thereby recapitulating and re-analysing the inundation boundaries and the areas that are uncertain
Pediatric Health-Related Quality of Life: A Structural Equation Modeling Approach
Villalonga-Olives, Ester; Kawachi, Ichiro; Almansa, Josué; Witte, Claudia; Lange, Benjamin; Kiese-Himmel, Christiane; von Steinbüchel, Nicole
2014-01-01
Objectives One of the most referenced theoretical frameworks to measure Health Related Quality of Life (HRQoL) is the Wilson and Cleary framework. With some adaptions this framework has been validated in the adult population, but has not been tested in pediatric populations. Our goal was to empirically investigate it in children. Methods The contributory factors to Health Related Quality of Life that we included were symptom status (presence of chronic disease or hospitalizations), functional status (developmental status), developmental aspects of the individual (social-emotional) behavior, and characteristics of the social environment (socioeconomic status and area of education). Structural equation modeling was used to assess the measurement structure of the model in 214 German children (3–5 years old) participating in a follow-up study that investigates pediatric health outcomes. Results Model fit was χ2 = 5.5; df = 6; p = 0.48; SRMR = 0.01. The variance explained of Health Related Quality of Life was 15%. Health Related Quality of Life was affected by the area education (i.e. where kindergartens were located) and development status. Developmental status was affected by the area of education, socioeconomic status and individual behavior. Symptoms did not affect the model. Conclusions The goodness of fit and the overall variance explained were good. However, the results between children' and adults' tests differed and denote a conceptual gap between adult and children measures. Indeed, there is a lot of variety in pediatric Health Related Quality of Life measures, which represents a lack of a common definition of pediatric Health Related Quality of Life. We recommend that researchers invest time in the development of pediatric Health Related Quality of Life theory and theory based evaluations. PMID:25415751
NASA Astrophysics Data System (ADS)
Tóthová, Jana; Lisý, Vladimír
2016-07-01
This paper is devoted to finding the fluctuation-dissipation relation (FDR) for the generalized Langevin equation (GLE) with the Boussinesq-Basset (BB) force in which the Stokes friction is generalized to a convolution of a memory kernel with the velocity of a Brownian particle. First, the solution of such GLE with hydrodynamic backflow is obtained. Using this solution, we find in a simple and easily controllable way the time correlation function of the thermal force driving the particles. If the GLE is used with the original BB force for pure liquids, the FDR known from the literature is corrected. It is shown that in this case the FDR contains, in addition to the known term ∼t - 3 / 2, a more slowly decaying contribution ∼t - 1 / 2.
Numerical study of a parametric parabolic equation and a related inverse boundary value problem
NASA Astrophysics Data System (ADS)
Mustonen, Lauri
2016-10-01
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the nonhomogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In the case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any linearized subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.
Shock Waves and Equations of State Related to Laser Plasma Interaction
NASA Astrophysics Data System (ADS)
Eliezer, Shalom
Equations of state (EOS) of are fundamental to numerous fields of science, such as astrophysics, geophysics, plasma physics, inertial confinement physics and more. Laser induced shock waves techniques enable the study of equations of states and related properties, expanding the thermodynamic range reached by conventional gas gun shock waves and static loading experiments. Two basic techniques are used in laser-induced shock wave research, direct drive and indirect drive. In direct drive, one or more beams irradiate the target. In the indirect drive, thermal x-rays generated in laser heated cavities create the shock wave. Most of the laser induced shock waves experiments in the last decade used the impedance matching. Both direct and indirect drive can be used to accelerate a small foil-flyer and collide it with the studied sample, creating a shock in the sample, similar to gas-gun accelerated plates experiments. These lectures describe the physics of laser induced shock waves and rarefaction waves. The different formulae of the ideal gas EOS are used in connection with shock waves and rarefaction waves. The critical problems in laser induced shock waves are pointed out and the shock wave stability is explained. A general description of the various thermodynamic EOS is given. In particular the Gruneisen EOS is derived fromEinstein and Debye models of the solid state of matter. Furthermore, the very useful phenomenological EOS, namely the linear relation between the shock wave velocity and the particle flow velocity, is analysed. This EOS is used to explain the ≈ 1 Gbar pressures in laser plasma induced shock waves. Last but not least, the shock wave jump conditions are derived in the presence of a magnetic field.
Environmental Conditions Influence Allometric Patterns in the Blow Fly, Chrysomya albiceps
Horenstein, M Battán; Peretti, Av
2011-01-01
The objective of this research was to study variations in allometry of body characters in females and males of two populations of blow flies, Chrysomya albiceps (Wiedemann) (Diptera: Calliphoridae), under different environmental conditions to establish patterns of morphological variation. Body size of both males and females in the experimental population was significantly higher than in the individuals of the natural population, indicating an important influence of food on body size. All genitalic and non-genitalic characters in males and females of the two populations showed a trend towards negative allometry rather than isometry. Allometric patterns were modified in both sexes and between populations. The data show generally larger allometric slopes in females than in males. We confirmed that the environmental conditions have an important effect on allometric patterns and body size. PMID:22224467
An allometric method for the projection of eelgrass leaf biomass production rates.
Echavarría-Heras, Hector; Solana-Arellano, Elena; Franco-Vizcaíno, Ernesto
2010-01-01
We demonstrate that an allometric model for eelgrass leaf-growth rates can be derived from data on leaf architecture and growth form. Using this construct, we produced indirect assessments of growth rates of leaves that we call projections, which can be easily obtained in terms of allometric parameters and proxy values for leaf area, expressed as the product of leaf length and width. These projections of leaf-growth rates displayed a high level of correspondence with values observed in our data, as well as with other sets of reference data. A comparison with growth rates obtained by using the plastochrone index method showed that our model provides more accurate estimations while using a simpler methodology. Our results also show that whenever allometric parameters for the scaling of eelgrass leaf dry weight in terms of leaf area are available, the proposed model provides an accurate, cost-effective and non-destructive alternative to assessments based on traditional or plastochrone methods.
Allometric scaling of chemical restraint associated with inhalant anesthesia in giant anteaters.
Carregaro, Adriano Bonfim; Gerardi, Patrícia Molina; Honsho, Daniel Kan
2009-04-01
This study describes the use of allometric scaling in five giant anteaters (Myrmecophaga tridactyla) submitted for osteosynthesis, gastrostomy, or treatment of burns. Chemical restraint was performed by allometric scaling using the dog as a reference; acepromazine (0.06 mg/kg), diazepam (0.3 mg/kg), ketamine (8.8 mg/kg), and buprenorphine (5.9 microg/kg) were combined, and the animals were maintained under isoflurane anesthesia. Heart rate, respiratory rate, hemoglobin oxygen saturation, temperature, and anesthetic depth were measured. Postoperative treatment consisted of ketoprofen, buprenorphine, and ceftiofur. Anesthetic induction was obtained in 10-15 min, achieving muscle relaxation and absence of excitement. Physiologic parameters were stable during the procedures, and postoperative treatment was effective. Allometric scaling was effective for chemical restraint and postoperative treatment.
NASA Astrophysics Data System (ADS)
Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P.
2015-02-01
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways. Many students represented the situation numerically without invoking negative numbers, whereas others wrote equations involving negative numbers. When asked to interpret equations involving negative numbers in relation to the story, students did so in two ways. Their responses reflect distinct perspectives concerning the relationship between arithmetic equations and borrowing/owing. We discuss these findings and their implications regarding the role of contexts in integer instruction.
Allometric scaling of strength scores in NCAA division I-A football athletes.
Oba, Yukiya; Hetzler, Ronald K; Stickley, Christopher D; Tamura, Kaori; Kimura, Iris F; Heffernan, Thomas P
2014-12-01
This study examined population-specific allometric exponents to control for the effect of body mass (BM) on bench press, clean, and squat strength measures among Division I-A collegiate football athletes. One repetition maximum data were obtained from a university pre-season football strength assessment (bench press, n = 207; clean, n = 88; and squat n = 86) and categorized into 3 groups by positions (line, linebacker, and skill). Regression diagnostics and correlations of scaled strength data to BM were used to assess the efficacy of the allometric scaling model and contrasted with that of ratio scaling and theoretically based allometric exponents of 0.67 and 0.33. The log-linear regression models yielded the following exponents (b): b = 0.559, 0.287, and 0.496 for bench press, clean, and squat, respectively. Correlations between bench press, clean, and squat to BM were r = -0.024, -0.047, and -0.018, respectively, suggesting that the derived allometric exponents were effective in partialling out the effect of BM on these lifts and removing between-group differences. Conversely, unscaled, ratio-scaled, and allometrically scaled (b = 0.67 or 0.33) data resulted in significant differences between groups. It is suggested that the exponents derived in the present study be used for allometrically scaling strength measures in National Collegiate Athletic Association Division I-A football athletes. Use of the normative percentile rank scores provide coaches and trainers with a valid means of judging the effectiveness of their training programs by allowing comparisons between individuals without the confounding influence of BM.
NASA Astrophysics Data System (ADS)
Dhakal, Y. P.; Kunugi, T.; Suzuki, W.; Aoi, S.
2014-12-01
Many of the empirical ground motion prediction equations (GMPE) also known as attenuation relations have been developed for absolute acceleration or pseudo relative velocity response spectra. For a small damping, pseudo and absolute acceleration response spectra are nearly identical and hence interchangeable. It is generally known that the relative and pseudo relative velocity response spectra differ considerably at very short or very long periods, and the two are often considered similar at intermediate periods. However, observations show that the period range at which the two spectra become comparable is different from site to site. Also, the relationship of the above two types of velocity response spectra with absolute velocity response spectra are not discussed well in literature. The absolute velocity response spectra are the peak values of time histories obtained by adding the ground velocities to relative velocity response time histories at individual natural periods. There exists many tall buildings on huge and deep sedimentary basins such as the Kanto basin, and the number of such buildings is growing. Recently, Japan Meteorological Agency (JMA) has proposed four classes of long-period ground motion intensity (http://www.data.jma.go.jp/svd/eew/data/ltpgm/) based on absolute velocity response spectra, which correlate to the difficulty of movement of people in tall buildings. As the researchers are using various types of response spectra for long-period ground motions, it is important to understand the relationships between them to take appropriate measures for disaster prevention applications. In this paper, we, therefore, obtain and discuss the empirical attenuation relationships using the same functional forms for the three types of velocity response spectra computed from observed strong motion records from moderate to large earthquakes in relation to JMA magnitude, hypocentral distance, sediment depths, and AVS30 as predictor variables at periods between
Multipolar equations of motion for extended test bodies in general relativity
Steinhoff, Jan; Puetzfeld, Dirk
2010-02-15
We derive the equations of motion of an extended test body in the context of Einstein's theory of gravitation. The equations of motion are obtained via a multipolar approximation method and are given up to the quadrupolar order. Special emphasis is put on the explicit construction of the so-called canonical form of the energy-momentum density. The set of gravitational multipolar moments and the corresponding equations of motion allow for a systematic comparison to competing multipolar approximation schemes.
Nonlocal Symmetry of the Lax Equation Related to Riccati-Type Pseudopotential
NASA Astrophysics Data System (ADS)
Wang, Yun-Hu; Chen, Yong; Xin, Xiang-Peng
2012-12-01
We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity. A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower integrable models from higher ones. It is interesting that this nonlocal symmetry links with its corresponding Riccati-type pseudopotential. By introducing suitable and simple auxiliary dependent variables, the nonlocal symmetry is localized and used to generate new solutions from trivial solutions. Meanwhile, this equation is reduced to an ordinary differential equation by means of this nonlocal symmetry and some local symmetries.
Miller, M.R.; Eadie, J. McA
2006-01-01
We examined the allometric relationship between resting metabolic rate (RMR; kJ day-1) and body mass (kg) in wild waterfowl (Anatidae) by regressing RMR on body mass using species means from data obtained from published literature (18 sources, 54 measurements, 24 species; all data from captive birds). There was no significant difference among measurements from the rest (night; n = 37), active (day; n = 14), and unspecified (n = 3) phases of the daily cycle (P > 0.10), and we pooled these measurements for analysis. The resulting power function (aMassb) for all waterfowl (swans, geese, and ducks) had an exponent (b; slope of the regression) of 0.74, indistinguishable from that determined with commonly used general equations for nonpasserine birds (0.72-0.73). In contrast, the mass proportionality coefficient (b; y-intercept at mass = 1 kg) of 422 exceeded that obtained from the nonpasserine equations by 29%-37%. Analyses using independent contrasts correcting for phylogeny did not substantially alter the equation. Our results suggest the waterfowl equation provides a more appropriate estimate of RMR for bioenergetics analyses of waterfowl than do the general nonpasserine equations. When adjusted with a multiple to account for energy costs of free living, the waterfowl equation better estimates daily energy expenditure. Using this equation, we estimated that the extent of wetland habitat required to support wintering waterfowl populations could be 37%-50% higher than previously predicted using general nonpasserine equations. ?? The Cooper Ornithological Society 2006.
De Esteban-Trivigno, Soledad; Mendoza, Manuel; De Renzi, Miquel
2008-10-01
The Magnorder Xenarthra includes strange extinct groups, like glyptodonts, similar to large armadillos, and ground sloths, terrestrial relatives of the extant tree sloths. They have created considerable paleobiological interest in the last decades; however, the ecology of most of these species is still controversial or unknown. The body mass estimation of extinct species has great importance for paleobiological reconstructions. The commonest way to estimate body mass from fossils is through linear regression. However, if the studied species does not have similar extant relatives, the allometric pattern described by the regression could differ from those shown by the extinct group. That is the case for glyptodonts and ground sloths. Thus, stepwise multiple regression were developed including extant xenarthrans (their taxonomic relatives) and ungulates (their size and ecological relatives). Cases were weighted to maximize the taxonomic evenness. Twenty-eight equations were obtained. The distribution of the percent of prediction error (%PE) was analyzed between taxonomic groups (Perissodactyla, Artiodactyla, and Xenarthra) and size groups (0-20 kg, 20-300 kg, and more than 300 kg). To assess the predictive power of the functions, equations were applied to species not included in the regression development [test set cross validation, (TSCV)]. Only five equations had a homogeneous %PE between the aforementioned groups. These were applied to five extinct species. A mean body mass of 80 kg was estimated for Propalaehoplophorus australis (Cingulata: Glyptodontidae), 594 kg for Scelidotherium leptocephalum (Phyllophaga: Mylodontidae), and 3,550.7 kg for Lestodon armatus (Phyllophaga: Mylodontidae). The high scatter of the body mass estimations obtained for Catonyx tarijensis (Phyllophaga: Mylodontidae) and Thalassocnus natans (Phyllophaga: Megatheriidae), probably due to different specializations, prevented us from predicting its body mass. Surprisingly, although obtained
De Esteban-Trivigno, Soledad; Mendoza, Manuel; De Renzi, Miquel
2008-10-01
The Magnorder Xenarthra includes strange extinct groups, like glyptodonts, similar to large armadillos, and ground sloths, terrestrial relatives of the extant tree sloths. They have created considerable paleobiological interest in the last decades; however, the ecology of most of these species is still controversial or unknown. The body mass estimation of extinct species has great importance for paleobiological reconstructions. The commonest way to estimate body mass from fossils is through linear regression. However, if the studied species does not have similar extant relatives, the allometric pattern described by the regression could differ from those shown by the extinct group. That is the case for glyptodonts and ground sloths. Thus, stepwise multiple regression were developed including extant xenarthrans (their taxonomic relatives) and ungulates (their size and ecological relatives). Cases were weighted to maximize the taxonomic evenness. Twenty-eight equations were obtained. The distribution of the percent of prediction error (%PE) was analyzed between taxonomic groups (Perissodactyla, Artiodactyla, and Xenarthra) and size groups (0-20 kg, 20-300 kg, and more than 300 kg). To assess the predictive power of the functions, equations were applied to species not included in the regression development [test set cross validation, (TSCV)]. Only five equations had a homogeneous %PE between the aforementioned groups. These were applied to five extinct species. A mean body mass of 80 kg was estimated for Propalaehoplophorus australis (Cingulata: Glyptodontidae), 594 kg for Scelidotherium leptocephalum (Phyllophaga: Mylodontidae), and 3,550.7 kg for Lestodon armatus (Phyllophaga: Mylodontidae). The high scatter of the body mass estimations obtained for Catonyx tarijensis (Phyllophaga: Mylodontidae) and Thalassocnus natans (Phyllophaga: Megatheriidae), probably due to different specializations, prevented us from predicting its body mass. Surprisingly, although obtained
Symmetry and singularity properties of the generalised Kummer-Schwarz and related equations
NASA Astrophysics Data System (ADS)
Leach, P. G. L.
2008-12-01
We examine the generalised Kummer-Schwarz equation and some of its generalisations from the viewpoints of symmetry and singularity analyses. We determine the Complete Symmetry Group of the general equation and show that different forms of the fourth-order representative illustrate the three possible classes of Laurent series to be expected in the course of the singularity analysis.
ERIC Educational Resources Information Center
Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P.
2015-01-01
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…
NASA Astrophysics Data System (ADS)
de Lira, José Jonathas Pereira Rodrigues; Calado, Tereza Cristina dos Santos; Rezende, Carla Ferreira; Silva, José Roberto Feitosa
2015-12-01
Geographic variation of phenotypic traits is common across species and is often associated with variation in environmental conditions. Here, we found larger bodies and larger size at maturity in a northward, lower latitude population of the crab Goniopsis cruentata, which inhabits a hotter, drier environment in comparison with a southward, higher latitude population. Furthermore, the juvenile male gonopods grow more relative to body size in the population characterized by maturation at a smaller size. In contrast, the female abdomen widens at a higher rate among the late maturing population. These results provide further evidence that local environmental conditions play a role in phenotypic variation between populations inhabiting different latitudes. Moreover, they also show that variation in size at maturity and body size can lead to divergent allometric patterns of sexual characteristics that can have a sex-specific response.
Rapidly rotating neutron stars in general relativity: Realistic equations of state
NASA Technical Reports Server (NTRS)
Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.
1994-01-01
We construct equilibrium sequences of rotating neutron stars in general relativity. We compare results for 14 nuclear matter equations of state. We determine a number of important physical parameters for such stars, including the maximum mass and maximum spin rate. The stability of the configurations to quasi-radial perturbations is assessed. We employ a numerical scheme particularly well suited to handle rapid rotation and large departures from spherical symmetry. We provide an extensive tabulation of models for future reference. Two classes of evolutionary sequences of fixed baryon rest mass and entropy are explored: normal sequences, which behave very much like Newtonian sequences, and supramassive sequences, which exist for neutron stars solely because of general relativistic effects. Adiabatic dissipation of energy and angular momentum causes a star to evolve in quasi-stationary fashion along an evolutionary sequence. Supramassive sequences have masses exceeding the maximum mass of a nonrotating neutron star. A supramassive star evolves toward eventual catastrophic collapse to a black hole. Prior to collapse, the star actually spins up as it loses angular momentum, an effect that may provide an observable precursor to gravitational collapse to a black hole.
We developed models to estimate the soft tissue content of benthic marine invertebrates that are prey for aquatic wildlife. Allometric regression models of tissue wet weight with shell length for 10 species of benthic invertebrates had r2 values ranging from 0.29 for hermit crabs...
Allometric scaling of UK urban emissions: interpretation and implications for air quality management
NASA Astrophysics Data System (ADS)
MacKenzie, Rob; Barnes, Matt; Whyatt, Duncan; Hewitt, Nick
2016-04-01
Allometry uncovers structures and patterns by relating the characteristics of complex systems to a measure of scale. We present an allometric analysis of air quality for UK urban settlements, beginning with emissions and moving on to consider air concentrations. We consider both airshed-average 'urban background' concentrations (cf. those derived from satellites for NO2) and local pollution 'hotspots'. We show that there is a strong and robust scaling (with respect to population) of the non-point-source emissions of the greenhouse gases carbon dioxide and methane, as well as the toxic pollutants nitrogen dioxide, PM2.5, and 1,3-butadiene. The scaling of traffic-related emissions is not simply a reflection of road length, but rather results from the socio-economic patterning of road-use. The recent controversy regarding diesel vehicle emissions is germane to our study but does not affect our overall conclusions. We next develop an hypothesis for the population-scaling of airshed-average air concentrations, with which we demonstrate that, although average air quality is expected to be worse in large urban centres compared to small urban centres, the overall effect is an economy of scale (i.e., large cities reduce the overall burden of emissions compared to the same population spread over many smaller urban settlements). Our hypothesis explains satellite-derived observations of airshed-average urban NO2 concentrations. The theory derived also explains which properties of nature-based solutions (urban greening) can make a significant contribution at city scale, and points to a hitherto unforeseen opportunity to make large cities cleaner than smaller cities in absolute terms with respect to their airshed-average pollutant concentration.
NASA Technical Reports Server (NTRS)
Jezewski, D.
1980-01-01
Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.
2014-01-01
Background Chemical restraint is of great importance in the clinical practice of wildlife animals. In such, interspecific allometric scaling proposes pharmacological doses to a wide range of species, based on previously known doses for domestic animals and the target animal’s body mass. The objective was to compare chemical restraint responses in the greater rhea (Rhea americana) with conventional doses of tiletamine/zolazepam, found in the literature for the species, and with doses calculated through interspecific allometric scaling extrapolation. From the Federal University of Piauí, six adult greater rheas (Rhea americana), three males and three females, were randomly selected to be subjects in this research. All six animals were submitted to two chemical restraint protocols with tiletamine and zolazepam, per intramuscular injection in the hind limb. The first protocol was composed of doses found on the literature for the species, while the second protocol used doses calculated by interspecific allometric scaling, with the domestic dog as model animal. Heart and respiratory rates, body temperature, eyelid reflex, digital pinch and metatarsal reflex were registered along with latency and ambulation times. Results The use of interspecific allometric scaling for chemical restraint with the combination tiletamine and zolazepam showed satisfying results, with great similarity to results obtained with conventional doses in Greater rheas. Conclusions Literature on chemical restraint and use of tiletamine and zolazepam in rheas is scarce. Chemical restraint is of extreme importance on these animals, due to their aggressive nature and low level of domesticity. This research may further establish the interspecific allometric scaling method as a viable tool for the veterinary physician in formulating anesthetic and chemical restraint protocols for wildlife animals. PMID:24625103
On the Equivalence of the Dirac Equation Between General Relativity and Teleparallel Gravity
Bagci, Meral; Havare, Ali; Soeguet, Kenan
2007-04-23
The Teleparellel Theory (TPT) is one of alternative ways of describing the gravitational field. Unlike the general relativistic description of gravitation in the TPT curvature is assumed to vanish instead of torsion. In general relativistic theory (GRT) the Riemann geometry is used to describe the equations while in the case of TPT the Weitzenboeck space-time is used. In this study we showed the equivalence of the Dirac equation between these two theories.
NASA Astrophysics Data System (ADS)
Ballesteros, C. A.; Herrmann, M.; Huang, H.
2011-12-01
The improvement of numerical weather prediction models in recent decades has led to a measurable decrease in forecast error, for instance as quantified by the 500-hPa geopotential height anomaly correlation. This improvement can be attributed in part to the refinements in the numerical architecture and the representation of physical processes in the model. It is more difficult to attribute the reduction in forecast error to improvements in the accuracy of the models' initial conditions, not least because of the complexity of the data assimilation process. As a contribution to this problem that will also be pedagogically useful, a reforecast experiment was conducted using a simple regional vorticity equation model for the 500-hPa flow over North America. This model is comparable in complexity to the Charney-Fjörtoft-von Neumann model used for the first numerical weather prediction experiment in 1949. Six-hourly predictions are made out to 36 hours for the period from 1948-2010, using the NCEP Reanalysis dataset for the initial conditions. Because initialization is trivial for this "filtered" model, one can clearly attribute the change in forecast skill to the changing quality of the initial state. The choice of the 500 hPa level is relevant since it will reflect the effect of the significant change in the density of upper-air observations from the mid- to late 20th Century. As an important byproduct of this exercise, a trend of improved forecast over time will imply an improved relative quality of the reanalysis data for the mid-troposphere. Therefore, the experiment serves two purposes of studying the forecast error and checking the quality of the reanalysis. An analysis of selected cases indicates that the predictions made for the 21st century have smaller errors compared to those made for the 1950s. A comprehensive analysis for the whole set of forecast is underway and the outcome will be discussed.
NASA Astrophysics Data System (ADS)
Arminjon, Mayeul
2005-10-01
The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg’s (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.
2016-01-01
Feeding adaptation, social behaviour, and interspecific interactions related to sexual dimorphism and allometric growth are particularly challenging to be investigated in the high sexual monomorphic Delphinidae. We used geometric morphometrics to extensively explore sexual dimorphism and ontogenetic allometry of different projections of the skull and the mandible of the bottlenose dolphin Tursiops truncatus. Two-dimensional landmarks were recorded on the dorsal, ventral, lateral, and occipital views of the skull, and on the lateral view of the left and the right mandible of 104 specimens from the Mediterranean and the North Seas, differing environmental condition and degree of interspecific associations. Landmark configurations were transformed, standardized and superimposed through a Generalized Procrustes Analysis. Size and shape differences between adult males and females were respectively evaluated through ANOVA on centroid size, Procrustes ANOVA on Procrustes distances, and MANOVA on Procrustes coordinates. Ontogenetic allometry was investigated by multivariate regression of shape coordinates on centroid size in the largest homogenous sample from the North Sea. Results evidenced sexual dimorphic asymmetric traits only detected in the adults of the North Sea bottlenose dolphins living in monospecific associations, with females bearing a marked incision of the cavity hosting the left tympanic bulla. These differences were related to a more refined echolocalization system that likely enhances the exploitation of local resources by philopatric females. Distinct shape in immature versus mature stages and asymmetric changes in postnatal allometry of dorsal and occipital traits, suggest that differences between males and females are established early during growth. Allometric growth trajectories differed between males and females for the ventral view of the skull. Allometric trajectories differed among projections of skull and mandible, and were related to dietary
Which electromagnetic equations apply in rotating coordinates. [frame transformations in relativity
NASA Technical Reports Server (NTRS)
Webster, D. L.; Whitten, R. C.
1973-01-01
It was discovered some years ago by Schiff that two equations for fields in vacuum do not carry over without change from an inertial frame to a frame with rotating axes of space coordinates, even for a region with all velocities much lower than the speed of light. However, the belief that all four of the field equations are invariant under such conditions is still prevalent and causes misconceptions in physical applications, including astrophysical and geophysical ones. The purpose of the present paper is therefore to call attention to Schiff's discovery, discussing its basis and its extension to fields in material media, and to interpret the additional terms that must be added to the equations in order to obtain valid transformations to rotating axes of coordinates.
Markel, Vadim A; Schotland, John C
2012-06-01
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half space and derive and implement a computationally efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically measurable quantities rather than to simply approximate certain coefficients in a partial differential equation. PMID:23005233
Fast methods for the Eikonal and related Hamilton- Jacobi equations on unstructured meshes.
Sethian, J A; Vladimirsky, A
2000-05-23
The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. The scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a Dijkstra-like programming approach. In this paper, we discuss several extensions to this technique, including higher order versions on unstructured meshes in Rn and on manifolds and connections to more general static Hamilton-Jacobi equations. PMID:10811874
Fast methods for the eikonal and related Hamilton-Jacobi equations on unstructured meshes
Sethian, J.A.; Vladimirsky, A.
1999-12-01
The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. The scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a Dijkstra-like programming approach. In this paper, we discuss several extensions to this technique, including higher order versions on unstructured meshes in R{sup n} and on manifolds and connections to more general static Hamilton-Jacobi equations.
Fast methods for the Eikonal and related Hamilton- Jacobi equations on unstructured meshes.
Sethian, J A; Vladimirsky, A
2000-05-23
The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. The scheme relies on an upwind finite difference approximation to the gradient and a resulting causality relationship that lends itself to a Dijkstra-like programming approach. In this paper, we discuss several extensions to this technique, including higher order versions on unstructured meshes in Rn and on manifolds and connections to more general static Hamilton-Jacobi equations.
NASA Astrophysics Data System (ADS)
Remiddi, Ettore; Tancredi, Lorenzo
2016-06-01
It is shown that the study of the imaginary part and of the corresponding dispersion relations of Feynman graph amplitudes within the differential equations method can provide a powerful tool for the solution of the equations, especially in the massive case. The main features of the approach are illustrated by discussing the simple cases of the 1-loop self-mass and of a particular vertex amplitude, and then used for the evaluation of the two-loop massive sunrise and the QED kite graph (the problem studied by Sabry in 1962), up to first order in the (d - 4) expansion.
ERIC Educational Resources Information Center
Sahin, Elvan; Ertepinar, Hamide; Teksoz, Gaye
2012-01-01
The purpose of this study is to construct a structural equation model to examine the links among attitudes, values, and behaviors pertaining to sustainability, participation in outdoor recreation as well as gender and tendency to follow mass media for university students. The data were collected by on-line administration of a survey to 958…
Student Interpretations of Equations Related to the First Law of Thermodynamics
ERIC Educational Resources Information Center
Hadfield, Linda C.; Wieman, Carl E.
2010-01-01
Student interpretations of the equation for the first law of thermodynamics, [delta]U = q + w, an expression defining work done on or by a gas, w = -[image omitted]PdV, and an expression defining heat, q = [image omitted]C[subscript v]dT were investigated through a multiple-choice survey, a free-response written survey, and interviews. The…
Translation of Algebraic Equations and Its Relation to Formal Operational Reasoning.
ERIC Educational Resources Information Center
Niaz, Mansoor
A large proportion of college students majoring in science are unable to translate even simple sentences into algebraic equations. Given the following sentence, "There are six times as many students (S) as professors (P) at this university," 37% of 150 freshmen engineering students in a study conducted in 1981 by Clement, Lockhead, and Monk wrote…
Allometric theory and the mechanical stability of large trees: proof and conjecture.
Niklas, Karl J; Spatz, Hanns-Christof
2006-06-01
Recent allometric theory has postulated that standing leaf mass will scale as the 3/4 power of stem mass and as the 3/4 power of root mass such that stem mass scales isometrically with respect to root mass across very large vascular plant species with self-supporting stems. We show that the isometric scaling of stem mass with respect to root mass (i.e., M(S) ∝ M(R)) can be derived directly from mechanical theory, specifically from the requirement that wind-induced bending moments acting at the base of stems must be balanced by a counter-resisting moment provided by the root system to prevent uprooting. This derivation provides indirect verification of the allometric theory. It also draws attention to the fact that leaf, stem, and root biomass partitioning patterns must accommodate the simultaneous performance of manifold functional obligations.
Generalized conditional symmetries and related solutions of the Grad-Shafranov equation
NASA Astrophysics Data System (ADS)
Cimpoiasu, Rodica
2014-04-01
The generalized conditional symmetry (GCS) method is applied to a specific case of the Grad-Shafranov (GS) equation, in cylindrical geometry assuming the existence of an axial symmetry. We investigate the conditions that yield the GS equation admitting a special class of second-order GCSs. The determining system for the unknown arbitrary functions is solved in several special cases and new exact solutions, including solitary waves, different in form and structure from the ones obtained using other nonclassical symmetry methods, are pointed out. Several plots of the level sets or flux surfaces of the new solutions as well as surfaces with vanishing flow are displayed. The obtained solutions can be useful for studying plasma equilibrium, transport phenomena, and magnetohydrodynamic stability.
Generalized conditional symmetries and related solutions of the Grad-Shafranov equation
Cimpoiasu, Rodica
2014-04-15
The generalized conditional symmetry (GCS) method is applied to a specific case of the Grad–Shafranov (GS) equation, in cylindrical geometry assuming the existence of an axial symmetry. We investigate the conditions that yield the GS equation admitting a special class of second-order GCSs. The determining system for the unknown arbitrary functions is solved in several special cases and new exact solutions, including solitary waves, different in form and structure from the ones obtained using other nonclassical symmetry methods, are pointed out. Several plots of the level sets or flux surfaces of the new solutions as well as surfaces with vanishing flow are displayed. The obtained solutions can be useful for studying plasma equilibrium, transport phenomena, and magnetohydrodynamic stability.
New Exact Solutions of the CDGSK Equation Related to a Non-local Symmetry
NASA Astrophysics Data System (ADS)
Lou, Senyue; Ruan, Hangyu; Chen, Weizhong; Wang, Zhenli; Chen, Lili
1994-10-01
A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation has been used for finding exact solution in two different ways. Firstly, using the standard prolongation approach, we obtain the finite Lie Bäcklund transformation and the single soliton solution. Secondly, combining some local symmetries and the nonlocal symmetry, we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.
Critical study of type II supernovae: equations of state and general relativity
Kahana, S.
1986-01-01
The relevance of relativistic gravitation and of the properties of nuclear matter at high density to supernova explosions is examined in detail. The existing empirical knowledge on the nuclear equation of state at densities greater than saturation, extracted from analysis of heavy ion collisions and from the breathing mode in heavy nuclei, is also considered. Particulars of the prompt explosions recently obtained theoretically by Baron, Cooperstein, and Kahana are presented. 40 refs., 9 figs., 3 tabs.
Suzuki, Maki; Hiura, Tsutom
2000-02-01
Current-year shoots are mostly made of primary tissues, whereas first-order branches comprise mainly secondary tissues. Differences in tissue composition of these units reflect differences in functional design. We compared the allometry of current-year shoots and first-order branches in eight deciduous broad-leaved tree species and examined the functional differences underlying the design of current-year shoots and first-order branches. Allometric relationships of first-order branches tended to be compatible with predictions of the pipe model and elastic similarity model. That is, allometric constants of the relationships between leaf mass and stem diameter at the branch base and between stem diameter and stem mass were 2.0 and 0.33-0.38, respectively, indicating that the functional regulation of stem form of first-order branches can be predicted by the two models. However, allometric relationships of current-year shoots were not compatible with the predictions of the pipe and elastic similarity models. Thus, the allometric constant of the relationship between leaf mass and stem diameter at the base of current-year shoots was larger than 2.0, and the allometric constant of the relationship between stem length and stem diameter of shoots was larger than 1.0 in all species examined. However, current-year shoots had an allometric constant of leaf mass against stem length that was less than 1.0, suggesting a functional demand on shoot design to reduce self-shading. Also, allometric constants of stem length against stem diameter at the shoot base were larger in monopodial species than in sympodial species, whereas allometric constants of leaf mass per shoot against stem length were smaller in monopodial species than in sympodial species. We propose that the allometries of current-year shoots reflect their function as disposable units for temporary leaf arrangement.
Ogle, Kiona; Pacala, Stephen W
2009-04-01
Predictions of forest succession, diversity and function require an understanding of how species differ in their growth, allocation patterns and susceptibility to mortality. These processes in turn are affected by allometric constraints and the physiological state of the tree, both of which are coupled to the tree's labile carbon status. Ultimately, insight into the hidden labile pools and the processes affecting the allocation of labile carbon to storage, maintenance and growth will improve our ability to predict tree growth, mortality and forest dynamics. We developed the 'Allometrically Constrained Growth and Carbon Allocation' (ACGCA) model that explicitly couples tree growth, mortality, allometries and labile carbon. This coupling results in (1) a semi-mechanistic basis for predicting tree death, (2) an allocation scheme that simultaneously satisfies allometric relationships and physiology-based carbon dynamics and (3) a range of physiological states that are consistent with tree behavior (e.g., healthy, static, shrinking, recovering, recovered and dead). We present the ACGCA model and illustrate aspects of its behavior by conducting simulations under different forest gap dynamics scenarios and with parameter values obtained for two ecologically dissimilar species: loblolly pine (Pinus taeda L.) and red maple (Acer rubrum L.). The model reproduces growth and mortality patterns of these species that are consistent with their shade-tolerance and succession status. The ACGCA framework provides an alternative, and potentially improved, approach for predicting tree growth, mortality and forest dynamics. PMID:19203984
Allometric ecological distributions in a local community of Hymenoptera
NASA Astrophysics Data System (ADS)
Ulrich, Werner
2004-05-01
The present paper describes basic ecological distributions in a community of beech forest Hymenoptera. It shows that the species diversity-body weight and the density-body weight distributions give rise to a new distribution that relates total community biomass to species diversity. For Hymenoptera this distribution follows a power function with a slope of 1.3. Combining this relation with the species-area and the individuals-area relations resulted in two other distributions that relate community biomass to area and individual numbers. It appeared that population densities decrease when computed over larger areas. The biomass-species diversity relation offers a new and simple way to estimate total community biomass from samples. The possible implications of this distribution to the productivity-diversity debate are discussed.
Dinh, Khanh N; Sidje, Roger B
2016-01-01
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP. PMID:27176781
NASA Astrophysics Data System (ADS)
Dinh, Khanh N.; Sidje, Roger B.
2016-06-01
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP.
Dinh, Khanh N; Sidje, Roger B
2016-05-13
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP.
Lochmiller, R L; Hellgren, E C; Grant, W E
1986-01-01
Selected morphological features of 8 adult male and 8 adult female collared peccaries (Tayassu tajacu) shot from southern Texas during March 1983 are described. A total of 16 adult peccaries with an average body mass of 18.68 +/- 0.61 (SE) Kg was examined. Significant differences between males and females were observed for absolute and relative mass of liver and lungs, and relative heart mass. These visceral organs were heavier among females than males. Significant sex effects were also found for absolute and relative mass of the dorsal scent gland. The dorsal scent gland contributed twice as much to total body mass in males as in females. No sexual dimorphisms of the gastrointestinal tract were noted. Females had a significantly greater portion of total visceral fat deposited around the kidneys than did males. Relative mass of the mandible was significantly greater in males than in females. Adult males had extremely large accessory sex glands. The bulbourethral and seminal vesicle glands comprised 0.27 per cent of the total body mass. Allometric growth coefficients (b) varied among the various organs and glands examined, ranging from below (eyes, b = 0.34) to well above (seminal vesicles, b = 1.87) unity. Growth coefficients of lungs, kidneys, pituitary gland, and thyroid gland during adulthood greatly exceeded respective values in developing nurslings.
NASA Astrophysics Data System (ADS)
Frank, T. D.
The Lotka-Volterra-Haken equations have been frequently used in ecology and pattern formation. Recently, the equations have been proposed by several research groups as amplitude equations for task-related patterns of brain activity. In this theoretical study, the focus is on the circular causality aspect of pattern formation systems as formulated within the framework of synergetics. Accordingly, the stable modes of a pattern formation system inhibit the unstable modes, whereas the unstable modes excite the stable modes. Using this circular causality principle it is shown that under certain conditions the Lotka-Volterra-Haken amplitude equations can be derived from a general model of brain activity akin to the Wilson-Cowan model. The model captures the amplitude dynamics for brain activity patterns in experiments involving several consecutively performed multiple-choice tasks. This is explicitly demonstrated for two-choice tasks involving grasping and walking. A comment on the relevance of the theoretical framework for clinical psychology and schizophrenia is given as well.
Flight speeds among bird species: allometric and phylogenetic effects.
Alerstam, Thomas; Rosén, Mikael; Bäckman, Johan; Ericson, Per G P; Hellgren, Olof
2007-08-01
Flight speed is expected to increase with mass and wing loading among flying animals and aircraft for fundamental aerodynamic reasons. Assuming geometrical and dynamical similarity, cruising flight speed is predicted to vary as (body mass)(1/6) and (wing loading)(1/2) among bird species. To test these scaling rules and the general importance of mass and wing loading for bird flight speeds, we used tracking radar to measure flapping flight speeds of individuals or flocks of migrating birds visually identified to species as well as their altitude and winds at the altitudes where the birds were flying. Equivalent airspeeds (airspeeds corrected to sea level air density, Ue) of 138 species, ranging 0.01-10 kg in mass, were analysed in relation to biometry and phylogeny. Scaling exponents in relation to mass and wing loading were significantly smaller than predicted (about 0.12 and 0.32, respectively, with similar results for analyses based on species and independent phylogenetic contrasts). These low scaling exponents may be the result of evolutionary restrictions on bird flight-speed range, counteracting too slow flight speeds among species with low wing loading and too fast speeds among species with high wing loading. This compression of speed range is partly attained through geometric differences, with aspect ratio showing a positive relationship with body mass and wing loading, but additional factors are required to fully explain the small scaling exponent of Ue in relation to wing loading. Furthermore, mass and wing loading accounted for only a limited proportion of the variation in Ue. Phylogeny was a powerful factor, in combination with wing loading, to account for the variation in Ue. These results demonstrate that functional flight adaptations and constraints associated with different evolutionary lineages have an important influence on cruising flapping flight speed that goes beyond the general aerodynamic scaling effects of mass and wing loading.
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Kundt, Wolfgang
2014-03-01
This is an English translation of a paper by Pascual Jordan and Wolfgang Kundt, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 3 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1, 2 and 4 of the series have already been reprinted, part 5 will be printed as a Golden Oldie in near future.) This third paper shows how solutions of the Einstein-Maxwell equations with null Maxwell field can be incorporated into the scheme of geometrodynamics. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Charles Misner.
Cheng, Hsien C
2004-07-01
Use of the Cheng-Prusoff equation for determination of the equilibrium dissociation constant, K(B), is based on an assumption that simple bi-molecular interaction kinetics are strictly followed. Under such circumstances, the slope parameters of the agonist concentration-response curve (K) and that of the inhibition curve (n) are unity. New equations are needed for calculating K(B) when slope parameters (K and n) deviate from unity. In this article, the slope parameters K and n are used as indexes of cooperativity. Thus, the following new equations are derived: (1) For calculation of K(B) from IC(50), the new equation which incorporates both cooperativity indexes is described as K(B) = (IC50)n/(1 + A(K)/K(A)) = (IC50)n/[1 + (A/EC50)K] where A is the concentration of the agonist against which the IC(50) is determined, and K(A) is the apparent equilibrium dissociation constant of the agonist. This new equation is applicable when the cooperativity indexes of K and n are less than, equal to, or greater than unity. This equation reduces to the Cheng-Prusoff equation when the cooperativity indexes K and n are unity. (2) For saturation binding assays, the enhanced Scatchard analysis is described by the equation: B/Fm = -B/K(D) + B(max)/K(D) where B and F are the concentrations of the bound and free ligand, respectively, and m is the cooperativity index of the ligand. A plot of B/F(m) versus B yields a straight line with a negative slope that equals 1/K(D), and an x-axis intercept that equals B(max). When m equals unity, the above analysis reduces to the traditional Scatchard analysis. (3) The importance of the slope parameters (K and n) on Schild analysis is illustrated by the equation: log(x(K) - 1) = log Bn - log K(B), where x is the concentration ratio, and B is the concentration of the antagonist. The modified pA(2) is now defined as the -logarithm of the molar concentration of the antagonist (B), power adjusted with the slope parameter (B(n)), that causes a two
Latitude-related changes in the amplitude of annual mortality rhythm. The biological equator in man.
Douglas, S; Rawles, J
1999-03-01
There is extensive literature describing the effect of season on mortality rates, especially in cardiovascular and respiratory disease. This study compares latitude with the extent of seasonal variation of monthly deaths from all causes. In developed countries, there is a peak of deaths in winter and a trough in summer. Monthly numbers of deaths were established in 89 countries in the Northern and Southern Hemisphere. Using cosinor analysis, the extent of seasonal variation (amplitude) was established and correlated with latitude. The amplitude of seasonality was greatest in mid-latitude around 35 degrees, but low or absent near the equator and subpolar regions. The amplitude can differ at the same latitude. The weather in equatorial regions and in habitations near the Arctic Circle is very different, but death has a similar seasonal rhythm. The purpose is to record this epidemiological finding even though no simple explanation is provided. Weather alone cannot explain it, and it is possible that day length (photoperiod) has an important, but complex, underlying role.
NASA Astrophysics Data System (ADS)
Lubuma, J. M.-S.; Mureithi, E.; Terefe, Y. A.
2011-11-01
The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.
Young, C.W.
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
NASA Technical Reports Server (NTRS)
Pan, Y. S.
1975-01-01
The aerodynamic sound described by the Lighthill-Curle solution is reexamined using a method of matched asymptotic expansions. The governing Navier-Stokes equations written in nondimensional form are expanded for a small Mach number. First- and second-order solutions for the pressure field are obtained, and the singular nature of the expansion at large distances is indicated. The nearfield pressure is governed by the Poisson equation, whereas the farfield equations describe a linear wave system in a dissipative medium. The pseudosound is related to the incompressible Reynolds stresses associated with a solenoidal velocity field, the velocity, the pressure perturbation, and their derivatives on the boundaries. A uniformly valid first-order solution for the pressure is obtained. It is shown that viscosity, thermal conductivity, and entropy in the flow do not contribute to the first-order noise generation, while the viscous stress contributes to noise only from some boundaries. The application of the proposed perturbation method to a subsonically moving surface and a hot jet is discussed.
Echavarría-Heras, Héctor; Solana-Arellano, Elena; Leal-Ramírez, Cecilia; Castillo, Oscar
2013-01-01
Estimation of leaf productivity in eelgrass (Zostera marina L.) is crucial for evaluating the ecological role of this important seagrass species. Although leaf marking techniques are widely used to obtain estimates of leaf productivity, the accuracy of these assessments, has been questioned mainly because these fail to account for leaf growth below the reference mark and also because they apparently disregard the contribution of mature leaf tissues to the growth rate of leaves. On the other hand, the plastochrone method is a simpler technique that has been considered to effectively capture growth in a more realistic way, thereby providing more accurate assessments of both above- and below-ground productivities. But since the actual values of eelgrass growth rates are difficult to obtain, the worth of the plastochrone method has been largely vindicated because it produces assessments that overestimate productivity as compared to estimates obtained by leaf marking. Additionally, whenever eelgrass leaf biomass can be allometrically scaled in terms of matching leaf length in a consistent way, the associated leaf growth rates can be also projected allometrically. In this contribution, we used that approach to derive an authentication of the plastochrone method and formally demonstrate that, as has been claimed to occur for leaf marking approaches, the plastochrone method itself underestimates actual values of eelgrass leaf growth rates. We also show that this unavoidable bias is mainly due to the inadequacy of single-leaf biomass assessments in providing a proxy for the growth of all leaf tissue in a shoot over a given interval. Moreover, the derived formulae give conditions under which assessments of leaf growth rates using the plastochrone method would systematically underestimate matching values obtained by leaf marking procedures. And, assessments of leaf growth rates obtained by using the present data show that plastochrone method estimations underestimated
2013-01-01
Estimation of leaf productivity in eelgrass (Zostera marina L.) is crucial for evaluating the ecological role of this important seagrass species. Although leaf marking techniques are widely used to obtain estimates of leaf productivity, the accuracy of these assessments, has been questioned mainly because these fail to account for leaf growth bellow the reference mark and also because they apparently disregard the contribution of mature leaf tissues to the growth rate of leaves. On the other hand, the plastochrone method is a simpler technique that has been considered to effectively capture growth in a more realistic way, thereby providing more accurate assessments of both above- and below-ground productivities. But since the actual values of eelgrass growth rates are difficult to obtain, the worth of the plastochrone method has been largely vindicated because it produces assessments that overestimate productivity as compared to estimates obtained by leaf marking. Additionally, whenever eelgrass leaf biomass can be allometrically scaled in terms of matching leaf length in a consistent way, the associated leaf growth rates can be also projected allometrically. In this contribution, we used that approach to derive an authentication of the plastochrone method and formally demonstrate that, as has been claimed to occur for leaf marking approaches, the plastochrone method itself underestimates actual values of eelgrass leaf growth rates. We also show that this unavoidable bias is mainly due to the inadequacy of single-leaf biomass assessments in providing a proxy for the growth of all leaf tissue in a shoot over a given interval. Moreover, the derived formulae give conditions under which assessments of leaf growth rates using the plastochrone method would systematically underestimate matching values obtained by leaf marking procedures. And, assessments of leaf growth rates obtained by using the present data show that plastochrone method estimations underestimated
NASA Astrophysics Data System (ADS)
Raychaudhuri, Debasree
2013-12-01
There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following question. Who succeeds at making the leap and can we describe the attributes that set them apart from the ones that do not? In this article, we offer a framework to categorize students as learners based on their individual approaches towards learning concepts in differential equations and related concepts - as demonstrated by their efforts to resolve a conflict, conserve and rebuild their cognitive structures.
Kaernbach, C; König, P; Schillen, T
1987-02-01
Recent experimental observations of otoacoustic emissions suggest the existence of spontaneous emitters of sound on the basilar membrane. These tend to send off waves not only in the normal direction of propagation. It is therefore significant to study the environmental conditions such an emitter finds inside the cochlea. The impedance relations seen by these emitters are described by the Riccati equation for an inhomogeneous transmission line. The results reported in this paper differ considerably for forward and backward excitation. This reflects the quite different behavior of the cochlea pertaining to waves traveling forward and backward. Because of reflections, backward waves cannot be treated with the Liouville-Green approximation.
Scaling relations in the equation of state, thermal expansion, and melting of metals
NASA Technical Reports Server (NTRS)
Guinea, F.; Rose, J. H.; Smith, J. R.; Ferrante, J.
1984-01-01
A simple and yet quite accurate prediction of volume as a function of pressure for metals and alloys is presented. Thermal expansion coefficients and melting temperatures are predicted by simple, analytic expressions and results compare favorably with experiment for a broad range of metals. All of these predictions are made possible by the discovery of universality in binding energy relations for metals.
Rogers, Allison G; Pritchett, Elizabeth M; Alphin, Robert L; Brannick, Erin M; Benson, Eric R
2015-03-01
This study evaluates the impact of light-emitting diode (LED), cold cathode fluorescent (CCFL), and incandescent lamps on broiler performance. Male Ross 708 broilers (n=672) were raised to 6 wk age in 8 black-out modified large colony houses, under identical intermittent lighting conditions using 4 unique types of lamps, which were gradually dimmed throughout the study. Incandescent lamps served as the control; experimental technologies tested included CCFL and 2 different LED lamps. Each technology was tested in duplicate for each of 4 trials (8 replications total per technology) conducted across the course of one year to account for seasonal variance. Live performance for each technology was evaluated using live broiler body weight (BW), weight gain, feed conversion, and mortality. Birds were removed from each house at 7, 14, 35, and 42 d to be humanely euthanized, weighed, and necropsied for allometric tissue sample analysis. Relative to the technologies tested, results indicate that birds raised under incandescent lamps had significantly higher BW by 42 d, compared to birds raised under CCFL lamps, which had poorer BW performance (P=0.03). Birds raised under both LED technologies grew to final BWs similar to those raised under incandescent light, with significant differences in neither feed conversion nor mortality.
NASA Astrophysics Data System (ADS)
Vlad, Marcel Ovidiu; Ross, John
2002-12-01
We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.
Tseng, Wan-Ling; Banny, Adrienne M; Kawabata, Yoshito; Crick, Nicki R; Gau, Susan Shur-Fen
2013-01-01
This short-term longitudinal study examined the associations among relational aggression, physical aggression, and peer status (i.e., acceptance, rejection, and perceived popularity) across three time points, six months apart, in a Taiwanese sample. Participants were 198 fifth grade students (94 girls and 104 boys; Mean age = 10.35 years) from Taipei, Taiwan. Study variables were assessed using peer nomination procedure. Results from the cross-lagged structural equation models demonstrated that there were longitudinal associations between relational aggression and each of the peer status constructs while only one longitudinal association was found for physical aggression such that physical aggression positively predicted subsequent peer rejection. The longitudinal associations did not vary with gender. Results also showed high stabilities of relational aggression, physical aggression, and the three peer status constructs over 1 year as well as high concurrent association between relational and physical aggression. In addition, relational aggression and physical aggression were concurrently related to less acceptance, more rejection, and less perceived popularity, especially at the outset of the study. Findings of this study demonstrated both similarities and differences in relation to previous literature in primarily Western cultures. This study also highlights the bidirectional and complex nature of the association between aggression and peer status, which appears to depend on the form of aggression and on the particular indicator of peer status under study.
NASA Astrophysics Data System (ADS)
Zhang, Yunlong; Wu, Qiaowan; Hu, Weihua; Wang, Fan; Shao, Weihan; Zhang, Chengming; Zhao, Zhongbo; He, Hui; Fan, Qixue; Gu, Zemao
2016-07-01
The length-weight relationship and allometric growth patterns of hatchery-reared Chinese loach, Paramisgurnus dabryanus (Dabry de Thiersant, 1872), were determined from hatching to 60 days after hatching. A best power model was estimated for the length-weight relationship during the early life stages. Positive allometric growth for the head segment, trunk length, tail length and eye diameter was also found in the early life stages, while body depth, tail depth, tail fin length, pectoral fin length and barbel length displayed a negative coefficient. During the subsequent early developmental stage, the growth coefficients showed a clear and common tendency towards isometry for all measured body ratios. The allometric growth changes in Chinese loach during the early stage are possibly the result of selective organogenesis directed towards survival priorities.
Warner, Nicholas A; Nøst, Therese H; Andrade, Hector; Christensen, Guttorm
2014-07-01
Spatial distribution and relationship of allometric measurements (length, weight and age) to liver concentrations of cyclic volatile methyl siloxanes (cVMS) including octamethylcyclotetrasiloxane (D4), decamethylcyclopentasiloxane (D5) and dodecamethylcyclosiloxane (D6) in Atlantic cod (Gadus morhua) collected near the community of Tromsø in Northern Norway were assessed. These congeners were benchmarked against known persistent polychlorinated biphenyls (PCBs 153 and 180) to assess accumulation behavior of cVMS. D5 was the dominate cVMS detected in all fish livers with lipid normalized concentrations up to 10 times or greater than those observed for PCB 153 and 180. D4 and D6 concentration were negatively correlated with fish length and weight, indicating a greater elimination capacity compared to uptake processes with increasing fish size for these chemicals. These results indicate relationships between allometric measurements and cVMS concentrations may account for concentration variations observed within fish and should be assessed in future studies evaluating cVMS bioaccumulation potential.
Allometric growth in juvenile marine turtles: possible role as an antipredator adaptation.
Salmon, Michael; Scholl, Joshua
2014-04-01
Female marine turtles produce hundreds of offspring during their lifetime but few survive because small turtles have limited defenses and are vulnerable to many predators. Little is known about how small turtles improve their survival probabilities with growth though it is assumed that they do. We reared green turtles (Chelonia mydas) and loggerheads (Caretta caretta) from hatchlings to 13 weeks of age and documented that they grew wider faster than they grew longer. This pattern of allometric growth might enable small turtles to more quickly achieve protection from gape-limited predators, such as the dolphinfish (Coryphaena hippurus). As a test of that hypothesis, we measured how dolphinfish gape increased with length, reviewed the literature to determine how dolphinfish populations were size/age structured in nearby waters, and then determined the probability that a small turtle would encounter a fish large enough to consume it if it grew by allometry vs. by isometry (in which case it retained its hatchling proportions). Allometric growth more quickly reduced the probability of a lethal encounter than did isometric growth. On that basis, we suggest that allometry during early ontogeny may have evolved because it provides a survival benefit for small turtles. PMID:24629459
NASA Astrophysics Data System (ADS)
Kiryakova, Virginia S.
2012-11-01
The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order
Armentrout, Matthew M.; Rainey, Emma S.G.; Kavner, Abby
2013-07-30
The high-pressure and high-temperature equation of state of rock salt-structured cobalt oxide was measured up to 65 GPa and 2600 K using synchrotron X-ray diffraction in conjunction with the laser heated diamond-anvil cell. Fitting a Mie-Grüneisen-Debye model to the data we find best-fit parameters V_{0} = 77.4 (fixed) Å^{3}, K_{0} = 190 (1) GPa, K' = 3.49 (4), γ_{0} = 1.54 (4), q = 2.87 (15), and θ_{0} = 517.8 K (fixed). We use this newly determined equation of state in conjunction with existing measurements of the thermoelastic parameters of cobalt metal to calculate the Gibbs free-energy difference between the cobalt oxide and cobalt metal phases as a function of pressure and temperature. A comparison of the energetics of the Co/CoO system with the Ni/NiO system predicts that below 58 GPa CoO+Ni is stable relative to NiO+Co, while above 58 GPa the reverse is true. This tipping point in energy can be mapped as a crossing point in the electrochemical potential of the two metal ions, suggesting that cobalt becomes more siderophile than nickel with increasing pressure. This result is in qualitative agreement with existing measurements of nickel and cobalt partition coefficients between mantle and core materials.
Qu, B; Guo, H Q; Liu, J; Zuo, T M; Zhang, Y; Sun, G
2009-01-01
This study explored the relationship between human immunodeficiency virus/acquired immune deficiency syndrome (HIV/AIDS)-related knowledge, attitudes and behaviour in migrant urban construction workers using structural equation modelling (SEM). A cross-sectional study was conducted among 428 male subjects on three building sites in Shenyang City. The SEM model of HIV/AIDS-related knowledge, attitudes and behaviour was built using LISREL version 8.5 and it fitted the data well, as shown by an adjusted goodness of fit index of 0.82 and a root mean square error of approximation of 0.094. Knowledge of HIV/AIDS was closely correlated with attitudes and behaviour. Age was an important factor affecting HIV/AIDS-related knowledge, attitudes and behaviour. These findings suggest that increasing HIV/AIDS-related knowledge could improve the attitude and behaviour of migrant urban construction workers, enabling them to avoid high-risk behaviour that increases the spread of HIV/AIDS. Any intervention used will need to take the important factor of age into consideration.
NASA Technical Reports Server (NTRS)
Watkins, Charles E; Berman, Julian H
1956-01-01
This report treats the Kernel function of the integral equation that relates a known or prescribed downwash distribution to an unknown lift distribution for harmonically oscillating wings in supersonic flow. The treatment is essentially an extension to supersonic flow of the treatment given in NACA report 1234 for subsonic flow. For the supersonic case the Kernel function is derived by use of a suitable form of acoustic doublet potential which employs a cutoff or Heaviside unit function. The Kernel functions are reduced to forms that can be accurately evaluated by considering the functions in two parts: a part in which the singularities are isolated and analytically expressed, and a nonsingular part which can be tabulated.
An allometric approach to quantify the extinction vulnerability of birds and mammals.
Hilbers, J P; Schipper, A M; Hendriks, A J; Verones, F; Pereira, H M; Huijbregts, M A J
2016-03-01
Methods to quantify the vulnerability of species to extinction are typically limited by the availability of species-specific input data pertaining to life-history characteristics and population dynamics. This lack of data hampers global biodiversity assessments and conservation planning. Here, we developed a new framework that systematically quantifies extinction risk based on allometric relationships between various wildlife demographic parameters and body size. These allometric relationships have a solid theoretical and ecological foundation. Extinction risk indicators included are (1) the probability of extinction, (2) the mean time to extinction, and (3) the critical patch size. We applied our framework to assess the global extinction vulnerability of terrestrial carnivorous and non-carnivorous birds and mammals. Irrespective of the indicator used, large-bodied species were found to be more vulnerable to extinction than their smaller counterparts. The patterns with body size were confirmed for all species groups by a comparison with IUCN data on the proportion of extant threatened species: the models correctly predicted a multimodal distribution with body size for carnivorous birds and a monotonic distribution for mammals and non-carnivorous birds. Carnivorous mammals were found to have higher extinction risks than non-carnivores, while birds were more prone to extinction than mammals. These results are explained by the allometric relationships, predicting the vulnerable species groups to have lower intrinsic population growth rates, smaller population sizes, lower carrying capacities, or larger dispersal distances, which, in turn, increase the importance of losses due to environmental stochastic effects and dispersal activities. Our study is the first to integrate population viability analysis and allometry into a novel, process-based framework that is able to quantify extinction risk of a large number of species without requiring data-intensive, species
An allometric approach to quantify the extinction vulnerability of birds and mammals.
Hilbers, J P; Schipper, A M; Hendriks, A J; Verones, F; Pereira, H M; Huijbregts, M A J
2016-03-01
Methods to quantify the vulnerability of species to extinction are typically limited by the availability of species-specific input data pertaining to life-history characteristics and population dynamics. This lack of data hampers global biodiversity assessments and conservation planning. Here, we developed a new framework that systematically quantifies extinction risk based on allometric relationships between various wildlife demographic parameters and body size. These allometric relationships have a solid theoretical and ecological foundation. Extinction risk indicators included are (1) the probability of extinction, (2) the mean time to extinction, and (3) the critical patch size. We applied our framework to assess the global extinction vulnerability of terrestrial carnivorous and non-carnivorous birds and mammals. Irrespective of the indicator used, large-bodied species were found to be more vulnerable to extinction than their smaller counterparts. The patterns with body size were confirmed for all species groups by a comparison with IUCN data on the proportion of extant threatened species: the models correctly predicted a multimodal distribution with body size for carnivorous birds and a monotonic distribution for mammals and non-carnivorous birds. Carnivorous mammals were found to have higher extinction risks than non-carnivores, while birds were more prone to extinction than mammals. These results are explained by the allometric relationships, predicting the vulnerable species groups to have lower intrinsic population growth rates, smaller population sizes, lower carrying capacities, or larger dispersal distances, which, in turn, increase the importance of losses due to environmental stochastic effects and dispersal activities. Our study is the first to integrate population viability analysis and allometry into a novel, process-based framework that is able to quantify extinction risk of a large number of species without requiring data-intensive, species
Szabó, András; Mézes, Miklós; Romvári, Róbert; Fébel, Hedvig
2010-03-01
The phospholipid (PL) fatty acyl chain (FA) composition (mol%) was determined in the kidney, liver, lung and brain of 8 avian species ranging in body mass from 150g (Japanese quail, Coturnix coturnix japonica) to 19kg (turkey, Meleagris gallopavo). In all organs except the brain, docosahexaenoic acid (C22:6 n3, DHA) was found to show a negative allometric scaling (allometric exponent: B=-0.18; -0.20 and -0.24, for kidney, liver and lung, respectively). With minor inter-organ differences, smaller birds had more n3 FAs and longer FA chains in the renal, hepatic and pulmonary PLs. Comparing our results with literature data on avian skeletal muscle, liver mitochondria and kidney microsomes and divergent mammalian tissues, the present findings in the kidney, liver and lung PLs seem to be a part of a general relationship termed "membranes as metabolic pacemakers". Marked negative allometric scaling was found furthermore for the tissue malondialdehyde concentrations in all organs except the brain (B=-0.17; -0.13 and -0.05, respectively). In the liver and kidney a strong correlation was found between the tissue MDA and DHA levels, expressing the role of DHA in shaping the allometric properties of membrane lipids.
Szabó, A; Fébel, Hedvig; Horn, P; Andrássy-Baka, G; Bázár, Gy; Romvári, R
2006-06-01
The growth-associated development of the m. pectoralis superficialis (MPS) phospholipid (PL) and triacylglycerol (TAG) fatty acyl (FA) chain composition was determined in BUT8 meat-type turkeys. Samples (3 d, 8, 12, 16 and 20 wk) of each 6 males were analysed by lipid fractionation and subsequent gas chromatography. Results were interpreted on an allometric basis. The MPS mass increased linearly (MPS weight = 0.2787 BW- 123.67; R2 = 0.9935, P<0.001, n = 30). In the total phospholipids 62-63% unsaturated fatty acids were found irrespective of the diet. A negative allometric alteration was found for the total saturated acyl chains (B = -0.012), while a positive value for the calculated unsaturation index (B = 0.026) was obtained. Within the PUFA chains, the n3- n6 balance was markedly changed, on the favour of the n3 fatty acyl chains, namely competitive allometric trends were found for the total n3 (B = 0.087) and n6 (B = 0.032) fatty acid groups. The alterations of the TAG FA chain composition were diet-dependent. The serum creatine kinase activity increased by over one class of magnitude during the trial. The allometric approach was found to be powerful in the characterization of the basic, non diet-dependent ontogenic alterations of the phospholipid fatty acyl chain composition.
DeSouza, Og; Araújo, Ana Paula Albano; Florencio, Daniela Faria; Rosa, Cassiano Sousa; Marins, Alessandra; Costa, Diogo Andrade; Rodrigues, Vinicius Barros; Cristaldo, Paulo Fellipe
2016-01-01
Structural and functional traits of organisms are known to be related to the size of individuals and to the size of their colonies when they belong to one. Among such traits, propensity to inquilinism in termites is known to relate positively to colony size. Larger termitaria hold larger diversity of facultative inquilines than smaller nests, whereas obligate inquilines seem unable to settle in nests smaller than a threshold volume. Respective underlying mechanisms, however, remain hypothetical. Here we test one of such hypotheses, namely, that nest defence correlates negatively to nest volume in Constrictotermes cyphergaster termites (Termitidae: Nasutitermitinae). As a surrogate to defence, we used ‘patrolling rate’, i.e., the number of termite individuals attending per unit time an experimentally damaged spot on the outer wall of their termitaria. We found that patrolling rate decayed allometrically with increasing nest size. Conspicuously higher patrolling rates occurred in smaller nests, while conspicuously lower rates occurred in larger nests presenting volumes in the vicinity of the threshold value for the establishment of inquilinism. This could be proven adaptive for the host and guest. At younger nest age, host colonies are smaller and presumably more vulnerable and unstable. Enhanced defence rates may, hence, prevent eventual risks to hosts from inquilinism at the same time that it prevents inquilines to settle in a still unstable nest. Conversely, when colonies grow and maturate enough to stand threats, they would invest in priorities other than active defence, opening an opportunity for inquilines to settle in nests which are more suitable or less risky. Under this two-fold process, cohabitation between host and inquiline could readily stabilize. PMID:26808197
DeSouza, Og; Araújo, Ana Paula Albano; Florencio, Daniela Faria; Rosa, Cassiano Sousa; Marins, Alessandra; Costa, Diogo Andrade; Rodrigues, Vinicius Barros; Cristaldo, Paulo Fellipe
2016-01-01
Structural and functional traits of organisms are known to be related to the size of individuals and to the size of their colonies when they belong to one. Among such traits, propensity to inquilinism in termites is known to relate positively to colony size. Larger termitaria hold larger diversity of facultative inquilines than smaller nests, whereas obligate inquilines seem unable to settle in nests smaller than a threshold volume. Respective underlying mechanisms, however, remain hypothetical. Here we test one of such hypotheses, namely, that nest defence correlates negatively to nest volume in Constrictotermes cyphergaster termites (Termitidae: Nasutitermitinae). As a surrogate to defence, we used 'patrolling rate', i.e., the number of termite individuals attending per unit time an experimentally damaged spot on the outer wall of their termitaria. We found that patrolling rate decayed allometrically with increasing nest size. Conspicuously higher patrolling rates occurred in smaller nests, while conspicuously lower rates occurred in larger nests presenting volumes in the vicinity of the threshold value for the establishment of inquilinism. This could be proven adaptive for the host and guest. At younger nest age, host colonies are smaller and presumably more vulnerable and unstable. Enhanced defence rates may, hence, prevent eventual risks to hosts from inquilinism at the same time that it prevents inquilines to settle in a still unstable nest. Conversely, when colonies grow and maturate enough to stand threats, they would invest in priorities other than active defence, opening an opportunity for inquilines to settle in nests which are more suitable or less risky. Under this two-fold process, cohabitation between host and inquiline could readily stabilize.
DeSouza, Og; Araújo, Ana Paula Albano; Florencio, Daniela Faria; Rosa, Cassiano Sousa; Marins, Alessandra; Costa, Diogo Andrade; Rodrigues, Vinicius Barros; Cristaldo, Paulo Fellipe
2016-01-01
Structural and functional traits of organisms are known to be related to the size of individuals and to the size of their colonies when they belong to one. Among such traits, propensity to inquilinism in termites is known to relate positively to colony size. Larger termitaria hold larger diversity of facultative inquilines than smaller nests, whereas obligate inquilines seem unable to settle in nests smaller than a threshold volume. Respective underlying mechanisms, however, remain hypothetical. Here we test one of such hypotheses, namely, that nest defence correlates negatively to nest volume in Constrictotermes cyphergaster termites (Termitidae: Nasutitermitinae). As a surrogate to defence, we used 'patrolling rate', i.e., the number of termite individuals attending per unit time an experimentally damaged spot on the outer wall of their termitaria. We found that patrolling rate decayed allometrically with increasing nest size. Conspicuously higher patrolling rates occurred in smaller nests, while conspicuously lower rates occurred in larger nests presenting volumes in the vicinity of the threshold value for the establishment of inquilinism. This could be proven adaptive for the host and guest. At younger nest age, host colonies are smaller and presumably more vulnerable and unstable. Enhanced defence rates may, hence, prevent eventual risks to hosts from inquilinism at the same time that it prevents inquilines to settle in a still unstable nest. Conversely, when colonies grow and maturate enough to stand threats, they would invest in priorities other than active defence, opening an opportunity for inquilines to settle in nests which are more suitable or less risky. Under this two-fold process, cohabitation between host and inquiline could readily stabilize. PMID:26808197
Choice of resolution by functional trait or taxonomy affects allometric scaling in soil food webs.
Sechi, Valentina; Brussaard, Lijbert; De Goede, Ron G M; Rutgers, Michiel; Mulder, Christian
2015-01-01
Belowground organisms often display a shift in their mass-abundance scaling relationships due to environmental factors such as soil chemistry and atmospheric deposition. Here we present new empirical data that show strong differences in allometric scaling according to whether the resolution at the local scale is based on a taxonomic or a functional classification, while only slight differences arise according to soil environmental conditions. For the first time, isometry (an inverse 1:1 proportion) is recognized in mass-abundance relationships, providing a functional signal for constant biomass distribution in soil biota regardless of discrete trophic levels. Our findings are in contrast to those from aquatic ecosystems, in that higher trophic levels in soil biota are not a direct function of increasing body mass.
Fifth dimension of life and the 4/5 allometric scaling law for human brain.
He, Ji-Huan; Zhang, Juan
2004-01-01
Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.
New allometric scaling relationships and applications for dose and toxicity extrapolation.
Cao, Qiming; Yu, Jimmy; Connell, Des
2014-01-01
Allometric scaling between metabolic rate, size, body temperature, and other biological traits has found broad applications in ecology, physiology, and particularly in toxicology and pharmacology. Basal metabolic rate (BMR) was observed to scale with body size and temperature. However, the mass scaling exponent was increasingly debated whether it should be 2/3, 3/4, or neither, and scaling with body temperature also attracted recent attention. Based on thermodynamic principles, this work reports 2 new scaling relationships between BMR, size, temperature, and biological time. Good correlations were found with the new scaling relationships, and no universal scaling exponent can be obtained. The new scaling relationships were successfully validated with external toxicological and pharmacological studies. Results also demonstrated that individual extrapolation models can be built to obtain scaling exponent specific to the interested group, which can be practically applied for dose and toxicity extrapolations.
Improved allometric models to estimate the aboveground biomass of tropical trees.
Chave, Jérôme; Réjou-Méchain, Maxime; Búrquez, Alberto; Chidumayo, Emmanuel; Colgan, Matthew S; Delitti, Welington B C; Duque, Alvaro; Eid, Tron; Fearnside, Philip M; Goodman, Rosa C; Henry, Matieu; Martínez-Yrízar, Angelina; Mugasha, Wilson A; Muller-Landau, Helene C; Mencuccini, Maurizio; Nelson, Bruce W; Ngomanda, Alfred; Nogueira, Euler M; Ortiz-Malavassi, Edgar; Pélissier, Raphaël; Ploton, Pierre; Ryan, Casey M; Saldarriaga, Juan G; Vieilledent, Ghislain
2014-10-01
Terrestrial carbon stock mapping is important for the successful implementation of climate change mitigation policies. Its accuracy depends on the availability of reliable allometric models to infer oven-dry aboveground biomass of trees from census data. The degree of uncertainty associated with previously published pantropical aboveground biomass allometries is large. We analyzed a global database of directly harvested trees at 58 sites, spanning a wide range of climatic conditions and vegetation types (4004 trees ≥ 5 cm trunk diameter). When trunk diameter, total tree height, and wood specific gravity were included in the aboveground biomass model as covariates, a single model was found to hold across tropical vegetation types, with no detectable effect of region or environmental factors. The mean percent bias and variance of this model was only slightly higher than that of locally fitted models. Wood specific gravity was an important predictor of aboveground biomass, especially when including a much broader range of vegetation types than previous studies. The generic tree diameter-height relationship depended linearly on a bioclimatic stress variable E, which compounds indices of temperature variability, precipitation variability, and drought intensity. For cases in which total tree height is unavailable for aboveground biomass estimation, a pantropical model incorporating wood density, trunk diameter, and the variable E outperformed previously published models without height. However, to minimize bias, the development of locally derived diameter-height relationships is advised whenever possible. Both new allometric models should contribute to improve the accuracy of biomass assessment protocols in tropical vegetation types, and to advancing our understanding of architectural and evolutionary constraints on woody plant development. PMID:24817483
NASA Astrophysics Data System (ADS)
Delmas, Magali; Gunnell, Yanni; Calvet, Marc
2015-01-01
When considering the morphometric attributes of a glacial cirque, imbalances between length, width, and amplitude have been deemed relevant tools for discriminating between two possible pathways of cirque growth: downwearing by glaciers or backwearing by freeze-thaw processes. Based on a sample of 1071 cirques in the French Pyrenees, we reframe the concern for climatic variables by also granting systematic consideration to cirque lithology. Insight into the factors that control cirque shape is gained from Principal Component Analysis, where maps of eigenvalues assigned to six classes of bedrock display spatial patterns of cirque form as a function of position along the regional climatic gradient. Among crystalline rocks (granite, gneiss, migmatite), cirque form is predominantly determined by climatic controls. This is highlighted in the contrast between the elevated core of the Pleistocene icefield, where cirque isometry prevails, and the more peripheral areas (external sierras of the Atlantic precipitation zone and high sierras of the drier Mediterranean zone) where the lighter imprint of glaciation on the landscape has failed to erase (through glacial deepening) the allometric signature of pre-Pleistocene topographic features such as shallow valley heads and etch-basins. As a result, wide and shallow cirques occur in these settings. Among schist outcrops, in contrast, cirque form appears randomly distributed, suggesting that bedrock characteristics (e.g., structure) rather than climate are the key controls on cirque growth patterns. Given the importance of geological structure and preglacial topographic inheritance, cirques are complex landforms for which assumptions of allometric growth may be spurious. It follows that form is not always a reliable guide to process.
Dynamic strain similarity in vertebrates; an alternative to allometric limb bone scaling.
Rubin, C T; Lanyon, L E
1984-03-21
Galileo (1638) observed that "nature cannot grow a tree nor construct an animal beyond a certain size, while retaining the proportions which suffice in the case of a smaller structure". However, subsequent measurement has shown that limb bone dimensions are scaled geometrically with body size (Alexander et al., 1979a), and that the material properties of their constituent bone tissue are similar in animals over a wide range of body weight (Sedlin & Hirsch, 1966; Yamada, 1970; Burstein et al., 1972; Biewener, 1982). If, as suggested in previous scaling arguments (McMahon, 1973; Biewener, 1982), vigorous locomotion involved the same proportional forces over a wide range of animal size, this would create a paradox since large animals would be in far greater danger of skeletal failure than small ones. However, in vivo strain gauge implantations have shown that, during high speed running, axial force as a proportion of body weight (G) in the limb bones of animals decreases as a function of body size from 6.9 G in a 7 kg turkey to 2.8 G in a small (130 kg) horse. Estimates of axial force in larger animals suggest that this is further reduced to 0.8 G in a 2500 kg elephant. Nevertheless, it appears that, regardless of animal size or locomotory style, the peak stresses in the bones of these animals are remarkably similar. Therefore, throughout the range of animals considered (350 times differences in mass), we suggest that similar safety factors to failure are maintained, not by allometrically scaling bone dimensions, but rather by allometrically scaling the magnitude of the peak forces applied to them during vigorous locomotion.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:6717041
Improved allometric models to estimate the aboveground biomass of tropical trees.
Chave, Jérôme; Réjou-Méchain, Maxime; Búrquez, Alberto; Chidumayo, Emmanuel; Colgan, Matthew S; Delitti, Welington B C; Duque, Alvaro; Eid, Tron; Fearnside, Philip M; Goodman, Rosa C; Henry, Matieu; Martínez-Yrízar, Angelina; Mugasha, Wilson A; Muller-Landau, Helene C; Mencuccini, Maurizio; Nelson, Bruce W; Ngomanda, Alfred; Nogueira, Euler M; Ortiz-Malavassi, Edgar; Pélissier, Raphaël; Ploton, Pierre; Ryan, Casey M; Saldarriaga, Juan G; Vieilledent, Ghislain
2014-10-01
Terrestrial carbon stock mapping is important for the successful implementation of climate change mitigation policies. Its accuracy depends on the availability of reliable allometric models to infer oven-dry aboveground biomass of trees from census data. The degree of uncertainty associated with previously published pantropical aboveground biomass allometries is large. We analyzed a global database of directly harvested trees at 58 sites, spanning a wide range of climatic conditions and vegetation types (4004 trees ≥ 5 cm trunk diameter). When trunk diameter, total tree height, and wood specific gravity were included in the aboveground biomass model as covariates, a single model was found to hold across tropical vegetation types, with no detectable effect of region or environmental factors. The mean percent bias and variance of this model was only slightly higher than that of locally fitted models. Wood specific gravity was an important predictor of aboveground biomass, especially when including a much broader range of vegetation types than previous studies. The generic tree diameter-height relationship depended linearly on a bioclimatic stress variable E, which compounds indices of temperature variability, precipitation variability, and drought intensity. For cases in which total tree height is unavailable for aboveground biomass estimation, a pantropical model incorporating wood density, trunk diameter, and the variable E outperformed previously published models without height. However, to minimize bias, the development of locally derived diameter-height relationships is advised whenever possible. Both new allometric models should contribute to improve the accuracy of biomass assessment protocols in tropical vegetation types, and to advancing our understanding of architectural and evolutionary constraints on woody plant development.
Rosas, Antonio; Bastir, Markus
2004-06-01
Allometry is an important factor of morphological integration that contributes to the organization of the phenotype and its variation. Variation in the allometric shape of the mandible is particularly important in hominid evolution because the mandible carries important taxonomic traits. Some of these traits are known to covary with size, particularly the retromolar space, symphyseal curvature, and position of the mental foramen. The mandible is a well studied system in the context of the evolutionary development of complex morphological structures because it is composed of different developmental units that are integrated within a single bone. In the present study, we investigated the allometric variation of two important developmental units that are separated by the inferior nerve (a branch of CN V3). We tested the null hypothesis that there would be no difference in allometric variation between the two components. Procrustes-based geometric morphometrics of 20 two-dimensional (2D) landmarks were analyzed by multivariate regressions of shape on size in samples from 121 humans, 48 chimpanzees, and 50 gorillas (all recent specimens), eight fossil hominids from Atapuerca, Sima de los Huesos (AT-SH), and 17 Neandertals. The findings show that in all of the examined species, there was significantly greater allometric variation in the supra-nerve unit than in the infra-nerve unit. The formation of the retromolar space exhibited an allometric relationship with the supra-nerve unit in all of the species studied. The formation of the chin-like morphology is an "apodynamic" feature of the infra-nerve unit in the AT-SH hominids. The results of this study support the hypothesis that allometry contributes to the organization of variation in complex morphological structures.
Doran, D A; Mc Geever, S; Collins, K D; Quinn, C; McElhone, R; Scott, M
2014-02-01
Dual-energy X-ray absorptiometry (DXA) and adipose tissue percentage estimates (AT%) derived from regression based skinfold equations were compared. 35 Gaelic games players [20.9 ± 1.7 years; 78.1 ± 8.6 kg; 179.5 ± 5.7 cm] underwent whole body fan beam DXA scans following a standardised protocol and assessment of skinfold thickness at 8 sites. Adipose tissue% from the sum of skinfolds and/or via body density were calculated for general and athlete specific equations (SKf-AT %). The relationship, i. e., proportional bias, fixed bias and random error (SEE) between DXA-AT % and AT % derived from the 6 skinfold equations were determined using least squares regression analysis. Skinfold AT% estimates were underestimated relative to DXA-AT % across all skinfold equations except that of Durnin and Wormersley [9] (D&W-∑(4AT %)) (16.7 ± 3.4 vs. 16.6 ± 4.0 %). All equations demonstrated 95 % prediction intervals ranges exceeding ~10 %. Each equation failed to predict AT% relative to DXA within an accepted ± 3.5 % anthropometric error rate. It is recommended that the conversion of absolute skinfold thickness to an AT % is avoided and that the skinfold equations assessed herein are not utilised in Gaelic games players. Alternate 'sum of skinfold' approaches should be considered.
Karpells, S.T.
1989-01-01
Storage proteins are the major nutritive intermediates in insects and although the serum storage proteins are relatively well studied, definitive roles for many of them have yet to be established. To further characterize their roles in development and to establish quantitative baselines for future studies, two serum proteins, arylphorin (Ap) and lipophorin (Lp), of the gypsy moth, Lymantria dispar, were studied. Ap and Lp, isolated from larval hemolymph, were partially characterized biochemically and immunologically. Hemolymph concentrations throughout larval development were determined using quantitative immunoelectrophoresis and absolute hemolymph amounts of protein were determined by measuring hemolymph volume. Cyclic fluctuations in hemolymph concentrations of Ap in particular correlated with each molting cycle and an increase in Lp levels just prior to pupation suggest a metamorphic change in the role or demand for the protein. Sexual dimorphism in protein concentrations are explained in part by the sexual dimorphism in the number of larval instars. In fact, an additional instar of Ap accumulation in the female gypsy moth is suggested to compensate for the lack of a female-specific storage protein in this species. The last two days of each instar were found to be the optimum time to sample protein concentration with minimum variance. Allometric relationships among Ap accumulation, Lp accumulation and weight gain were uncovered. Ap labelled with ({sup 14}C)-N-ethylmaleimide was shown to be incorporated into newly synthesized cuticle and setae during a larval-larval molt. The antiserum developed against L. dispar Ap was used to identify the Ap of Trichoplusia in and study Ap titers in parasitized T. in larvae. The antiserum was also used to determine the immunological relatedness of 5 species of Lepidoptera.
Chen, Guangshui; Yang, Yusheng; Robinson, David
2014-05-01
To fully understand how soil respiration is partitioned among its component fluxes and responds to climate, it is essential to relate it to belowground carbon allocation, the ultimate carbon source for soil respiration. This remains one of the largest gaps in knowledge of terrestrial carbon cycling. Here, we synthesize data on gross and net primary production and their components, and soil respiration and its components, from a global forest database, to determine mechanisms governing belowground carbon allocation and their relationship with soil respiration partitioning and soil respiration responses to climatic factors across global forest ecosystems. Our results revealed that there are three independent mechanisms controlling belowground carbon allocation and which influence soil respiration and its partitioning: an allometric constraint; a fine-root production vs. root respiration trade-off; and an above- vs. belowground trade-off in plant carbon. Global patterns in soil respiration and its partitioning are constrained primarily by the allometric allocation, which explains some of the previously ambiguous results reported in the literature. Responses of soil respiration and its components to mean annual temperature, precipitation, and nitrogen deposition can be mediated by changes in belowground carbon allocation. Soil respiration responds to mean annual temperature overwhelmingly through an increasing belowground carbon input as a result of extending total day length of growing season, but not by temperature-driven acceleration of soil carbon decomposition, which argues against the possibility of a strong positive feedback between global warming and soil carbon loss. Different nitrogen loads can trigger distinct belowground carbon allocation mechanisms, which are responsible for different responses of soil respiration to nitrogen addition that have been observed. These results provide new insights into belowground carbon allocation, partitioning of soil
Rault, Jacques
2015-08-01
The dynamical properties of glass formers (GFs) as a function of P, V, and T are reanalyzed in relation with the equations of state (EOS) proposed recently (Eur. Phys. J. E 37, 113 (2014)). The relaxation times τ of the cooperative non-Arrhenius α process and the individual Arrhenius β process are coupled via the Kohlrausch exponent n S(T, P). In the model n S is the sigmoidal logistic function depending on T (and P, and the α relaxation time τ α of GFs above T g verifies the pressure-modified VFT law: log τ α ∼ E β /nsRT, which can be put into a form with separated variables: log τ α ∼ f(T)g(P). From the variation of n S and τ α with T and P the Vogel temperature T 0 (τ α → ∝, n S = 0) and the crossover temperature (also called the merging or splitting temperature) T B (τ α ∼ τ β, n S ∼ 1) are determined. The proposed sm-VFT equation fits with excellent accuracy the experimental data of fragile and strong GFs under pressure. The properties generally observed in organic mineral and metallic GFs are explained: a) The Vogel temperature is independent of P (as suggested by the EOS properties), the crossover is pressure-dependent. b) In crystallizable GFs the T B (P) and Clapeyron curves T m(P) coincide. c) The α and β processes have the same ratio of the activation energies and volume, E*/V* (T- and P-independent), the compensation law is observed, this ratio depends on the anharmonicity Slater-Grüneisen parameter and on the critical pressure P* deduced from the EOS. d) The properties of the Fan Structure of the Tangents (FST) to the isotherms and isobars curves log τ versus P and T and to the isochrones curves P(T). e) The scaling law log τ = f(V (Λ) ) and the relation between Γ and γ. We conclude that these properties should be studied in detail in GFs submitted to negative pressures.
Hassanzadeh, Jafar; Asadi-Lari, Mohsen; Baghbanian, Abdolvahab; Ghaem, Haleh; Kassani, Aziz; Rezaianzadeh, Abbas
2016-01-01
Aim To explore the association(s) between demographic factors, socioeconomic status (SES), social capital, health-related quality of life (HRQoL), and mental health among residents of Tehran, Iran. Methods The pooled data (n = 31 519) were extracted from a population-based survey Urban Health Equity Assessment and Response Tool-2 (Urban HEART-2) conducted in Tehran in 2011. Mental health, social capital, and HRQoL were assessed using the 28-item General Health Questionnaire (GHQ-28), social capital questionnaire, and Short-Form Health Survey (SF-12), respectively. The study used a multistage sampling method. Social capital, HRQoL, and SES were considered as latent variables. The association between these latent variables, demographic factors, and mental health was determined by structural-equation modeling (SEM). Results The mean age and mental health score were 44.48 ± 15.87 years and 23.33 ± 11.10 (range, 0-84), respectively. The prevalence of mental disorders was 41.76% (95% confidence interval 41.21-42.30). The SEM model showed that age was directly associated with social capital (P = 0.016) and mental health (P = 0.001). Sex was indirectly related to mental health through social capital (P = 0.018). SES, HRQoL, and social capital were associated both directly and indirectly with mental health status. Conclusion This study suggests that changes in social capital and SES can lead to positive changes in mental health status and that individual and contextual determinants influence HRQoL and mental health. PMID:26935615
DOE R&D Accomplishments Database
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
NASA Astrophysics Data System (ADS)
Nguyen, Quan Minh
2011-12-01
We investigate the propagation of solitons of the perturbed nonlinear Schrodinger equation (NLSE) via asymptotic perturbation techniques and numerical simulations. The dissertation consists of several inter-related projects [22, 98, 103, 108, 109] that are focused on the effects of nonlinear processes and randomness on dynamics of pulses of light in optical waveguides. We particularly consider two of the most important nonlinear processes affecting pulse dynamics in multichannel optical waveguides: weak cubic loss and delayed Raman response. In the presence of weak cubic loss [98], we obtain the analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Furthermore, we show that amplitude dynamics in an N-channel waveguide system is described by a Lotka-Volterra model for N competing species. We find the conditions on the time slot width and the soliton's equilibrium amplitude value under which the transmission is stable. The predictions of the reduced Lotka-Volterra model are confirmed by numerical solution of a coupled-NLSE model, which takes into account intra-pulse and inter-pulse effects due to cubic nonlinearity and cubic loss. These results uncover an interesting analogy between the dynamics of energy exchange in pulse collisions and population dynamics in Lotka-Volterra models. In the presence of delayed Raman response [103,108,109], we show that the dynamics of pulse amplitudes in an N-channel transmission system in differential phase shift keying (DPSK) scheme is described by an N-dimensional predator-prey model. We find the equilibrium states with non-zero amplitudes and prove their stability by obtaining the Lyapunov function. We then show that stable transmission can be achieved by a proper choice of the frequency profile of linear amplifier gain. We also investigate the impact of Raman self- and collsion
Mouahid, Gabriel; Faliex, Elisabeth; Allienne, Jean-François; Cribb, Thomas H; Bray, Rodney A
2012-05-01
The present paper deals with Proctophantastes nettastomatis (Digenea: Zoogonidae; Lepidophyllinae) found in the intestine of three species of deep-sea fish, Dicrolene longimana (Ophidiidae, Ophidiiformes), Bathyuroconger sp. (Congridae, Anguilliformes), and Venefica tentaculata (Nettastomatidae, Anguilliformes). The fish were collected near the islands of Espiritu Santo, Erromango, and Epi, respectively, in the archipelago of Vanuatu (Southern Pacific Ocean) at depths ranging from 561 to 990 m. Morphological and histological analyses showed that the Vanuatu specimens differ from Proctophantastes abyssorum, Proctophantastes gillissi, Proctophantastes glandulosum, Proctophantastes infundibulum, and Proctophantastes brayi but are close to P. nettastomatis discovered in Suruga Bay, Japan. P. nettastomatis is redescribed based both on the observations of our specimens and of the Japanese holotype and paratype. The morphological variability of the species is described. Morphometric data allowed the identification of positive allometric growth for the hindbody, negative allometric growth for the ventral sucker, and a growth phenotypic plasticity between Ophidiiformes and Anguilliformes definitive hosts. PMID:22089085
Comparative Pharmacokinetics and Allometric Scaling of Carboplatin in Different Avian Species
De Baere, Siegrid; Hellebuyck, Tom; Van de Maele, Isabel; Rouffaer, Lieze; Stemkens, Hendrickus J. J.; De Backer, Patrick; Martel, An; Croubels, Siska
2015-01-01
The use of chemotherapeutics as a possible treatment strategy in avian oncology is steadily increasing over the last years. Despite this, literature reports regarding dosing strategies and pharmacokinetic behaviour of chemotherapeutics in avian species are lacking. The aim of the present study was to investigate the pharmacokinetics of carboplatin in a representative species of the order of Galliformes, Anseriformes, Columbiformes and Psittaciformes. Eight chickens, ducks and pigeons and twenty-eight parakeets were administered carboplatin intravenously (5 mg/kg body weight). A specific and sensitive liquid chromatography-tandem mass spectrometry method was developed and validated for quantification of the free carboplatin in plasma of the four birds species (limit of quantification: 20 ng/mL for chicken and duck, 50 ng/mL for pigeon and 100 ng/mL for parakeets). Non-compartmental pharmacokinetic analysis and allometric scaling demonstrated a significant correlation (R² = 0.9769) between body weight (BW) and elimination half-life (T1/2el). T1/2el ranged from 0.41 h in parakeets (BW: 61 ± 8 g) to 1.16 h chickens (BW: 1909 ± 619 g). T1/2el is a good parameter for dose optimization of carboplatin in other avian species, since also the previously reported T1/2el in cockatoos (average BW: 769 ± 68 g) of 1.00 h corresponds to the results obtained in the present study. PMID:26222777
Final Harvest of Above-Ground Biomass and Allometric Analysis of the Aspen FACE Experiment
Mark E. Kubiske
2013-04-15
The Aspen FACE experiment, located at the US Forest Service Harshaw Research Facility in Oneida County, Wisconsin, exposes the intact canopies of model trembling aspen forests to increased concentrations of atmospheric CO2 and O3. The first full year of treatments was 1998 and final year of elevated CO2 and O3 treatments is scheduled for 2009. This proposal is to conduct an intensive, analytical harvest of the above-ground parts of 24 trees from each of the 12, 30 m diameter treatment plots (total of 288 trees) during June, July & August 2009. This above-ground harvest will be carefully coordinated with the below-ground harvest proposed by D.F. Karnosky et al. (2008 proposal to DOE). We propose to dissect harvested trees according to annual height growth increment and organ (main stem, branch orders, and leaves) for calculation of above-ground biomass production and allometric comparisons among aspen clones, species, and treatments. Additionally, we will collect fine root samples for DNA fingerprinting to quantify biomass production of individual aspen clones. This work will produce a thorough characterization of above-ground tree and stand growth and allocation above ground, and, in conjunction with the below ground harvest, total tree and stand biomass production, allocation, and allometry.
Craniodental features in male Mandrillus may signal size and fitness: an allometric approach.
Klopp, Emily B
2012-04-01
According to a hypothesis in the broader mammalian literature, secondary sexual characteristics that have evolved to signal fitness and size to other conspecifics should exhibit positive allometry across adult males within a species. Here this hypothesis is tested in the genus Mandrillus. The overbuilding of bony features in larger individuals necessitates a functional explanation as bone is metabolically expensive to produce and maintain. Canine size and size of the maxillary ridge are scaled against a body size surrogate in intraspecific samples of male Mandrillus sphinx (mandrills) and Mandrillus leucophaeus (drills). Areal dimensions are weighted more heavily as they represent the size of a feature as it is viewed by individuals. Measures of the maxillary ridge and canine tooth are significantly correlated with the size surrogate and scale with positive allometry in both samples supporting the hypothesis that these features function to advertise a male's body size and fitness to other males competing for mates and potential discerning females. This is the first study in primates to test for intraspecific positive allometric scaling of bony facial features in adult males based on a theory of fitness signaling and sexual selection. PMID:22328467
Craniodental features in male Mandrillus may signal size and fitness: an allometric approach.
Klopp, Emily B
2012-04-01
According to a hypothesis in the broader mammalian literature, secondary sexual characteristics that have evolved to signal fitness and size to other conspecifics should exhibit positive allometry across adult males within a species. Here this hypothesis is tested in the genus Mandrillus. The overbuilding of bony features in larger individuals necessitates a functional explanation as bone is metabolically expensive to produce and maintain. Canine size and size of the maxillary ridge are scaled against a body size surrogate in intraspecific samples of male Mandrillus sphinx (mandrills) and Mandrillus leucophaeus (drills). Areal dimensions are weighted more heavily as they represent the size of a feature as it is viewed by individuals. Measures of the maxillary ridge and canine tooth are significantly correlated with the size surrogate and scale with positive allometry in both samples supporting the hypothesis that these features function to advertise a male's body size and fitness to other males competing for mates and potential discerning females. This is the first study in primates to test for intraspecific positive allometric scaling of bony facial features in adult males based on a theory of fitness signaling and sexual selection.
Solari, Cristian A; Kessler, John O; Goldstein, Raymond E
2013-03-01
The transition from unicellular, to colonial, to larger multicellular organisms has benefits, costs, and requirements. Here we present a model inspired by the volvocine green algae that explains the dynamics involved in the unicellular-multicellular transition using life-history theory and allometry. We model the two fitness components (fecundity and viability) and compare the fitness of hypothetical colonies of different sizes with varying degrees of cellular differentiation to understand the general principles that underlie the evolution of multicellularity. We argue that germ-soma separation may have evolved to counteract the increasing costs and requirements of larger multicellular colonies. The model shows that the cost of investing in soma decreases with size. For lineages such as the Volvocales, as reproduction costs increase with size for undifferentiated colonies, soma specialization benefits the colony indirectly by decreasing such costs and directly by helping reproductive cells acquire resources for their metabolic needs. Germ specialization is favored once soma evolves and takes care of vegetative functions. To illustrate the model, we use some allometric relationships measured in Volvocales. Our analysis shows that the cost of reproducing an increasingly larger group has likely played an important role in the transition to multicellularity and cellular differentiation.
Cheng, Dongliang; Ma, Yuzhu; Zhong, Quanling; Xu, Weifeng
2014-01-01
Allometric biomass allocation theory predicts that leaf biomass (ML) scaled isometrically with stem (MS) and root (MR) biomass, and thus above-ground biomass (leaf and stem) (MA) and root (MR) scaled nearly isometrically with below-ground biomass (root) for tree seedlings across a wide diversity of taxa. Furthermore, prior studies also imply that scaling constant should vary with species. However, litter is known about whether such invariant isometric scaling exponents hold for intraspecific biomass allocation, and how variation in scaling constants influences the interspecific scaling relationship between above- and below-ground biomass. Biomass data of seedlings from five evergreen species were examined to test scaling relationships among biomass components across and within species. Model Type II regression was used to compare the numerical values of scaling exponents and constants among leaf, stem, root, and above- to below-ground biomass. The results indicated that ML and MS scaled in an isometric or a nearly isometric manner with MR, as well as MA to MR for five woody species. Significant variation was observed in the Y-intercepts of the biomass scaling curves, resulting in the divergence for intraspecific scaling and interspecific scaling relationships for ML versus MS and ML versus MR, but not for MS versus MR and MA versus MR. We conclude, therefore, that a nearly isometric scaling relationship of MA versus MR holds true within each of the studied woody species and across them irrespective the negative scaling relationship between leaf and stem. PMID:25505524
Comparative Pharmacokinetics and Allometric Scaling of Carboplatin in Different Avian Species.
Antonissen, Gunther; Devreese, Mathias; De Baere, Siegrid; Hellebuyck, Tom; Van de Maele, Isabel; Rouffaer, Lieze; Stemkens, Hendrickus J J; De Backer, Patrick; Martel, An; Croubels, Siska
2015-01-01
The use of chemotherapeutics as a possible treatment strategy in avian oncology is steadily increasing over the last years. Despite this, literature reports regarding dosing strategies and pharmacokinetic behaviour of chemotherapeutics in avian species are lacking. The aim of the present study was to investigate the pharmacokinetics of carboplatin in a representative species of the order of Galliformes, Anseriformes, Columbiformes and Psittaciformes. Eight chickens, ducks and pigeons and twenty-eight parakeets were administered carboplatin intravenously (5 mg/kg body weight). A specific and sensitive liquid chromatography-tandem mass spectrometry method was developed and validated for quantification of the free carboplatin in plasma of the four birds species (limit of quantification: 20 ng/mL for chicken and duck, 50 ng/mL for pigeon and 100 ng/mL for parakeets). Non-compartmental pharmacokinetic analysis and allometric scaling demonstrated a significant correlation (R² = 0.9769) between body weight (BW) and elimination half-life (T1/2el). T1/2el ranged from 0.41 h in parakeets (BW: 61 ± 8 g) to 1.16 h chickens (BW: 1909 ± 619 g). T1/2el is a good parameter for dose optimization of carboplatin in other avian species, since also the previously reported T1/2el in cockatoos (average BW: 769 ± 68 g) of 1.00 h corresponds to the results obtained in the present study.
NASA Astrophysics Data System (ADS)
Vinokurov, N. A.
2015-03-01
Equations of motion that preserve a given function (called energy) of generalized coordinates and velocities are derived. These equations differ from Lagrange equations by the presence of additional terms describing generalized gyroscopic forces. The relation between energy conservation and the d'Alembert principle is noted.
NASA Astrophysics Data System (ADS)
Ghamarian, Iman; Samimi, Peyman; Dixit, Vikas; Collins, Peter C.
2015-11-01
While it is useful to predict properties in metallic materials based upon the composition and microstructure, the complexity of real, multi-component, and multi-phase engineering alloys presents difficulties when attempting to determine constituent-based phenomenological equations. This paper applies an approach based upon the integration of three separate modeling approaches, specifically artificial neural networks, genetic algorithms, and Monte Carlo simulations to determine a mechanism-based equation for the yield strength of α+ β processed Ti-6Al-4V (all compositions in weight percent) which consists of a complex multi-phase microstructure with varying spatial and morphological distributions of the key microstructural features. Notably, this is an industrially important alloy yet an alloy for which such an equation does not exist in the published literature. The equation ultimately derived in this work not only can accurately describe the properties of the current dataset but also is consistent with the limited and dissociated information available in the literature regarding certain parameters such as intrinsic yield strength of pure hexagonal close-packed alpha titanium. In addition, this equation suggests new interesting opportunities for controlling yield strength by controlling the relative intrinsic strengths of the two phases through solid solution strengthening.
Interspecies allometric scaling. Part I: prediction of clearance in large animals.
Mahmood, I; Martinez, M; Hunter, R P
2006-10-01
Interspecies scaling is a useful tool for the prediction of pharmacokinetic parameters from animals to humans, and it is often used for estimating a first-time in human dose. The knowledge of pharmacokinetics in veterinary species is important for dosage selection, particularly in the treatment of large zoo animal species, such as elephants, giant cats and camels, for which pharmacokinetic data are scant. Therefore, the accuracy in clearance predictions in large animal species, with and without the use of correction factors (rule of exponents), and the impact of species selection in the prediction of clearance in large animal species was examined. Based upon this analysis, it was determined that there is a much larger risk of inaccuracies in the clearance estimates in large animal species when compared with that observed for humans. Unlike in humans, for large animal species, correction factors could not be applied because there was no trend between the exponents of simple allometry and the appropriate correction factor for improving our predictions. Nevertheless, we did see an indication that the exponents of simple allometry may alert us as to when the predicted clearance in the large animal may be underestimated or overpredicted. For example, if a large animal is included in the scaling, the predicted clearance in a large animal should be considered overestimated if the exponent of simple allometry is >1.3. Despite the potential for extrapolation error, the reality is that allometric scaling is needed across many veterinary practice situations, and therefore will be used. For this reason, it is important to consider mechanisms for reducing the risk of extrapolation errors that can seriously affect target animal safety, therapeutic response, or the accuracy of withdrawal time predictions. PMID:16958787
Kelehear, Crystal; Spratt, David M.; Dubey, Sylvain; Brown, Gregory P.; Shine, Richard
2011-01-01
Taxonomic studies of parasites can be severely compromised if the host species affects parasite morphology; an uncritical analysis might recognize multiple taxa simply because of phenotypically plastic responses of parasite morphology to host physiology. Pentastomids of the genus Raillietiella are endoparasitic crustaceans primarily infecting the respiratory system of carnivorous reptiles, but also recorded from bufonid anurans. The delineation of pentastomids at the generic level is clear, but the taxonomic status of many species is not. We collected raillietiellids from lungs of the invasive cane toad (Rhinella marina), the invasive Asian house gecko (Hemidactylus frenatus), and a native tree frog (Litoria caerulea) in tropical Australia, and employed a combination of genetic analyses, and traditional and novel morphological methods to clarify their identity. Conventional analyses of parasite morphology (which focus on raw values of morphological traits) revealed two discrete clusters in terms of pentastome hook size, implying two different species of pentastomes: one from toads and a tree frog (Raillietiella indica) and another from lizards (Raillietiella frenatus). However, these clusters disappeared in allometric analyses that took pentastome body size into account, suggesting that only a single pentastome taxon may be involved. Our molecular data revealed no genetic differences between parasites in toads versus lizards, confirming that there was only one species: R. frenatus. This pentastome (previously known only from lizards) clearly is also capable of maturing in anurans. Our analyses show that the morphological features used in pentastomid taxonomy change as the parasite transitions through developmental stages in the definitive host. To facilitate valid descriptions of new species of pentastomes, future taxonomic work should include both morphological measurements (incorporating quantitative measures of body size and hook bluntness) and molecular data
A method for describing the canopy architecture of coppice poplar with allometric relationships.
Casella, Eric; Sinoquet, Hervé
2003-12-01
A multi-scale biometric methodology for describing the architecture of fast-growing short-rotation woody crops is used to describe 2-year-old poplar clones during the second rotation. To allow for expressions of genetic variability observed within this species (i.e., growth potential, leaf morphology, coppice and canopy structure), the method has been applied to two clones: Ghoy (Gho) (Populus deltoides Bartr. ex Marsh. x Populus nigra L.) and Trichobel (Tri) (Populus trichocarpa Torr. & A. Gray x Populus trichocarpa). The method operates at the stool level and describes the plant as a collection of components (shoots and branches) described as a collection of metameric elements, themselves defined as a collection of elementary units (internode, petiole, leaf blade). Branching and connection between the plant units (i.e., plant topology) and their spatial location, orientation, size and shape (i.e., plant geometry) describe the plant architecture. The methodology has been used to describe the plant architecture of 15 selected stools per clone over a 5-month period. On individual stools, shoots have been selected from three classes (small, medium and large) spanning the diameter distribution range. Using a multi-scale approach, empirical allometric relationships were used to parameterize elementary units of the plant, topological relationships and geometry (e.g., distribution of shoot diameters on stool, shoot attributes from shoot diameter). The empirical functions form the basis of the 3-D Coppice Poplar Canopy Architecture model (3-D CPCA), which recreates the architecture and canopy structure of fast-growing coppice crops at the plot scale. Model outputs are assessed through visual and quantitative comparisons between actual photographs of the coppice canopy and simulated images. Overall, results indicate a good predictive ability of the 3-D CPCA model.
Beaty, Lynne E; Salice, Christopher J
2013-10-01
Invasive species are costly and difficult to control. In order to gain a mechanistic understanding of potential control measures, individual-based models uniquely parameterized to reflect the salient life-history characteristics of invasive species are useful. Using invasive Australian Rhinella marina as a case study, we constructed a cohort- and individual-based population simulation that incorporates growth and body size of terrestrial stages. We used this allometric approach to examine the efficacy of nontraditional control methods (i.e., tadpole alarm chemicals and native meat ants) that may have indirect effects on population dynamics mediated by effects on body size. We compared population estimates resulting from these control methods with traditional hand removal. We also conducted a sensitivity analysis to investigate the effect that model parameters, specifically those associated with growth and body size, had on adult population estimates. Incremental increases in hand removal of adults and juveniles caused nonlinear decreases in adult population estimates, suggesting less return with increased investment in hand-removal efforts. Applying tadpole alarm chemicals or meat ants decreased adult population estimates on the same level as removing 15-25% of adults and juveniles by hand. The combined application of tadpole alarm chemicals and meat ants resulted in approximately 80% decrease in adult abundance, the largest of any applied control method. In further support of the nontraditional control methods, which greatly affected the metamorph stage, our model was most sensitive to changes in metamorph survival, juvenile survival, metamorph growth rate, and adult survival. Our results highlight the use and insights that can be gained from individual-based models that incorporate growth and body size and the potential success that nontraditional control methods could have in controlling established, invasive Rhinella marina populations. PMID:24261039
Roda, Amy L; Oldham, Neil J; Svatos, Ales; Baldwin, Ian T
2003-02-01
Trichomes excrete secondary metabolites that may alter the chemical composition of the leaf surface, reducing damage caused by herbivores, pathogens and abiotic stresses. We examined the surface exudates produced by Nicotiana attenuata Torr. Ex Wats., a plant known to contain and secrete a number of secondary metabolites that are toxic or a deterrent to herbivorous insects. Extractions specific to the leaf surface, the trichomes, and the laminar components demonstrated the localization of particular compounds. Diterpene glycosides occurred exclusively in leaf mesophyll, whereas nicotine was found in both the trichomes and mesophyll. Neither rutin nor nicotine was found on the leaf surface. Quercetin and 7 methylated derivatives were found in the glandular trichomes and appeared to be excreted onto the leaf surface. We examined the elicitation of these flavonols on the leaf surface with a surface-area allometric analysis, which measures changes in metabolites independent of the effects of leaf expansion. The flavonols responded differently to wounding, methyl jasmonate (MeJA), herbivore attack and UV-C radiation, and the response patterns corresponded to their compound-specific allometries. Finding greater amounts of quercetin on younger leaves and reduced amounts after herbivore feeding and MeJA treatment, we hypothesized that quercetin may function as an attractant, helping the insects locate a preferred feeding site. Consistent with this hypothesis, mirids (Tupiocoris notatus) were found more often on mature leaves sprayed with quercetin at a concentration typical of young leaves than on unsupplemented mature leaves. The composition of metabolites on the leaf surface of N. attenuata changes throughout leaf development and in response to herbivore attack or environmental stress, and these changes are mediated in part by responses of the glandular trichomes.
NASA Astrophysics Data System (ADS)
Rukolaine, Sergey A.
2016-05-01
In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE.
Bertini, G; Fransozo, A
1999-11-01
The purpose of this paper is to investigate the relative growth and heterochely in the hermit crab Petrochirus diogenes. Hermit crabs were collected in the Ubatuba region, SP, from 1993 to 1996; using a commercial fishing boat equipped with two double-rig nets. Body mass of each individual was weighed and their cephalothoracic shield and chelar propodus size were measured. Body mass and chelar propodus size were regarded as dependent variables and plotted against length of cephalothoracic shield according to the allometric equation y = a x x(b). A total of 479 individuals were obtained being 307 males and 172 females. Cephalothoracic shield width follows an isometric growth for both sexes. Otherwise, right cheliped dimensions show different relative growth patterns and left cheliped ones present a positive allometry in males and females. Unlike brachyurans, ontogenetic changes in the growth rate of chelar propodus are not clearly discernible, which prevents the accurate detection of allometric variations. In both sexes, the right cheliped is larger than the right one. Cheliped size is a sexual dimorphic feature with males bearing larger chelipeds than females. Heterochely may be particularly adaptive in agonistic interactions and precopulatory behaviour in P diogenes.
Jayasundara, Nishad; Kozal, Jordan S; Arnold, Mariah C; Chan, Sherine S L; Di Giulio, Richard T
2015-01-01
Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO2), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO2 scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO2) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism's vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate-a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in
Jayasundara, Nishad; Kozal, Jordan S.; Arnold, Mariah C.; Chan, Sherine S. L.; Di Giulio, Richard T.
2015-01-01
Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO2), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO2 scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO2) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism’s vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate—a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in
NASA Astrophysics Data System (ADS)
Levin, A. M.; Olshanetsky, M. A.; Zotov, A. V.
2016-08-01
We construct twisted Calogero-Moser systems with spins as Hitchin systems derived from the Higgs bundles over elliptic curves, where the transition operators are defined by arbitrary finite-order automorphisms of the underlying Lie algebras. We thus obtain a spin generalization of the twisted D'Hoker-Phong and Bordner-Corrigan-Sasaki-Takasaki systems. In addition, we construct the corresponding twisted classical dynamical r-matrices and the Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of Lie algebras.
Allometric comparison of Georgia dairy heifers on farms and at youth shows.
White, D S; Duberstein, K J; Fain Bohlen, J L; Bertrand, J K; Nelson, A H; Froetschel, M A; Davidson, B E; Graves, W M
2015-02-01
Studies were conducted to determine the relationship between allometric measures of growth of Holstein dairy heifers and placing in the show ring, and to compare differences in growth between Holstein heifers that are shown and not shown. In the first study, 494 Holstein show heifers were evaluated at the 2012 and 2013 Georgia Junior National Livestock Shows. Measurements were obtained for weight, head length, withers height, hip height, thurl width, and tail length. Heifer mass index (HMI), average daily gain (ADG), and age were calculated. In total, 72.5% of Holstein show heifers were underweight. Average ADG was 0.63 kg/d, which is below the industry recommendation of 0.7 to 0.8 kg/d. Variables were ranked and converted to percentages to account for differences in class size. Withers height, head length, and HMI were most indicative of show placing. In the second study, we compared differences between growth patterns of show heifers and non-show heifers. An additional 293 non-show Holstein heifers were evaluated on 3 Georgia dairy farms during the same period as the show. In total, 43.3% of non-show heifers were underweight. Average ADG for non-show heifers was 0.71 kg/d, which is within the industry recommendation of 0.7 to 0.8 kg/d. Show heifers weighed less for their age than non-show heifers and tended to be taller at the withers than non-show heifers. The HMI scores were similar for younger show and non-show heifers, but older show heifers had lower HMI scores than non-show heifers of the same age. Show heifers had HMI scores that were lower than values calculated from standard growth data. As show heifers matured, ADG decreased, whereas as non-show heifers matured, ADG increased. Youth, leaders, and parents need to be aware of the importance of growing replacement heifers correctly so that heifers calve at 22 to 24 mo of age at an acceptable size and scale and become profitable members of the milking herd. PMID:25434340
Allometric comparison of Georgia dairy heifers on farms and at youth shows.
White, D S; Duberstein, K J; Fain Bohlen, J L; Bertrand, J K; Nelson, A H; Froetschel, M A; Davidson, B E; Graves, W M
2015-02-01
Studies were conducted to determine the relationship between allometric measures of growth of Holstein dairy heifers and placing in the show ring, and to compare differences in growth between Holstein heifers that are shown and not shown. In the first study, 494 Holstein show heifers were evaluated at the 2012 and 2013 Georgia Junior National Livestock Shows. Measurements were obtained for weight, head length, withers height, hip height, thurl width, and tail length. Heifer mass index (HMI), average daily gain (ADG), and age were calculated. In total, 72.5% of Holstein show heifers were underweight. Average ADG was 0.63 kg/d, which is below the industry recommendation of 0.7 to 0.8 kg/d. Variables were ranked and converted to percentages to account for differences in class size. Withers height, head length, and HMI were most indicative of show placing. In the second study, we compared differences between growth patterns of show heifers and non-show heifers. An additional 293 non-show Holstein heifers were evaluated on 3 Georgia dairy farms during the same period as the show. In total, 43.3% of non-show heifers were underweight. Average ADG for non-show heifers was 0.71 kg/d, which is within the industry recommendation of 0.7 to 0.8 kg/d. Show heifers weighed less for their age than non-show heifers and tended to be taller at the withers than non-show heifers. The HMI scores were similar for younger show and non-show heifers, but older show heifers had lower HMI scores than non-show heifers of the same age. Show heifers had HMI scores that were lower than values calculated from standard growth data. As show heifers matured, ADG decreased, whereas as non-show heifers matured, ADG increased. Youth, leaders, and parents need to be aware of the importance of growing replacement heifers correctly so that heifers calve at 22 to 24 mo of age at an acceptable size and scale and become profitable members of the milking herd.
NASA Technical Reports Server (NTRS)
Nathenson, M.; Baganoff, D.; Yen, S. M.
1974-01-01
Data obtained from a numerical solution of the Boltzmann equation for shock-wave structure are used to test the accuracy of accepted approximate expressions for the two moments of the collision integral Delta (Q) for general intermolecular potentials in systems with a large translational nonequilibrium. The accuracy of the numerical scheme is established by comparison of the numerical results with exact expressions in the case of Maxwell molecules. They are then used in the case of hard-sphere molecules, which are the furthest-removed inverse power potential from the Maxwell molecule; and the accuracy of the approximate expressions in this domain is gauged. A number of approximate solutions are judged in this manner, and the general advantages of the numerical approach in itself are considered.
Makowitz, H.
1992-10-01
We have studied various formulations of the concept of pressure, in the context of the usual Six-Equation Model of thermal-hydraulics. A different concept of pressure, than the usual one, has been used. This new pressure concept is Galilean Invariant, and results for the One-Pressure Model with the same complex characteristic roots as the Basic III-Posed Model,'' discussed in the literature for the cases we have investigated. We have also examined several Two-Pressure formulations and shown that two pressures are a necessary but not sufficient condition for obtaining a Well-Posed system. Several counter examples are presented. We have shown that the standard theory is not Galilean Invariant and suggested that the origin of III-Posedness is due to our closure relationships. We also question whether the current theory can satisfy conservation principles for mass, energy, and momentum.
Craig, Jaquelyn M.; Thomas, Michael V.; Nichols, S. Jerrine
2005-01-01
Several USA state, federal, and Canadian agencies study lake sturgeon (Acipenser fulvescens) within the St Clair River and Lake St Clair, collectively referred to hereafter as the St Clair River (SCR) system. Previously, there has been no set standard for determining condition for SCR system lake sturgeon. Condition measures the variation from the expected weight for length as an indicator of fatness, general well-being, gonad development, etc. The aim of this project was to determine the length-weight relationship of lake sturgeon caught from the SCR system, from which a relative condition factor (Kn) equation could be derived. Total length (TL, mm) and weight (W, kg) were measured for 1074 lake sturgeon (101 males and 16 females were identifiable) collected by setline and bottom trawl from the SCR system in May-September, 1997-2002. Analysis of covariance found no difference in the length-weight relationship between sampling gear or sex. Least-squares regression of log10W x log10TL produced the overall equation logW = 3.365logTL - 9.320. Using the exponential form of the slope and y-intercept, relative condition factor for lake sturgeon from the SCR system can be calculated as Kn = W/ [(4.786 x 10-10)(TL3.365)]. Equations for males and females were also developed. Overall, body condition was significantly correlated with both age and girth; no significant difference in Kn by sex was found. In general, the SCR lake sturgeon population was near the upper ends of growth and condition ranges listed in the literature, comparable with those populations that are at similar latitudes. Although condition factors should be interpreted with caution, proper use of a standard equation provides a non-lethal measure of overall fish health that can be used by biologists and managers in ongoing efforts to restore lake sturgeon throughout the Great Lakes.
Craig, J.M.; Thomas, M.V.; Nichols, S.J.
2005-01-01
Several USA state, federal, and Canadian agencies study lake sturgeon (Acipenser fulvescens) within the St Clair River and Lake St Clair, collectively referred to hereafter as the St Clair River (SCR) system. Previously, there has been no set standard for determining condition for SCR system lake sturgeon. Condition measures the variation from the expected weight for length as an indicator of fatness, general well-being, gonad development, etc. The aim of this project was to determine the length weight relationship of lake sturgeon caught from the SCR system, from which a relative condition factor (Kn) equation could be derived. Total length (TL, mm) and weight (W, kg) were measured for 1074 lake sturgeon (101 males and 16 females were identifiable) collected by setline and bottom trawl from the SCR system in May-September, 1997-2002. Analysis of covariance found no difference in the length-weight relationship between sampling gear or sex. Least-squares regression of log10W ?? log10TL produced the overall equation logW = 3.365logTL - 9.320. Using the exponential form of the slope and y-intercept, relative condition factor for lake sturgeon from the SCR system can be calculated as Kn - W/[(4.786 ?? 10-10)(TL3.365)]. Equations for males and females were also developed. Overall, body condition was significantly correlated with both age and girth; no significant difference in Kn by sex was found. In general, the SCR lake sturgeon population was near the upper ends of growth and condition ranges listed in the literature, comparable with those populations that are at similar latitudes. Although condition factors should be interpreted with caution, proper use of a standard equation provides a non-lethal measure of overall fish health that can be used by biologists and managers in ongoing efforts to restore lake sturgeon throughout the Great Lakes. ?? 2005 Blackwell Verlag, Berlin.
de Camargo, Nícholas Ferreira; Corrêa, Danilo do Carmo Vieira; de Camargo, Amabílio J. Aires; Diniz, Ivone Rezende
2015-01-01
Sexual dimorphism is a pronounced pattern of intraspecific variation in Lepidoptera. However, moths of the family Sphingidae (Lepidoptera: Bombycoidea) are considered exceptions to this rule. We used geometric morphometric techniques to detect shape and size sexual dimorphism in the fore and hindwings of seven hawkmoth species. The shape variables produced were then subjected to a discriminant analysis. The allometric effects were measured with a simple regression between the canonical variables and the centroid size. We also used the normalized residuals to assess the nonallometric component of shape variation with a t-test. The deformations in wing shape between sexes per species were assessed with a regression between the nonreduced shape variables and the residuals. We found sexual dimorphism in both wings in all analyzed species, and that the allometric effects were responsible for much of the wing shape variation between the sexes. However, when we removed the size effects, we observed shape sexual dimorphism. It is very common for females to be larger than males in Lepidoptera, so it is expected that the shape of structures such as wings suffers deformations in order to preserve their function. However, sources of variation other than allometry could be a reflection of different reproductive flight behavior (long flights in search for sexual mates in males, and flight in search for host plants in females). PMID:26206895
Wang, Lei; Qiang, Wei; Cheng, Zeneng
2016-03-01
Allometric scaling has been widely used for predictions of human pharmacokinetic (PK) parameters in the development of monoclonal antibody (mAb) drugs, and some correction factors have been proposed to improve the estimations. However, classic correction factors fail to offer a complete explanation of the additional differences among species besides the body weight and, thus, lack enough power to further improve the predictions. In this study, the antigen concentration was initially set as a new correction factor to predict the human clearance (CL) of mAbs. Bevacizumab was intravenously injected into 2 animal species and humans to obtain PK data to predict human CL from the animal data. Additionally, a new approach was also validated with data from 3 other mAbs which were collected through a literature review of published work. Accordingly, allometric scaling with a correction factor of the antigen concentration generated accurate estimations of the human CL of 4 mAbs, which were superior to the results obtained by other classic scaling methods. More importantly, the proposed method also achieved good predictions of individual human CL of bevacizumab. In conclusion, the potential of this method as a powerful tool for human PK estimation of mAbs in species translation has been demonstrated. PMID:26886347
de Camargo, Willian Rogers Ferreira; de Camargo, Nícholas Ferreira; Corrêa, Danilo do Carmo Vieira; de Camargo, Amabílio J Aires; Diniz, Ivone Rezende
2015-01-01
Sexual dimorphism is a pronounced pattern of intraspecific variation in Lepidoptera. However, moths of the family Sphingidae (Lepidoptera: Bombycoidea) are considered exceptions to this rule. We used geometric morphometric techniques to detect shape and size sexual dimorphism in the fore and hindwings of seven hawkmoth species. The shape variables produced were then subjected to a discriminant analysis. The allometric effects were measured with a simple regression between the canonical variables and the centroid size. We also used the normalized residuals to assess the nonallometric component of shape variation with a t-test. The deformations in wing shape between sexes per species were assessed with a regression between the nonreduced shape variables and the residuals. We found sexual dimorphism in both wings in all analyzed species, and that the allometric effects were responsible for much of the wing shape variation between the sexes. However, when we removed the size effects, we observed shape sexual dimorphism. It is very common for females to be larger than males in Lepidoptera, so it is expected that the shape of structures such as wings suffers deformations in order to preserve their function. However, sources of variation other than allometry could be a reflection of different reproductive flight behavior (long flights in search for sexual mates in males, and flight in search for host plants in females). PMID:26206895
ERIC Educational Resources Information Center
Xiong, Yao; Li, Hongli; Kornhaber, Mindy L.; Suen, Hoi K.; Pursel, Barton; Goins, Deborah D.
2015-01-01
Students who are enrolled in MOOCs tend to have different motivational patterns than fee-paying college students. A majority of MOOC students demonstrate characteristics akin more to "tourists" than formal learners. As a consequence, MOOC students' completion rate is usually very low. The current study examines the relations among…
Octonic Massive Field Equations
NASA Astrophysics Data System (ADS)
Demir, Süleyman; Kekeç, Seray
2016-07-01
In the present paper we propose the octonic form of massive field equations based on the analogy with electromagnetism and linear gravity. Using the advantages of octon algebra the Maxwell-Dirac-Proca equations have been reformulated in compact and elegant way. The energy-momentum relations for massive field are discussed.
NASA Astrophysics Data System (ADS)
Molinari, Vincenzo; Mostacci, Domiziano
2015-10-01
He-4 is known to become superfluid at very low temperatures. This effect is now generally accepted to be connected with BEC (Bose-Einstein Condensation). The dispersion relation of pressure waves in superfluid He-4 has been determined at 1.1 °K by Yarnell et al., and exhibits a non monotonic behavior-with a maximum and a minimum-usually explained in terms of excitations called rotons, introduced by Landau. In the present work an attempt is made to describe the phenomenon within the Bohmian interpretation of QM. To this end, the effects of the intermolecular potential, taken to be essentially of the Lennard-Jones type modified to account for molecule finiteness, are included as a Vlasov-type self-consistent field. A dispersion relation is found, that is in quite good agreement with Yarnell's curve.
Mohamadian, Hashem; Eftekhar, Hasan; Rahimi, Abas; Mohamad, Hosein Taghdisi; Shojaiezade, Davod; Montazeri, Ali
2011-06-01
Predicting the significant determinants of health-related quality of life through the application of structural equation modeling in adolescents has received little attention in the health education and health promotion literature. The purpose of this study was to investigate the relationships between self-efficacy, barriers, social support, health-promoting lifestyle, and health-related quality of life among Iranian adolescent girls. Pender's health promotion model guided this study. This was a cross-sectional survey of 500 students who were recruited in Kashan, Iran. Their health-related quality of life was measured by using the Short Form Health Survey. A path analysis was conducted to predict the health-related quality of life determinants. The results indicated that 71% of the variance in health-related quality of life could be predicted by the variables. The results affirmed that self-efficacy was the most significant predictor of the students' health-related quality of life. It was concluded that interventions that are aimed at improving self-efficacy can lead to the enhancement of health-related quality of life among adolescent girls in the developing country of Iran.
NASA Astrophysics Data System (ADS)
Franceries, X.; Doyon, B.; Chauveau, N.; Rigaud, B.; Celsis, P.; Morucci, J.-P.
2003-03-01
In electroencephalography (EEG) and event related potentials (ERP), localizing the electrical sources at the origin of scalp potentials (inverse problem) imposes, in a first step, the computation of scalp potential distribution from the simulation of sources (forward problem). This article proposes an alternative method for mimicing both the electrical and geometrical properties of the head, including brain, skull, and scalp tissue with resistors. Two resistor mesh models have been designed to reproduce the three-sphere reference model (analytical model). The first one (spherical resistor mesh) closely mimics the geometrical and electrical properties of the analytical model. The second one (cubic resistor mesh) is designed to conveniently handle anatomical data from magnetic resonance imaging. Both models have been validated, in reference to the analytical solution calculated on the three-sphere model, by computing the magnification factor and the relative difference measure. Results suggest that the mesh models can be used as robust and user-friendly simulation or exploration tools in EEG/ERP.
Nambiar, P; Bridges, T E; Brown, K A
1991-06-01
As a result of a systematic morphometric study of shark dentitions, a system of notation for describing the location of shark teeth has been developed and is proposed as a standard to be adopted for use in similar studies in the future. The macroscopic morphology of White Shark teeth has been characterised in order to gain quantitative data which might assist in identification of these sharks from bite marks on victims or objects or from shark carcasses. Using these data, a nomogram has been developed which can be used to estimate the body length of a White Shark from measurements of tooth or bite mark morphology. An example of the forensic application of such allometric data is provided as it applied to a recent fatal attack on a diver by a White Shark.
NASA Technical Reports Server (NTRS)
Eades, J. B., Jr.
1974-01-01
The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.
Craig, Jaquelyn; Thomas, Michael V.; Nichols, Susan Jerrine
2005-01-01
Several USA state, federal, and Canadian agencies study lake sturgeon (Acipenser fulvescens) within the St Clair River and Lake St Clair, collectively referred to hereafter as the St Clair River (SCR) system. Previously, there has been no set standard for determining condition for SCR system lake sturgeon. Condition measures the variation from the expected weight for length as an indicator of fatness, general well-being, gonad development, etc. The aim of this project was to determine the length–weight relationship of lake sturgeon caught from the SCR system, from which a relative condition factor (Kn) equation could be derived. Total length (TL, mm) and weight (W, kg) were measured for 1074 lake sturgeon (101 males and 16 females were identifiable) collected by setline and bottom trawl from the SCR system in May–September, 1997–2002. Analysis of covariance found no difference in the length–weight relationship between sampling gear or sex. Least-squares regression of log10W × log10TL produced the overall equation logW = 3.365logTL − 9.320. Using the exponential form of the slope and y-intercept, relative condition factor for lake sturgeon from the SCR system can be calculated as Kn = W/[(4.786 × 10−10)(TL3.365)]. Equations for males and females were also developed. Overall, body condition was significantly correlated with both age and girth; no significant difference in Kn by sex was found. In general, the SCR lake sturgeon population was near the upper ends of growth and condition ranges listed in the literature, comparable with those populations that are at similar latitudes. Although condition factors should be interpreted with caution, proper use of a standard equation provides a non-lethal measure of overall fish health that can be used by biologists and managers in ongoing efforts to restore lake sturgeon throughout the Great Lakes.
Jia, Mei-yu; Li, Xue-hua; Oh, Choong-hyeon; Park, Hong-chul; Miao, Chun-ping; Han, Xu
2015-10-01
Research on fine scale pattern and characteristics of allometric growth could contribute to better understanding plants' adaptation in moving sandy dunes. The abundance, height and biomass of 3 species Agriophilum aquarrosum, Corispermum candelabrum and Setaria viridis in twenty-eight 1 m x 1 m quadrats of Horqin Sandy Land were identified, mapped and described. The nearest neighbor method and O-ring O(r) function analysis were applied to analyze the spatial patterns. The results showed that the individual spatial pattern was mainly aggregated in 1 m x 1 m quadrat at community level but mainly random at population level. At 0-50 cm individual distance scale, both intraspecific and interspecific relationship were facilitation and aggregated distribution occurred at some scales and varied with increasing plant abundance in 1 m x 1 m quadrat. In 0-40 cm, the aggregated distribution of S. viridis and A. aquarrosum increased obviously; in 10-20 cm, both intraspecific and interspecific aggregation increased; in 10-30 cm, the occurrence possibility of positive correlations between S. viridis and A. aquarrosum, S. viridis and C. candelabrum all increased; in 40-50 cm, the possibility of positive correlations between A. squarrosum and S. viridis, A. squarrosum and C. candelabrum all increased. Research on the three species components indicated that the growth rate of above-ground was faster than that of underground. S. viridis had the highest ratio of under-ground biomass to above-ground biomass but its nutritional organs' biomass ratio was medium. C. candelabrum allocated more biomass to propagative organs and stem, but A. squarrosum allocated more biomass to nutritional organs. Based on the spatial distribution and allometric characteristics, the three common species in moving sand dunes preferred r strategy in their life history. PMID:26995902
Benítez, Hugo A.; Bravi, Raffaella; Parra, Luis E.; Sanzana, Maria-Jose; Sepúlveda-Zúñiga, Einer
2013-01-01
Bees and wasps could exhibit shape and size sexual dimorphism, and most of their morphological variation could depend on phenotypic responses due to environmental pressure during ontogenetic development. More complex measurement techniques related to size and shape rather than simply to mass and length should be required to analyze such a complex sexual dimorphism. In this study, differences related to wing shape and size of males and females of Ophion intricatus Brullé (Hymenoptera: Ichneumonidae) were evaluated using geometric morphometrics. Right and left wings of specimens were used, and a photographic matrix was constructed in which 18 morphological landmarks based on shape and vein patterns of the wings were digitalized. A multivariate analysis of wing shape showed significant differences between sexes and sites. The geometric variation demonstrated that the points at the intersection of radial and cubital-anal veins might be key characters to differentiate between sexes. This study also showed the presence of two clearly different male morphotypes coexisting in the same study site. However, it should be noted that the results of this study showed that the variation in wing shape is an analytical character in the determination of sexual differences in the family Ichneumonidae. These differences raise the question of whether sexual dimorphism of wing shape may be modulated by natural selection. PMID:24766555
NASA Technical Reports Server (NTRS)
Watkins, Charles E; Runyan, Harry L; Woolston, Donald S
1955-01-01
This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.
NASA Astrophysics Data System (ADS)
Fibich, Gadi; Merle, Frank; Raphaël, Pierre
2006-08-01
We give a proof of a Spectral Property related to the description of the singularity formation for the L2 critical nonlinear Schrödinger equation iut+Δu+u|=0 in dimensions N=2,3,4. Assuming this property, the rigorous mathematical analysis developed in a recent series of papers by Merle and Raphaël provides a complete description of the collapse dynamics for a suitable class of initial data. In particular, this implies in dimension N=2 the existence of a large class of solutions blowing up with the log-log speed |∼√{{log|log(T-t)}/{T-t}} where T>0 is the blow up time. This Spectral Property is equivalent to the coercivity of some Schrödinger type operators. An analytic proof is given in [F. Merle, P. Raphaël, Blow up dynamic and upper bound on the blow up rate for critical nonlinear Schrödinger equation, Ann. of Math. 161 (1) (2005) 157-222] in dimension N=1 and in this paper, we give a computer assisted proof in dimensions N=2,3,4. We propose in particular a rigorous mathematical frame to reduce the check of this type of coercivity property to accessible and robust numerical results.
NASA Astrophysics Data System (ADS)
Palchik, V.
2014-11-01
The axial, crack and total volumetric strains, porosity, elastic constants, crack damage stresses, uniaxial compressive strengths, as well as fracture apertures and number of fracture traces in rock samples surface after compression were defined for different chalk, basalt, dolomite, granite, limestone and sandstone samples exhibiting negative total volumetric strain at failure. It is established that the total (summed) aperture of vertical fractures obtained on the lateral surface of rock sample is related to three characteristic strain parameters: axial strain at the onset of negative total volumetric strain, axial failure strain and negative total volumetric strain at failure. The relation is based on Descartes folium equation, where the length of the loop of folium is equal to axial strain coordinate at the onset of negative total volumetric strain. This relation shows that the total aperture increases according to power law with increasing difference between axial failure strain and axial strain at the onset of negative total volumetric strain. Simultaneously, an increase in this difference leads to an increase in the value of negative total volumetric strain at failure. It is found that a direct correlation between total aperture of fractures and negative total volumetric strain at failure is relatively weak. Nevertheless, total aperture of fractures tends to increase with increasing absolute value of negative total volumetric strain at failure. It is revealed that there is no connection between the number of fracture traces and negative total volumetric strain at failure.
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Ehlers, Jürgen; Sachs, Rainer K.
2013-12-01
This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.
Vatsalya, Vatsalya; Arora, Kashmiri L.
2014-01-01
The Japanese quail is a very valuable animal model for research in a variety of biological disciplines. The purpose of this study was to characterize and interrelate age-dependent testicular parameters with various blood constituents: blood glucose, plasma proteins and packed cell volume that are developing concurrently in the growing bird. Another objective of the study was to identify selective physioanatomical markers for predicting the testicular growth and the onset of sexual maturity. Male Japanese quail hatchlings were raised in temperature controlled brooders for up to 3 weeks of age under a constant light and then shifted to hanging cages in an air conditioned room set at ~73° F under a 14L: 10D lighting system and ad libitum access to feed and water. Starting d8, a group of 8–10 birds of uniform size and weight were selected randomly at 4-day intervals up to d52 of age for the project. The birds were weighed and blood sampled using the brachial vein and Blood Glucose (BGL), Total Plasma Proteins (PP) and Packed Cell Volume (PCV) levels were measured prior to euthanization. The testes were removed and measured for weight, length, width and Volume (VOL). All the testicular measurements were then correlated with age and body weight. The left testes were larger than the right testes and their differences were evident at d36 of age. Testicular measurements also reflected two distinct growth surges at d28, d32 and d36 of age. Combined Testes Weight (CTW) and Combined Testes Volume (CTV) revealed a strong positive correlation with PCV and PP and a negative correlation with Blood Glucose Level (BGL). Accordingly, these measurements could serve as reliable markers of growth rate and sexual maturation in male Japanese quail. PMID:25243007
Vatsalya, Vatsalya; Arora, Kashmiri L
2012-01-01
The Japanese quail is a very valuable animal model for research in a variety of biological disciplines. The purpose of this study was to characterize and interrelate age-dependent testicular parameters with various blood constituents: blood glucose, plasma proteins and packed cell volume that are developing concurrently in the growing bird. Another objective of the study was to identify selective physioanatomical markers for predicting the testicular growth and the onset of sexual maturity. Male Japanese quail hatchlings were raised in temperature controlled brooders for up to 3 weeks of age under a constant light and then shifted to hanging cages in an air conditioned room set at ~73° F under a 14L: 10D lighting system and ad libitum access to feed and water. Starting d8, a group of 8-10 birds of uniform size and weight were selected randomly at 4-day intervals up to d52 of age for the project. The birds were weighed and blood sampled using the brachial vein and Blood Glucose (BGL), Total Plasma Proteins (PP) and Packed Cell Volume (PCV) levels were measured prior to euthanization. The testes were removed and measured for weight, length, width and Volume (VOL). All the testicular measurements were then correlated with age and body weight. The left testes were larger than the right testes and their differences were evident at d36 of age. Testicular measurements also reflected two distinct growth surges at d28, d32 and d36 of age. Combined Testes Weight (CTW) and Combined Testes Volume (CTV) revealed a strong positive correlation with PCV and PP and a negative correlation with Blood Glucose Level (BGL). Accordingly, these measurements could serve as reliable markers of growth rate and sexual maturation in male Japanese quail.
Logie, Carmen H.; Jenkinson, Jesse I. R.; Earnshaw, Valerie; Tharao, Wangari; Loutfy, Mona R.
2016-01-01
African and Caribbean Black women in Canada have new HIV infection rates 7 times higher than their white counterparts. This overrepresentation is situated in structural contexts of inequities that result in social, economic and health disparities among African and Caribbean Black populations. Economic insecurity is a distal driver of HIV vulnerability, reducing access to HIV testing, prevention and care. Less is known about how economic insecurity indicators, such as housing security, continue to influence the lives of women living with HIV following HIV-positive diagnoses. The aim of this study was to test a conceptual model of the pathways linking HIV-related stigma, racial discrimination, housing insecurity, and wellbeing (depression, social support, self-rated health). We implemented a cross-sectional survey with African and Caribbean Black women living with HIV in 5 Ontario cities, and included 157 participants with complete data in the analyses. We conducted structural equation modeling using maximum likelihood estimation to evaluate the hypothesized conceptual model. One-fifth (22.5%; n = 39) of participants reported housing insecurity. As hypothesized, racial discrimination had significant direct effects on: HIV-related stigma, depression and social support, and an indirect effect on self-rated health via HIV-related stigma. HIV-related stigma and housing insecurity had direct effects on depression and social support, and HIV-related stigma had a direct effect on self-rated health. The model fit the data well: χ2 (45, n = 154) = 54.28, p = 0.387; CFI = 0.997; TLI = 0.996; RMSEA = 0.016. Findings highlight the need to address housing insecurity and intersecting forms of stigma and discrimination among African and Caribbean Black women living with HIV. Understanding the complex relationships between housing insecurity, HIV-related stigma, racial discrimination, and wellbeing can inform multi-level interventions to reduce stigma and enhance health. PMID
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
Optimization of one-way wave equations.
Lee, M.W.; Suh, S.Y.
1985-01-01
The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors
Relativistic Guiding Center Equations
White, R. B.; Gobbin, M.
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
NASA Astrophysics Data System (ADS)
Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul
2014-07-01
In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).
NASA Astrophysics Data System (ADS)
Silveira, Andréa P.; Martins, Fernando R.; Araújo, Francisca S.
2012-08-01
In temperate and tropical rainforests, ontogenetic structure and allometry during tree ontogeny are often associated with light gradients. Light is not considered a limiting resource in deciduous thorny woodland (DTW), but establishment and growth occur during a short rainy period, when the canopy is fully leaved and light in the understory may be modified. Our aim was to investigate whether the light gradient in DTW and the biomechanical limitations of tree growth would be enough to produce an ontogenetic structure and allometric growth similar to rainforest canopy trees. We investigated the ontogenetic stages and diameter-height relationship of Cordia oncocalyx (Boraginaceae), a dominant canopy tree of the DTW of semiarid northeastern Brazil. We tagged, measured and classified the ontogenetic stages of 2.895 individuals in a 1 ha area (5°6'58.1″S and 40°52'19.4″W). In the rainy season only 4.7% of the light falling on the canopy reached the ground. Initial ontogenetic stages, mainly infant (50.9%) and seedling (42.1%), were predominant in the population, with the remaining 7% distributed among juvenile, immature, virginile and reproductive. The ontogenetic structure was similar to that of rainforest tree species, but the population formed both permanent seed and infant banks in response to long dry periods and erratic rainy spells. Like many other Boraginaceae tree species in tropical rainforests, C. oncocalyx has a Prévost architectural model, but allometric growth was quite different from rainforest trees. C. oncocalyx invested slightly more in diameter at first, then in height and finally invested greatly in diameter and attained an asymptotic height. The continued high investment in diameter growth at late stages and the asymptotic height point to low tree density and more frequent xylem embolism as the main drivers of tree allometric shape in DTW. This indicates that tree ontogenetic structure and allometric relationships depend on vegetation
The compressible adjoint equations in geodynamics: equations and numerical assessment
NASA Astrophysics Data System (ADS)
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Kelly, Clint D
2015-08-01
Sexual dimorphism in shape and size is widespread across animal taxa and arises when natural or sexual selection operates differently on the sexes. Male and female common geckos (Woodworthia maculatus; formerly Hoplodactylus maculatus) in New Zealand do not appear to experience different viability selection pressure, nor do males appear to be under intense pre-copulatory sexual selection. It was therefore predicted that this species would be sexually monomorphic with regard to body size and the size and shape of the head. In line with the prediction, there was no sexual difference in head width, depth, or length or in lateral head shape. However, contrary to prediction, males had a larger body and lateral head size than females. This study suggests that males, at least on Maud Island, NZ, might be under stronger pre-copulatory sexual selection than previously recognized and thus have evolved larger heads (i.e. lateral head size) for use in male combat for females. Allometric scaling patterns do not differ between the sexes and suggest that head width and depth are under directional selection whereas lateral head size is under stabilizing selection. Diet ecology - an agent of natural selection common to both sexes - is likely largely responsible for the observed patterns of head size and shape and the lack of sexual dimorphism in them.
Valente-dos-Santos, J; Coelho-e-Silva, M J; Duarte, J; Pereira, J; Rebelo-Gonçalves, R; Figueiredo, A; Mazzuco, M A; Sherar, L B; Elferink-Gemser, M T; Malina, R M
2014-08-01
This study evaluates the contributions of age, skeletal maturation, body size and composition, training and playing position to the development of agility and dribbling speed in young male soccer players (10-18 years) followed longitudinally. 83 players [defenders (n=35), midfielders (n=27), forwards (n=21)] were followed annually over 5 years (average: 4.4 observations per player). Skeletal age (SA), stature, body mass, triceps and subscapular skinfolds, agility and dribbling speed were measured annually. Body composition was estimated from the 2 skinfolds. Annual training volume was estimated from weekly participation forms completed by coaches. The multiplicative allometric models with the best statistical fit showed that statural growth of 1 cm predicts 1.334 s and 1.927 s of improvement in agility and dribbling speed, respectively. Significant independent effects of fat-free mass and annual volume training were found for agility and dribbling speed, respectively (P<0.05). Predicted agility (from 12 to 18 years of SA) and dribbling speed (from 13 to 18 years of SA) differed significantly among players by playing positions (midfielders>forwards>defenders). The present results provide developmental models for the interpretation of intra- and inter-individual variability in agility and dribbling speed among youth soccer players across adolescence, and may provide a framework for trainers and coaches to develop and evaluate individualized training protocols.
Elliott, K.J.; Clinton, B.D.
1993-03-31
Allometric equations were developed to predict aboveground dry weight of herbaceous and woody species on prescribe-burned sites in the Southern Appalachians. Best-fit least-square regression models were developed using diameter, height, or both, as the independent variables and dry weight as the dependent variable. Coefficients of determination for the selected total biomass models ranged from 0.620 to 0.992 for herbaceous species and from 0.698 to 0.999 for the wood species. Equations for foliage biomass generally had lower coefficients of determination than did equations for either stem or total biomass of woody species.
Parallel tridiagonal equation solvers
NASA Technical Reports Server (NTRS)
Stone, H. S.
1974-01-01
Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.
Vandorpe, G; Kühn, E R; Gevaerts, H
1990-09-01
Females of the giant swamp frog Dicroglossus occipitalis were captured in Zaïre close to the equator in the course of 1 month. During this period, females with fully developed eggs were found, together with females of which the eggs were still in the first developmental stages. A close relationship was established between the maturation of the eggs and the studied gonadal factors: the gonadosomatic index, the oviduct weight, plasma estradiol-17 beta (E2) concentrations, plasma testosterone concentrations, and the total ovarian E2 concentrations. At the level of the thyroidal axis, the studied factors (plasma thyroxine (T4), plasma triiodothyronine (T3), plasma T3/T4 ratio, T4 and T3 concentrations, and the T3/T4 ratio in the thyroids and the 5'-monodeiodination activity (5'-D-activity) in the skin and kidney homogenates) did not show parallel changes with the maturation process of the eggs. These results indicate that no causal relation has to exist between the annual variation in thyroid hormones and the annual reproductive patterns as found in frogs from the tropical or temperate climatic region.
NASA Astrophysics Data System (ADS)
Kundt, Wolfgang; Trümper, Manfred
2016-04-01
This is an English translation of a paper by Wolfgang Kundt and Manfred Trümper, first published in 1962 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was the last of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (All the other parts of the series have already been re-published as Golden Oldies.) This fifth contribution summarizes key points of the earlier papers and applies them, in particular results from papers II and IV in the series, in the context of the propagation of gravitational radiation when matter is present. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Malcolm A.H. MacCallum and by a brief autobiography of Manfred Trümper.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
NASA Astrophysics Data System (ADS)
Zhu, Jinlong; Xu, Hongwu; Zhang, Jianzhong; Jin, Changqing; Wang, Liping; Zhao, Yusheng
2011-10-01
The phase relation of tetragonal and cubic PbTiO3 and their unit-cell parameters have been determined by synchrotron x-ray diffraction at pressures up to 7.8 GPa and temperatures up to 1074 K with a cubic anvil apparatus. From these measurements, a pressure-temperature phase boundary between the tetragonal and cubic phases has been established. With increasing temperature or pressure, the c/a ratio of the ferroelectric, tetragonal PbTiO3 becomes closer to unity, suggesting that both heating and compression favor the paraelectric, cubic structure. Using a modified high-T Birch-Murnaghan equation of state and a thermal-pressure approach, we have derived the thermoelastic parameters of tetragonal and cubic PbTiO3, including the ambient bulk modulus K0, temperature derivative of bulk modulus at constant pressure, volumetric thermal expansivity, pressure derivative of thermal expansion, and temperature derivative of bulk modulus at constant volume. Our obtained K0 value for tetragonal PbTiO3 is consistent with previously reported results, while that for cubic PbTiO3 is smaller than earlier results probably due to differences in the experimental techniques used (cubic anvil apparatus versus diamond anvil cell) and related stress conditions of the samples. All other thermoelastic parameters for both tetragonal and cubic PbTiO3 have been determined for the first time. Compared with previous high-temperature data at atmospheric pressure, our P-V-T dataset for tetragonal PbTiO3 infers a pressure-induced crossover in volumetric thermal expansion from negative to positive between 0 and 1 GPa, an phenomenon that is of fundamentally interest and practically important.
2014-01-01
Background Although studies suggest the relevance of intimate partner violence (IPV) and other health-related social characteristics as risk factors for postpartum mental health, literature lacks evidence about how these are effectively connected. This study thus aims to explore how socio-economic position, maternal age, household and marital arrangements, general stressors, alcohol misuse and illicit drug abuse, and especially psychological and physical IPV relate in a framework leading to postpartum common mental disorder (CMD). Methods The study was carried out in five primary health care units of Rio de Janeiro, Brazil, and included 810 randomly selected mothers of children up to five postpartum months waiting for pediatric visits. The postulated pathways between exposures and outcome were based on literature evidence and were further examined using structural equation models. Results Direct pathways to postpartum CMD arose from a latent variable depicting socio-economic position, a general stressors score, and both IPV variables. Notably, the effect of psychological IPV on postpartum CMD ran partly through physical IPV. The effect of teenage pregnancy, conjugal instability and maternal burden apparently happens solely through substance use, be it alcohol misuse, illicit drug abuse or both in tandem. Moreover, the effect of the latter on CMD seems to be entirely mediated through both types of IPV. Conclusion Although the theoretical model underlying the analysis still requires in-depth detailing, results of this study may have shed some light on the role of both psychological and physical IPV as part of an intricate network of events leading to postpartum CMD. Health initiatives may want to make use of this knowledge when designing preventive and intervention approaches. PMID:24884951
NASA Astrophysics Data System (ADS)
Villar, Ricardo G.; Pelayo, Jigg L.; Mozo, Ray Mari N.; Salig, James B., Jr.; Bantugan, Jojemar
2016-06-01
Leaning on the derived results conducted by Central Mindanao University Phil-LiDAR 2.B.11 Image Processing Component, the paper attempts to provides the application of the Light Detection and Ranging (LiDAR) derived products in arriving quality Landcover classification considering the theoretical approach of data analysis principles to minimize the common problems in image classification. These are misclassification of objects and the non-distinguishable interpretation of pixelated features that results to confusion of class objects due to their closely-related spectral resemblance, unbalance saturation of RGB information is a challenged at the same time. Only low density LiDAR point cloud data is exploited in the research denotes as 2 pts/m2 of accuracy which bring forth essential derived information such as textures and matrices (number of returns, intensity textures, nDSM, etc.) in the intention of pursuing the conditions for selection characteristic. A novel approach that takes gain of the idea of object-based image analysis and the principle of allometric relation of two or more observables which are aggregated for each acquisition of datasets for establishing a proportionality function for data-partioning. In separating two or more data sets in distinct regions in a feature space of distributions, non-trivial computations for fitting distribution were employed to formulate the ideal hyperplane. Achieving the distribution computations, allometric relations were evaluated and match with the necessary rotation, scaling and transformation techniques to find applicable border conditions. Thus, a customized hybrid feature was developed and embedded in every object class feature to be used as classifier with employed hierarchical clustering strategy for cross-examining and filtering features. This features are boost using machine learning algorithms as trainable sets of information for a more competent feature detection. The product classification in this
Wu Shuangqing
2008-09-15
The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations. The general solution is expressed as a superposition of solutions derived from these two decoupled ordinary differential equations. By separating variables for the massive Klein-Gordon equation in the same spacetime background, I derive a simple and elegant form for the Staeckel-Killing tensor, which can be easily written as the square of a rank-three Killing-Yano tensor. I have also explicitly constructed a symmetry operator that commutes with the scalar Laplacian by using the Staeckel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.
``Riemann equations'' in bidifferential calculus
NASA Astrophysics Data System (ADS)
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
Large uncertainty in soil carbon modelling related to carbon input calculation method
NASA Astrophysics Data System (ADS)
Keel, Sonja G.; Leifeld, Jens; Taghizadeh-Toosi, Arezoo; Oleson, Jørgen E.
2016-04-01
A model-based inventory for carbon (C) sinks and sources in agricultural soils is being established for Switzerland. As part of this project, five frequently used allometric equations that estimate soil C inputs based on measured yields are compared. To evaluate the different methods, we calculate soil C inputs for a long-term field trial in Switzerland. This DOK experiment (bio-Dynamic, bio-Organic, and conventional (German: Konventionell)) compares five different management systems, that are applied to identical crop rotations. Average calculated soil C inputs vary largely between allometric equations and range from 1.6 t C ha-1 yr-1 to 2.6 t C ha-1 yr-1. Among the most important crops in Switzerland, the uncertainty is largest for barley (difference between highest and lowest estimate: 3.0 t C ha-1 yr-1). For the unfertilized control treatment, the estimated soil C inputs vary less between allometric equations than for the treatment that received mineral fertilizer and farmyard manure. Most likely, this is due to the higher yields in the latter treatment, i.e. the difference between methods might be amplified because yields differ more. To evaluate the influence of these allometric equations on soil C dynamics we simulate the DOK trial for the years 1977-2004 using the model C-TOOL (Taghizadeh-Toosi et al. 2014) and the five different soil C input calculation methods. Across all treatments, C-TOOL simulates a decrease in soil C in line with the experimental data. This decline, however, varies between allometric equations (-2.4 t C ha-1 to -6.3 t C ha-1 for the years 1977-2004) and has the same order of magnitude as the difference between treatments. In summary, the method to estimate soil C inputs is identified as a significant source of uncertainty in soil C modelling. Choosing an appropriate allometric equation to derive the input data is thus a critical step when setting up a model-based national soil C inventory. References Taghizadeh-Toosi A et al. (2014) C
Briki, Walid; Chaouachi, Anis; Patrick, Thomas; Chamari, Karim
2015-01-01
Aim The present study attempted to test McCullough and Willoughby’s hypothesis that self-control mediates the relationships between religiosity and psychosocial outcomes. Specifically, this study examined whether trait self-control (TSC) mediates the relationship of identified-introjected religiosity with positive and negative health-related-feelings (HRF) in healthy Muslims. Methods Two hundred eleven French-speaking participants (116 females, 95 males; Mage = 28.15, SDage = 6.90) answered questionnaires. One hundred ninety participants were retained for the analyses because they reported to be healthy (105 females, 85 males; Mage = 27.72, SDage = 6.80). To examine the relationships between religiosity, TSC and HRF, two competing mediation models were tested using structural equation model analysis: While a starting model used TSC as mediator of the religiosity-HRF relationship, an alternative model used religiosity as mediator of the TSC-HRF relationship. Results The findings revealed that TSC mediated the relationship between identified religiosity and positive HRF, and that identified religiosity mediated the relationship between TSC and positive and negative HRF, thereby validating both models. Moreover, the comparison of both models showed that the starting model explained 13.211% of the variance (goodness of fit = 1.000), whereas the alternative model explained 6.877% of the variance (goodness of fit = 0.987). Conclusion These results show that the starting model is the most effective model to account for the relationships between religiosity, TSC, and HRF. Therefore, this study provides initial insights into how religiosity influences psychological health through TSC. Important practical implications for the religious education are suggested. PMID:25962179
Soil acidity, ecological stoichiometry and allometric scaling in grassland food webs
MULDER, CHRISTIAN; ELSER, JAMES J
2009-01-01
The factors regulating the structure of food webs are a central focus of community and ecosystem ecology, as trophic interactions among species have important impacts on nutrient storage and cycling in many ecosystems. For soil invertebrates in grassland ecosystems in the Netherlands, the site-specific slopes of the faunal biomass to organism body mass relationships reflected basic biochemical and biogeochemical processes associated with soil acidity and soil C : N : P stoichiometry. That is, the higher the phosphorus availability in the soil, the higher, on average, the slope of the faunal biomass size spectrum (i.e., the higher the biomass of large-bodied invertebrates relative to the biomass of small invertebrates). While other factors may also be involved, these results are consistent with the growth rate hypothesis from biological stoichiometry that relates phosphorus demands to ribosomal RNA and protein production. Thus our data represent the first time that ecosystem phosphorus availability has been associated with allometry in soil food webs (supporting information available online). Our results have broad implications, as soil invertebrates of different size have different effects on soil processes.
Deformation of the Dirac equation
NASA Astrophysics Data System (ADS)
Faizal, Mir; Kruglov, Sergey I.
2016-10-01
In this paper, we will first clarify the physical meaning of having a minimum measurable time. Then we will combine the deformation of the Dirac equation due to the existence of minimum measurable length and time scales with its deformation due to the doubly special relativity. We will also analyze this deformed Dirac equation in curved spacetime, and observe that this deformation of the Dirac equation also leads to a nontrivial modification of general relativity. Finally, we will analyze the stochastic quantization of this deformed Dirac equation on curved spacetime.
Modelling by Differential Equations
ERIC Educational Resources Information Center
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Structural Equation Model Trees
ERIC Educational Resources Information Center
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Allometric Relationships in Soybean to Estimate the Effect of Vegetation on Microwave Remote Sensing
NASA Astrophysics Data System (ADS)
Spencer, A. J.; Hornbuckle, B. K.; Patton, J.
2011-12-01
Microwave remote sensing is capable of developing soil moisture maps through satellite data. The resulting maps are useful indicators of hydrologic conditions. Water concentrations are deterministic of flooding events and potential agricultural resources. The emitted microwave radiation of soil is influenced by its moisture content. Models have been developed to incorporate parameters besides soil moisture that affect the emitted microwave radiation. We are interested in one of these parameters known as the optical depth. Optical depth is the effect of the canopy on the observed emission of microwaves. The vegetation directly competes with soil moisture as a contributor to the emitted microwave radiation and the optical depth appears within every term in the present satellite retrieval algorithm. Optical depth has been shown to be directly proportional to the amount of water contained within vegetation tissue. Allometry is a way to effectively and efficiently measure vegetation water content through the way the parts of the organism change in proportion to each other in response to growth. Vegetation water content is difficult to measure without taking destructive measurements, in addition to involving too much time and manual labor. Therefore, another component of vegetation can be measured in relation to vegetation water content which can then be related to optical depth. In our study we worked in soybean, a major crop in many areas of the world. We compared soybean vegetation water content to an estimate of the volume of an individual plant expressed as the product of canopy height and stem diameter squared (Zc*Sd2), both of which can be measured easily and nondestructively. We also wished to determine whether vegetation water content remained constant as a percentage to total biomass over the length of the growing season. Agricultural yield is most likely a function of the total dry mass of vegetation. Establishing the relationship between vegetation water
NASA Technical Reports Server (NTRS)
Markley, F. Landis
1995-01-01
Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.
Martínez, M; Dutil, J D; Guderley, H
2000-06-15
This study evaluated whether indicators of metabolic capacity of cod white muscle differ along the length of the body, whether this variation persists over a large range of body sizes, and whether the allometry of metabolic capacities is similar along the length of the body. We examined the maximal activities of two glycolytic enzymes, phosphofructokinase (PFK) and lactate dehydrogenase (LDH), a mitochondrial enzyme, cytochrome C oxidase (CCO), and the biosynthetic enzyme nucleotide diphosphate kinase (NDPK). All enzymes examined showed significant size dependence, which was generally apparent in all regions. The activity of glycolytic enzymes increased with size, whereas that of CCO and NDPK decreased with size. For PFK and LDH, the size dependence decreased caudally, whereas for CCO and NDPK it was strongest in the caudal sample. For each size range, the activities of PFK, LDH, and CCO were higher in the last third of the body than in the middle or just behind the head. In contrast, NDPK activity was higher just behind the head than at the middle or in the last third of the body, suggesting that nuclear proliferation is more rapid in this zone. The high capacity for adenosine triphosphate (ATP) generation in the caudal region suggests that increases in mass-specific ATP output are advantageous in this relatively thin section of the body. PMID:10861548
Error analysis of leaf area estimates made from allometric regression models
NASA Technical Reports Server (NTRS)
Feiveson, A. H.; Chhikara, R. S.
1986-01-01
Biological net productivity, measured in terms of the change in biomass with time, affects global productivity and the quality of life through biochemical and hydrological cycles and by its effect on the overall energy balance. Estimating leaf area for large ecosystems is one of the more important means of monitoring this productivity. For a particular forest plot, the leaf area is often estimated by a two-stage process. In the first stage, known as dimension analysis, a small number of trees are felled so that their areas can be measured as accurately as possible. These leaf areas are then related to non-destructive, easily-measured features such as bole diameter and tree height, by using a regression model. In the second stage, the non-destructive features are measured for all or for a sample of trees in the plots and then used as input into the regression model to estimate the total leaf area. Because both stages of the estimation process are subject to error, it is difficult to evaluate the accuracy of the final plot leaf area estimates. This paper illustrates how a complete error analysis can be made, using an example from a study made on aspen trees in northern Minnesota. The study was a joint effort by NASA and the University of California at Santa Barbara known as COVER (Characterization of Vegetation with Remote Sensing).
Local Linear Observed-Score Equating
ERIC Educational Resources Information Center
Wiberg, Marie; van der Linden, Wim J.
2011-01-01
Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…
Behavioral and phylogenetic implications of a narrow allometric study of Ardipithecus ramidus.
Sarmiento, E E; Meldrum, D J
2011-04-01
Narrow allometry is used to compare Ardipithecus ramidus molar and body segment lengths and proportions to those of living primates, with the goal of reconstructing fossil behavior and exploring how lengths and proportions bear on phylogeny. Comparatively short hands and upper limbs suggest Ardipithecus was less adept at forelimb suspension and vertical climbing than are great apes. Its tibial and tarsal lengths, suggest bonobo-like leaping ability. Its short lower limbs, but long toes relative to humans, are not conducive to habitual bipedality. When terrestrial, Ardipithecus would have engaged in palmigrade quadrupedality. Compared to the semi-digitigrade baboon its long fingers and toes suggest a less marked terrestrial commitment and agree with carpal anatomy reflecting full palmigrady. Molar dimensions and surface areas are similar to those of baboons and drills, but greater than in chimpanzees, indicating a diet with less fruit and more roughage than that of chimpanzees. Ardipithecus dimensions reflect a generalized ape, able to move in trees and on the ground, and exploit food sources in woodlands, grasslands and/or flooded terrain. These abilities are well-suited to the mosaic habitats that characterize Africa at 11°N. Parsimonious reconstruction of the common human/African ape ancestor suggests the short upper limbs and metacarpals of Ardipithecus are too derived to belong to an exclusive human ancestor. Because parsimony is a theoretical construct and not an evolutionary reality, derived segment lengths alone do not prove conclusively Ardipithecus is not such an ancestor. Description in Ardipithecus of complex anatomy uniquely shared by humans and African apes, that leaves a record of reversals or parallelisms, would be a first step in showing whether this fossil qualifies as such an ancestor.
ERIC Educational Resources Information Center
McInerney, Valentina; Marsh, Herbert W.; McInerney, Dennis M.
This paper discusses the process through which a powerful multidimensional measure of affect and cognition in relation to adult learning of computing skills was derived from its early theoretical stages to its validation using structural equation modeling. The discussion emphasizes the importance of ensuring a strong substantive base from which to…
Nonlocal electrical diffusion equation
NASA Astrophysics Data System (ADS)
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.
2016-07-01
In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.
Phillips, Darci; Covian, Raul; Aponte, Angel M.; Glancy, Brian; Taylor, Joni F.; Chess, David
2012-01-01
The concentration of mitochondrial oxidative phosphorylation complexes (MOPCs) is tuned to the maximum energy conversion requirements of a given tissue; however, whether the activity of MOPCs is altered in response to acute changes in energy conversion demand is unclear. We hypothesized that MOPCs activity is modulated by tissue metabolic stress to maintain the energy-metabolism homeostasis. Metabolic stress was defined as the observed energy conversion rate/maximum energy conversion rate. The maximum energy conversion rate was assumed to be proportional to the concentration of MOPCs, as determined with optical spectroscopy, gel electrophoresis, and mass spectrometry. The resting metabolic stress of the heart and liver across the range of resting metabolic rates within an allometric series (mouse, rabbit, and pig) was determined from MPOCs content and literature respiratory values. The metabolic stress of the liver was high and nearly constant across the allometric series due to the proportional increase in MOPCs content with resting metabolic rate. In contrast, the MOPCs content of the heart was essentially constant in the allometric series, resulting in an increasing metabolic stress with decreasing animal size. The MOPCs activity was determined in native gels, with an emphasis on Complex V. Extracted MOPCs enzyme activity was proportional to resting metabolic stress across tissues and species. Complex V activity was also shown to be acutely modulated by changes in metabolic stress in the heart, in vivo and in vitro. The modulation of extracted MOPCs activity suggests that persistent posttranslational modifications (PTMs) alter MOPCs activity both chronically and acutely, specifically in the heart. Protein phosphorylation of Complex V was correlated with activity inhibition under several conditions, suggesting that protein phosphorylation may contribute to activity modulation with energy metabolic stress. These data are consistent with the notion that metabolic
Simplified Relativistic Force Transformation Equation.
ERIC Educational Resources Information Center
Stewart, Benjamin U.
1979-01-01
A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…
Isothermal Equation Of State For Compressed Solids
NASA Technical Reports Server (NTRS)
Vinet, Pascal; Ferrante, John
1989-01-01
Same equation with three adjustable parameters applies to different materials. Improved equation of state describes pressure on solid as function of relative volume at constant temperature. Even though types of interatomic interactions differ from one substance to another, form of equation determined primarily by overlap of electron wave functions during compression. Consequently, equation universal in sense it applies to variety of substances, including ionic, metallic, covalent, and rare-gas solids. Only three parameters needed to describe equation for given material.
Shore, B.W.
1981-01-30
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence.
NASA Astrophysics Data System (ADS)
Yesilova, Abdullah; Yilmaz, Ayhan
In this study, the Poison regression, negative binomial regression and generalized estimating equations were applied to the repeated measurements based on count data obtained from the sexual behaviors of ram lambs. Negative binomial regression was more effective to handle the over dispersion that causes bias in parameter estimations in Poison regression. The generalized estimating equations were used for analyzing repeated categorical data. GEE estimates were obtained by using the exchangeable working correlation. As a result of GEE analyses, it was concluded that flehmen lip curl response, tail raising, mount duration, vocalization and weight of the ram lamb were statistically important (p<0.05) for mount frequent. However, the anogenital sniff found be not significant.
Higher derivative gravity: Field equation as the equation of state
NASA Astrophysics Data System (ADS)
Dey, Ramit; Liberati, Stefano; Mohd, Arif
2016-08-01
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. The extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher-curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism-invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.
Investigation of the kinetic model equations
NASA Astrophysics Data System (ADS)
Liu, Sha; Zhong, Chengwen
2014-03-01
Currently the Boltzmann equation and its model equations are widely used in numerical predictions for dilute gas flows. The nonlinear integro-differential Boltzmann equation is the fundamental equation in the kinetic theory of dilute monatomic gases. By replacing the nonlinear fivefold collision integral term by a nonlinear relaxation term, its model equations such as the famous Bhatnagar-Gross-Krook (BGK) equation are mathematically simple. Since the computational cost of solving model equations is much less than that of solving the full Boltzmann equation, the model equations are widely used in predicting rarefied flows, multiphase flows, chemical flows, and turbulent flows although their predictions are only qualitatively right for highly nonequilibrium flows in transitional regime. In this paper the differences between the Boltzmann equation and its model equations are investigated aiming at giving guidelines for the further development of kinetic models. By comparing the Boltzmann equation and its model equations using test cases with different nonequilibrium types, two factors (the information held by nonequilibrium moments and the different relaxation rates of high- and low-speed molecules) are found useful for adjusting the behaviors of modeled collision terms in kinetic regime. The usefulness of these two factors are confirmed by a generalized model collision term derived from a mathematical relation between the Boltzmann equation and BGK equation that is also derived in this paper. After the analysis of the difference between the Boltzmann equation and the BGK equation, an attempt at approximating the collision term is proposed.
NASA Astrophysics Data System (ADS)
Simos, T. E.; Aguiar, Jesus Vigo
In this paper, a new approach for developing efficient Runge-Kutta-Nyström methods is introduced. This new approach is based on the requirement of annihilation of the phase-lag (i.e., the phase-lag is of order infinity) and on a modification of Runge-Kutta-Nyström methods. Based on this approach, a new modified Runge-Kutta-Nyström fourth algebraic order method is developed for the numerical solution of Schrödinger equation and related problems. The new method has phase-lag of order infinity and extended interval of periodicity. Numerical illustrations on the radial Schrödinger equation and related problems with oscillating solutions indicate that the new method is more efficient than older ones.
NASA Astrophysics Data System (ADS)
Drozd-Rzoska, Aleksandra; Rzoska, Sylwester J.
A consistent set of temperature- (T), pressure- (P), volume- (V) and density- (ρ) related VFT-type equations for portraying the evolution of the structural relaxation time or viscosity is presented, namely: andτ (V) = τ 0 exp[D T (V SL — V)(V 0 V SL )/(V — V 0)], where T 0,P 0,V 0 and ρ0 are VFT estimates of the ideal glass loci and T SL , P SL , V SL and ρ SL are estimates of the location of the absolute stability limit, partially hidden in the negative pressures domain (P<0). For these equations prefactors are well defined via ρ 0 = ρ (T SL ,P SL , V SL ,ρ SL ), ie. they are linked to the absolute stability limit loci (gas-liquid spinodal). Noteworthy is their smooth transformation into VFT-type equations, used so far, on approaching the glass transition, and into Arrhenius-type equations remote from the glass transition, on approaching the absolute stability limit. The latter may suggest the re-examination of experimental data suggesting the VFT-to-Arrhenius crossover far away from the glass transition. Novel VFT counterparts also lead to the consistent set of fragility strength coefficients (D T ,D P ,D V ,D ρ) and fragilities associated with the slope (steepness index) at appropriate "Angell plot" counterparts.
Fitness consequences of artificial selection on relative male genital size.
Booksmythe, Isobel; Head, Megan L; Keogh, J Scott; Jennions, Michael D
2016-01-01
Male genitalia often show remarkable differences among related species in size, shape and complexity. Across poeciliid fishes, the elongated fin (gonopodium) that males use to inseminate females ranges from 18 to 53% of body length. Relative genital size therefore varies greatly among species. In contrast, there is often tight within-species allometric scaling, which suggests strong selection against genital-body size combinations that deviate from a species' natural line of allometry. We tested this constraint by artificially selecting on the allometric intercept, creating lines of males with relatively longer or shorter gonopodia than occur naturally for a given body size in mosquitofish, Gambusia holbrooki. We show that relative genital length is heritable and diverged 7.6-8.9% between our up-selected and down-selected lines, with correlated changes in body shape. However, deviation from the natural line of allometry does not affect male success in assays of attractiveness, swimming performance and, crucially, reproductive success (paternity). PMID:27188478
Makowitz, H.
1992-10-01
We have studied various formulations of the concept of pressure, in the context of the usual Six-Equation Model of thermal-hydraulics. A different concept of pressure, than the usual one, has been used. This new pressure concept is Galilean Invariant, and results for the One-Pressure Model with the same complex characteristic roots as the ``Basic III-Posed Model,`` discussed in the literature for the cases we have investigated. We have also examined several Two-Pressure formulations and shown that two pressures are a necessary but not sufficient condition for obtaining a Well-Posed system. Several counter examples are presented. We have shown that the standard theory is not Galilean Invariant and suggested that the origin of III-Posedness is due to our closure relationships. We also question whether the current theory can satisfy conservation principles for mass, energy, and momentum.
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1981-01-01
Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.
Students' Equation Understanding and Solving in Iran
ERIC Educational Resources Information Center
Barahmand, Ali; Shahvarani, Ahmad
2014-01-01
The purpose of the present article is to investigate how 15-year-old Iranian students interpret the concept of equation, its solution, and studying the relation between the students' equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between…
Local Observed-Score Kernel Equating
ERIC Educational Resources Information Center
Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.
2014-01-01
Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…
Pavement performance equations. Final report
Mahoney, J.P.; Kay, R.K.; Jackson, N.C.
1988-03-01
The WSDOT PMS data base was used to develop regression equations for three pavement surface types: bituminous surface treatments, asphalt concrete, and portland-cement concrete. The primary regression equations developed were to predict Pavement Condition Rating (PCR) which is a measure of the pavement surface distress (ranges from 100 (no distress) to below 0 (extensive distress)). Overall, the equations fit the data rather well given the expected variation of pavement performance information. The relative effects of age (time since construction or reconstruction) were illustrated for the three surface types.
Silva, Simonete; Bustamante, Alcibíades; Nevill, Alan; Katzmarzyk, Peter T.; Freitas, Duarte; Prista, António; Maia, José
2016-01-01
Children from developed and developing countries differ in their body size and shape due to marked differences across their life history caused by social, economic and cultural differences which are also linked to their motor performance (MP). We used allometric models to identify size/shape characteristics associated with MP tests between Brazilian and Peruvian schoolchildren. A total of 4,560 subjects, 2,385 girls and 2,175 boys aged 9–15 years were studied. Height and weight were measured; biological maturation was estimated with the maturity offset technique; MP measures included the 12 minute run (12MR), handgrip strength (HG), standing long jump (SLJ) and the shuttle run speed (SR) tests; physical activity (PA) was assessed using the Baecke questionnaire. A multiplicative allometric model was adopted to adjust for body size differences across countries. Reciprocal ponderal index (RPI) was found to be the most suitable body shape indicator associated with the 12MR, SLJ, HG and SR performance. A positive maturation offset parameter was also associated with a better performance in SLJ, HG and SR tests. Sex differences were found in all motor tests. Brazilian youth showed better scores in MP than their Peruvian peers, even when controlling for their body size differences The current study identified the key body size associated with four body mass-dependent MP tests. Biological maturation and PA were associated with strength and motor performance. Sex differences were found in all motor tests, as well as across countries favoring Brazilian children even when accounting for their body size/shape differences. PMID:26939118
Silva, Simonete; Bustamante, Alcibíades; Nevill, Alan; Katzmarzyk, Peter T; Freitas, Duarte; Prista, António; Maia, José
2016-01-01
Children from developed and developing countries differ in their body size and shape due to marked differences across their life history caused by social, economic and cultural differences which are also linked to their motor performance (MP). We used allometric models to identify size/shape characteristics associated with MP tests between Brazilian and Peruvian schoolchildren. A total of 4,560 subjects, 2,385 girls and 2,175 boys aged 9-15 years were studied. Height and weight were measured; biological maturation was estimated with the maturity offset technique; MP measures included the 12 minute run (12MR), handgrip strength (HG), standing long jump (SLJ) and the shuttle run speed (SR) tests; physical activity (PA) was assessed using the Baecke questionnaire. A multiplicative allometric model was adopted to adjust for body size differences across countries. Reciprocal ponderal index (RPI) was found to be the most suitable body shape indicator associated with the 12MR, SLJ, HG and SR performance. A positive maturation offset parameter was also associated with a better performance in SLJ, HG and SR tests. Sex differences were found in all motor tests. Brazilian youth showed better scores in MP than their Peruvian peers, even when controlling for their body size differences The current study identified the key body size associated with four body mass-dependent MP tests. Biological maturation and PA were associated with strength and motor performance. Sex differences were found in all motor tests, as well as across countries favoring Brazilian children even when accounting for their body size/shape differences. PMID:26939118
ERIC Educational Resources Information Center
Cetin, Bayram; Eroglu, Yuksel; Peker, Adem; Akbaba, Sirri; Pepsoy, Sevim
2012-01-01
The aim of this study is to investigate the effect of relational-interdependent self-construal on cyberbullying and the effect of cyberbullying on psychological disharmony. Participants were 258 high school students. In this study, the Relational-Interdependent Self-Construal Scale, the Revised Cyberbullying Inventory, and the Depression, Anxiety,…
Militzer, B.; Hubbard, W. B.
2013-09-10
Using density functional molecular dynamics simulations, we determine the equation of state (EOS) for hydrogen-helium mixtures spanning density-temperature conditions typical of giant-planet interiors, {approx}0.2-9 g cm{sup -3} and 1000-80,000 K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy using an ab initio thermodynamic integration technique. A comprehensive EOS table with 391 density-temperature points is constructed and the results are presented in the form of a two-dimensional free energy fit for interpolation. Deviations between our ab initio EOS and the semi-analytical EOS model by Saumon and Chabrier are analyzed in detail, and we use the results for initial revision of the inferred thermal state of giant planets with known values for mass and radius. Changes are most pronounced for planets in the Jupiter mass range and below. We present a revision to the mass-radius relationship that makes the hottest exoplanets increase in radius by {approx}0.2 Jupiter radii at fixed entropy and for masses greater than {approx}0.5 Jupiter mass. This change is large enough to have possible implications for some discrepant ''inflated giant exoplanets''.
NASA Astrophysics Data System (ADS)
Zeyer, Albert; Bölsterli, Katrin; Brovelli, Dorothee; Odermatt, Freia
2012-03-01
Sex is considered to be one of the most significant factors influencing attitudes towards science. However, the so-called brain type approach from cognitive science suggests that the difference in motivation to learn science does not primarily differentiate the girls from the boys, but rather the so-called systemisers from the empathizers. The present study investigates this hypothesis by using structural equation modelling on a sex-stratified sample of 500 male and female students of secondary II level. The results show, that the motivation to learn science is directly influenced by the systemizing quotient SQ, but not by sex. The impact of sex on the motivation to learn science, measured by five key concepts, only works indirectly, namely through the influence of sex on the SQ. The empathizing quotient (EQ) has no impact on the motivation to learn science. The SQ explains between 13 and 23 percent of the variation of the five key constructs. In female students, the impact of the SQ is very similar for all key concepts. In male students, it is highest for self-efficacy and lowest for assessment anxiety. The motivation to learn science is significantly larger for male students in all involved SMQ key concepts, but the difference is small. The interpretation of these findings and conclusions for science teaching and further research are discussed.
NASA Astrophysics Data System (ADS)
Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem
2016-05-01
``The nature has two magnitudes and two elongations, one is gradual being (wavy-like motion) which belongs to the time and dividable to the former and the next times in mind, and the other one is jerky-like motion which belongs to the space and dividable to the former and the next places'' [Asfar, Mulla Sadra, (1571/2-1640)]. These two separated natures of space-time are matched on wave-particle duality. Therefore, the nature of time can be wavy-like and the nature of space can be jerky-like. So, there are two independent variable sources of particle(s)' flow while they are match exactly with each other. These two sources are potential of flow and potential of time (relative time) which vary with respect to both space and time. Here, we propose two additional parts to Schrodinger's equation with respect to relative time: HΨ + ∇t' = EΨ + ∂t' / ∂t , where t is time and t' is relative time: t' = t +/- Δt [Gholibeigian et al., APS March Meeting 2016], which for each atom becomes: tatom = ∑mnucleons + ∑melectrons where m is momentum [Gholibeigian, APS March Meeting 2015, abstract #V1.023]. Using time's relativity in Schrodinger equation will give us more precious results. AmirKabir University of Technology,Tehran, Iran.
ERIC Educational Resources Information Center
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Titon, Braz; Gomes, Fernando Ribeiro
2015-01-01
Amphibian species richness increases toward the equator, particularly in humid tropical forests. This relation between amphibian species richness and environmental water availability has been proposed to be a consequence of their high rates of evaporative water loss. In this way, traits that estimate water balance are expected to covary with climate and constrain a species’ geographic distribution. Furthermore, we predicted that coexisting species of anurans would have traits that are adapted to local hydric conditions. We compared the traits that describe water balance in 17 species of anurans that occur in the mesic Atlantic Forest and xeric Cerrado (savannah) habitats of Brazil. We predicted that species found in the warmer and dryer areas would show a lower sensitivity of locomotor performance to dehydration (SLPD), increased resistance to evaporative water loss (REWL) and higher rates of water uptake (RWU) than species restricted to the more mesic areas. We estimated the allometric relations between the hydric traits and body mass using phylogenetic generalized least squares. These regressions showed that REWL scaled negatively with body mass, whereas RWU scaled positively with body mass. Additionally, species inhabiting areas characterized by higher and more seasonally uniform temperatures, and lower and more seasonally concentrated precipitation, such as the Cerrado, had higher RWU and SLPD than species with geographical distributions more restricted to mesic environments, such as the Atlantic Forest. These results support the hypothesis that the interspecific variation of physiological traits shows an adaptation pattern to abiotic environmental traits. PMID:26469787
Kinetic energy equations for the average-passage equation system
NASA Technical Reports Server (NTRS)
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
The zero dispersion limits of nonlinear wave equations
Tso, T.
1992-01-01
In chapter 2 the author uses functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schroedinger equation for initial data that satisfy some suitable conditions. In chapter 3 the energy estimates are used to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H[sup 3](R) as [epsilon] [yields] 0; also, it is shown that the strong L[sup 2](R)-limit of the solutions of the BBM equation as [epsilon] [yields] 0 before a critical time. In chapter 4 the author uses the Whitham modulation theory and averaging method to find the 2[pi]-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. It is shown that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, the relations are studied of the KdV equation and the mKdV equation. Finally, the author studies the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.
Asymptotic-preserving Boltzmann model equations for binary gas mixture.
Liu, Sha; Liang, Yihua
2016-02-01
An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations. PMID:26986408
IKT for quantum hydrodynamic equations
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Ellero, Marco; Nicolini, Piero
2007-11-01
A striking feature of standard quantum mechanics (SQM) is its analogy with classical fluid dynamics. In fact, it is well-known that the Schr"odinger equation is equivalent to a closed set of partial differential equations for suitable real-valued functions of position and time (denoted as quantum fluid fields) [Madelung, 1928]. In particular, the corresponding quantum hydrodynamic equations (QHE) can be viewed as the equations of a classical compressible and non-viscous fluid, endowed with potential velocity and quantized velocity circulation. In this reference, an interesting theoretical problem, in its own right, is the construction of an inverse kinetic theory (IKT) for such a type of fluids. In this note we intend to investigate consequences of the IKT recently formulated for QHE [M.Tessarotto et al., Phys. Rev. A 75, 012105 (2007)]. In particular a basic issue is related to the definition of the quantum fluid fields.
ERIC Educational Resources Information Center
Chen, Haiwen
2012-01-01
In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…
Reflections on Chemical Equations.
ERIC Educational Resources Information Center
Gorman, Mel
1981-01-01
The issue of how much emphasis balancing chemical equations should have in an introductory chemistry course is discussed. The current heavy emphasis on finishing such equations is viewed as misplaced. (MP)
Interpretation of Bernoulli's Equation.
ERIC Educational Resources Information Center
Bauman, Robert P.; Schwaneberg, Rolf
1994-01-01
Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)
NASA Astrophysics Data System (ADS)
Gholibeigian, Hassan; Gholibeigian, Kazem
2016-03-01
In Sadra's theory, the relative time for an atom (body) which is varying continuously becomes momentums of its involved fundamental particles (strings), (time's relativity) [Gholibeigian, APS March Meeting 2015, abstract #V1.023]. Einstein's theory of special relativity might be special form of Sadra's theory. ``The nature has two magnitudes and two elongations, the one is gradual being (wavy-like motion) which belongs to the time and dividable to the former and the next times in mind, and the other is jerky-like motion which belongs to the space and dividable to the former and the next places'' [Asfar, Mulla Sadra, (1571/2-1640)]. Sadra separated the nature of time from nature of space. Therefore we can match these two natures on wave-particle duality. It means that the nature of time might be wavy-like and the nature of space might be jerky-like. So, there are two independent variable sources for particle(s)' flow with respect of its two natures such as potential of flow and relative time which vary with respect of both space and time. Consequently we propose two additional parts to Schrodinger's equation: H⌢ Ψ +tp ∇t' = ih/2 π ∂/∂t Ψ +tp∂/∂t t' , where tp is Planck's time and t' is relative time: t' = f (m , v , t) = t +/- Δt , in which t is time, m is mass and vis speed of particle . AmirKabir University of Technology, Tehran, Iran.
NASA Astrophysics Data System (ADS)
Cardona, Carlos; Gomez, Humberto
2016-06-01
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
Differential Equations for Morphological Amoebas
NASA Astrophysics Data System (ADS)
Welk, Martin; Breuß, Michael; Vogel, Oliver
This paper is concerned with amoeba median filtering, a structure-adaptive morphological image filter. It has been introduced by Lerallut et al. in a discrete formulation. Experimental evidence shows that iterated amoeba median filtering leads to segmentation-like results that are similar to those obtained by self-snakes, an image filter based on a partial differential equation. We investigate this correspondence by analysing a space-continuous formulation of iterated median filtering. We prove that in the limit of vanishing radius of the structuring elements, iterated amoeba median filtering indeed approximates a partial differential equation related to self-snakes and the well-known (mean) curvature motion equation. We present experiments with discrete iterated amoeba median filtering that confirm qualitative and quantitative predictions of our analysis.
NASA Astrophysics Data System (ADS)
Kostov, Ivan; Serban, Didina; Volin, Dmytro
2008-08-01
We give a realization of the Beisert, Eden and Staudacher equation for the planar Script N = 4 supersymetric gauge theory which seems to be particularly useful to study the strong coupling limit. We are using a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotański. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.
Einstein equation at singularities
NASA Astrophysics Data System (ADS)
Stoica, Ovidiu-Cristinel
2014-02-01
Einstein's equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein's equation and the metric tensor).
Solving Ordinary Differential Equations
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Euler's Amazing Way to Solve Equations.
ERIC Educational Resources Information Center
Flusser, Peter
1992-01-01
Presented is a series of examples that illustrate a method of solving equations developed by Leonhard Euler based on an unsubstantiated assumption. The method integrates aspects of recursion relations and sequences of converging ratios and can be extended to polynomial equation with infinite exponents. (MDH)
How Should Equation Balancing Be Taught?
ERIC Educational Resources Information Center
Porter, Spencer K.
1985-01-01
Matrix methods and oxidation-number methods are currently advocated and used for balancing equations. This article shows how balancing equations can be introduced by a third method which is related to a fundamental principle, is easy to learn, and is powerful in its application. (JN)
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
Some remarks on unilateral matrix equations
Cerchiai, Bianca L.; Zumino, Bruno
2001-02-01
We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials.
On some differential transformations of hypergeometric equations
NASA Astrophysics Data System (ADS)
Hounkonnou, M. N.; Ronveaux, A.
2015-04-01
Many algebraic transformations of the hypergeometric equation σ(x)z"(x) + τ(x)z'(x) + lz(x) = 0, where σ, τ, l are polynomial functions of degrees 2 (at most), 1, 0, respectively, are well known. Some of them involve x = x(t), a polynomial of degree r, in order to recover the Heun equation, extension of the hypergeometric equation by one more singularity. The case r = 2 was investigated by K. Kuiken (see 1979 SIAM J. Math. Anal. 10 (3) 655-657) and extended to r = 3,4, 5 by R. S. Maier (see 2005 J. Differ. Equat. 213 171 - 203). The transformations engendered by the function y(x) = A(x)z(x), also very popular in mathematics and physics, are used to get from the hypergeometric equation, for instance, the Schroedinger equation with appropriate potentials, as well as Heun and confluent Heun equations. This work addresses a generalization of Kimura's approach proposed in 1971, based on differential transformations of the hypergeometric equations involving y(x) = A(x)z(x) + B(x)z'(x). Appropriate choices of A(x) and B(x) permit to retrieve the Heun equations as well as equations for some exceptional polynomials. New relations are obtained for Laguerre and Hermite polynomials.
Stochastic differential equation model to Prendiville processes
Granita; Bahar, Arifah
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Yagi, M.; Horton, W. )
1994-07-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite [beta] that the perpendicular component of Ohm's law be solved to ensure [del][center dot][bold j]=0 for energy conservation.
Uniqueness of Maxwell's Equations.
ERIC Educational Resources Information Center
Cohn, Jack
1978-01-01
Shows that, as a consequence of two feasible assumptions and when due attention is given to the definition of charge and the fields E and B, the lowest-order equations that these two fields must satisfy are Maxwell's equations. (Author/GA)
Explicit integration of Friedmann's equation with nonlinear equations of state
NASA Astrophysics Data System (ADS)
Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong
2015-05-01
In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of important, yet not previously touched, problems will be worked out which include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born-Infeld, two-fluid models, and Chern-Simons modified gravity theory models. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution which may also offer clues to a profound understanding of the problems in general settings. For example, in the Chaplygin gas universe, a few integrable cases lead us to derive a universal formula for the asymptotic exponential growth rate of the scale factor, of an explicit form, whether the Friedmann equation is integrable or not, which reveals the coupled roles played by various physical sectors and it is seen that, as far as there is a tiny presence of nonlinear matter, conventional linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.
NASA Astrophysics Data System (ADS)
Sullivan, F. B.; Palace, M. W.; Ducey, M.; Czarnecki, C.; Zanin Shimbo, J.; Mota e Silva, J.
2012-12-01
Tropical forests are considered to be some of the most structurally complex forests in the world. Understanding vegetation height structure in these forests can aid in understanding the spatial temporal components of disturbance, from blowdowns to gap dynamics. Vegetation profiles can be used to better estimate carbon storage and flux across the landscape. Using light detection and ranging (lidar) data collected at La Selva, Costa Rica from four instruments (three airborne, one terrestrial) at four times since 2005, and field data collected in January 2012, we generated relative vegetation profiles for twenty plots in La Selva. Relative vegetation profiles were derived from lidar data by accounting for obscured plant material through a log transformation of the cumulative proportion of observations (percent canopy closure). Profiles were derived from field data using two different sets of allometric equations describing crown shape and tree height. We conducted a cluster analysis on similarity matrices developed in R (version 2.14.1) using three different metrics (sum of squares, Kullback-Leibler divergence, Kolmogorov-Smirnov D statistic) and identified general similarity between lidar profiles. Results were consistent across each of the three similarity metrics. Three distinct clusters were found, with profiles from three airborne lidar instruments, two profiles from a terrestrial lidar instrument, and profiles derived from field data forming the clusters. Our results indicate that although estimating lidar relative vegetation profiles from field data was not possible, terrestrial lidar relative vegetation profiles are generally similar to airborne relative vegetation profiles. Given the rapidity and repeatability of terrestrial lidar measurements, these results show promise for terrestrial lidar instruments to collect plot-specific data on forest structure and vertical distribution of plant material. Furthermore, identifying relationships between terrestrial and
NASA Astrophysics Data System (ADS)
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Perceptions of the Schrodinger equation
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2014-03-01
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived as the quantum equivalent of the non-relativistic classical energy relation. We argue that the Schrodinger equation cannot be a physical postulate, and we show explicitly that its second space derivative term is wrongly associated with the kinetic energy of the particle. The kinetic energy of a particle at a point is proportional to the square of the momentum, that is, to the square of the first space derivative of the wavefunction. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. In simple interaction settings we can tell what particle motions arise and can explain the outcomes in direct and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.
A generalized simplest equation method and its application to the Boussinesq-Burgers equation.
Sudao, Bilige; Wang, Xiaomin
2015-01-01
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.
A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation
Sudao, Bilige; Wang, Xiaomin
2015-01-01
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605
NASA Astrophysics Data System (ADS)
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Nonlinear differential equations
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Baker, J F; Bryson, W L; Sanders, J O; Dahm, P F; Cartwright, T C; Ellis, W C; Long, C R
1991-08-01
Slaughter and carcass data were obtained on 197 bulls produced in a diallel involving Angus, Brahman, Hereford, Holstein and Jersey that were slaughtered at either 6, 9, 12, 15, 18, 24, or 30 mo of age. Bulls were given ad libitum access to a 72% TDN diet on an individual basis from 6 mo of age until slaughter. Empty body weight (EBWT) was determined as the sum of the weights of blood, hide, hard drop, soft drop (minus contents of the digestive tract), and carcass weight (CWT), which were recorded at slaughter. Carcass protein (CPROT) and fat (CFAT) were based on weights and chemical analyses of lean and fat tissue and bone of the carcass. Empty body protein (EBPROT) and fat (EBFAT) were based on weights and chemical estimates of the components of the empty body. Growth of EBWT, EBPROT, EBFAT, CWT, CPROT, and CFAT relative to either live weight (LWT), EBWT, or CWT were investigated using the allometric equation. Breed-type differences existed (P less than .01) for the growth of EBWT relative to LWT. Comparisons of general combining abilities revealed that Angus, Hereford, and Jersey generally had lower maturing rates of EBWT relative to LWT and that Brahman and Holstein had higher maturing rates. Across breed-type, relative growth rates indicated that fat and protein were later-maturing components relative to LWT, EBWT, or CWT, which implies that other components mature relatively earlier. Relative maturing rates of components studied were not important in explaining differences in body composition that have been previously reported for these breed-types. PMID:1894551
Baker, J F; Bryson, W L; Sanders, J O; Dahm, P F; Cartwright, T C; Ellis, W C; Long, C R
1991-08-01
Slaughter and carcass data were obtained on 197 bulls produced in a diallel involving Angus, Brahman, Hereford, Holstein and Jersey that were slaughtered at either 6, 9, 12, 15, 18, 24, or 30 mo of age. Bulls were given ad libitum access to a 72% TDN diet on an individual basis from 6 mo of age until slaughter. Empty body weight (EBWT) was determined as the sum of the weights of blood, hide, hard drop, soft drop (minus contents of the digestive tract), and carcass weight (CWT), which were recorded at slaughter. Carcass protein (CPROT) and fat (CFAT) were based on weights and chemical analyses of lean and fat tissue and bone of the carcass. Empty body protein (EBPROT) and fat (EBFAT) were based on weights and chemical estimates of the components of the empty body. Growth of EBWT, EBPROT, EBFAT, CWT, CPROT, and CFAT relative to either live weight (LWT), EBWT, or CWT were investigated using the allometric equation. Breed-type differences existed (P less than .01) for the growth of EBWT relative to LWT. Comparisons of general combining abilities revealed that Angus, Hereford, and Jersey generally had lower maturing rates of EBWT relative to LWT and that Brahman and Holstein had higher maturing rates. Across breed-type, relative growth rates indicated that fat and protein were later-maturing components relative to LWT, EBWT, or CWT, which implies that other components mature relatively earlier. Relative maturing rates of components studied were not important in explaining differences in body composition that have been previously reported for these breed-types.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Set Equation Transformation System.
2002-03-22
Version 00 SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protectionmore » requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. Two auxiliary programs, SEP and FTD, are included. SEP performs the quantitative analysis of reduced Boolean equations (minimal cut sets) produced by SETS. The user can manipulate and evaluate the equations to find the probability of occurrence of any desired event and to produce an importance ranking of the terms and events in an equation. FTD is a fault tree drawing program which uses the proprietary ISSCO DISSPLA graphics software to produce an annotated drawing of a fault tree processed by SETS. The DISSPLA routines are not included.« less
Planck-scale corrections to Friedmann equation
NASA Astrophysics Data System (ADS)
Awad, Adel; Ali, Ahmed
2014-04-01
Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde's proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde's proposal and two known models of GUPs, we obtain modifications to Newton's law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.
Solution Methods for Certain Evolution Equations
NASA Astrophysics Data System (ADS)
Vega-Guzman, Jose Manuel
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value
Introducing Chemical Formulae and Equations.
ERIC Educational Resources Information Center
Dawson, Chris; Rowell, Jack
1979-01-01
Discusses when the writing of chemical formula and equations can be introduced in the school science curriculum. Also presents ways in which formulae and equations learning can be aided and some examples for balancing and interpreting equations. (HM)
The Bernoulli-Poiseuille Equation.
ERIC Educational Resources Information Center
Badeer, Henry S.; Synolakis, Costas E.
1989-01-01
Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)
Constitutive equations for discrete electromagnetic problems over polyhedral grids
Codecasa, Lorenzo . E-mail: codecasa@elet.polimi.it; Trevisan, Francesco . E-mail: trevisan@uniud.it
2007-08-10
In this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field problem. The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations. In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual grid. Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations of the electromagnetic field.
Pierantozzi, T.; Vazquez, L.
2005-11-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
Maxwell Equations and the Redundant Gauge Degree of Freedom
ERIC Educational Resources Information Center
Wong, Chun Wa
2009-01-01
On transformation to the Fourier space (k,[omega]), the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the…
The structure of constitutive equations for semiconductor devices
Buchanan, G.R.; Girrens, S.P.; Bennett, J.G.
1987-01-01
The fundamental equations that describe carrier transport in semiconductor materials are developed using the methods of continuum mixture theory and Maxwell's equations for electrodynamics. There are five basic equations that govern the behavior of current flux, electrostatic potential, electrons, and holes. The bahavior of the electrical chemical potentials are introduced and their relation to the current flux is discussed.
Using worksheets to solve the Einstein equation
NASA Astrophysics Data System (ADS)
Moore, Thomas A.
2016-05-01
This article describes how one can use worksheets to guide undergraduate students through the process of finding solutions to specific cases of the Einstein equation of general relativity. The worksheets provide expressions for a metric's Christoffel symbols and Ricci tensor components for fairly general metrics. Students can use a worksheet to adapt these expressions to specific cases where symmetry or other considerations constrain the metric components' dependencies, and then use the worksheet's results to reduce the Einstein equation to a set of simpler differential equations that they can solve. This article illustrates the process for both a diagonal metric and a metric with one off-diagonal element.
Fractional diffusion equations coupled by reaction terms
NASA Astrophysics Data System (ADS)
Lenzi, E. K.; Menechini Neto, R.; Tateishi, A. A.; Lenzi, M. K.; Ribeiro, H. V.
2016-09-01
We investigate the behavior for a set of fractional reaction-diffusion equations that extend the usual ones by the presence of spatial fractional derivatives of distributed order in the diffusive term. These equations are coupled via the reaction terms which may represent reversible or irreversible processes. For these equations, we find exact solutions and show that the spreading of the distributions is asymptotically governed by the same the long-tailed distribution. Furthermore, we observe that the coupling introduced by reaction terms creates an interplay between different diffusive regimes leading us to a rich class of behaviors related to anomalous diffusion.
NASA Technical Reports Server (NTRS)
Brown, James L.; Naughton, Jonathan W.
1999-01-01
A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.
Braverman, Eric R; Chen, Thomas J H; Prihoda, Thomas J; Sonntag, William; Meshkin, Brian; Downs, B William; Mengucci, Julie F; Blum, Seth H; Notaro, Alison; Arcuri, Vanessa; Varshavskiy, Michael; Blum, Kenneth
2007-09-01
A review of the literature in both animals and humans reveals that changes in sex hormone have often been associated with changes in behavioral and mental abilities. Previously published research from our laboratory, and others, provides strong evidence that P300 (latency) event-related potential (ERP), a marker of neuronal processing speed, is an accurate predictor of early memory impairment in both males and females across a wide age range. It is our hypothesis, given the vast literature on the subject, that coupling growth hormones (insulin-like growth factor-I, (IGF-I) and insulin-like growth factor binding protein 3 (IGF-BP3)), P300 event-related potential and test of variables of attention (TOVA) are important neuroendocrinological predictors of early cognitive decline in a clinical setting. To support this hypothesis, we utilized structural equation modeling (SEM) parameter estimates to determine the relationship between aging and memory, as mediated by growth hormone (GH) levels (indirectly measured through the insulin-like growth factor system), P300 latency and TOVA, putative neurocognitive predictors tested in this study. An SEM was developed hypothesizing a causal directive path, leading from age to memory, mediated by IGF-1 and IGF-BP3, P300 latency (speed), and TOVA decrements. An increase in age was accompanied by a decrease in IGF-1 and IGF-BP3, an increase in P300 latency, a prolongation in TOVA response time, and a decrease in memory functioning. Moreover, independent of age, decreases in IGF-1 and IGF-BP3, were accompanied by increases in P300 latency, and were accompanied by increases in TOVA response time. Finally, increases in P300 latency were accompanied by decreased memory function, both directly and indirectly through mediation of TOVA response time. In summary, this is the first report utilizing SEM to reveal the finding that aging affects memory function negatively through mediation of decreased IGF-1 and IGF-BP3, and increased P300
Braverman, Eric R.; Chen, Thomas J. H.; Prihoda, Thomas J.; Sonntag, William; Meshkin, Brian; Downs, B. William; Mengucci, Julie F.; Blum, Seth H.; Notaro, Alison; Arcuri, Vanessa; Varshavskiy, Michael
2007-01-01
A review of the literature in both animals and humans reveals that changes in sex hormone have often been associated with changes in behavioral and mental abilities. Previously published research from our laboratory, and others, provides strong evidence that P300 (latency) event-related potential (ERP), a marker of neuronal processing speed, is an accurate predictor of early memory impairment in both males and females across a wide age range. It is our hypothesis, given the vast literature on the subject, that coupling growth hormones (insulin-like growth factor-I, (IGF-I) and insulin-like growth factor binding protein 3 (IGF-BP3)), P300 event-related potential and test of variables of attention (TOVA) are important neuroendocrinological predictors of early cognitive decline in a clinical setting. To support this hypothesis, we utilized structural equation modeling (SEM) parameter estimates to determine the relationship between aging and memory, as mediated by growth hormone (GH) levels (indirectly measured through the insulin-like growth factor system), P300 latency and TOVA, putative neurocognitive predictors tested in this study. An SEM was developed hypothesizing a causal directive path, leading from age to memory, mediated by IGF-1 and IGF-BP3, P300 latency (speed), and TOVA decrements. An increase in age was accompanied by a decrease in IGF-1 and IGF-BP3, an increase in P300 latency, a prolongation in TOVA response time, and a decrease in memory functioning. Moreover, independent of age, decreases in IGF-1 and IGF-BP3, were accompanied by increases in P300 latency, and were accompanied by increases in TOVA response time. Finally, increases in P300 latency were accompanied by decreased memory function, both directly and indirectly through mediation of TOVA response time. In summary, this is the first report utilizing SEM to reveal the finding that aging affects memory function negatively through mediation of decreased IGF-1 and IGF-BP3, and increased P300
The Statistical Drake Equation
NASA Astrophysics Data System (ADS)
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
Comparison of Kernel Equating and Item Response Theory Equating Methods
ERIC Educational Resources Information Center
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Accumulative Equating Error after a Chain of Linear Equatings
ERIC Educational Resources Information Center
Guo, Hongwen
2010-01-01
After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…
Dirac equations for generalised Yang-Mills systems
NASA Astrophysics Data System (ADS)
Lechtenfeld, O.; Nahm, W.; Tchrakian, D. H.
1985-11-01
We present Dirac equations in 4 p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a “BPST” background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results.
NASA Astrophysics Data System (ADS)
Ho, Choon-Lin; Hosotani, Yutaka
Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gauge transformation.
Parallel Multigrid Equation Solver
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
Do Differential Equations Swing?
ERIC Educational Resources Information Center
Maruszewski, Richard F., Jr.
2006-01-01
One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…
ERIC Educational Resources Information Center
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Generalized reduced magnetohydrodynamic equations
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Evolution equation for quantum coherence
NASA Astrophysics Data System (ADS)
Hu, Ming-Liang; Fan, Heng
2016-07-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures.
Evolution equation for quantum coherence
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Evolution equation for quantum coherence.
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Space Time Defined by Stress Equation
NASA Astrophysics Data System (ADS)
Yanagisawa, H.
2004-07-01
Time can never be measured directly. Time is calculated from changed lengths and angles by using all clocks. In addition, an atomic absolute clock and an atomic absolute telemeter have a contradictory relation to depend on each other. Of course, there is no absolute time. The time of all clocks are changed by energy states such as gravity or temperature. Here, I report an equation relating time to energy. It was deduced from my stress equation (dE/dt=kE). t=log E(t)/E(0)/k The relation of time to changed energy was shown.
NASA Astrophysics Data System (ADS)
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
Exact solutions of the nonlinear Boltzmann equation
NASA Astrophysics Data System (ADS)
Ernst, Matthieu H.
1984-03-01
A review is given of research activities since 1976 on the nonlinear Boltzmann equation and related equations of Boltzmann type, in which several rediscoveries have been made and several conjectures have been disproved. Subjects are (i) the BKW solution of the Boltzmann equation for Maxwell molecules, first discovered by Krupp in 1967, and the Krook-Wu conjecture concerning the universal significance of the BKW solution for the large (v, t) behavior of the velocity distribution function f (v, t); (ii) moment equations and polynomial expansions of f (v, t); (iii) model Boltzmann equation for a spatially uniform system of very hard particles, that can be solved in closed form for general initial conditions; (iv) for Maxwell and non-Maxwell-type molecules there exist solutions of the nonlinear Boltzmann equation with algebraic decrease at υ→∞; connections with nonuniqueness and violation of conservation laws; (v) conjectured super- H-theorem and the BKW solution; (vi) exactly soluble one-dimensional Boltzmann equation with spatial dependence.
Brownian motion from Boltzmann's equation.
NASA Technical Reports Server (NTRS)
Montgomery, D.
1971-01-01
Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.
Supersymmetric fifth order evolution equations
Tian, K.; Liu, Q. P.
2010-03-08
This paper considers supersymmetric fifth order evolution equations. Within the framework of symmetry approach, we give a list containing six equations, which are (potentially) integrable systems. Among these equations, the most interesting ones include a supersymmetric Sawada-Kotera equation and a novel supersymmetric fifth order KdV equation. For the latter, we supply some properties such as a Hamiltonian structures and a possible recursion operator.
Nikolaevskiy equation with dispersion.
Simbawa, Eman; Matthews, Paul C; Cox, Stephen M
2010-03-01
The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral "Goldstone" mode, including electroconvection and reaction-diffusion systems. It is known to exhibit chaotic dynamics at the onset of pattern formation, at least when the dispersive terms in the equation are suppressed, as is commonly the practice in previous analyses. In this paper, the effects of reinstating the dispersive terms are examined. It is shown that such terms can stabilize some of the spatially periodic traveling waves; this allows us to study the loss of stability and transition to chaos of the waves. The secondary stability diagram ("Busse balloon") for the traveling waves can be remarkably complicated. PMID:20365845
Causal electromagnetic interaction equations
Zinoviev, Yury M.
2011-02-15
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
Viscous Boussinesq equations for internal waves
NASA Astrophysics Data System (ADS)
Liu, Chi-Min
2016-04-01
In this poster, Boussinesq wave equations for internal wave propagation in a two-fluid system bounded by two impermeable plates are derived and analyzed. Using the perturbation method as well as the Padé approximation, a set of three equations accurate up to the fourth order are derived and displayed by three unknowns: the interfacial elevation, upper and lower velocity potentials at arbitrary vertical positions. No limitation on nonlinearity is made while weakly dispersive effects are originally considered in the derivation. The derived equations are examined by comparing its dispersion relation with those of existing models to verify the accuracy. The results show that present model equations provide an excellent base for simulating internal waves not only in shallower configuration but also medium configuration.
Reinforcing Net Ionic Equation Writing: Second Semester
NASA Astrophysics Data System (ADS)
Wruck, Betty J.
1996-02-01
It is important to actively illustrate that total and net ionic equation writing is a way of learning and expressing an enormous amount of chemistry. There is, however, a major problem with students retaining their ability to write net ionic equations in the second semester. So, we start this semester with a review and a special, long range assignment. In the lecture, we stress net ionic equation writing in as many topics as possible such as hydrolysis, Ksp chemistry, and electrochemistry. In the laboratory, we have revised experiments such as metal chromatography and designed new experiments such as Relative Strengths of Hydroxides and Complex Ions, in which net ionic equation writing is the major tool used in interpreting and answering laboratory questions.
Generalized reduced MHD equations
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson.
NASA Astrophysics Data System (ADS)
Konesky, Gregory
2009-08-01
In the almost half century since the Drake Equation was first conceived, a number of profound discoveries have been made that require each of the seven variables of this equation to be reconsidered. The discovery of hydrothermal vents on the ocean floor, for example, as well as the ever-increasing extreme conditions in which life is found on Earth, suggest a much wider range of possible extraterrestrial habitats. The growing consensus that life originated very early in Earth's history also supports this suggestion. The discovery of exoplanets with a wide range of host star types, and attendant habitable zones, suggests that life may be possible in planetary systems with stars quite unlike our Sun. Stellar evolution also plays an important part in that habitable zones are mobile. The increasing brightness of our Sun over the next few billion years, will place the Earth well outside the present habitable zone, but will then encompass Mars, giving rise to the notion that some Drake Equation variables, such as the fraction of planets on which life emerges, may have multiple values.
Entropic corrections to Friedmann equations
Sheykhi, Ahmad
2010-05-15
Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In Verlinde's argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton's law of gravitation as well as modified Friedmann equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde's model.
Entropic corrections to Friedmann equations
NASA Astrophysics Data System (ADS)
Sheykhi, Ahmad
2010-05-01
Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In Verlinde’s argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton’s law of gravitation as well as modified Friedmann equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde’s model.
Onsager's-principle-consistent 13-moment transport equations.
Singh, Narendra; Agrawal, Amit
2016-06-01
A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.
Maxwell's equations, quantum physics and the quantum graviton
NASA Astrophysics Data System (ADS)
Gersten, Alexander; Moalem, Amnon
2011-12-01
Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of "relativistic quaternions". Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.
Double-Plate Penetration Equations
NASA Technical Reports Server (NTRS)
Hayashida, K. B.; Robinson, J. H.
2000-01-01
This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.
ERIC Educational Resources Information Center
Moses, Tim; Liu, Jinghua
2011-01-01
In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…
Riccati equations for bounded radiating systems
NASA Astrophysics Data System (ADS)
Maharaj, S. D.; Tiwari, A. K.; Mohanlal, R.; Narain, R.
2016-09-01
We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of restrictions on the gravitational potentials. One category of solution can be related to the horizon function transformation which was recently introduced. A Lie symmetry analysis of the resulting Riccati equation shows that several new classes of exact solutions are possible. The relationship between the horizon function, Euclidean star models, and other earlier investigations is clarified.
Reduction operators of Burgers equation
Pocheketa, Oleksandr A.; Popovych, Roman O.
2013-01-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special “no-go” case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf–Cole transformation to a parameterized family of Lie reductions of the linear heat equation. PMID:23576819
New application to Riccati equation
NASA Astrophysics Data System (ADS)
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
Disconjugacy of fourth-order equations on graphs
NASA Astrophysics Data System (ADS)
Kulaev, R. Ch
2015-12-01
This paper develops the theory of disconjugacy of fourth-order equations on geometric graphs which arises in modelling rod structures. The disconjugacy of an equation is defined in terms of a special fundamental system of solutions of the homogeneous equation. The disconjugacy property is shown to be related to the positivity property of the Green's functions for certain classes of boundary value problems for a fourth-order equation on a graph. A maximum principle for a fourth-order equation on a graph is formulated, and some properties of differential inequalities are proved. Bibliography: 25 titles.
Scaling of ballistic deposition from a Langevin equation.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2006-04-01
An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions. PMID:16711773
Differential Equations Compatible with Boundary Rational qKZ Equation
NASA Astrophysics Data System (ADS)
Takeyama, Yoshihiro
2011-10-01
We give diffierential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (Cěen, Cn) which in the case of type GLn was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case.
Estimating Equating Error in Observed-Score Equating. Research Report.
ERIC Educational Resources Information Center
van der Linden, Wim J.
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and in the population of examinees. This definition underlies, for example, the well-known approximation to the standard error of equating by Lord (1982).…
NASA Astrophysics Data System (ADS)
Taff, L. G.; Brennan, T. A.
1989-06-01
Intrigued by the recent advances in research on solving Kepler's equation, we have attacked the problem too. Our contributions emphasize the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques in both mean anomaly/eccentricity space and eccentric anomaly/eccentricity space, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions. The very close second is Broucke's bounds coupled with Newton's second-order scheme.
The Arrhenius equation revisited.
Peleg, Micha; Normand, Mark D; Corradini, Maria G
2012-01-01
The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T
Makkonen, Lasse
2016-04-01
Young's construction for a contact angle at a three-phase intersection forms the basis of all fields of science that involve wetting and capillary action. We find compelling evidence from recent experimental results on the deformation of a soft solid at the contact line, and displacement of an elastic wire immersed in a liquid, that Young's equation can only be interpreted by surface energies, and not as a balance of surface tensions. It follows that the a priori variable in finding equilibrium is not the position of the contact line, but the contact angle. This finding provides the explanation for the pinning of a contact line. PMID:26940644
Relationships between basic soils-engineering equations and basic ground-water flow equations
Jorgensen, Donald G.
1980-01-01
The many varied though related terms developed by ground-water hydrologists and by soils engineers are useful to each discipline, but their differences in terminology hinder the use of related information in interdisciplinary studies. Equations for the Terzaghi theory of consolidation and equations for ground-water flow are identical under specific conditions. A combination of the two sets of equations relates porosity to void ratio and relates the modulus of elasticity to the coefficient of compressibility, coefficient of volume compressibility, compression index, coefficient of consolidation, specific storage, and ultimate compaction. Also, transient ground-water flow is related to coefficient of consolidation, rate of soil compaction, and hydraulic conductivity. Examples show that soils-engineering data and concepts are useful to solution of problems in ground-water hydrology.
Solving Equations of Multibody Dynamics
NASA Technical Reports Server (NTRS)
Jain, Abhinandan; Lim, Christopher
2007-01-01
Darts++ is a computer program for solving the equations of motion of a multibody system or of a multibody model of a dynamic system. It is intended especially for use in dynamical simulations performed in designing and analyzing, and developing software for the control of, complex mechanical systems. Darts++ is based on the Spatial-Operator- Algebra formulation for multibody dynamics. This software reads a description of a multibody system from a model data file, then constructs and implements an efficient algorithm that solves the dynamical equations of the system. The efficiency and, hence, the computational speed is sufficient to make Darts++ suitable for use in realtime closed-loop simulations. Darts++ features an object-oriented software architecture that enables reconfiguration of system topology at run time; in contrast, in related prior software, system topology is fixed during initialization. Darts++ provides an interface to scripting languages, including Tcl and Python, that enable the user to configure and interact with simulation objects at run time.
Higher order equations of motion and gravity
NASA Astrophysics Data System (ADS)
Lämmerzahl, Claus; Rademaker, Patricia
2012-12-01
Standard fundamental equations of motion for point particles are of second order in the time derivative. Here we are exploring the consequences of fundamental equations of motion with an additional small even higher order term to the standard formulation. This is related to two issues: (i) higher order equations of motion will have influence on the definition of the structure of possible interactions and in particular of the gravitational interaction, and (ii) such equations of motion provide a framework to test the validity of Newton’s second law which is the basis for the definition of forces but which assumes from the very beginning that the fundamental equations of motion are of second order. We will show that starting with our generalized equations of motions it is possible to introduce the space-time metric describing the gravitational interaction by means of a standard gauge principle. Another main result within our model of even higher order derivatives is that for slowly varying and smooth fields the higher order derivatives either lead to runaway solutions or induces a zitterbewegung. We confront this higher order scheme with experimental data.
New integral equation for simple fluids
NASA Astrophysics Data System (ADS)
Kang, Hong Seok; Ree, Francis H.
1995-09-01
We present a new integral equation for the radial distribution function of classical fluids. It employs the bridge function for a short-range repulsive reference system which was used earlier in our dense fluid perturbation theory. The bridge function is evaluated using Ballone et al.'s closure relation. Applications of the integral equation to the Lennard-Jones and inverse nth-power (n=12, 9, 6, and 4) repulsive systems show that it can predict thermodynamic and structural properties in close agreement with results from computer simulations and the reference-hypernetted-chain equation. We also discuss thermodynamic consistency tests on the new equation and comparisons with the integral equations of Rogers and Young and of Zerah and Hansen. The present equation has no parameter to adjust. This unique feature offers a significant advantage as it eliminates a time-consuming search to optimize such parameters appearing in other theories. It permits practical applications needing complex intermolecular potentials and for multicomponent systems.
Conservational PDF Equations of Turbulence
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Solitons and nonlinear wave equations
Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.
1982-01-01
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Solving Nonlinear Coupled Differential Equations
NASA Technical Reports Server (NTRS)
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Successfully Transitioning to Linear Equations
ERIC Educational Resources Information Center
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
The Forced Hard Spring Equation
ERIC Educational Resources Information Center
Fay, Temple H.
2006-01-01
Through numerical investigations, various examples of the Duffing type forced spring equation with epsilon positive, are studied. Since [epsilon] is positive, all solutions to the associated homogeneous equation are periodic and the same is true with the forcing applied. The damped equation exhibits steady state trajectories with the interesting…
Equating with Miditests Using IRT
ERIC Educational Resources Information Center
Fitzpatrick, Joseph; Skorupski, William P.
2016-01-01
The equating performance of two internal anchor test structures--miditests and minitests--is studied for four IRT equating methods using simulated data. Originally proposed by Sinharay and Holland, miditests are anchors that have the same mean difficulty as the overall test but less variance in item difficulties. Four popular IRT equating methods…
Fitness consequences of artificial selection on relative male genital size
Booksmythe, Isobel; Head, Megan L.; Keogh, J. Scott; Jennions, Michael D.
2016-01-01
Male genitalia often show remarkable differences among related species in size, shape and complexity. Across poeciliid fishes, the elongated fin (gonopodium) that males use to inseminate females ranges from 18 to 53% of body length. Relative genital size therefore varies greatly among species. In contrast, there is often tight within-species allometric scaling, which suggests strong selection against genital–body size combinations that deviate from a species' natural line of allometry. We tested this constraint by artificially selecting on the allometric intercept, creating lines of males with relatively longer or shorter gonopodia than occur naturally for a given body size in mosquitofish, Gambusia holbrooki. We show that relative genital length is heritable and diverged 7.6–8.9% between our up-selected and down-selected lines, with correlated changes in body shape. However, deviation from the natural line of allometry does not affect male success in assays of attractiveness, swimming performance and, crucially, reproductive success (paternity). PMID:27188478
On stochastic diffusion equations and stochastic Burgers' equations
NASA Astrophysics Data System (ADS)
Truman, A.; Zhao, H. Z.
1996-01-01
In this paper we construct a strong solution for the stochastic Hamilton Jacobi equation by using stochastic classical mechanics before the caustics. We thereby obtain the viscosity solution for a certain class of inviscid stochastic Burgers' equations. This viscosity solution is not continuous beyond the caustics of the corresponding Hamilton Jacobi equation. The Hopf-Cole transformation is used to identify the stochastic heat equation and the viscous stochastic Burgers' equation. The exact solutions for the above two equations are given in terms of the stochastic Hamilton Jacobi function under a no-caustic condition. We construct the heat kernel for the stochastic heat equation for zero potentials in hyperbolic space and for harmonic oscillator potentials in Euclidean space thereby obtaining the stochastic Mehler formula.
Relaxation: from Laplace's equation to the heat equation and discretely back again
NASA Astrophysics Data System (ADS)
Low, Robert J.
2015-05-01
We see how the relaxation method for Laplace's equation is related to a numerical solution of the heat equation, which is in turn motivated by thinking of the Hamiltonian as the the time evolution operator in quantum mechanics. This gives some physical insight into what the relaxation method is doing. We also use this to suggest investigative work for a student learning about computational methods in physics.
'Footballs', conical singularities, and the Liouville equation
Redi, Michele
2005-02-15
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.
The Use of Transformations in Solving Equations
ERIC Educational Resources Information Center
Libeskind, Shlomo
2010-01-01
Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…
Power Series Solution to the Pendulum Equation
ERIC Educational Resources Information Center
Benacka, Jan
2009-01-01
This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…
Generalized Klein-Kramers equations
NASA Astrophysics Data System (ADS)
Fa, Kwok Sau
2012-12-01
A generalized Klein-Kramers equation for a particle interacting with an external field is proposed. The equation generalizes the fractional Klein-Kramers equation introduced by Barkai and Silbey [J. Phys. Chem. B 104, 3866 (2000), 10.1021/jp993491m]. Besides, the generalized Klein-Kramers equation can also recover the integro-differential Klein-Kramers equation for continuous-time random walk; this means that it can describe the subdiffusive and superdiffusive regimes in the long-time limit. Moreover, analytic solutions for first two moments both in velocity and displacement (for force-free case) are obtained, and their dynamic behaviors are investigated.
Multinomial Diffusion Equation
Balter, Ariel I.; Tartakovsky, Alexandre M.
2011-06-01
We have developed a novel stochastic, space/time discrete representation of particle diffusion (e.g. Brownian motion) based on discrete probability distributions. We show that in the limit of both very small time step and large concentration, our description is equivalent to the space/time continuous stochastic diffusion equation. Being discrete in both time and space, our model can be used as an extremely accurate, efficient, and stable stochastic finite-difference diffusion algorithm when concentrations are so small that computationally expensive particle-based methods are usually needed. Through numerical simulations, we show that our method can generate realizations that capture the statistical properties of particle simulations. While our method converges converges to both the correct ensemble mean and ensemble variance very quickly with decreasing time step, but for small concentration, the stochastic diffusion PDE does not, even for very small time steps.
On nonautonomous Dirac equation
Hovhannisyan, Gro; Liu Wen
2009-12-15
We construct the fundamental solution of time dependent linear ordinary Dirac system in terms of unknown phase functions. This construction gives approximate representation of solutions which is useful for the study of asymptotic behavior. Introducing analog of Rayleigh quotient for differential equations we generalize Hartman-Wintner asymptotic integration theorems with the error estimates for applications to the Dirac system. We also introduce the adiabatic invariants for the Dirac system, which are similar to the adiabatic invariant of Lorentz's pendulum. Using a small parameter method it is shown that the change in the adiabatic invariants approaches zero with the power speed as a small parameter approaches zero. As another application we calculate the transition probabilities for the Dirac system. We show that for the special choice of electromagnetic field, the only transition of an electron to the positron with the opposite spin orientation is possible.
Linear partial difference equations of hypergeometric type
NASA Astrophysics Data System (ADS)
Rodal, J.; Area, I.; Godoy, E.
2007-03-01
In this paper a systematic study of the orthogonal polynomial solutions of a second order partial difference equation of hypergeometric type of two variables is done. The Pearson's systems for the orthogonality weight of the solutions and also for the difference derivatives of the solutions are presented. The orthogonality property in subspaces is treated in detail, which leads to an analog of the Rodrigues-type formula for orthogonal polynomials of two discrete variables. A classification of the admissible equations as well as some examples related with bivariate Hahn, Kravchuk, Meixner, and Charlier families, and their algebraic and difference properties are explicitly given.
Thermoelastic constitutive equations for chemically hardening materials
NASA Technical Reports Server (NTRS)
Shaffer, B. W.; Levitsky, M.
1974-01-01
Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.
Constitutive equations of ageing polymeric materials
NASA Technical Reports Server (NTRS)
Peng, S. T. J.
1985-01-01
The constitutive equation for the relaxation behavior of time-dependent, chemically unstable materials developed by Valanis and Peng (1983), which used the irreversible thermodynamics of internal variables in Eyring's absolute reaction theory and yielded a theoretical expression for the effect of chemical crosslink density on the relaxation rate, is presently applied to the creep behavior of a network polymer which is undergoing a scission process. In particular, two equations are derived which may for the first time show the relations between mechanical models and internal variables in the creep expressions, using a three-element model with a Maxwell element.
Integrability of Lie Systems Through Riccati Equations
NASA Astrophysics Data System (ADS)
Cariñena, José F.; de Lucas, Javier
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.
Langevin Equations for Reaction-Diffusion Processes.
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems. PMID:27636462
Langevin Equations for Reaction-Diffusion Processes
NASA Astrophysics Data System (ADS)
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A.
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.
Entwined paths, difference equations, and the Dirac equation
Ord, G.N.; Mann, R.B.
2003-02-01
Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper, we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are ''self-quantizing.'' We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process, in the same sense that the diffusion and telegraph equations are phenomenological descriptions of stochastic processes.
An accurate equation of state for fluids of linear homonuclear fused hard spheres
NASA Astrophysics Data System (ADS)
Maeso, M. J.; Solana, J. R.
1994-12-01
A model relating the equation of state of linear homonuclear fused hard sphere fluids to the equation of state of the hard sphere fluid is derived from the pressure equation. The equation of state reproduces simulation data practically within their accuracy for diatomic and linear triatomic hard molecular fluids.
Linear integral transformations and hierarchies of integrable nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Nijhoff, Frank W.
1988-07-01
Integrable hierarchies of nonlinear evolution equations are investigated on the basis of linear integral equations. These are (Riemann-Hilbert type of) integral transformations which leave invariant an infinite sequence of ordinary differential matrix equations of increasing order in an (indefinite) parameter k. The potential matrices in these equations obey a set of nonlinear recursion relations, leading to a heirarchy of nonlinear partial differential equations. In decreasing order the same equations give rise to a “reciprocal” hierarchy, associated with Heisenberg ferromagnet type of equations. Central in the treatment is an embedding of the hierarchy into an infinite-matrix structure, which is constructed on the basis of the integral equations. In terms of this infinite-matrix structure the equations governing the hierarchies become quite simple. Furthermore, it leads in a straightforward way to various generalizations, such as to other types of linear spectral problems, multicomponent system and lattice equations. Generalizations to equations associated with noncommuting flows follow as a direct consequence of the treatment. Finally, some results on conserved densities and the Hamiltonian structure are briefly discussed.
On inter-tidal transport equation
Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi
1989-01-01
The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the Eulerian residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the Lagrangian residual current suggest that the long-term transport problem is more closely related to the Lagrangian residual current than to the Eulerian residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.
Magnetic monopoles, Galilean invariance, and Maxwell's equations
Crawford, F.S. . Physics Department)
1992-02-01
Maxwell's equations have space reserved for magnetic monopoles. Whether or not they exist in our part of the universe, monopoles provide a useful didactic tool to help us recognize relations among Maxwell's equations less easily apparent in the approach followed by many introductory textbooks, wherein Coulomb's law, Biot and Savart's law, Ampere's law, Faraday's law, Maxwell's displacement current, etc., are introduced independently, as demanded by experiment.'' Instead a conceptual path that deduces all of Maxwell's equations from the near-minimal set of assumptions: (a) Inertial frames exist, in which Newton's laws hold, to a first approximation; (b) the laws of electrodynamics are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities {ital v}{much lt}{ital c} are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula.
Boundary transfer matrices and boundary quantum KZ equations
Vlaar, Bart
2015-07-15
A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.
Modeling some real phenomena by fractional differential equations
NASA Astrophysics Data System (ADS)
Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.
2016-11-01
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.
Newtonian hydrodynamic equations with relativistic pressure and velocity
NASA Astrophysics Data System (ADS)
Hwang, Jai-chan; Noh, Hyerim; Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried
2016-07-01
We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.
2013-01-01
Background The extent to which psychosocial and diet behavior factors affect dietary self-report remains unclear. We examine the contribution of these factors to measurement error of self-report. Methods In 450 postmenopausal women in the Women’s Health Initiative Observational Study doubly labeled water and urinary nitrogen were used as biomarkers of objective measures of total energy expenditure and protein. Self-report was captured from food frequency questionnaire (FFQ), four day food record (4DFR) and 24 hr. dietary recall (24HR). Using regression calibration we estimated bias of self-reported dietary instruments including psychosocial factors from the Stunkard-Sorenson Body Silhouettes for body image perception, the Crowne-Marlowe Social Desirability Scale, and the Three Factor Eating Questionnaire (R-18) for cognitive restraint for eating, uncontrolled eating, and emotional eating. We included a diet behavior factor on number of meals eaten at home using the 4DFR. Results Three categories were defined for each of the six psychosocial and diet behavior variables (low, medium, high). Participants with high social desirability scores were more likely to under-report on the FFQ for energy (β = -0.174, SE = 0.054, p < 0.05) and protein intake (β = -0.142, SE = 0.062, p < 0.05) compared to participants with low social desirability scores. Participants consuming a high percentage of meals at home were less likely to under-report on the FFQ for energy (β = 0.181, SE = 0.053, p < 0.05) and protein (β = 0.127, SE = 0.06, p < 0.05) compared to participants consuming a low percentage of meals at home. In the calibration equations combining FFQ, 4DFR, 24HR with age, body mass index, race, and the psychosocial and diet behavior variables, the six psychosocial and diet variables explained 1.98%, 2.24%, and 2.15% of biomarker variation for energy, protein, and protein density respectively. The variations explained are
NASA Astrophysics Data System (ADS)
Sokolova, Tatiana S.; Dorogokupets, Peter I.; Dymshits, Anna M.; Danilov, Boris S.; Litasov, Konstantin D.
2016-09-01
We present Microsoft Excel spreadsheets for calculation of thermodynamic functions and P-V-T properties of MgO, diamond and 9 metals, Al, Cu, Ag, Au, Pt, Nb, Ta, Mo, and W, depending on temperature and volume or temperature and pressure. The spreadsheets include the most common pressure markers used in in situ experiments with diamond anvil cell and multianvil techniques. The calculations are based on the equation of state formalism via the Helmholtz free energy. The program was developed using Visual Basic for Applications in Microsoft Excel and is a time-efficient tool to evaluate volume, pressure and other thermodynamic functions using T-P and T-V data only as input parameters. This application is aimed to solve practical issues of high pressure experiments in geosciences and mineral physics.
Absorbing layers for the Dirac equation
Pinaud, Olivier
2015-05-15
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Braces and the Yang-Baxter Equation
NASA Astrophysics Data System (ADS)
Cedó, Ferran; Jespers, Eric; Okniński, Jan
2014-04-01
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In particular, for each positive integer n a finite square-free multipermutation solution of the Yang-Baxter equation with multipermutation level n and an abelian involutive Yang-Baxter group is constructed. This answers a problem of Gateva-Ivanova and Cameron. It is proved that finite non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation whose associated involutive Yang-Baxter group is abelian are multipermutation solutions. Earlier the authors proved this with the additional square-free hypothesis on the solutions. It is also proved that finite square-free non-degenerate involutive set-theoretic solutions associated to a left brace are multipermutation solutions.
Lorentz Abraham Force and Power Equations
NASA Astrophysics Data System (ADS)
Yaghjian, Arthur D.
Toward the end of the nineteenth century Lorentz modeled the electron (“vibrating charged particle,” as he called it) by a spherical shell of uniform surface charge density and set about the difficult task of deriving the equation of motion of this electron model by determining, from Maxwell's equations and the Lorentz force law, the retarded self electromagnetic force that the fields of the accelerating charge distribution exert upon the charge itself [1]. (This initial work of Lorentz in 1892 on a moving charged sphere appeared five years before J.J. Thomson's “discovery” of the electron. It is summarized in English by J.Z. Buchwald [2, app. 7].) With the help of Abraham,1 a highly successful theory of the moving electron model was completed by the early 1900's [3, 4]. Before Einstein's papers [5, 6] on special relativity appeared in 1905, they had derived the following force equation of motion
Mode decomposition evolution equations
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Integral equation study of liquid hydrogen fluoride
NASA Astrophysics Data System (ADS)
Martín, C.; Lombardero, M.; Anta, J. A.; Lomba, E.
2001-01-01
Liquid hydrogen fluoride is a well-known hydrogen bonded substance, in many aspects related to liquid water, and for which a wide variety of interaction models have recently been proposed. We have studied two of these models by means of a reference hypernetted chain equation in order to assess the ability of this latter approach to describe the properties of this highly associative system. Our calculations, when compared with molecular dynamic results, show that the integral equation reproduces quantitatively both the structure and the thermodynamics of liquid hydrogen fluoride over a wide range of thermodynamic states. However, the integral equation approach is apparently unable to produce estimates for the phase diagram since the low-density (gas phase) side of the binodal curve lies inside the nonsolution region of the equation. This failure can be understood as the result of the inability of standard integral equation theories to account for the behavior of low density strongly associative systems like highly charged electrolytes or, in this case, the gaseous phase of hydrogen fluoride.
Non relativistic limit of the Landau-Lifshitz equation: A new equation
NASA Astrophysics Data System (ADS)
Ares de Parga, G.; Domínguez-Hernández, S.; Salinas-Hernández, E.
2016-06-01
It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1 /c2 is proposed for the constant electric and magnetic fields.
What physics is encoded in Maxwell's equations?
NASA Astrophysics Data System (ADS)
Kosyakov, B. P.
2005-08-01
We reconstruct Maxwell's equations showing that a major part of the information encoded in them is taken from topological properties of spacetime, and the residual information, divorced from geometry, which represents the physical contents of electrodynamics, %these equations, translates into four assumptions:(i) locality; (ii) linearity; %of the dynamical law; (iii) identity of the charge-source and the charge-coupling; and (iv) lack of magnetic monopoles. However, a closer inspection of symmetries peculiar to electrodynamics shows that these assumptions may have much to do with geometry. Maxwell's equations tell us that we live in a three-dimensional space with trivial (Euclidean) topology; time is a one-dimensional unidirectional and noncompact continuum; and spacetime is endowed with a light cone structure readable in the conformal invariance of electrodynamics. Our geometric feelings relate to the fact that Maxwell's equations are built in our brain, hence our space and time orientation, our visualization and imagination capabilities are ensured by perpetual instinctive processes of solving Maxwell's equations. People are usually agree in their observations of angle relations, for example, a right angle is never confused with an angle slightly different from right. By contrast, we may disagree in metric issues, say, a colour-blind person finds the light wave lengths quite different from those found by a man with normal vision. This lends support to the view that conformal invariance of Maxwell's equations is responsible for producing our notion of space. Assuming that our geometric intuition is guided by our innate realization of electrodynamical laws, some abnormal mental phenomena, such as clairvoyance, may have a rational explanation.
Menikoff, Ralph
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
On the generalized Jacobi equation
NASA Astrophysics Data System (ADS)
Perlick, Volker
2008-05-01
The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to the coordinates, but not with respect to the velocities. The resulting equation has been studied by several authors in some detail for timelike geodesics in a Lorentzian manifold. Here we begin by briefly considering the generalized Jacobi equation on affine manifolds, without a metric; then we specify to lightlike geodesics in a Lorentzian manifold. We illustrate the latter case by considering particular lightlike geodesics (a) in Schwarzschild spacetime and (b) in a plane-wave spacetime.
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2015-06-01
It is shown that a nonlinear reformulation of time-dependent and time-independent quantum mechanics in terms of Riccati equations not only provides additional information about the physical system, but also allows for formal comparison with other nonlinear theories. This is demonstrated for the nonlinear Burgers and Korteweg-de Vries equations with soliton solutions. As Riccati equations can be linearized to corresponding Schrödinger equations, this also applies to the Riccati equations that can be obtained by integrating the nonlinear soliton equations, resulting in a time-independent Schrödinger equation with Rosen-Morse potential and its supersymmetric partner. Because both soliton equations lead to the same Riccati equation, relations between the Burgers and Korteweg-de Vries equations can be established. Finally, a connection with the inverse scattering method is mentioned.
Equations of the Randomizer's Dynamics
NASA Astrophysics Data System (ADS)
Strzałko, Jarosław; Grabski, Juliusz; Perlikowski, Przemysław; Stefanski, Andrzej; Kapitaniak, Tomasz
Basing on the Newton-Euler laws of mechanics we derive the equations which describe the dynamics of the coin toss, the die throw, and roulette run. The equations for full 3D models and for lower dimensional simplifications are given. The influence of the air resistance and energy dissipation at the impacts is described. The obtained equations allow for the numerical simulation of the randomizer's dynamics and define the mapping of the initial conditions into the final outcome.
Solving Differential Equations in R
NASA Astrophysics Data System (ADS)
Soetaert, Karline; Meysman, Filip; Petzoldt, Thomas
2010-09-01
The open-source software R has become one of the most widely used systems for statistical data analysis and for making graphs, but it is also well suited for other disciplines in scientific computing. One of the fields where considerable progress has been made is the solution of differential equations. Here we first give an overview of the types of differential equations that R can solve, and then demonstrate how to use R for solving a 2-Dimensional partial differential equation.
A note on "Kepler's equation".
NASA Astrophysics Data System (ADS)
Dutka, J.
1997-07-01
This note briefly points out the formal similarity between Kepler's equation and equations developed in Hindu and Islamic astronomy for describing the lunar parallax. Specifically, an iterative method for calculating the lunar parallax has been developed by the astronomer Habash al-Hasib al-Marwazi (about 850 A.D., Turkestan), which is surprisingly similar to the iterative method for solving Kepler's equation invented by Leonhard Euler (1707 - 1783).
Quaternion Dirac Equation and Supersymmetry
NASA Astrophysics Data System (ADS)
Rawat, Seema; Negi, O. P. S.
2009-08-01
Quaternion Dirac equation has been analyzed and its supersymmetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, nonzero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.
Electronic representation of wave equation
NASA Astrophysics Data System (ADS)
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Squared eigenfunctions for the Sasa-Satsuma equation
NASA Astrophysics Data System (ADS)
Yang, Jianke; Kaup, D. J.
2009-02-01
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.
Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations
Hashemiparast, S. M.; Avazpour, L.
2008-09-01
There are many procedures for the numerical solution of Fredholm integral equations. The main idea in these procedures is accuracy of the solution. In this paper, we use Gaussian quadrature with multiple nodes to improve the solution of these integral equations. The application of this method is illustrated via some examples, the related tables are given at the end.
Observed-Score Equating with a Heterogeneous Target Population
ERIC Educational Resources Information Center
Duong, Minh Q.; von Davier, Alina A.
2012-01-01
Test equating is a statistical procedure for adjusting for test form differences in difficulty in a standardized assessment. Equating results are supposed to hold for a specified target population (Kolen & Brennan, 2004; von Davier, Holland, & Thayer, 2004) and to be (relatively) independent of the subpopulations from the target population (see…
A Reciprocal Transformation for the Constant Astigmatism Equation
NASA Astrophysics Data System (ADS)
Hlaváč, Adam; Marvan, Michal
2014-08-01
We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation z_{yy} + (1/z)_{xx} + 2 = 0. The transformation is related to the special case of the famous Bäcklund transformation of the sine-Gordon equation with the Bäcklund parameter λ = ±1. It is also a nonlocal symmetry.
Representing Rate Equations for Enzyme-Catalyzed Reactions
ERIC Educational Resources Information Center
Ault, Addison
2011-01-01
Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…
Equations and the Equal Sign in Elementary Mathematics Textbooks
ERIC Educational Resources Information Center
Powell, Sarah R.
2012-01-01
To promote a relational understanding of the equal sign (=), students may require exposure to a variety of equation types (i.e., 3 = 8 - 5; 2 + 3 = 1 + 4; 9 - 3 = 6). The purpose of this study was to evaluate 8 elementary curricula for degree of exposure to equation types. Across 6 elementary grade levels, curricula were coded for the number of…
A reciprocal transformation for the Geng-Xue equation
Li, Nianhua Niu, Xiaoxing
2014-05-15
In this paper, we construct a reciprocal transformation for the Geng-Xue equation and show that, with help of this transformation, we relate the first negative flow of the modified Boussinesq hierarchy to the Geng-Xue equation. Furthermore, we analyze the construction of conserved quantities and present new ones.
Hamiltonian structures for the Ostrovsky-Vakhnenko equation
NASA Astrophysics Data System (ADS)
Brunelli, J. C.; Sakovich, S.
2013-01-01
We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko (OV) equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed.
Factorization of the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.
2005-01-01
The Navier-Stokes equations for a Newtonian ideal gas are examined to determine the factorizable form of the equations relevant to the construction of a factorizable relaxation scheme. The principal linearization of the equations is found by examining the relative magnitude of the terms for short-wavelength errors. The principal part of the operator is then found. Comparison of the factors of the Navier-Stokes and Euler equations differ qualitatively because of the coupling of entropy and pressure through thermal diffusion. Special cases of the factorization are considered.
A Maxwell formulation for the equations of a plasma
Thompson, Richard J.; Moeller, Trevor M.
2012-01-15
In light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid equations of motion may be reformulated as a set of Maxwell equations. This analogy has been explored in the literature for incompressible turbulent flow and compressible flow but has not been widely explored in relation to plasmas. This letter introduces the analogous fluid Maxwell equations and formulates a set of Maxwell equations for a plasma in terms of the species canonical vorticity and its cross product with the species velocity. The form of the source terms is presented and the magnetohydrodynamic (MHD) limit restores the typical variety of MHD waves.
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
New Formulation of the Governing Equations for Analyzing Outrigger Structures
NASA Astrophysics Data System (ADS)
Er, Guo-Kang
2010-05-01
In this paper, an easily comprehensible solution procedure is proposed for the analysis of outrigger-braced structures. The idea is based on the compatibility of the columns' axial deformation. The unknowns are selected to be the axial forces in the columns. The resulted governing equations and the equations for the optimum analysis of the outrigger locations are different from the conventional ones, but numerical analysis shows that the results obtained with the new equations are same as those obtained with conventional equations. The relations between the new equations and the conventional ones are also figured out. The new procedure of formulating the governing equations can be easily extended to more complicated cases of outrigger-braced structures.
Generalized Langevin theory for inhomogeneous fluids: The equations of motion
NASA Astrophysics Data System (ADS)
Grant, Martin; Desai, Rashmi C.
1982-05-01
We use the generalized Langevin approach to study the dynamical correlations in an inhomogeneous system. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor, and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamiclike quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low-density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We also indicate how the resulting general set of equations would simplify for systems in which the inhomogeneity is unidirectional, e.g., a liquid-vapor interface.
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.