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
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
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
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., III; 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.
NASA Astrophysics Data System (ADS)
Watanabe, Hayafumi; Takayasu, Hideki; Takayasu, Misako
2013-02-01
To elucidate allometric scaling in complex systems, we investigated the underlying scaling relationships between typical three-scale indicators for approximately 500,000 Japanese firms; namely, annual sales, number of employees, and number of business partners. First, new scaling relations including the distributions of fluctuations were discovered by systematically analyzing conditional statistics. Second, we introduced simple probabilistic models that reproduce all these scaling relations, and we derived relations between scaling exponents and the magnitude of fluctuations.
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. PMID:26094447
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
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
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.
NASA Astrophysics Data System (ADS)
Riisgård, Hans Ulrik; Larsen, Poul S.; Pleissner, Daniel
2014-03-01
The relationship between body dry weight ( W) and shell length ( L) of blue mussels, Mytilus edulis, can be expressed by the condition index (CI = W/ L 3) which varies from population to population and during the year. Here, we examine the influence of CI on the relationships between maximum filtration rate ( F, l h-1), W (g), and L (mm) as described by the equations: F W = aW b and F L = cL d , respectively. This is done by using available and new experimental laboratory data on M. edulis obtained by members of the same research team using different methods and controlled diets of cultivated algal cells. For all data, it was found that F W = 6.773 W 0.678 and F L = 0.00135 L 2.088 which are very similar to equations for mussels with `medium condition' (CI = 4-6 mg cm-3): F W = 6.567 W 0.681 and F L = 0.00150 L 2.051, with b- and d-values within a few percent of the theoretically expected of 2/3 and 2, respectively. Further, based on the present data, we propose a correction factor expressed by the empirical relation F W / F L = 0.3562CI2/3 which implies that F W tends to underestimate the actual filtration rate ( F L ) when CI < 4.70 and to overestimate the filtration rate when CI > 4.70.
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.
Adding constraints to predation through allometric relation of scats to consumption.
Chakrabarti, Stotra; Jhala, Yadvendradev V; Dutta, Sutirtha; Qureshi, Qamar; Kadivar, Riaz F; Rana, Vishwadipsinh J
2016-05-01
A thorough understanding of mechanisms of prey consumption by carnivores and the constraints on predation help us in evaluating the role of carnivores in an ecosystem. This is crucial in developing appropriate management strategies for their conservation and mitigating human-carnivore conflict. Current models on optimal foraging suggest that mammalian carnivores would profit most from killing the largest prey that they can subdue with minimal risk of injury to themselves. Wild carnivore diets are primarily estimated through analysis of their scats. Using extensive feeding experiments (n = 68) on a wide size range (4·5-130 kg) of obligate carnivores - lion, leopard, jungle cat and domestic cat, we parameterize biomass models that best relate consumption to scat production. We evaluate additional constraints of gut fill, prey digestibility and carcass utilization on carnivory that were hereto not considered in optimal foraging studies. Our results show that patterns of consumption to scat production against prey size are similar and asymptotic, contrary to established linear models, across these carnivores after accounting for the effect of carnivore size. This asymptotic, allometric relationship allowed us to develop a generalized model: biomass consumed per collectable scat/predator weight = 0·033-0·025exp(-4·284(prey weight/predator weight)) , which is applicable to all obligate carnivores to compute prey biomass consumed from scats. Our results also depict a relationship for prey digestibility which saturates at about 90% for prey larger than predator size. Carcass utilization declines exponentially with prey size. These mechanisms result in digestible biomass saturating at prey weights approximately equal to predator weight. Published literature on consumption by tropical carnivores that has relied on linear biomass models is substantially biased. We demonstrate the nature of these biases by correcting diets of tiger, lion and leopard in recent
Romiti, Federico; Tini, Massimiliano; Redolfi De Zan, Lara; Chiari, Stefano; Zauli, Agnese; Carpaneto, Giuseppe M
2015-10-01
Enlarged weapons and ornamental traits under sexual selection often show a positive allometric relationship with the overall body size. The present study explores the allometry of mandibles and their supporting structure, the head, in males of the European stag beetle, Lucanus cervus. This species shows a remarkable dimorphism in mandible shape and size that are used by males in intraspecific combats. Stag beetles were captured, measured, weighed, and released in the framework of a capture-mark-recapture study. The relationship of mandible length (ML) and head width in respect to the overall body size was described by a segmented regression model. A linear relationship was detected between ML and head width. The scaling relationships for both ML and head width identified the same switchpoint, highlighting the advantages of using combined results of weapons and their supporting structures in such analysis. These results led to a more consistent distinction of males in two morphologies: minor and major. The survival probability of individuals was dependent on the morphological class and was higher for minor males than for major. Elytron length and body mass of the individuals did not show any significant variation during the season. Differences in predatory pressure were detected between morphs by the collection and analysis of body fragments due to the predatory activity of corvids. Morphological differences and shift in demographic and ecological parameters between the two classes suggested that selection continues to favor intrasexual dimorphism in this species throughout a trade-off mechanism between costs and benefits of carrying exaggerated traits. PMID:26220669
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 physiology. 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 by the Department of Energy in developing generic methods for evaluating radiation dose to biota, we have examined the utility of applying allometric techniques to predicting radionuclide tissue concentration across a large range of terrestrial and riparian species of animals. This particular study examined 23 radionuclides. Initial investigations suggest that the allometric approach can provide a useful tool to derive limiting values of uptake and elimination factors for animals. PMID:12590070
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. PMID:24724476
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 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
The allometric model in chronic myocardial infarction
2012-01-01
Background An allometric relationship between different electrocardiogram (ECG) parameters and infarcted ventricular mass was assessed in a myocardial infarction (MI) model in New Zealand rabbits. Methods A total of fifteen animals were used, out of which ten underwent left anterior descending coronary artery ligation to induce infarction (7–35% area). Myocardial infarction (MI) evolved and stabilized during a three month-period, after which, rabbits were sacrificed and the injured area was histologically confirmed. Right before sacrifice, ECGs were obtained to correlate several of its parameters to the infarcted mass. The latter was normalized after combining data from planimetry measurements and heart weight. The following ECG parameters were studied: RR and PR intervals, P-wave duration (PD), QRS duration (QRSD) and amplitude (QRSA), Q-wave (QA), R-wave (RA) and S-wave (SA) amplitudes, T-wave peak amplitude (TA), the interval from the peak to the end of the T-wave (TPE), ST-segment deviation (STA), QT interval (QT), corrected QT and JT intervals. Corrected QT was analyzed with different correction formulae, i.e., Bazett (QTB), Framingham (QTFRA), Fridericia (QTFRI), Hodge (QTHO) and Matsunaga (QTMA) and compared thereafter. The former variables and infarcted ventricular mass were then fitted to the allometric equation in terms of deviation from normality, in turn derived after ECGs in 5 healthy rabbits. Results Six variables (JT, QTB, QA, SA, TA and STA) presented statistical differences among leads. QT showed the best allometric fit (r = 0.78), followed by TA (r = 0.77), STA (r = 0.75), QTFRA (r = 0.72), TPE (r = 0.69), QTFRI (r = 0.68) and QTMA (r = 0.68). Corrected QT’s (QTFRA, QTFRI and QTMA) performed worse than the uncorrected counterpart (QT), the former scaling allometrically with similar goodness of fits. Conclusions QT, TA, STA and TPE could possibly be used to assess infarction extent in an old MI event through the
Julian Huxley, Uca pugnax and the allometric method.
Packard, Gary C
2012-02-15
The allometric method, which often is attributed to Julian Huxley, entails fitting a straight line to logarithmic transformations of the original bivariate data and then back-transforming the resulting equation to form a power function in the arithmetic scale. Development of the technique was strongly influenced by Huxley's own research on growth by the enlarged 'crusher' claw in male fiddler crabs (Uca pugnax). Huxley reported a discontinuity in the log-log plot of chela mass vs body mass, which he interpreted as an abrupt change in relative growth of the chela at about the time crabs attain sexual maturity. My analysis of Huxley's arithmetic data indicates, however, that the discontinuity was an artifact caused by logarithmic transformation and that dynamics of growth by the crusher claw do not change at any point during development. Arithmetic data are well described by a power function fitted by nonlinear regression but not by one estimated by back-transforming a line fitted to logarithms. This finding and others like it call into question the continued reliance on the allometric method in contemporary research. PMID:22279062
Allometric control of human gait
NASA Astrophysics Data System (ADS)
Griffin, Lori Ann
The purpose of the study was to extract the information contained in the fluctuations in the stride interval time series and the correlation properties of walking. To determine if the time series had memory or long-time correlation properties, the decay (loss) of correlation of the data across time was studied. The information acquired was to determine if control of walking could be better understood, by studying statistics of stride intervals. Furthermore, it was determined if the time series for walking was stable enough to establish a baseline for future studies. Allometric analysis was done on relaxed walking for 10 individuals. The data obtained during the experiments consisted of the time interval for a given stride and the number of strides in the sequence of steps. The maximal extension of the right leg, the ``stride interval'' versus the stride number, yielded a graph that has all the characteristics of a time series. Insight into the stride interval time series was obtained using relative dispersion, also know as the coefficient of variation, the ratio of the standard deviation to the mean. The results indicated memory in the control of walking for all subjects. Furthermore, memory was not maintained once the data was randomized suggesting the order of strides is important. The amount of memory differed for each subject, whereby some subjects had significant memory (high correlation coefficients = 0.693) while others showed low correlation coefficients. The relative dispersion for all subjects decreased with increasing aggregation number. This straight line with a negative slope depicted an inverse power-law relation between the relative dispersion and the aggregation number. The data does not have a dominant scale and can be evaluated on many scales without information lost. Although these data alone do not establish a baseline, the data analyzed using allometric analysis appears sufficiently stable to establish a baseline norm for walking. Finally, the
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
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.
Allometric secular change in the long bones from the 1800s to the present.
Meadows, L; Jantz, R L
1995-09-01
Allometric secular changes in the six long limb bones for White and Black males from the mid 1800s to the present are examined. Long bone lengths are available from the Terry collection and WWII casualties. We conducted two types of analysis to reveal secular changes. First, allometry scaling coefficients were derived by regressing log bone length onto log stature. These showed that the femur, tibia and fibula were positively allometric with stature, while the humerus, radius and ulna were isometric. The lower limb bones were more positively allometric in the WWII sample than in the Terry sample. Second, secular changes in length of femur and tibia and in the tibia/femur ratio were evaluated, using modern forensic cases in addition to the Terry and WWII samples. This analysis shows that secular increase in lower limb bone length is accompanied by relatively longer tibiae. Secular changes in proportion may render stature formulae based on nineteenth century samples, such as the Terry collection, inappropriate for modern forensic cases. The positive allometry of the lower limb bones argues against using simple femur/stature ratio, which assumes constant proportionality, as an alternative to regression equations. PMID:7595319
The Einstein Relation for the KPZ Equation
NASA Astrophysics Data System (ADS)
Gonçalves, Patrícia; Jara, Milton
2015-03-01
We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying microscopic dynamics. In particular, we derive the second-order Einstein relation for the transport coefficient of the KPZ equation, in terms of the conserved quantity , the diffusion coefficient , the strength of the asymmetry and the static compressibility of the system.
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.…
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
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.
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
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
Left Ventricular Hypertrophy: An allometric comparative analysis of different ECG markers
NASA Astrophysics Data System (ADS)
Bonomini, M. P.; Ingallina, F.; Barone, V.; Valentinuzzi, M. E.; Arini, P. D.
2011-12-01
Allometry, in general biology, measures the relative growth of a part in relation to the whole living organism. Left ventricular hypertrophy (LVH) is the heart adaptation to excessive load (systolic or diastolic). The increase in left ventricular mass leads to an increase in the electrocardiographic voltages. Based on clinical data, we compared the allometric behavior of three different ECG markers of LVH. To do this, the allometric fit AECG = δ + β (VM) relating left ventricular mass (estimated from ecocardiographic data) and ECG amplitudes (expressed as the Cornell-Voltage, Sokolow and the ECG overall voltage indexes) were compared. Besides, sensitivity and specifity for each index were analyzed. The more sensitive the ECG criteria, the better the allometric fit. In conclusion: The allometric paradigm should be regarded as the way to design new and more sensitive ECG-based LVH markers.
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
Anatomical and physiological basis for the allometric scaling of cisplatin clearance in dogs.
Achanta, S; Sewell, A; Ritchey, J W; Broaddus, K; Bourne, D W A; Clarke, C R; Maxwell, L K
2016-06-01
Cisplatin is a platinum-containing cytotoxic drug indicated for the treatment of solid tumors in veterinary and human patients. Several of the algorithms used to standardize the doses of cytotoxic drugs utilize allometry, or the nonproportional relationships between anatomical and physiological variables, but the underlying basis for these relationships is poorly understood. The objective of this proof of concept study was to determine whether allometric equations explain the relationships between body weight, kidney weight, renal physiology, and clearance of a model, renally cleared anticancer agent in dogs. Postmortem body, kidney, and heart weights were collected from 364 dogs (127 juveniles and 237 adults, including 51 dogs ≥ 8 years of age). Renal physiological and cisplatin pharmacokinetic studies were conducted in ten intact male dogs including two juvenile and eight adult dogs (4-55 kg). Glomerular filtration rate (GFR), effective renal plasma flow, effective renal blood flow, renal cisplatin clearance, and total cisplatin clearance were allometrically related to body weight with powers of 0.75, 0.59, 0.61, 0.71, and 0.70, respectively. The similar values of these diverse mass exponents suggest a common underlying basis for the allometry of kidney size, renal physiology, and renal drug handling. PMID:26440900
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
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
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. PMID:24347386
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.
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.
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.
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.
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
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
Runciman, S; Seymour, RS; Baudinette, RV; Pearson, JT
2005-01-01
Pelicans produce altricial chicks that develop into some of the largest birds capable of sustained flight. We traced pulmonary morphological development in the Australian pelican, Pelicanus conspicillatus, from third trimester embryos to adults. We described growth and development with allometric relationships between lung components and body mass or lung volume, according to the equation y = axb. Pelican lung volume increased faster than body mass (b = 1.07). Relative to lung volume, the airways and vascular spaces increased allometrically (b > 1) in embryos, but isometrically (b ≈ 1) after hatching. Parabronchial mantle volume decreased (b < 1) prior to hatching and increased isometrically thereafter. Surface area of air capillaries, blood capillaries and the blood–gas barrier increased relative to lung volume (b > 0.67) before and after hatching. Barrier thickness decreased before hatching, remained constant in juveniles and decreased by adulthood. The anatomical diffusing capacity significantly increased before hatching (b = 4.44) and after hatching (b = 1.26). Although altricial pelicans developed pulmonary complexity later than precocial turkeys, the volume-specific characteristics were similar. However, lungs of volant adult pelicans became significantly larger, with a greater capacity for gas exchange, than lungs of terrestrial turkeys. Exchange characteristics of growing pelican lungs were inferior to those of adult birds of 26 other species, but converged with them at maturity. PMID:16191165
Quadratic relations in continuous and discrete Painlevé equations
NASA Astrophysics Data System (ADS)
Ramani, A.; Grammaticos, B.; Tamizhmani, T.
2000-04-01
The quadratic relations between the solutions of a Painlevé equation and that of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the quadratic relations existing for the continuous PII , PIII , PV and PVI have analogues as well as consequences in the discrete case. Moreover, the discrete Painlevé equations have quadratic relations of their own without any reference to the continuous case.
An allometric scaling relationship in the brain of preterm infants
Paul, Rachel A; Smyser, Christopher D; Rogers, Cynthia E; English, Ian; Wallendorf, Michael; Alexopoulos, Dimitrios; Meyer, Erin J; Van Essen, David C; Neil, Jeffrey J; Inder, Terrie E
2014-01-01
Allometry has been used to demonstrate a power–law scaling relationship in the brain of premature born infants. Forty-nine preterm infants underwent neonatal MRI scans and neurodevelopmental testing at age 2. Measures of cortical surface area and total cerebral volume demonstrated a power–law scaling relationship (α = 1.27). No associations were identified between these measures and investigated clinical variables. Term equivalent cortical surface area and total cerebral volume measures and scaling exponents were not related to outcome. These findings confirm a previously reported allometric scaling relationship in the preterm brain, and suggest that scaling is not a sensitive indicator of aberrant cortical maturation. PMID:25540808
Discrete systems related to the sixth Painlevé equation
NASA Astrophysics Data System (ADS)
Ramani, A.; Ohta, Y.; Grammaticos, B.
2006-09-01
We present discrete Painlevé equations which can be obtained as contiguity relations of the solutions of the continuous Painlevé VI. The derivation is based on the geometry of the affine Weyl group D(1)4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau-Ablowitz-Fokas equation, which is a Miura transformed, 'modified', PVI.
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
Snelling, Edward P; Matthews, Philip G D; Seymour, Roger S
2012-10-01
The discontinuous gas exchange cycle (DGC) is a three-phase breathing pattern displayed by many insects at rest. The pattern consists of an extended breath-hold period (closed phase), followed by a sequence of rapid gas exchange pulses (flutter phase), and then a period in which respiratory gases move freely between insect and environment (open phase). This study measured CO(2) emission in resting locusts Locusta migratoria throughout ontogeny, in normoxia (21 kPa P(O2)), hypoxia (7 kPa P(O2)) and hyperoxia (40 kPa P(O2)), to determine whether body mass and ambient O(2) affect DGC phase duration. In normoxia, mean CO(2) production rate scales with body mass (M(b); g) according to the allometric power equation , closed phase duration (C; min) scales with body mass according to the equation C=8.0M(b)(0.38±0.29), closed+flutter period (C+F; min) scales with body mass according to the equation C+F=26.6M (0.20±0.25)(b) and open phase duration (O; min) scales with body mass according to the equation O=13.3M(b) (0.23±0.18). Hypoxia results in a shorter C phase and longer O phase across all life stages, whereas hyperoxia elicits shorter C, C+F and O phases across all life stages. The tendency for larger locusts to exhibit longer C and C+F phases might arise if the positive allometric scaling of locust tracheal volume prolongs the time taken to reach the minimum O(2) and maximum CO(2) set-points that determine the duration of these respective periods, whereas an increasingly protracted O phase could reflect the additional time required for larger locusts to expel CO(2) through a relatively longer tracheal pathway. Observed changes in phase duration under hypoxia possibly serve to maximise O(2) uptake from the environment, whereas the response of the DGC to hyperoxia is difficult to explain, but could be affected by elevated levels of reactive oxygen species. PMID:22735346
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
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.
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. PMID:21230596
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.
Allometric and metameric shape variation in Pan mandibular molars: a digital morphometric analysis.
Singleton, Michelle; Rosenberger, Alfred L; Robinson, Chris; O'neill, Rob
2011-02-01
The predominance of molar teeth in fossil hominin assemblages makes the patterning of molar shape variation a topic of bioanthropological interest. Extant models are the principal basis for understanding dental variation in the fossil record. As the sister taxon to the hominin clade, Pan is one such model and the only widely accepted extant hominid model for both interspecific and intraspecific variation. To explore the contributions of allometric scaling and meristic variation to molar variation in Pan, we applied geometric shape analysis to 3D landmarks collected from virtual replicas of chimpanzee and bonobo mandibular molars. Multivariate statistical analysis and 3D visualization of metameric and allometric shape vectors were used to characterize shape differences and test the hypothesis that species of Pan share patterns of metameric variation and molar shape allometry. Procrustes-based shape variables were found to effectively characterize crown shape, sorting molars into species and tooth-row positions with ≥ 95% accuracy. Chimpanzees and bonobos share a common pattern of M(1) -M(2) metameric variation, which is defined by differences in the relative position of the metaconid, size of the hypoconulid, curvature of the buccal wall, and proportions of the basins and foveae. Allometric scaling of molar shape is homogeneous for M(1) and M(2) within species, but bonobo and chimpanzee allometric vectors are significantly different. Nevertheless, the common allometric shape trend explains most molar-shape differences between P. paniscus and P. troglodytes. When allometric effects are factored out, chimpanzee and bonobo molars are not morphometrically distinguishable. Implications for hominid taxonomy and dietary reconstruction are discussed. PMID:21235007
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.
Electromagnetic Klein-Gordon and Dirac Equations in Scale Relativity
NASA Astrophysics Data System (ADS)
Célérier, Marie-Noëlle; Nottale, Laurent
We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scale-covariant derivative tool. Finally, the electromagnetic Klein-Gordon equation has been recovered with a covariant derivative constructed by combining the quantum-covariant velocity operator and the scale-covariant derivative. We show here that if one tries to derive the electromagnetic Dirac equation from the Klein-Gordon one as for the free particle motion, i.e. as a square root of the time part of the Klein-Gordon operator, one obtains an additional term which is the relativistic analog of the spin-magnetic field coupling term of the Pauli equation. However, if one first applies the quantum covariance, then implements the scale covariance through the scale-covariant derivative, one obtains the electromagnetic Dirac equation in its usual form. This method can also be applied successfully to the derivation of the electromagnetic Klein-Gordon equation. This suggests it rests on more profound roots of the theory, since it encompasses naturally the spin-charge coupling.
The relation between Hill's equation and individual muscle properties.
Thaller, S; Wagner, H
2004-12-01
In this paper we deal with movement-independent individual muscle properties derived from Hill's equation. Relations between these properties are found by theoretical considerations. We define a dimensionless quantity that turns out to play a major role in characterizing individual muscle properties, and we analyse normalization and symmetry behaviour of the parameters in Hill's equation. This leads to a systematic, transparent, and useful overview of mathematical relations involving muscle parameters. We examine the experimentally determined parameters of 62 subjects to find additional empirical relations between the muscle properties described by the parameters of Hill's equation. In the light of the theoretical end empirical results we investigate the connections between maximum efficiency, endurance, and fibre composition. PMID:15501465
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. PMID:27322124
The Complexity of Relating Quantum Channels to Master Equations
NASA Astrophysics Data System (ADS)
Cubitt, Toby S.; Eisert, Jens; Wolf, Michael M.
2012-03-01
Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.
Clausius relation and Friedmann equation in FRW universe model
Cao, Qiao-Jun; Chen, Yi-Xin; Shao, Kai-Nan E-mail: yxchen@zimp.zju.edu.cn
2010-05-01
It has been shown that Friedmann equation of FRW universe can be derived from the first law of thermodynamics in Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, scalar-tensor gravity and f(R) gravity. Moreover, it was pointed out that the temperature of the apparent horizon can be obtained using the tunneling formalism for the corresponding observers defined by Kodama vector. In this article, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics associated with the apparent horizon in FRW universe is relative to the Kodama observers. We illustrate the derivation of Friedmann equation, and also extend the study to the cases of Hořava-Lifshitz gravity and IR modified Hořava-Lifshitz gravity.
Popović, Zoran B; Sun, Jing Ping; Yamada, Hirotsugu; Drinko, Jeannie; Mauer, Karin; Greenberg, Neil L; Cheng, Yuanna; Moravec, Christine S; Penn, Marc S; Mazgalev, Todor N; Thomas, James D
2005-10-01
While the heart size maintains a constant proportion to body size, heart function parameters, such as heart rate and cardiac output, show a more complex scaling pattern. How these phenomena affect the long-axis left ventricular (LV) function is unknown. We studied 10 mice, 15 rats, 6 rabbits, 8 mongrel dogs and 38 human volunteers. Doppler tissue echocardiography data were postprocessed to reconstruct mitral annulus (MA) peak systolic velocity and displacement. The relationship between MA peak velocity, MA displacement and LV ejection time, and LV end-diastolic volume (and mass) were fit to an allometric (power-law) equation Y=kMbeta. LV mass varied from 0.062 to 255 g, while end-diastolic volume varied from 0.014 to 205 ml. beta values of the relation between LV ejection time and LV end-diastolic volume and mass were 0.247+/-0.017 and 0.267+/-0.018, respectively. beta values of the relationship between MA displacement and LV end-diastolic volume and mass were 0.358+/-0.047 and 0.390+/-0.051 (P<0.023 versus beta of LV ejection time). beta values of the relationship between MA peak systolic velocity and LV end-diastolic volume and mass were 0.096+/-0.012 and 0.100+/-0.013, respectively (P<0.0001 versus 0). Finally, beta values of the relationship between the long-to-short axis displacement ratio and LV end-diastolic volume and mass were 0.077+/-0.017 and 0.086+/-0.019 (P<0.0001 versus 0). We conclude that MA velocity, displacement, and long-to-short axis displacement ratio scale allometrically to heart size. This reduces the relative long-axis contribution to heart function in small mammals. PMID:16002448
Doherty, M; Dimitriou, L
1997-01-01
OBJECTIVE: To compare lung volumes in a large cross sectional sample of Greek swimmers, land based athletes, and sedentary controls by means of allometric scaling. METHODS: Four hundred and fifty nine asymptomatic Greek children and young adults (age 10-21 years), including 159 swimmers, 130 land based athletes, and 170 sedentary controls, performed forced expiratory manoeuvres into a portable spirometer. Measurements included forced vital capacity, forced expiratory volume in one second (FEV1.0), and peak expiratory flow. Body mass and stature were also measured using standardised anthropometric techniques. RESULTS: Logarithmic transformations showed that in FEV1.0 was highly related to in stature in males and females (r = 0.93 and 0.86 respectively, P < 0.001) and were used to determine the exponent in an allometric equation which also included age and age. Resulting power functions, FEV1.0/stature, were 0.64 (0.18) litres/m2.69 and 0.33 (0.24) litres/m2.32 for males and females respectively (mean (SE)). The male and female swimming groups had larger FEV1.0 than both land based athletes and sedentary controls (one way analysis of variance, P < 0.001). In addition, male national standard swimmers (n = 38) had superior FEV1.0 in comparison with male non-national standard swimmers (n = 24; t test, P < 0.05). However, when years of swimming training was controlled for by analysis of covariance, the difference in FEV1.0 between the two groups was no longer evident. CONCLUSIONS: Swimmers have superior FEV1.0 independent of stature and age in comparison with both land based athletes and sedentary controls. In addition, male national standard swimmers have superior FEV1.0 independent of stature and age in comparison with male non-national standard swimmers. When years of training is controlled for, the difference in FEV1.0 between the two groups is no longer evident. This suggests that the years of swimming training and/or the earlier age at which training begins may
Reciprocal relations based on the non-stationary Boltzmann equation
NASA Astrophysics Data System (ADS)
Sharipov, Felix
2012-03-01
The reciprocal relations for open gaseous systems are obtained on the basis of main properties of the non-stationary Boltzmann equation and gas-surface interaction law. It is shown that the main principles to derive the kinetic coefficients satisfying the reciprocal relations remain the same as those used for time-independent gaseous systems [F. Sharipov, Onsager-Casimir reciprocal relations based on the Boltzmann equation and gas-surface interaction law single gas, Phys. Rev. 73 (2006) 026110]. First, the kinetic coefficients are obtained from the entropy production expression; then it is proved that the coefficient matrix calculated for time reversed source functions is symmetric. The proof is based on the reversibility of the gas-gas and gas-surface interactions. Three examples of applications of the present theory are given. None of these examples can be treated in the frame of the classical Onsager-Casimir reciprocal relations, which are valid only in a particular case, when the kinetic coefficients are odd or even with respect to the time reversion. The approach is generalized for gaseous mixtures.
Stochastic Equation of Fragmentation and Branching Processes Related to Avalanches
NASA Astrophysics Data System (ADS)
Beznea, Lucian; Deaconu, Madalina; Lupaşcu, Oana
2016-02-01
We give a stochastic model for the fragmentation phase of an avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by Bertoin. A fractal property of this process is emphasized. We also establish a specific stochastic differential equation of fragmentation. It turns out that specific branching Markov processes on finite configurations of particles with sizes bigger than a strictly positive threshold are convenient for describing the continuous time evolution of the number of the resulting fragments. The results are obtained by combining analytic and probabilistic potential theoretical tools.
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
Perturbative Solutions of the Extended Constraint Equations in General Relativity
NASA Astrophysics Data System (ADS)
Butscher, Adrian
2007-05-01
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface {mathcal{Z}} in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on {mathcal{Z}} , and are equivalent to the usual constraint equations that {mathcal{Z}} satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.
Sup-t-norm and inf-residuum are a single type of relational equations
NASA Astrophysics Data System (ADS)
Bartl, Eduard; Belohlavek, Radim
2011-08-01
We show that the sup-t-norm and inf-residuum types of fuzzy relational equations, considered in the literature as two different types, are in fact two particular instances of a single, more general type of equations. We demonstrate that several pairs of corresponding results on the sup-t-norm and inf-residuum types of equations are simple consequences of single results regarding the more general type of equations. We also show that the new type of equations subsumes other types of equations such as equations with constraints on solutions, examples of which are fuzzy relational equations whose solutions are required to be crisp (ordinary) relations.
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. PMID:25333341
Riviere, J E; Martin-Jimenez, T; Sundlof, S F; Craigmill, A L
1997-12-01
correlation, or be inconclusive due to the lack of quality data or excessive variability due to the multi-laboratory origin of the FARAD data. The results of this study show that interspecies scaling is applicable to certain veterinary drugs. The experimental determination of the coefficients of the allometric equation for relevant pharmacokinetic parameters (clearance and volume of distribution) could be an important tool in estimating dose in species where the drug has never been studied. This could have important consequences in terms of avoiding the use of dose-titration studies in Phase I of drug development, for drugs that are experimentally 'well behaved.' PMID:9430769
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)
İsmail, Aslan
2014-05-01
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before.
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 constraints on Sr/Ca and Ba/Ca partitioning in terrestrial mammalian trophic chains.
Balter, Vincent
2004-03-01
In biological systems, strontium (Sr) and barium (Ba) are two non-essential elements, in comparison to calcium (Ca) which is essential. The Sr/Ca and Ba/Ca ratios tend to decrease in biochemical pathways which include Ca as an essential element, and these processes are termed biopurification of Ca. The quantitative pathway of the biopurification of Ca in relation to Sr and Ba between two biological reservoirs ( Rn and R(n -1)) is measured with an observed ratio (OR) expressed by the (Sr/Ca) Rn /(Sr/Ca)( Rn-1) and (Ba/Ca) Rn /(Ba/Ca)( Rn-1) ratios. For a mammalian organism, during the whole biopurification of Ca starting with the diet to the ultimate reservoir of Ca which is the bone, the mean values for ORSr and ORBa are 0.25 and 0.2, respectively. In this study, published Sr/Ca and Ba/Ca ratios are used for three sets of soils, plants, and bones of herbivorous and carnivorous mammals, each comprising a trophic chain, to illustrate the biopurification of Ca at the level of trophic chains. Calculated ORSr and ORBa of herbivore bones in relation to plants and of bones of carnivores in relation to bones of herbivores give ORSr=0.30+/-0.08 and ORBa=0.16+/-0.08, thus suggesting that trophic chains reflect the Sr/Ca and Ba/Ca fluxes that are prevalent at the level of a mammalian organism. The slopes of the three regression equations of log(Sr/Ca) vs. log(Ba/Ca) are similar, indicating that the process of biopurification of Ca with respect to Sr and Ba is due to biological processes and is independent of the geological settings. Modifications of the logarithmic expression of the Sr/Ca and Ba/Ca relationship allow a new formula of the biopurification process to be deduced, leading to the general equation ORBa=ORSr(1.79+/-0.33), where the allometric coefficient is the mean of the slopes of the three regression equations. Some recent examples are used to illustrate this new analysis of predator-prey relations between mammals. This opens up new possibilities for the
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.
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
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
Early development and allometric growth patterns of the grumatã (Prochilodus vimboides Kner, 1859).
Souza, Guilherme; Melo, Edésio J T; Caramaschi, Erica P; Andrade, Dalcio R; Monteiro, Leandro R
2016-06-01
The objective of this study was to characterize the early development and allometric growth of the grumatã (Prochilodus vimboides). We describe a sample of 266 eggs and larvae obtained through induced spawning. The eggs were spherical (mean 3.7 mm diameter), exhibited a yellow yolk and were non-adhesive and pelagic after fertilization and hydration. The time elapsed between the early cleavage and post-flexion stages was considered short (328 hours, 8054 hour-degrees) in regard to the development times of other Neotropical rheophilic species, but time to hatching was considerably longer than in other Prochilodus species. The most notable anatomical changes were observed between the end of the yolk larval stage and the beginning of the pre-flexion stage, when the larvae displayed directed swimming and the digestive system became functional, enabling the transition from endogenous to exogenous feeding. After hatching, the larvae grew from 6.04 to 15.15 mm in total length average. Two growth phases were observed at this stage: a non-linear asymptotic curve in yolk-sac larvae, and a linear constant-rate growth phase after exogenous feeding started. Allometric growth related to standard length was positive for head length, negative for eye diameter, and switched between phases from negative to positive in body depth and head height. Morphological development and allometric growth in different larval phases impose drastic anatomical and physiological changes that are synchronic with habitat changes and the flood cycles during the reproductive period. PMID:26199146
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. PMID:27284070
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
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
Arab, Hossein-Ali; Muhammadnejad, Samad; Naeimi, Saeideh; Arab, Attieh
2013-06-01
This study aimed to establish an allometric scaling relationship between the frequency of intestinal contractions and body mass of different mammalian species. The frequency of intestinal contractions of rabbit, guinea pig, rat and mouse were measured using an isolated organ system. The isolated rings were prepared from proximal segments of jejunums and the frequency of contractions was recorded by an isometric force procedure. The coefficients of the obtained allometric equation were ascertained by computation of least squares after logarithmic transformation of both body mass and frequency. Significant differences (p less than 0.001) were shown in the frequency of contractions between different species. The highest frequency that corresponded to the mice was 57.7 min-1 and the 95 percent confidence interval (CI) ranged from 45.4 to 70, while rabbits showed the lowest frequency (12.71 min-1, CI: 8.6-16.8). Logarithms of frequency were statistically proportional to logarithms of body mass (r00.99; p less than 0.001). The data fitted an equation F 1/4 18:51B 0:31 and the 95 percent confidence interval of the exponent ranged from -0.30 to -0.32. The results of this study suggest that it is probably possible to extrapolate the intestinal contraction frequency of other mammalian species by the means of allometry scaling. PMID:23660674
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.
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. PMID:27114057
A note on Verhulst's logistic equation and related logistic maps
NASA Astrophysics Data System (ADS)
Ranferi Gutiérrez, M.; Reyes, M. A.; Rosu, H. C.
2010-05-01
We consider the Verhulst logistic equation and a couple of forms of the corresponding logistic maps. For the case of the logistic equation we show that using the general Riccati solution only changes the initial conditions of the equation. Next, we consider two forms of corresponding logistic maps reporting the following results. For the map xn + 1 = rxn(1 - xn) we propose a new way to write the solution for r = -2 which allows better precision of the iterative terms, while for the map xn + 1 - xn = rxn(1 - xn + 1) we show that it behaves identically to the logistic equation from the standpoint of the general Riccati solution, which is also provided herein for any value of the parameter r.
Fractional Klein-Gordon Equations and Related Stochastic Processes
NASA Astrophysics Data System (ADS)
Garra, Roberto; Orsingher, Enzo; Polito, Federico
2014-03-01
This paper presents finite-velocity random motions driven by fractional Klein-Gordon equations of order α in (0,1] . A key tool in the analysis is played by the McBride's theory which converts fractional hyper-Bessel operators into Erdélyi-Kober integral operators. Special attention is payed to the fractional telegraph process whose space-dependent distribution solves a non-homogeneous fractional Klein-Gordon equation. The distribution of the fractional telegraph process for α = 1 coincides with that of the classical telegraph process and its driving equation converts into the homogeneous Klein-Gordon equation. Fractional planar random motions at finite velocity are also investigated, the corresponding distributions obtained as well as the explicit form of the governing equations. Fractionality is reflected into the underlying random motion because in each time interval a binomial number of deviations B(n,α ) (with uniformly-distributed orientation) are considered. The parameter n of B(n,α ) is itself a random variable with fractional Poisson distribution, so that fractionality acts as a subsampling of the changes of direction. Finally the behaviour of each coordinate of the planar motion is examined and the corresponding densities obtained. Extensions to N -dimensional fractional random flights are envisaged as well as the fractional counterpart of the Euler-Poisson-Darboux equation to which our theory applies.
Allometric scaling of infraorbital surface topography in Homo.
Maddux, Scott D; Franciscus, Robert G
2009-02-01
Infraorbital morphology is often included in phylogenetic and functional analyses of Homo. The inclusion of distinct infraorbital configurations, such as the "canine fossa" in Homo sapiens or the "inflated" maxilla in Neandertals, is generally based on either descriptive or qualitative assessments of this morphology, or simple linear chord and subtense measurements. However, the complex curvilinear surface of the infraorbital region has proven difficult to quantify through these traditional methods. In this study, we assess infraorbital shape and its potential allometric scaling in fossil Homo (n=18) and recent humans (n=110) with a geometric morphometric method well-suited for quantifying complex surface topographies. Our results indicate that important aspects of infraorbital shape are correlated with overall infraorbital size across Homo. Specifically, individuals with larger infraorbital areas tend to exhibit relatively flatter infraorbital surface topographies, taller and narrower infraorbital areas, sloped inferior orbital rims, anteroinferiorly oriented maxillary body facies, posteroinferiorly oriented maxillary processes of the zygomatic, and non-everted lateral nasal margins. In contrast, individuals with smaller infraorbital regions generally exhibit relatively depressed surface topographies, shorter and wider infraorbital areas, projecting inferior orbital rims, posteroinferiorly oriented maxillary body facies, anteroinferiorly oriented maxillary processes, and everted lateral nasal margins. These contrasts form a continuum and only appear dichotomized at the ends of the infraorbital size spectrum. In light of these results, we question the utility of incorporating traditionally polarized infraorbital morphologies in phylogenetic and functional analyses without due consideration of continuous infraorbital and facial size variation in Homo. We conclude that the essentially flat infraorbital surface topography of Neandertals is not unique and can be
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.
Tredennick, Andrew T.; Bentley, Lisa Patrick; Hanan, Niall P.
2013-01-01
Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those
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.
Xu, Liangwen; Snelling, Edward P; Seymour, Roger S
2014-11-01
Burrowing is an important life strategy for many insects, yet the energetic cost of constructing burrows has never been studied in insects of different sizes. Open flow respirometry was used to determine the allometric scaling of standard metabolic rate (MRS) and burrowing metabolic rate (MRB) in the heaviest extant cockroach species, the Giant Burrowing Cockroach Macropanesthia rhinoceros, at different stages of development. At 10 °C, MRS (mW) scales with body mass (M; g) according to the allometric power equation, MRS=0.158M(0.74), at 20 °C the equation is MRS=0.470M(0.53), and at 30 °C the equation is MRS=1.22M(0.49) (overall Q10=2.23). MRS is much lower in M. rhinoceros compared to other insect species, which is consistent with several aspects of their life history, including flightlessness, extreme longevity (>5 years), burrowing, parental behaviour, and an energy-poor diet (dry eucalypt leaf litter). Energy expenditure during burrowing at 25 °C scales according to MRB=16.9M(0.44), and is approximately 17 times higher than resting rates measured at the same temperature, although the metabolic cost over a lifetime is probably low, because the animal does not burrow to find food. The net cost of transport by burrowing (Jm(-1)) scales according to NCOT=120M(0.49), and reflects the energetically demanding task of burrowing compared to other forms of locomotion. The net cost of excavating the soil (J cm(-3)) is statistically independent of body size. PMID:25257537
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. PMID:25759244
An equivalence relation for the Ginzburg-Landau equations of superconductivity.
Kaper, H. G.; Takac, P.; Mathematics and Computer Science; Univ. Rostock
1997-01-01
Gauge invariance is used to establish an equivalence relation between solutions of the time-independent and time-dependent Ginzburg-Landau equations that describe the same physical state of a superconductor. The equivalence relation shows how equilibrium configurations are obtained as large-time asymptotic limits of solutions of the time-dependent Ginzburg-Landau equations.
On discrete three-dimensional equations associated with the local Yang-Baxter relation
NASA Astrophysics Data System (ADS)
Kashaev, R. M.
1996-12-01
The local Yang-Baxter equation (YBE), introduced by Maillet and Nijhoff, is a proper generalization to three dimensions of the zero curvature relation. Recently, Korepanov has constructed an infinite set of integrable three-dimensional lattice models, and has related them to solutions to the local YBE. The simplest Korepanov model is related to the star-triangle relation in the Ising model. In this Letter the corresponding discrete equation is derived. In the continuous limit it leads to a differential three-dimensional equation, which is symmetric with respect to all permutations of the three coordinates. A similar analysis of the star-triangle transformation in electric networks leads to the discrete bilinear equation of Miwa, associated with the BKP hierarchy. Some related operator solutions to the tetrahedron equation are also constructed.
Sexual size dimorphism and allometric growth of Morelet's crocodiles in captivity.
Barrios-Quiroz, Gabriel; Casas-Andreu, Gustavo; Escobedo-Galván, Armando H
2012-03-01
Few studies have conducted morphological analyses of crocodilians, and little information exists on differences between size-classes and sexes in Neotropical crocodilians. In this study, we measured nine morphological traits in 121 captive Morelet's crocodiles Crocodylus moreletii (81 females and 40 males). Our results revealed that individuals < 2 m total length do not exhibit sexual dimorphism in morphometric characteristics. However, for crocodiles over 2 m in length, males were significantly larger than females in terms of dorsal-cranial length, cranial width, snout width and snout-ventral length. In general, morphological traits demonstrated a strongly significant relationship with total length at the smaller size class of 150-200 cm length. However, in the highest size class of 250-300 cm length (large adult males), morphological traits were no longer significantly related with total length. Male crocodiles demonstrated allometric growth of cranial morphology with significantly greater increase in cranial width, snout width, and mid-snout width relative to total length at higher size classes. Morphological dimorphism and allometric growth may be associated with adaptive strategies for reproductive success. PMID:22379988
Bruner, Emiliano; de la Cuétara, José Manuel; Colom, Roberto; Martin-Loeches, Manuel
2012-01-01
The corpus callosum displays considerable morphological variability between individuals. Although some characteristics are thought to differ between male and female brains, there is no agreement regarding the source of this variation. Biomedical imaging and geometric morphometrics have provided tools to investigate shape and size variation in terms of integration and correlation. Here we analyze variations at the midsagittal outline of the corpus callosum in a sample of 102 young adults in order to describe and quantify the pattern of covariation associated with its morphology. Our results suggest that the shape of the corpus callosum is characterized by low levels of morphological integration, which explains the large variability. In larger brains, a minor allometric component involves a relative reduction of the splenium. Small differences between males and?females are associated with this allometric pattern, induced primarily by size variation rather than gender-specific characteristics. PMID:22296183
Bruner, Emiliano; de la Cuétara, José Manuel; Colom, Roberto; Martin-Loeches, Manuel
2012-04-01
The corpus callosum displays considerable morphological variability between individuals. Although some characteristics are thought to differ between male and female brains, there is no agreement regarding the source of this variation. Biomedical imaging and geometric morphometrics have provided tools to investigate shape and size variation in terms of integration and correlation. Here we analyze variations at the midsagittal outline of the corpus callosum in a sample of 102 young adults in order to describe and quantify the pattern of covariation associated with its morphology. Our results suggest that the shape of the corpus callosum is characterized by low levels of morphological integration, which explains the large variability. In larger brains, a minor allometric component involves a relative reduction of the splenium. Small differences between males and?females are associated with this allometric pattern, induced primarily by size variation rather than gender-specific characteristics. PMID:22296183
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
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
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.
ERIC Educational Resources Information Center
Asiru, M. A.
2007-01-01
Under predetermined conditions on the roots and coefficients, necessary and sufficient conditions relating the coefficients of a given cubic equation x[cubed] + ax[squared] + bx + c = 0 can be established so that the roots possess desired properties. In this note, the condition for one root of a cubic equation to be "the negative reciprocal of…
Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation
NASA Astrophysics Data System (ADS)
Boiti, M.; Leon, J. J.-P.; Pempinelli, F.
1989-10-01
We define a new spectral transform r(k, l) of the potential u in the time dependent Schrödinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schrödinger equation are used to express the spectral transform f( k, l) previously introduced by Manakov and Fokas and Ablowitz in terms of r( k, l). The main advantage of the new spectral transform r( k, l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r( k, l) are also obtained.
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.
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
The form-invariance of wave equations without requiring a priori relations between field variables
NASA Astrophysics Data System (ADS)
Xiang, ZhiHai
2014-12-01
According to the principle of relativity, the equations describing the laws of physics should have the same forms in all admissible frames of reference, i.e., form-invariance is an intrinsic property of correct wave equations. However, so far in the design of metamaterials by transformation methods, the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation. The main contribution of this paper is to give general proofs of form-invariance of electromagnetic, sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables. The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant, but traditional elastodynamic equations are not. As a by-product, one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media. The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak. These findings are important for solving inverse scattering problems in many fields such as seismology, nondestructive evaluation and metamaterials.
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
Gálvez-López, Eloy; Casinos, Adrià
2012-01-01
Six mechanically significant skeletal variables were measured on the calcanei from 60 Felidae specimens (22 species) to determine whether these variables were scaled to body mass, and to assess whether differential scaling exists. The power equation (y = a · xb) was used to analyse the scaling of the six variables to body mass; we compared traditional regression methods (standardised major axis) to phylogenetically independent contrasts. In agreement with previous studies that compared these methodologies, we found no significant differences between methods in the allometric coefficients (b) obtained. Overall, the scaling pattern of the felid calcaneus conformed to the predictions of the geometric similarity hypothesis, but not entirely to those of the elastic similarity hypothesis. We found that the moment arm of the ankle extensors scaled to body mass with an exponent not significantly different from 0.40. This indicated that the tuber calcanei scaled to body mass faster than calcaneus total length. This explained why the effective mechanical advantage of the ankle extensors increased with body mass, despite the fact that limb posture does not change in felid species. Furthermore, this finding was consistent with the hypothesis of the isometric scaling of ground reaction forces. No evidence for differential scaling was found in any of the variables studied. We propose that this reflected the similar locomotor pattern of all felid species. Thus, our results suggested that the differences in allometric coefficients for ‘large’ and ‘small’ mammals were in fact caused by different types of locomotion among the species included in each category. PMID:22463377
Gálvez-López, Eloy; Casinos, Adrià
2012-06-01
Six mechanically significant skeletal variables were measured on the calcanei from 60 Felidae specimens (22 species) to determine whether these variables were scaled to body mass, and to assess whether differential scaling exists. The power equation (y = a · x(b) ) was used to analyse the scaling of the six variables to body mass; we compared traditional regression methods (standardised major axis) to phylogenetically independent contrasts. In agreement with previous studies that compared these methodologies, we found no significant differences between methods in the allometric coefficients (b) obtained. Overall, the scaling pattern of the felid calcaneus conformed to the predictions of the geometric similarity hypothesis, but not entirely to those of the elastic similarity hypothesis. We found that the moment arm of the ankle extensors scaled to body mass with an exponent not significantly different from 0.40. This indicated that the tuber calcanei scaled to body mass faster than calcaneus total length. This explained why the effective mechanical advantage of the ankle extensors increased with body mass, despite the fact that limb posture does not change in felid species. Furthermore, this finding was consistent with the hypothesis of the isometric scaling of ground reaction forces. No evidence for differential scaling was found in any of the variables studied. We propose that this reflected the similar locomotor pattern of all felid species. Thus, our results suggested that the differences in allometric coefficients for 'large' and 'small' mammals were in fact caused by different types of locomotion among the species included in each category. PMID:22463377
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.
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
NASA Astrophysics Data System (ADS)
Kravchenko, Vladislav V.
2005-01-01
Given a particular solution of a one-dimensional stationary Schrödinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schrödinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schrödinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schrödinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schrödinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schrödinger equation. Moreover, for an ample
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.
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.
Muscle contraction: energy rate equations in relation to efficiency and step-size distance.
Worthington, C R; Elliott, G F
2003-09-01
We derive the energy rate equation for muscle contraction. Our equation has only two parameters m, the maintenance heat rate and 1/S, the shortening heat coefficient. The impulsive model (previously described in earlier papers) provides a physical basis for parameter 1/S as well as for constants a and b in Hill's force-velocity equation. We develop new theory and relate the efficiency and the step-size distance to our energy rate equation. Correlation between the efficiency and the step-size distance is established. The various numbers are listed in Table 1: we use data from five different muscles in the literature. In summary, our analysis strongly supports the impulsive model as the correct model of contraction. PMID:12957311
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
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
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
Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae
Yang, Xi; Yu, Hao-Ran; Zhang, Tong-Jie E-mail: yu@bnu.edu.cn
2013-06-01
Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter α to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the Distance-Duality (DD) relation, D{sub L}(z)(1+z){sup −2}/D{sub A}(z) = 1, should be valid for all cosmological models that are described by Riemannian geometry, where D{sub L} and D{sub A} are, respectively, the luminosity and angular distance distances. Therefore, it is necessary to test whether if the Dyer-Roeder approximate equation can satisfy the Distance-Duality relation. In this paper, we use Union2.1 SNe Ia data to constrain the smoothness parameter α and test whether the Dyer-Roeder equation meet the DD relation. By using χ{sup 2} minimization, we get α = 0.92{sub −0.32}{sup +0.08} at 1σ and 0.92{sub −0.65}{sup +0.08} at 2σ, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at 1σ.
Krenek, Lauren; Rudolf, Volker H W
2014-11-01
Non-consumptive effects (NCES) frequently lead to non-independent effects of multiple predators. While such emergent predator effects are ubiquitous in natural communities, the strength of these effects varies among studies and systems, making it difficult to predict a priory how changes in predator diversity influence prey suppression. Thus, identifying general scaling rules which can explain this variation of non-independent effects is vital for modelling natural communities and how they respond to biodiversity loss. Body size is a key trait determining the nature and strength of ecological interactions. While great progress has been made using allometric relationships to predict the interaction strength of predator-prey pairs, it is unknown whether similar relationships explain variation in the strength of NCEs, and how they are related to consumptive effects. Here, we experimentally manipulate the relative size difference of multiple predators to determine whether NCEs follow general allometric scaling relationships in an aquatic multi-predator system. Results demonstrate that the presence and strength of NCEs can vary dramatically across predator combinations. However, this variation scaled predictably with the size ratio of predators, increasing the size difference among predators increased NCEs. This pattern was driven by a size-mediated shift in 'food web motif' from competition to intraguild predation and a positive correlation of NCEs and intraguild predation rate. Results indicate that models which assume that consumers have independent effects are particularly likely to make erroneous predictions when predators differ substantially in size, but simple allometric relationships of NCEs could be used to correct this bias. PMID:24910170
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.
Intertwining relations and Darboux transformations for Schroedinger equations in (n+1) dimensions
Schulze-Halberg, Axel
2010-03-15
We evaluate the intertwining relation for Schroedinger equations in (n+1) dimensions. The conditions for the existence of a Darboux transformation are analyzed and compared to their (1+1) dimensional counterparts. A complete solution of the conditions is given for (2+1) dimensions, and a Darboux transformation is constructed.
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…
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,…
SUN, SHUCUN; JIN, DONGMEI; SHI, PEILI
2006-01-01
• Background and Aims The leaf size–twig size spectrum is one of the leading dimensions of plant ecological variation, and now it is under development. The purpose of this study was to test whether the relationship between leaf size and twig size is isometric or allometric, and to examine the relationship between plant allometric growth and life history strategies in the spectrum. • Methods Leaf and stem characters—including leaf and stem mass, total leaf area, individual leaf area, stem cross-sectional area, leaf number and stem length—at the twig level for 59 woody species were investigated along an altitudinal gradient on Changbaishan Mountain in the temperate zone of China. The environmental gradient ranges from temperate broad-leaved mixed forest at low altitude, to conifer forest at middle altitude, and to sub-alpine birch forest at high altitude. The scaling relationships between stem cross-sectional area and stem mass, stem mass and leaf mass, and leaf mass and leaf area at the twig level were simultaneously determined. • Key Results Twig cross-sectional area was found to have invariant allometric scaling relationships with the stem mass, leaf mass, total leaf area and individual leaf area, all with common slopes being significantly larger than 1, for three altitudinal-zoned vegetation types under investigation. However, leaf mass was found to be isometrically related to stem mass and leaf area along the environmental gradient. Based on the predictions of previous models, the exponent value of the relationship between twig cross-sectional area and total leaf area can be inferred to be 1·5, which falls between the confidence intervals of the relationship at each altitude, and between the confidence intervals of the common slope value (1·17–1·56) of this study. This invariant scaling relationship is assumed to result from the fractural network and/or developmental constraints of plants. The allometric constants (y-intercepts) of the
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.
Solution of inverse problem of fuzzy relational equation by using perceptron model
NASA Technical Reports Server (NTRS)
Hirota, Kaoru; Ikoma, Norikazu
1991-01-01
A Max-Min fuzzy system can be regarded as a network of max and min operational elements. Thus, the inverse problem of a fuzzy relational equation is interpreted as an input estimation problem from output values in the corresponding network. An approximate network model of a fuzzy relational system is proposed. An algorithm for obtaining an approximate solution of the system is presented for using a neural network technique.
A 3+1 formalism for quantum electrodynamical corrections to Maxwell equations in general relativity
NASA Astrophysics Data System (ADS)
Pétri, J.
2015-08-01
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover, strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of BQ = 4.4 × 109 T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polarization properties, it is important to include general relativistic (GR) effects simultaneously with non-linear electrodynamics. This can be achieved through a 3+1 formalism known in general relativity and that incorporates QED perturbations to Maxwell equations. Starting from the lowest order corrections to the Lagrangian for the electromagnetic field, as given for instance by Born-Infeld or Euler-Heisenberg theory, we derive the non-linear Maxwell equations in general relativity including quantum vacuum effects. We also derive a prescription for the force-free limit and show that these equations can be solved with classical finite volume methods for hyperbolic conservation laws. It is therefore straightforward to include general relativity and QED in the description of neutron star magnetospheres by using standard classical numerical techniques borrowed from Maxwell and Newton theory. As an application, we show that spin-down luminosity corrections associated with QED effects are negligible with respect to GR corrections.
NASA Astrophysics Data System (ADS)
Sharipov, Felix
2011-12-01
The Boltzmann equation subject to a general boundary condition is expanded in a power series with respect to a thermodynamic force disturbing a gaseous system. Recurrence relations between the terms of the expansion are obtained using the main properties of the collision integral and of the gas-surface interaction kernel. The reciprocal relation for nonlinear irreversible phenomena, i.e., a relation between the terms of different orders, is obtained. The relations can be used to estimate the range of applicability of linearized solutions and to predict nonlinear phenomena in gaseous systems.
NASA Astrophysics Data System (ADS)
Si, Jianguo; Zhao, Houyu
2007-11-01
In this paper, we are concerned with the existence of analytic solutions of a class of iterative differential equation in the complex field , where , , fi(z) denotes ith iterate of f(z), i=1,2,...,n. The above equation is closely related to a discrete derivatives sequence F'(m) (see [Y.-F.S. Pétermann, Jean-Luc Rémy, Ilan Vardi, Discrete derivative of sequences, Adv. in Appl. Math. 27 (2001) 562-584]). We first give the existence of analytic solutions of the form of power functions for such an equation. Then by constructing a convergent power series solution y(z) of an auxiliary equation of the formx'(z)=K[alpha]x'([alpha]z)(x([alpha]z))a1(x([alpha]2z))a2...(x([alpha]nz))an, invertible analytic solutions of the form f(z)=x([alpha]x-1(z)) for the original equation are obtained. We discuss not only the constant [alpha] at resonance, i.e. at a root of the unity, but also those [alpha] near resonance (near a root of the unity) under the Brjuno condition.
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.
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.
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
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
An allometric analysis of the number of muscle spindles in mammalian skeletal muscles.
Banks, R W
2006-06-01
An allometric analysis of the number of muscle spindles in relation to muscle mass in mammalian (mouse, rat, guinea-pig, cat, human) skeletal muscles is presented. It is shown that the trend to increasing number as muscle mass increases follows an isometric (length) relationship between species, whereas within a species, at least for the only essentially complete sample (human), the number of spindles scales, on average, with the square root rather than the cube root of muscle mass. An attempt is made to reconcile these apparently discrepant relationships. Use of the widely accepted spindle density (number of spindles g(-1) of muscle) as a measure of relative abundance of spindles in different muscles is shown to be grossly misleading. It is replaced with the residuals of the linear regression of ln spindle number against ln muscle mass. Significant differences in relative spindle abundance as measured by residuals were found between regional groups of muscles: the greatest abundance is in axial muscles, including those concerned with head position, whereas the least is in muscles of the shoulder girdle. No differences were found between large and small muscles operating in parallel, or between antigravity and non-antigravity muscles. For proximal vs. distal muscles, spindles were significantly less abundant in the hand than the arm, but there was no difference between the foot and the leg. PMID:16761976
Kapellou, Olga; Counsell, Serena J; Kennea, Nigel; Dyet, Leigh; Saeed, Nadeem; Stark, Jaroslav; Maalouf, Elia; Duggan, Philip; Ajayi-Obe, Morenike; Hajnal, Jo; Allsop, Joanna M; Boardman, James; Rutherford, Mary A; Cowan, Frances; Edwards, A. David
2006-01-01
Background We postulated that during ontogenesis cortical surface area and cerebral volume are related by a scaling law whose exponent gives a quantitative measure of cortical development. We used this approach to investigate the hypothesis that premature termination of the intrauterine environment by preterm birth reduces cortical development in a dose-dependent manner, providing a neural substrate for functional impairment. Methods and Findings We analyzed 274 magnetic resonance images that recorded brain growth from 23 to 48 wk of gestation in 113 extremely preterm infants born at 22 to 29 wk of gestation, 63 of whom underwent neurodevelopmental assessment at a median age of 2 y. Cortical surface area was related to cerebral volume by a scaling law with an exponent of 1.29 (95% confidence interval, 1.25–1.33), which was proportional to later neurodevelopmental impairment. Increasing prematurity and male gender were associated with a lower scaling exponent (p < 0.0001) independent of intrauterine or postnatal somatic growth. Conclusions Human brain growth obeys an allometric scaling relation that is disrupted by preterm birth in a dose-dependent, sexually dimorphic fashion that directly parallels the incidence of neurodevelopmental impairments in preterm infants. This result focuses attention on brain growth and cortical development during the weeks following preterm delivery as a neural substrate for neurodevelopmental impairment after premature delivery. PMID:16866579
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. PMID:26630347
Yanovitskii, E.G.
1981-01-01
The general invariance principle (GIP) for arbitrary plane inhomogeneous atmospheres is formulated on the basis of ideas contained in (V. V. Ivanov, Sov. Astron. 19, 137 (1975)). All the known invariance relations follow as particular cases from the GIP. The problem of diffuse light reflection by a semi-infinite atmosphere and the Milne problem are analyzed in detail. The existence of a number of integrals, quadratic with respect to intensity, of the transfer equation is shown, the majority of which are invariant relative to optical depth.
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
Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients
Khmelnytskaya, K.V.; Rosu, H.C. Gonzalez, A.
2010-03-15
We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically coupled second-order differential equations. We solve analytically these parametric periodic problems along the whole real axis. Next, the analytically solved model is used as a case study for a powerful numerical approach that is employed here for the first time in the investigation of the energy band structure of periodic not necessarily regular potentials. The approach is based on the well-known self-matching procedure of James (1949) and implements the spectral parameter power series solutions introduced by Kravchenko (2008). We obtain additionally an efficient series representation of the Hill discriminant based on Kravchenko's series.
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.
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
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
Massively parallel fast elliptic equation solver for three dimensional hydrodynamics and relativity
Sholl, P.L.; Wilson, J.R.; Mathews, G.J.; Avila, J.H.
1995-01-01
Through the work proposed in this document we expect to advance the forefront of large scale computational efforts on massively parallel distributed-memory multiprocessors. We will develop tools for effective conversion to a parallel implementation of sequential numerical methods used to solve large systems of partial differential equations. The research supported by this work will involve conversion of a program which does state of the art modeling of multi-dimensional hydrodynamics, general relativity and particle transport in energetic astrophysical environments. The proposed parallel algorithm development, particularly the study and development of fast elliptic equation solvers, could significantly benefit this program and other applications involving solutions to systems of differential equations. We shall develop a data communication manager for distributed memory computers as an aid in program conversions to a parallel environment and implement it in the three dimensional relativistic hydrodynamics program discussed below; develop a concurrent system/concurrent subgrid multigrid method. Currently, five systems are approximated sequentially using multigrid successive overrelaxation. Results from an iteration cycle of one multigrid system are used in following multigrid systems iterations. We shall develop a multigrid algorithm for simultaneous computation of the sets of equations. In addition, we shall implement a method for concurrent processing of the subgrids in each of the multigrid computations. The conditions for convergence of the method will be examined. We`ll compare this technique to other parallel multigrid techniques, such as distributed data/sequential subgrids and the Parallel Superconvergent Multigrid of Frederickson and McBryan. We expect the results of these studies to offer insight and tools both for the selection of new algorithms as well as for conversion of existing large codes for massively parallel architectures.
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.
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.
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
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.
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.
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.
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
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
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.
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.
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.
Topics in general relativity: Binary black holes and hyperbolic formulations of Einstein's equations
NASA Astrophysics Data System (ADS)
Alvi, Kashif
2002-09-01
This thesis consists of three projects in general relativity on topics related to binary black holes and the gravitational waves they emit. The first project involves calculating a four-metric that is an approximate solution to Einstein's equations representing two widely separated nonrotating black holes in a circular orbit. This metric is constructed by matching a post-Newtonian metric to two tidally distorted Schwarzschild metrics using the framework of matched asymptotic expansions. The four-metric presented here provides physically realistic initial data that are tied to the binary's inspiral phase and can be evolved numerically to determine the gravitational wave output during the late stages of inspiral as well as the merger. The second project is on the tidal interaction of binary black holes during the inspiral phase. The holes' tidal distortion results in the flow of energy and angular momentum into or out of the holes in a process analogous to Newtonian tidal friction in a planet-moon system. The changes in the black holes' masses, spins, and horizon areas during inspiral are calculated for a circular binary with holes of possibly comparable masses. The absorption or emission of energy and angular momentum by the holes is shown to have a negligible influence on the binary's orbital evolution when the holes have comparable masses. The tidal-interaction analysis presented in this thesis is applicable to a black hole in a binary with any companion body (e.g., a neutron star) that is well separated from the hole. The final project is on first-order hyperbolic formulations of Einstein's equations, which are promising as a basis for numerical simulation of binary black holes. This thesis presents two first-order symmetrizable hyperbolic systems that include the lapse and shift as dynamical fields and have only physical characteristic speeds. The first system may be useful in numerical work; the second system allows one to show that any solution to Einstein
THE NEUTRON STAR MASS-RADIUS RELATION AND THE EQUATION OF STATE OF DENSE MATTER
Steiner, Andrew W.; Brown, Edward F.; Lattimer, James M. E-mail: ebrown@pa.msu.edu
2013-03-01
The equation of state (EOS) of dense matter has been a long-sought goal of nuclear physics. EOSs generate unique mass versus radius (M-R) relations for neutron stars, the ultra-dense remnants of stellar evolution. In this work, we determine the neutron star mass-radius relation and, based on recent observations of both transiently accreting and bursting sources, we show that the radius of a 1.4 solar mass neutron star lies between 10.4 and 12.9 km, independent of assumptions about the composition of the core. We show, for the first time, that these constraints remain valid upon removal from our sample of the most extreme transient sources or of the entire set of bursting sources; our constraints also apply even if deconfined quark matter exists in the neutron star core. Our results significantly constrain the dense matter EOS and are furthermore consistent with constraints from both heavy-ion collisions and theoretical studies of neutron matter. We predict a relatively weak dependence of the symmetry energy on the density and a value for the neutron skin thickness of lead which is less than 0.20 fm, results that are testable in forthcoming experiments.
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...
Prediction of glucuronidated drug clearance in pediatrics (≤5 years): An allometric approach.
Mahmood, Iftekhar
2015-03-01
Children are not small adults. The differences between children of different age groups and adults are not merely due to body weight, but also due to physiological and biochemical differences resulting in different rates of drug metabolism or renal clearance. Glucuronidation is an important pathway of drug metabolism. Therefore, the objective of this study is to evaluate the predictive performance of several allometric exponents in children of ≤5 years for the total clearance of drugs which are mainly metabolized by glucuronidation. Four exponents (0.75, 1.0, 1.2, or 1.4) on the body weights and an allometric model developed from adults were evaluated. The four exponents and the allometric model were examined to determine the suitability of the method(s) to predict the clearances of drugs which are glucuronidated in children ≤5 years of age. Based on the analysis of ten drugs, it was noted that the combination of two allometric exponents 1.2 (for children ≤3 months) and 1.0 (for children ≥3 months ≤5 years) can be used to predict mean clearances of drugs which are mainly metabolized by glucuronidation. The suggested approach may be used to estimate a first-in-pediatric dose to initiate a pediatric clinical trial. PMID:24519316
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
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.
Allometric Prediction of Energy Expenditure in Infants and Children
Blinman, Thane; Cook, Robin
2011-01-01
Predicting energy needs in children is complicated by the wide range of patient sizes, confusing traditional estimation equations, nonobjective stress-activity factors, and so on. These complications promote errors in bedside estimates of nutritional needs by rendering the estimation methods functionally unavailable to bedside clinicians. Here, the authors develop a simple heuristic energy prediction equation that requires only body mass (not height, age, or sex) as input. Expert estimation of energy expenditure suggested a power-law relationship between mass and energy. A similar mass-energy expenditure relationship was derived from published pediatric echocardiographic data using a Monte Carlo model of energy expenditure based on oxygen delivery and consumption. A simplified form of the equation was compared with energy required for normal growth in a cohort of historical patients weighing 2 to 70 kg. All 3 methods demonstrate that variation in energy expenditure in children is dominated by mass and can be estimated by the following equation: Power(kcal/kg/d) = 200 × [Mass(kg)(−0.4)]. This relationship explains 85% of the variability in energy required to maintain expected growth over a broad range of surgical clinical contexts. A simplified power-law equation predicts real-world energy needs for growth in patients over a wide range of body sizes and clinical contexts, providing a more useful bedside tool than traditional estimators. PMID:22308194
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
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
NASA Astrophysics Data System (ADS)
Levin, A.; Olshanetsky, M.; Zotov, A.
2014-10-01
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum R-matrices. Here we study the simplest case - the 11-vertex R-matrix and related gl2 rational models. The corresponding top is equivalent to the 2-body Ruijsenaars-Schneider (RS) or the 2-body Calogero-Moser (CM) model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries). The known relation between the top and CM (or RS) models allows to rewrite the Gaudin models (or the spin chains) in the canonical variables. Then they assume the form of n-particle integrable systems with 2n constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau-Lifshitz type equation. The latter can be treated as non-trivial deformation of the classical continuous Heisenberg model. In a similar way the deformation of the principal chiral model is described.
Brustein, Ram; Hadad, Merav
2009-09-01
We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation deltaQ=TdeltaS. Our proof relies on extending previous arguments by using a more general definition of the Noether charge entropy. We have thus completed the implementation of Jacobson's proposal to express Einstein's equations as a thermodynamic equation of state. Additionally, we find that the Noether charge entropy obeys the second law of thermodynamics if the energy-momentum tensor obeys the null energy condition. Our results support the idea that gravitation on a macroscopic scale is a manifestation of the thermodynamics of the vacuum. PMID:19792292
NASA Astrophysics Data System (ADS)
Van den Bergh, Norbert; Slobodeanu, Radu
2016-04-01
The present status of the shear-free fluid conjecture in general relativity is discussed: a review is given of recent partial proofs, a new and complete proof is given for the case of a linear equation of state, including a non-zero cosmological constant, and a number of useful results are presented which might help in proving the conjecture for a general equation of state.
Basu, Abhik; Naji, Ali; Pandit, Rahul
2014-01-01
We generalize the method of A. M. Polyakov, [ Phys. Rev. E 52 6183 (1995)] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analogs of MHD in one dimension [ Eur. Phys. J. B 9 725 (1999)], and in three dimensions (3DMHD and 3D Hall MHD). Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure functions and their derivatives; these expressions are the analogs of the von Kármán-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD. PMID:24580182
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.
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.
Soliton equations related to the affine Kac-Moody algebra D{4/(1)}
NASA Astrophysics Data System (ADS)
Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K.
2015-06-01
We have derived the hierarchy of soliton equations associated with the untwisted affine Kac-Moody algebra D {4/(1)} by calculating the corresponding recursion operators. The Hamiltonian formulation of the equations from the hierarchy is also considered. As an example we have explicitly presented the first non-trivial member of the hierarchy, which is an one-parameter family of mKdV equations. We have also considered the spectral properties of the Lax operator and introduced a minimal set of scattering data.
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.
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.
Eu, Byung Chan
2008-09-01
In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel. PMID:19044872
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
Arminjon, Mayeul
2005-10-15
The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase and 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 {eta}, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order {eta}{sup 3} 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 {eta}{yields}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.
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
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.
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.
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…
A Structural Equation Model at the Individual and Group Level for Assessing Faking-Related Change
ERIC Educational Resources Information Center
Ferrando, Pere Joan; Anguiano-Carrasco, Cristina
2011-01-01
This article proposes a comprehensive approach based on structural equation modeling for assessing the amount of trait-level change derived from faking-motivating situations. The model is intended for a mixed 2-wave 2-group design, and assesses change at both the group and the individual level. Theoretically the model adopts an integrative…
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…
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…
Allometric patterns of cranial bone thickness in fossil hominids.
Gauld, S C
1996-07-01
The interspecific allometry of five measures of total cranial bone thickness is examined in 10 extant catarrhine genera and two fossil hominid samples representing A. africanus and Asian H. erectus. Analysis of the modern sample shows that most interspecific variation in vault thickness can be accounted for by variation in body size. Correlation values are moderate to high (r = 0.75-0.98), and all variables exhibit positive allometry. The bone thickness: body mass relationship of modern humans broadly conforms with that of other primates. However, in the distribution of relative thickness throughout the skull, H. sapiens is distinguished by relative thickening of the parietal and extreme relative thinning of the temporal squama. The bone thickness: body mass relationship in the two early hominid species is examined using published mean body weight estimates generated from post-cranial predictor variables. A. africanus exhibits great similarity to modern humans in its relation to the catarrhine regression data and in the distribution of relative thickness throughout the skull. H. erectus also shows a modern human-like pattern in the distribution of its relative thickness; however, its bone thickness: body mass relationship is dissimilar to that displayed by all other taxa, including the other hominid species. On the basis of these results, it is suggested that the published body weight estimate assigned to H. erectus greatly underestimates actual mean body size for Asian members of this species. PMID:8798997
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.
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.
NASA Astrophysics Data System (ADS)
Zhao, Xueyan; Deng, Feiqi
2016-07-01
In this paper, a particular property of Lyapunov functions for functional differential equations (FDEs) is developed, that is the direct dependence of the signs of the derivatives of the Lyapunov functions on the initial data. This property implies that the derivatives of the Lyapunov functions for FDEs cannot be guaranteed to be negative definite generally, and then makes the FDEs differ from the ordinary differential equations constitutionally. With this property, we give some enlightenments for the research methods for establishing stability theorems or criteria for FDEs, which may help us to form a common view about the choice of the investigation methods on the stability of FDEs. The conclusion is stated in both the deterministic and stochastic versions. Two illustrative examples are given to show and verify our conclusion through the paper.
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.
NASA Astrophysics Data System (ADS)
Bilonick, Richard A.; Connell, Daniel P.; Talbott, Evelyn O.; Rager, Judith R.; Xue, Tao
2015-02-01
The objective of this study was to remove systematic bias among fine particulate matter (PM2.5) mass concentration measurements made by different types of samplers used in the Pittsburgh Aerosol Research and Inhalation Epidemiology Study (PARIES). PARIES is a retrospective epidemiology study that aims to provide a comprehensive analysis of the associations between air quality and human health effects in the Pittsburgh, Pennsylvania, region from 1999 to 2008. Calibration was needed in order to minimize the amount of systematic error in PM2.5 exposure estimation as a result of including data from 97 different PM2.5 samplers at 47 monitoring sites. Ordinary regression often has been used for calibrating air quality measurements from pairs of measurement devices; however, this is only appropriate when one of the two devices (the "independent" variable) is free from random error, which is rarely the case. A group of methods known as "errors-in-variables" (e.g., Deming regression, reduced major axis regression) has been developed to handle calibration between two devices when both are subject to random error, but these methods require information on the relative sizes of the random errors for each device, which typically cannot be obtained from the observed data. When data from more than two devices (or repeats of the same device) are available, the additional information is not used to inform the calibration. A more general approach that often has been overlooked is the use of a measurement error structural equation model (SEM) that allows the simultaneous comparison of three or more devices (or repeats). The theoretical underpinnings of all of these approaches to calibration are described, and the pros and cons of each are discussed. In particular, it is shown that both ordinary regression (when used for calibration) and Deming regression are particular examples of SEMs but with substantial deficiencies. To illustrate the use of SEMs, the 7865 daily average PM2.5 mass
NASA Astrophysics Data System (ADS)
Hellig, Christoph J.; Kerschbaumer, Michaela; Sefc, Kristina M.; Koblmüller, Stephan
2010-07-01
The morphological versatility of the pharyngeal jaw of cichlid fishes is assumed to represent a key factor facilitating their unparalleled trophic diversification and explosive radiation. It is generally believed that the functional design of an organism relates to its ecology, and thus, specializations to different diets are typically associated with distinct morphological designs, especially manifested in the cichlids’ pharyngeal jaw apparatus. Thereby, the lower pharyngeal jaw (LPJ) incorporates some of the most predictive features for distinct diet-related morphotypes. Thus, considering that piscivorous cichlids experience an ontogenetic dietary shift from typically various kinds of invertebrates to fish, concomitant morphological changes in the LPJ are expected. Using Lepidiolamprologus elongatus, a top predator in the shallow rocky habitat of Lake Tanganyika, as model, and applying geometric and traditional morphometric techniques, we demonstrate an allometric change in ontogenetic LPJ shape development coinciding with the completion of the dietary shift toward piscivory. The piscivorous LPJ morphotype is initiated in juvenile fish by increasing elongation and narrowing of the LPJ and—when the fish reach a size of 80-90 mm standard length—further refined by the elongation of the posterior muscular processes, which serve as insertion for the fourth musculus levator externus. The enlarged muscular processes of the fully mature piscivorous morphotype provide for the construction of a powerful lever system, which allows the large individuals to process large prey fish and rely on exclusive piscivory.
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.
Anastassi, Z. A.; Simos, T. E.
2010-09-30
We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.
Xia, Youshen; Feng, Gang; Wang, Jun
2004-09-01
This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications. PMID:15312842
NASA Astrophysics Data System (ADS)
Alrachid, Houssam; Lelièvre, Tony; Talhouk, Raafat
2016-05-01
We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non-linear term is related to a conditional expectation, and is thus non-local. The proof uses tools from the theory of semigroups of linear operators for the local existence result, and an a priori estimate based on a supersolution for the global existence result.
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
Testing for size and allometric differences in fossil hominin body mass estimation.
Uhl, Natalie M; Rainwater, Christopher W; Konigsberg, Lyle W
2013-06-01
Body size reconstructions of fossil hominins allow us to infer many things about their evolution and lifestyle, including diet, metabolic requirements, locomotion, and brain/body size relationships. The importance of these implications compels anthropologists to attempt body mass estimation from fragmentary fossil hominin specimens. Most calculations require a known "calibration" sample usually composed of modern humans or other extant apes. Caution must be taken in these analyses, as estimates are sensitive to overall size and allometric differences between the fossil hominin and the reference sample. PMID:23588924
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. PMID:25628420
Dai, Boyi; Ware, William B; Giuliani, Carol A
2012-01-01
The current study used a structural equation model to investigate the interrelationships among physical function, pain, IM, and falls in 511 American older adults. The model included 11 measurement variables (tandem stance, single leg stance, 360° turn, chair stand, arm curl, sit and reach, back scratch, normative score of 6-min walk or 2-min step, timed up and go, pain, and fall) and four latent variables (balance, strength, flexibility, and IM). The final model with the combined sample demonstrated good fit with the participant data (χ(2)(31)=30.0, N=499, p=0.52; Goodness of Fit Index (GFI)=0.99). Balance had a significant and the largest effect on IM (standardized regression weights=-1.05, p<0.001). Strength, endurance, flexibility, and pain had small effects on IM (standardized regression weights<0.2). The findings suggest that balance and mobility testing should be a priority in fall screening and prevention programs. PMID:22766209
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.
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.
Stability and bifurcations of relative equilibria of a pendulum suspended on the equator
NASA Astrophysics Data System (ADS)
Burov, A. A.; Kosenko, I. I.
2013-05-01
The problem of equilibria of a pendulum suspended at an equatorial point relative to the rotating Earth is considered. An altitude is determined at which the degree of instability of the inverted pendulum changes from two to unity. Relative equilibria are investigated that bifurcate from the radial one when its degree of instability changes. Their stability properties are studied.
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.
Muir, Christopher D; Thomas-Huebner, Meret
2015-09-01
The West-Brown-Enquist (WBE) metabolic scaling theory posits that many organismal features scale predictably with body size because of selection to minimize transport costs in resource distribution networks. Many scaling exponents are quarter-powers, as predicted by WBE, but there are also biologically significant deviations that could reflect adaptation to different environments. A central but untested prediction of the WBE model is that wide deviation from optimal scaling is penalized, leading to a pattern of constraint on scaling exponents. Here, we demonstrate, using phylogenetic comparative methods, that variation in allometric scaling between mass and leaf area across 17 wild tomato taxa is constrained around a value indistinguishable from that predicted by WBE but significantly greater than 2/3 (geometric-similarity model). The allometric-scaling exponent was highly correlated with fecundity, water use, and drought response, suggesting that it is functionally significant and therefore could be under selective constraints. However, scaling was not strictly log-log linear but rather declined during ontogeny in all species, as has been observed in many plant species. We caution that although our results supported one prediction of the WBE model, it did not strongly test the model in other important respects. Nevertheless, phylogenetic comparative methods such as those used here are powerful but underutilized tools for metabolic ecology that complement existing methods to adjudicate between models. PMID:26655358
Nevill, A M; Allen, S V; Ingham, S A
2011-02-01
Previous studies have investigated the determinants of indoor rowing using correlations and linear regression. However, the power demands of ergometer rowing are proportional to the cube of the flywheel's (and boat's) speed. A rower's speed, therefore, should be proportional to the cube root (0.33) of power expended. Hence, the purpose of the present study was to explore the relationship between 2000 m indoor rowing speed and various measures of power of 76 elite rowers using proportional, curvilinear allometric models. The best single predictor of 2000 m rowing ergometer performance was power at VO(2max)(WVO(2max))(0.28), that explained R(2)=95.3% in rowing speed. The model realistically describes the greater increment in power required to improve a rower's performance by the same amount at higher speeds compared with that at slower speeds. Furthermore, the fitted exponent, 0.28 (95% confidence interval 0.226-0.334) encompasses 0.33, supporting the assumption that rowing speed is proportional to the cube root of power expended. Despite an R(2)=95.3%, the initial model was unable to explain "sex" and "weight-class" differences in rowing performances. By incorporating anaerobic as well as aerobic determinants, the resulting curvilinear allometric model was common to all rowers, irrespective of sex and weight class. PMID:19883389
Allometric scaling of foraging rate with trail dimensions in leaf-cutting ants
Bruce, Andrew I.; Burd, Martin
2012-01-01
Leaf-cutting ants (Atta spp.) create physical pathways to support the transport of resources on which colony growth and reproduction depend. We determined the scaling relationship between the rate of resource acquisition and the size of the trail system and foraging workforce for 18 colonies of Atta colombica and Atta cephalotes. We examined conventional power-law scaling patterns, but did so in a multivariate analysis that reveals the simultaneous effects of forager number, trail length and trail width. Foraging rate (number of resource-laden ants returning to the nest per unit time) scaled at the 0.93 power of worker numbers, the –1.02 power of total trail length and the 0.65 power of trail width. These scaling exponents indicate that individual performance declines only slightly as more foragers are recruited to the workforce, but that trail length imposes a severe penalty on the foraging rate. A model of mass traffic flow predicts the allometric patterns for workforce and trail length, although the effect of trail width is unexpected and points to the importance of the little-known mechanisms that regulate a colony's investment in trail clearance. These results provide a point of comparison for the role that resource flows may play in allometric scaling patterns in other transport-dependent entities, such as human cities. PMID:22337696
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
Martinez, M; Mahmood, I; 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. However, it is important to appreciate the mathematical underpinnings of this scaling procedure when using it to predict pharmacokinetic parameter values across animal species. When cautiously applied, allometry can be a tool for estimating clearance in veterinary species for the purpose of dosage selection. It is particularly valuable during the selection of dosages in large zoo animal species, such as elephants, large cats and camels, for which pharmacokinetic data are scant. In Part I, allometric predictions of clearance in large animal species were found to pose substantially greater risks of inaccuracies when compared with that observed for humans. In this report, we examine the factors influencing the accuracy of our clearance estimates from the perspective of the relationship between prediction error and such variables as the distribution of body weight values used in the regression analysis, the influence of a particular observation on the clearance estimate, and the 'goodness of fit' (R(2)) of the regression line. Ultimately, these considerations are used to generate recommendations regarding the data to be included in the allometric prediction of clearance in large animal species. PMID:16958788
Ott, C D; Dimmelmeier, H; Marek, A; Janka, H-T; Hawke, I; Zink, B; Schnetter, E
2007-06-29
We present 2D and 3D simulations of the collapse of rotating stellar iron cores in general relativity employing a nuclear equation of state and an approximate treatment of deleptonization. We compare fully general relativistic and conformally flat evolutions and find that the latter treatment is sufficiently accurate for the core-collapse supernova problem. We focus on gravitational wave (GW) emission from rotating collapse, bounce, and early postbounce phases. Our results indicate that the GW signature of these phases is much more generic than previously estimated. We also track the growth of a nonaxisymmetric instability in one model, leading to strong narrow-band GW emission. PMID:17678077
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.
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. PMID:23606625
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
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. PMID:26808197
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
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. PMID:15164343
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. PMID:15563403
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.
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.
Li, Fang; Lee, Jung Ho; Grishaev, Alexander; Ying, Jinfa; Bax, Ad
2015-01-01
3JC′C′ and 3JHNHα couplings are related to the intervening backbone torsion angle ϕ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ϕ, including H-bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small. The solution NMR structure of protein GB3, newly refined by using extensive sets of residual dipolar couplings (RDCs), yields 50–60% better Karplus equation agreement between ϕ angles and experimental 3JC′C′ and 3JHNHα values than does the high resolution X-ray structure. In intrinsically disordered proteins, 3JC′C′ and 3JHNHα couplings can be measured at even higher accuracy, and the impact of factors other than the intervening torsion angle on 3J will be smaller than in folded proteins, making these couplings exceptionally valuable reporters on the ensemble of ϕ angles sampled by each residue. PMID:25511552
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.
Park, Byung-Chan; Kim, Eun-A; Kim, Soo Geun
2010-01-01
Objectives This study was conducted to develop a model describing the interaction between lifestyle, job, and postural factors and parts of the upper extremities in shipyard workers. Methods A questionnaire survey was given to 2,140 workers at a shipyard in Ulsan City. The questionnaire consisted of questions regarding the subjects' general characteristics, lifestyle, tenure, physical burden, job control, posture and musculoskeletal symptoms. The overall relationship between variables was analyzed by a structural equation model (SEM). Results The positive rate of upper extremity musculoskeletal symptoms increased in employees who worked longer hours, had severe physical burden, and did not have any control over their job. Work with a more frequent unstable posture and for longer hours was also associated with an increased positive rate of musculoskeletal symptoms. Multiple logistic regression analysis showed that unstable posture and physical burden were closely related to the positive rate of musculoskeletal symptoms after controlling for age, smoking, drinking, exercise, tenure, and job control. In SEM analysis, work-related musculoskeletal disease was influenced directly and indirectly by physical and job stress factors, lifestyle, age, and tenure (p < 0.05). The strongest correlations were found between physical factors and work-related musculoskeletal disease. Conclusion The model in this study provides a better approximation of the complexity of the actual relationship between risk factors and work-related musculoskeletal disorders. Among the variables evaluated in this study, physical factors (work posture) had the strongest association with musculoskeletal disorders. PMID:22953172
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.
Flamm, W Gary; Blackburn, George L; Comer, C Phil; Mayhew, Dale A; Stargel, W Wayne
2003-10-01
In long-term safety studies with neotame, a new high-intensity sweetener 7000-13,000 times sweeter than sucrose, the percent changes (%Delta) in body weight gain (BWG) in Sprague-Dawley rats were several-fold greater than the %Delta in overall food consumption (FC). This study investigates the question of whether the changes in BWG were adverse or secondary to small, long-term decrements in FC. The hypothesis tested in Sprague-Dawley rats was that the relationship between long-term %Delta in FC and %Delta in BWG is linear and in a ratio of 1:1. The %Delta in FC were compared to %Delta in BWG after 52 weeks on study in one saccharin (825 rats), two sucralose (480 rats), two neotame (630 rats), and five dietary restriction (>1000 rats) studies. Non-transformed plotting of data points demonstrated an absence of linearity between %Delta in FC and %Delta in BWG; however, log-log evaluation demonstrated a robust (R2=0.97) linear relationship between %Delta in FC and %Delta in BWG. This relationship followed the well-known allometric equation, y=bxa where x is %DeltaFC, y is %DeltaBWG, b is %DeltaBWG when DeltaFC=1, and a is the log-log slope. Thus, in Sprague-Dawley rats at week 52, the long-term relationship between %Delta in FC and %Delta in BWG was determined to be: %DeltaBWG=3.45(%DeltaFC0.74) for males and %DeltaBWG=5.28(%DeltaFC0.68) for females. Sexes were statistically different but study types, i.e., the high-intensity sweeteners saccharin and sucralose versus dietary restriction, were not. The %Delta in BWG are allometrically consistent with the observed %Delta in FC for these high-intensity sweeteners, including neotame. BW parameters are not appropriate endpoints for setting no-observed-effect levels (NOELs) when materials with intense taste are admixed into food. An approach using objective criteria is proposed to delineate BW changes due to toxicity from those secondary to reduced FC. PMID:14550756
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
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. PMID:26314261
Zhao, Ning; Yu, Guirui; He, Nianpeng; Xia, Fucai; Wang, Qiufeng; Wang, Ruili; Xu, Zhiwei; Jia, Yanlong
2016-07-01
Nitrogen (N) to phosphorus (P) allocation in plant organs is of particular interest, as both elements are important to regulate plant growth. We analyzed the scaling relationship of N and P in leaves, stems and fine roots of 224 plant species along an altitudinal transect (500-2,300 m) on the northern slope of Changbai Mountain, China. We tested whether the scaling relationships of N and P were conserved in response to environmental variations. We found that the N and P concentrations of the leaves, stems and fine roots decreased, whereas the N:P ratios increased with increasing altitude. Allometric scaling relationships of N and P were found in the leaves, stems and fine roots, with allometric exponents of 0.78, 0.71 and 0.87, respectively. An invariant allometric scaling of N and P in the leaves, stems and fine roots was detected for woody plants along the altitudinal gradient. These results may advance our understanding of plant responses to climate change, and provide a basis for practical implication of various ecological models. PMID:26943163
Allometric scaling of mammalian blood pressure: A comment on White and Seymour (2014).
Packard, Gary C
2015-12-01
White and Seymour examined the scaling of central arterial blood pressure against body mass in mammals ranging in size from a 30 g mouse to a 4080 kg elephant. Exponents in power functions fitted to each of three datasets (systolic, diastolic, and mean arterial pressure) were reported to be significantly greater than zero and indistinguishable from 0.33. The first of these outcomes would indicate that blood pressure increases with body size, whereas the second is consistent with the heart working against gravity to move blood to the head. Taken together, these results seemingly refute the notion that the cephalic circulation functions as an energy-neutral siphon. However, the main findings by White and Seymour were presented in the form of graphs that distorted the relationships between the variables of interest. I use simple graphics to show that the data were unsuited from the outset for use in allometric analyses and that conclusions of the investigation are not well supported. PMID:26462730
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
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
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. PMID:26222777
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. PMID:23448886
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
Prediction of human drug clearance from two species: a comparison of several allometric methods.
Goteti, Kosalaram; Garner, C Edwin; Mahmood, Iftekhar
2010-03-01
The objective of the study was to assess the degree of accuracy in human drug clearance prediction from two species using four different allometric approaches: simple allometry (SA), multiexponential allometry (ME), rule of exponents (ROE), and fixed exponents (FE) as suggested by Tang et al. There were 45 compounds in this analysis and the two species used were either rat-dog or rat-monkey. In addition, > or = 3 species scaling was also performed to evaluate the comparative accuracy in the prediction of human drug clearance between two or more than two-species scaling. The results of the study indicated that the two-species scaling with different methods provided different degrees of accuracy in the prediction of clearance. Prediction by a particular method was also species dependent. For example, a given drug with rat-dog scaling provided a reasonably accurate prediction of clearance whereas with rat-monkey scaling the prediction of clearance was highly erratic or vice versa. The results of the study indicated that the two-species scaling can be useful for prediction purposes but the prediction of clearance from > or = 3 species was far more accurate than two-species scaling. PMID:19827101
Pollman, Curtis D
2014-11-15
Structural equation modeling (SEM) provides a framework that can more properly handle complex variable interactions inherent in mercury cycling and its bioaccumulation compared to more traditional regression-based methods. SEM was applied to regional data sets for three different types of aquatic ecosystems within Florida, USA--lakes, streams, and the Everglades--to evaluate the underlying nature (i.e., indirect and direct) of the relationships between fish mercury concentrations and trophic state related variables such as nutrients, dissolved organic carbon (DOC), sulfate, and alkalinity. The modeling results indicated some differences in key variable relationships--for example, the effect of nutrients on fish mercury in lakes and streams was uniformly negative through direct and indirect pathways consistent with biodilution or eutrophication-associated effects on food web structure. Somewhat surprisingly, however, was that total phosphorus did not serve as a meaningful variable in the Everglades model, apparently because its effects were masked or secondary to the effects of DOC. What is perhaps a more important result were two key similarities across the three systems. First, the modeling clearly indicates that the dominant influence on fish tissue mercury concentrations in all three systems is related to variations in the methylmercury signal. Second, the modeling demonstrated that the effect of DOC on fish mercury concentrations was exerted through multiple and antagonistic pathways, including facilitated transport of total mercury and methylmercury, enhanced rates of methylation, and limitations imposed on bioavailability. Indeed, while the individual DOC pathways in the models were all highly significant (generally p<0.001), the net effect of DOC in each model was greatly reduced or insignificant. These results can help explain contradictory results obtained previously by other researchers in other systems, and illustrate the importance of SEM as a modeling
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
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
Daws, Matthew I; Ballard, Christopher; Mullins, Christopher E; Garwood, Nancy C; Murray, Brian; Pearson, Timothy R H; Burslem, David F R P
2007-12-01
A seed size-seed number trade-off exists because smaller seeds are produced in greater number but have a lower probability of establishment. This reduced establishment success of smaller-seeded species may be determined by biophysical constraints imposed by scaling rules. Root and shoot diameter, root growth extension rate (RGER) and shoot length at death for dark-grown seedlings are predicted to scale with the cube root of seed embryo and endosperm mass (m). We confirmed this expectation for ten neotropical gap-dependent tree species with an embryo and endosperm dry mass>1 mg. However, for nine smaller seeded species (m<1 mg) with photoblastic germination, root and shoot diameters were larger than expected, and consequently, RGER was slower than expected. The maximum shoot thrust of seedlings from seeds with masses>or=1 mg was comparable to the estimated force required to displace overlying litter, supporting the hypothesis that photoblastic behaviour only occurs in seeds with insufficient shoot thrust to displace overlying leaves. Using the model soil water, energy and transpiration to predict soil drying in small and large gaps, we showed that: (1) gaps that receive a significant amount of direct sunlight will dry more quickly than small gaps that do not, (2) compared to the wet-season, soil that is already dry at depth (i.e. the dry-season) will dry faster after rainfall (this drying would most likely kill seedlings from small seeds) and (3) even during the wet-season, dry periods of a few days in large gaps can kill shallow-rooted seedlings. We conclude that the smaller the seed, the more vulnerable its seedling would be to both covering by litter and soil drying because it can only emerge from shallow depths and has a slow RGER. Consequently, we suggest that these allometrically related factors contribute to the reduced establishment success of smaller-seeded species that underpins the seed size-seed number trade-off. PMID:17846798
NASA Astrophysics Data System (ADS)
Pattnaik, S.; Nayak, R. C.
2014-04-01
We obtain here a new relation for the reduced electric quadrupole transition probability B(E2)↑ of a given nucleus in terms of its derivatives with respect to neutron and proton numbers based on a similar local energy relation in the Infinite Nuclear Matter (INM) model of atomic nuclei, which is essentially built on the foundation of the Hugenholtz-Van Hove (HVH) theorem of many-body theory. Obviously, such a relation in the form of a differential equation is expected to be more powerful than the usual algebraic difference equations. Although the relation for B(E2)↑ has been perceived simply on the basis of a corresponding differential equation for the local energy in the INM model, its theoretical foundation otherwise has been clearly demonstrated. We further exploit the differential equation in using the very definitions of the derivatives to obtain two different recursion relations for B(E2)↑, connecting in each case three neighboring even-even nuclei from lower to higher mass numbers and vice versa. We demonstrate their numerical validity using available data throughout the nuclear chart and also explore their possible utility in predicting B(E2)↑ values.
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.
1998-11-01
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.
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
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
Mahmood, Iftekhar
2016-06-01
The objective of this study was to evaluate the predictive performance of 4 allometric models to predict clearance in pediatric ages ranging from premature neonates to children ≤2 years of age. Four allometric models were used to predict clearances of 28 drugs in children from preterm neonates to 2 years of age (n = 564). The 4 models are (1) basal metabolic rate-dependent model; (2) age-dependent exponent model; (3) an allometric model based on kidney and liver weights as well as kidney and liver blood flow; and (4) an allometric model based on a fixed exponent of 0.75. The predictive performance of these models was evaluated by comparing the predicted clearance of the studied drugs with the observed clearance in an individual child. The results of the study indicated that the 3 new proposed models predicted the mean clearance of the drugs with reasonable accuracy (≤50% prediction error). On the other hand, the exponent of 0.75 produced substantial prediction error. Predicted individual clearance values were ≥50% in approximately 30% of the children by the proposed 3 methods and 73% by exponent 0.75. The 3 new proposed allometric models can predict mean clearances of drugs in children from premature neonates to ≤2 years of age with reasonable accuracy and are of practical value during pediatric drug development. PMID:26437918
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)
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.
Wotherspoon, Danny; Burgin, Shelley
2011-02-01
The functional significance of allometric change in reptiles has received limited attention and the reason for such changes has been regarded as 'obscure'. In this paper we report data on the Australian Pogona barbata, the eastern bearded dragon, from across their range and review changes in allometric growth among juveniles, and adult males and females and consider the functional relevance of these changes. There were significant differences in the population for mass, tail length, tail width, rear leg length and jaw length. These differences were consistent with differences required in locomotor performance and thus habitat use, together with access to different preferred dietary components. PMID:21236651
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
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
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.
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, 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.
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.
NASA Astrophysics Data System (ADS)
Tsuboi, Zengo
2014-09-01
We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of Uq(gl(M|N)) in the FRT formulation and obtain explicit solutions of the graded Yang-Baxter equation in terms of q-oscillator superalgebras. These solutions correspond to L-operators for Baxter Q-operators. We also discuss an extension of these representations to the ones for contracted algebras of Uq(glˆ(M|N)) by considering the action of renormalized generators of the other side of the Borel subalgebra. We define model independent universal Q-operators as the supertrace of the universal R-matrix and write universal T-operators in terms of these Q-operators based on shift operators on the supercharacters. These include our previous work on Uq(slˆ(2|1)) case [1] in part, and also give a cue for the operator realization of our Wronskian-like formulas on T- and Q-functions in [2,3].
Charlton, R A; Landau, S; Schiavone, F; Barrick, T R; Clark, C A; Markus, H S; Morris, R G
2008-10-01
Cognitive changes in normal aging have been explained by the frontal-executive hypothesis, but the assumptions made by this hypothesis concerning the neurobiological causes are still a matter of debate. Executive functions (EF) may activate neural networks that include disparate grey matter regions, and rely on the integrity of white matter connections. In 118 adults (50-90 years old) from the GENIE study, white matter integrity was measured using diffusion tensor imaging, and information processing speed, fluid intelligence and EF were assessed. A theory-driven structural equation model was developed to test associations between variables. The model was revised, removing non-significant paths. The adjusted model explained well the covariance in our data; and suggested that the reduction in white matter integrity associated with age directly affected only working memory. Fluid intelligence was mediated by all measured cognitive variables. The results suggest that white matter integrity may be particularly important for abilities activating complex neural networks, as occurs in working memory. Integration of the information processing speed and frontal-executive hypotheses may provide important information regarding common, unique, and mediating factors in cognitive aging. PMID:17451845
Wang, Chenguang; Allegaert, Karel; Peeters, Mariska Y M; Tibboel, Dick; Danhof, Meindert; Knibbe, Catherijne A J
2014-01-01
Aim For scaling clearance between adults and children, allometric scaling with a fixed exponent of 0.75 is often applied. In this analysis, we performed a systematic study on the allometric exponent for scaling propofol clearance between two subpopulations selected from neonates, infants, toddlers, children, adolescents and adults. Methods Seven propofol studies were included in the analysis (neonates, infants, toddlers, children, adolescents, adults1 and adults2). In a systematic manner, two out of the six study populations were selected resulting in 15 combined datasets. In addition, the data of the seven studies were regrouped into five age groups (FDA Guidance 1998), from which four combined datasets were prepared consisting of one paediatric age group and the adult group. In each of these 19 combined datasets, the allometric scaling exponent for clearance was estimated using population pharmacokinetic modelling (nonmem 7.2). Results The allometric exponent for propofol clearance varied between 1.11 and 2.01 in cases where the neonate dataset was included. When two paediatric datasets were analyzed, the exponent varied between 0.2 and 2.01, while it varied between 0.56 and 0.81 when the adult population and a paediatric dataset except for neonates were selected. Scaling from adults to adolescents, children, infants and neonates resulted in exponents of 0.74, 0.70, 0.60 and 1.11 respectively. Conclusions For scaling clearance, ¾ allometric scaling may be of value for scaling between adults and adolescents or children, while it can neither be used for neonates nor for two paediatric populations. For scaling to neonates an exponent between 1 and 2 was identified. PMID:23772816
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. PMID:1814935
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
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…
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.
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.
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.
Octonic Massive Field Equations
NASA Astrophysics Data System (ADS)
Demir, Süleyman; Kekeç, Seray
2016-03-01
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.
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.
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.
NASA Astrophysics Data System (ADS)
Dashora, Nirvikar
2012-07-01
Ionospheric models are of prime interest for applications like satellite based navigation and a near real time forecasting of grid based ionospheric delays. The physical processes that govern low latitude ionospheric variability are, at large, known, however, there remains a certain degree of uncertainty in many variables that are not measurable in each longitude sector on day-to-day basis like thermospheric neutral winds and drifts, diffusion and conductivity distribution etc. To study the day-to-day and seasonal variation of peak electron density and TEC in low latitude we used a physics based model, SAMI2, for three years 2001, 2005 and 2009 representing respectively the peak, moderate and lowest levels of solar activity in past solar cycle, besides for some geomagnetic storms. The model is run for Indian longitude sector under various controlled conditions like meridional winds and equatorial ExB drifts. The diurnal and seasonal variations of various quantities have been obtained as 2D meridional cross-section of ionosphere. There is a renewed interest in the variable nature of relation between time of maximization of equatorial ionization anomaly in terms of electron density (and TEC) and the time of maximization of ExB drift over equator. A dramatic variation is found in the time-lag between the maximization of ExB drift over equator and peak density occurrence in low latitudes (even in case of zero meridional winds). We found that single linear relation neither exists for any season nor for any year during any epoch of solar cycle. Specifically, equinoctial months exhibit greater day-to-day variability than other seasons, the reasons to be still quantified. Simulations for geomagnetic storms were separately performed. TEC observations show a direct response to penetration electric fields. The model results under disturbed ExB conditions show that the imminent enhancements in low latitude TEC are result of enhanced density due to mechanical up-lifting of F
NASA Astrophysics Data System (ADS)
Stephani, Hans
2004-02-01
Preface; Notation; Part I. Special Relativity: 1. Introduction: inertial systems and Galilei invariance of classical mechanics; 2. Light propagation in moving coordinate systems and Lorentz transformations; 3. Our world as a Minkowski space; 4. Mechanics of special relativity; 5. Optics of plane waves; 6. Four-dimensional vectors and tensors; 7. Electrodynamics in vacuo; 8. Transformation properties of electromagnetic fields: examples; 9. Null vectors and the algebraic properties of electromagnetic field tensors; 10. Charged point particles and their field; 11. Pole-dipole particles and their field; 12. Electrodynamics in media; 13. Perfect fluids and other physical theories; Part II. Riemannian Geometry: 14. Introduction: the force-free motion of particles in Newtonian mechanics; 15. Why Riemannian geometry?; 16. Riemannian space; 17. Tensor algebra; 18. The covariant derivative and parallel transport; 19. The curvature tensor; 20. Differential operators, integrals and integral laws; 21. Fundamental laws of physics in Riemannian spaces; Part III. Foundations of Einstein's Theory of Gravitation: 22. The fundamental equations of Einstein's theory of gravitation; 23. The Schwarzschild solution; 24. Experiments to verify the Schwarzschild metric; 25. Gravitational lenses; 26. The interior Schwarzschild solution; Part IV. Linearized Theory of Gravitation, Far Fields and Gravitational Waves: 27. The linearized Einstein theory of gravity; 28. Far fields due to arbitrary matter distributions and balance equations for momentum and angular momentum; 29. Gravitational waves; 30. The Cauchy problem for the Einstein field equations; Part V. Invariant Characterization of Exact Solutions: 31. Preferred vector fields and their properties; 32. The Petrov classification; 33. Killing vectors and groups of motion; 34. A survey of some selected classes of exact solutions; Part VI. Gravitational Collapse and Black Holes: 35. The Schwarzschild singularity; 36. Gravitational collapse
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 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.
Equating Training to Education.
ERIC Educational Resources Information Center
Davis, Lansing J.
1993-01-01
Distinguishes between education and employer-sponsored training in terms of process, purpose, and providers. Concludes that work-related training and postsecondary education are cognates within the classification education, and equating their learning outcomes is appropriate. (SK)
Smith, David; Woodman, Richard; Drummond, Aaron; Battersby, Malcolm
2016-03-30
Knowledge of a problem gambler's underlying gambling related cognitions plays an important role in treatment planning. The Gambling Related Cognitions Scale (GRCS) is therefore frequently used in clinical settings for screening and evaluation of treatment outcomes. However, GRCS validation studies have generated conflicting results regarding its latent structure using traditional confirmatory factor analyses (CFA). This may partly be due to the rigid constraints imposed on cross-factor loadings with traditional CFA. The aim of this investigation was to determine whether a Bayesian structural equation modelling (BSEM) approach to examination of the GRCS factor structure would better replicate substantive theory and also inform model re-specifications. Participants were 454 treatment-seekers at first presentation to a gambling treatment centre between January 2012 and December 2014. Model fit indices were well below acceptable standards for CFA. In contrast, the BSEM model which included small informative priors for the residual covariance matrix in addition to cross-loadings produced excellent model fit for the original hypothesised factor structure. The results also informed re-specification of the CFA model which provided more reasonable model fit. These conclusions have implications that should be useful to both clinicians and researchers evaluating measurement models relating to gambling related cognitions in treatment-seekers. PMID:26921058
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)
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
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.
Wilson, R S; Franklin, C E; James, R S
2000-06-01
We constructed a force platform to investigate the scaling relationships of the detailed dynamics of jumping performance in striped marsh frogs (Limnodynastes peronii). Data were used to test between two alternative models that describe the scaling of anuran jumping performance; Hill's model, which predicts mass- independence of jump distance, and Marsh's model, which predicts that jump distance increases as M(0.2), where M is body mass. From the force platform, scaling relationships were calculated for maximum jumping force (F(max)), acceleration, take-off velocity (U(max)), mass-specific jumping power (P(max)), total jumping distance (D(J)) and total contact time for 75 L. peronii weighing between 2.9 and 38. 4 g. F(max) was positively correlated with body mass and was described by the equation F(max)=0.16M(0.61), while P(max) decreased significantly with body mass and was described by the equation P(max)=347M(-)(0.46). Both D(J) and U(max) were mass-independent over the post-metamorph size range, and thus more closely resembled Hill's model for the scaling of locomotion. We also examined the scaling relationships of jumping performance in metamorph L. peronii by recording the maximum jump distance of 39 animals weighing between 0.19 and 0.58 g. In contrast to the post-metamorphic L. peronii, D(J) and U(max) were highly dependent on body mass in metamorphs and were described by the equations D(J)=38M(0.53) and U(max)=1.82M(0.23), respectively. Neither model for the scaling of anuran jumping performance resembled data from metamorph L. peronii. Although the hindlimbs of post-metamorphic L. peronii scaled geometrically (body mass exponent approximately 0.33), the hindlimbs of metamorphs showed greater proportional increases with body mass (mass exponents of 0.41-0.42). PMID:10821750
ERIC Educational Resources Information Center
Nibbelink, William H.
1990-01-01
Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)
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. PMID:25958103
2011-01-01
Background It is hypothesized that dietary linoleic acid (LA) promotes chronic and acute diseases in humans by enriching tissues with arachidonic acid (AA), its downstream metabolite, and dietary studies with rodents have been useful for validation. However, levels of LA in research diets of rodents, as published in the literature, are notoriously erratic making interspecies comparisons unreliable. Therefore, the ability to extrapolate the biological effects of dietary LA from experimental rodents to humans necessitates an allometric scaling model that is rooted within a human equivalent context. Methods To determine the physiological response of dietary LA on tissue AA, a mathematical model for extrapolating nutrients based on energy was used, as opposed to differences in body weight. C57BL/6J mice were divided into 9 groups fed a background diet equivalent to that of the US diet (% energy) with supplemental doses of LA or AA. Changes in the phospholipid fatty acid compositions were monitored in plasma and erythrocytes and compared to data from humans supplemented with equivalent doses of LA or AA. Results Increasing dietary LA had little effect on tissue AA, while supplementing diets with AA significantly increased tissue AA levels, importantly recapitulating results from human trials. Conclusions Thus, interspecies comparisons for dietary LA between rodents and humans can be achieved when rodents are provided human equivalent doses based on differences in metabolic activity as defined by energy consumption. PMID:21702942
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.
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
Santiago-Torres, Margarita; Cui, Yuchen; Adams, Alexandra K; Allen, David B; Carrel, Aaron L; Guo, Jessica Y; LaRowe, Tara L; Schoeller, Dale A
2016-06-01
Hispanic children are disproportionally affected by obesity-related risk of metabolic disease. We used the structural equation modeling to examine the associations between specific diet and physical activity (PA) behaviors at home and Hispanic children's metabolic health. A total of 187 Hispanic children and their parents from an urban community in Wisconsin participated in the study. Exposure variables included, children's daily intake of sugar-sweetened beverages (SSB) and PA; home availability of SSB and PA areas/equipment; and parents' intake of SSB and PA, assessed through self-administered questionnaires. Outcome variables for children's metabolic health included, measured anthropometrics; cardiovascular fitness assessed using the Progressive Aerobic Cardiovascular Endurance Run (PACER); and insulin resistance determined with the homeostasis model assessment of insulin resistance (HOMAIR). We found that children's daily intake of SSB was positively associated with BMI z-score, which in turn, was positively associated with HOMAIR (P < 0.05). Specific diet behaviors at home associated with children's intake of SSB, included home availability of SSB, which mediated the association between parents' and children's intake of SSB (P < 0.05). Children's PA was positively associated with PACER z-score, which in turn, was inversely associated with HOMAIR (P < 0.05). Specific PA behaviors at home associated with children's PA, included home availability of PA areas/equipment, which mediated the association between parents' and children's PA (P < 0.05). The structural equation model indices suggested a satisfactory model fit (Chi-square, X(2) = 53.1, comparative fix index = 0.92, root-mean-squared error associated = 0.04). The findings confirm the need for interventions at the family level that promotes healthier home environments by targeting poor diet and low levels of PA in all family members. PMID:26850309
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
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.
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.
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
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).
Trabecular bone microstructure scales allometrically in the primate humerus and femur
Ryan, Timothy M.; Shaw, Colin N.
2013-01-01
Most analyses of trabecular microarchitecture in mammals have focused on the functional significance of interspecific variation, but they have not effectively considered the influence of body size or phylogeny on bone architecture. The goals of this study were to determine the relationship between trabecular bone and body size in the humeral and femoral heads of extant primates, and to assess the influence of phylogeny on bone microstructure. Using a sample of 235 individuals from 34 primate species, ranging in body size from 0.06 to 130 kg, the relationships between trabecular bone structure and body size were assessed by using conventional and phylogenetic regression analyses. Bone volume fraction, trabecular thickness and trabecular spacing increase with body size, whereas bone surface-area-to-volume ratio decreases. Shape variables such as trabecular number, connectivity density and degree of anisotropy scale inversely with size. Most of these variables scale with significant negative allometry, except bone surface-area-to-volume ratio, which scales with slight positive allometry. Phylogenetic regressions indicate a relatively weak phylogenetic signal in some trabecular bone variables. These data demonstrate that, relative to body size, large primates have thinner and more tightly packed trabeculae than small primates. The relatively thin trabeculae in large primates and other mammals, coupled with constraints on trabecular thickness related to osteocyte function, suggest that increased skeletal loads in the postcranial joints of large mammals are probably mitigated not only through alterations in trabecular microarchitecture, but also through other mechanisms such as changes in cortical bone distribution, limb posture and gait speed. PMID:23486443
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.
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.
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
The ontogeny of the chin: an analysis of allometric and biomechanical scaling.
Holton, N E; Bonner, L L; Scott, J E; Marshall, S D; Franciscus, R G; Southard, T E
2015-06-01
The presence of a prominent chin in modern humans has been viewed by some researchers as an architectural adaptation to buttress the anterior corpus from bending stresses during mastication. In contrast, ontogenetic studies of mandibular symphyseal form suggest that a prominent chin results from the complex spatial interaction between the symphysis and surrounding soft tissue and skeletal anatomy during development. While variation in chin prominence is clearly influenced by differential growth and spatial constraints, it is unclear to what degree these developmental dynamics influence the mechanical properties of the symphysis. That is, do ontogenetic changes in symphyseal shape result in increased symphyseal bending resistance? We examined ontogenetic changes in the mechanical properties and shape of the symphysis using subjects from a longitudinal cephalometric growth study with ages ranging from 3 to 20+ years. We first examined whether ontogenetic changes in symphyseal shape were correlated with symphyseal vertical bending and wishboning resistance using multivariate regression. Secondly, we examined ontogenetic scaling of bending resistance relative to bending moment arm lengths. An ontogenetic increase in chin prominence was associated with decreased vertical bending resistance, while wishboning resistance was uncorrelated with ontogenetic development of the chin. Relative to bending moment arm lengths, vertical bending resistance scaled with significant negative allometry whereas wishboning resistance scaled isometrically. These results suggest a complex interaction between symphyseal ontogeny and bending resistance, and indicate that ontogenetic increases in chin projection do not provide greater bending resistance to the mandibular symphysis. PMID:25865897
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.
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
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 Astrophysics Data System (ADS)
Wu, Shuang-Qing
2008-09-01
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 Stäckel-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 Stäckel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.
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.
Prediction intervals: Placing real bounds on regression-based allometric estimates of biomass.
Ward, Peter J
2015-07-01
Biomass allometry studies routinely assume that regression models can be applied across species and sites, and that goodness of fit of a regression model to its derivation dataset indicates both the relevance of the model to a new dataset and the likely error. Assuming that a model is relevant for a new sample, a prediction interval is a useful error measure for stand mass. Prediction coverage tests whether the model and hence the interval are appropriate in the new sample. Data for three similar shrubby species from four similar sites were combined in various ways to test the impact of varying levels of biodiverse heterogeneity on the performance of the four models most commonly used in published biomass studies. No one model performed consistently well predicting new data, and validation checks were not good indicators of prediction coverage. The highly variable results suggest that the common models might contain insufficient variables. Euclidean distance was used to quantify the relative similarity of samples as a possible means of estimating prediction coverage; it proved unsuccessful with these data. PMID:25974741
Predicting Maximum Tree Heights and Other Traits from Allometric Scaling and Resource Limitations
Kempes, Christopher P.; West, Geoffrey B.; Crowell, Kelly; Girvan, Michelle
2011-01-01
Terrestrial vegetation plays a central role in regulating the carbon and water cycles, and adjusting planetary albedo. As such, a clear understanding and accurate characterization of vegetation dynamics is critical to understanding and modeling the broader climate system. Maximum tree height is an important feature of forest vegetation because it is directly related to the overall scale of many ecological and environmental quantities and is an important indicator for understanding several properties of plant communities, including total standing biomass and resource use. We present a model that predicts local maximal tree height across the entire continental United States, in good agreement with data. The model combines scaling laws, which encode the average, base-line behavior of many tree characteristics, with energy budgets constrained by local resource limitations, such as precipitation, temperature and solar radiation. In addition to predicting maximum tree height in an environment, our framework can be extended to predict how other tree traits, such as stomatal density, depend on these resource constraints. Furthermore, it offers predictions for the relationship between height and whole canopy albedo, which is important for understanding the Earth's radiative budget, a critical component of the climate system. Because our model focuses on dominant features, which are represented by a small set of mechanisms, it can be easily integrated into more complicated ecological or climate models. PMID:21695189
Phylogenetic, ecological, and allometric correlates of cranial shape in Malagasy lemuriforms.
Baab, Karen L; Perry, Jonathan M G; Rohlf, F James; Jungers, William L
2014-05-01
Adaptive radiations provide important insights into many aspects of evolution, including the relationship between ecology and morphological diversification as well as between ecology and speciation. Many such radiations include divergence along a dietary axis, although other ecological variables may also drive diversification, including differences in diel activity patterns. This study examines the role of two key ecological variables, diet and activity patterns, in shaping the radiation of a diverse clade of primates, the Malagasy lemurs. When phylogeny was ignored, activity pattern and several dietary variables predicted a significant proportion of cranial shape variation. However, when phylogeny was taken into account, only typical diet accounted for a significant proportion of shape variation. One possible explanation for this discrepancy is that this radiation was characterized by a relatively small number of dietary shifts (and possibly changes in body size) that occurred in conjunction with the divergence of major clades. This pattern may be difficult to detect with the phylogenetic comparative methods used here, but may characterize not just lemurs but other mammals. PMID:24451053
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).
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
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
NASA Astrophysics Data System (ADS)
CHOI, S.; Shi, Y.; Ni, X.; Simard, M.; Myneni, R. B.
2013-12-01
Sparseness in in-situ observations has precluded the spatially explicit and accurate mapping of forest biomass. The need for large-scale maps has raised various approaches implementing conjugations between forest biomass and geospatial predictors such as climate, forest type, soil property, and topography. Despite the improved modeling techniques (e.g., machine learning and spatial statistics), a common limitation is that biophysical mechanisms governing tree growth are neglected in these black-box type models. The absence of a priori knowledge may lead to false interpretation of modeled results or unexplainable shifts in outputs due to the inconsistent training samples or study sites. Here, we present a gray-box approach combining known biophysical processes and geospatial predictors through parametric optimizations (inversion of reference measures). Total aboveground biomass in forest stands is estimated by incorporating the Forest Inventory and Analysis (FIA) and Parameter-elevation Regressions on Independent Slopes Model (PRISM). Two main premises of this research are: (a) The Allometric Scaling and Resource Limitations (ASRL) theory can provide a relationship between tree geometry and local resource availability constrained by environmental conditions; and (b) The zeroth order theory (size-frequency distribution) can expand individual tree allometry into total aboveground biomass at the forest stand level. In addition to the FIA estimates, two reference maps from the National Biomass and Carbon Dataset (NBCD) and U.S. Forest Service (USFS) were produced to evaluate the model. This research focuses on a site-scale test of the biomass model to explore the robustness of predictors, and to potentially improve models using additional geospatial predictors such as climatic variables, vegetation indices, soil properties, and lidar-/radar-derived altimetry products (or existing forest canopy height maps). As results, the optimized ASRL estimates satisfactorily
``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.
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…
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…
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…
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
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.
ERIC Educational Resources Information Center
Finlay, Karen; Finlay, Thomas
1996-01-01
Reports on a study of 101 Canadian librarians that tested individual differences important to enhanced use of the Internet. Analysis of covariance, hierarchical regression, and structural equation modeling provided evidence that technical and procedural knowledge had a significant influence on attitudes toward the Internet and the frequency of…
NASA Astrophysics Data System (ADS)
Russell, John
2003-11-01
I will use the abbreviation BMHR equation (for uc(Bussman,) Münz, Hughes & Reid) to denote the modified uc(Orr-Sommerfeld) equation that applies when the mean flow is the asymptotic suction boundary layer. uc(Dieter) Grohne (1950) and uc(Paul) Baldwin (1970) found several integral representations of exact solutions of the uc(Orr-Sommerfeld) and BMHR equations, respectively. In the mean time uc(W.D.) Lakin & W.H. Reid (1982) derived uniformly-valid asymptotic solutions of the BMHR equation. Following uc(W.) Wasow (1953) they found it useful to define a family of seven canonical solutions (one of which is well-balanced, three of which are balanced and three of which are dominant-recessive). As uc(Baldwin) pointed out in a 1985 paper the family of integral representations found by uc(Grohne) and uc(Baldwin,) though large enough to represent the general solution, does not immediately permit a one-to-one correlation with seven solutions of uc(Lakin) & Reid. A careful correlation must enlarge the family of exact solutions given by uc(Grohne) and uc(Baldwin) and must, moreover, include suitable conformal transfomations between the planes of the uc(Langer) variable used by uc(Lakin) & Reid and the independent variable that arises most naturally in the exact integral representations. The present work addresses these problems.
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.
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.
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.
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.
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.
Oxborough, David; Ghani, Saqib; Harkness, Allan; Lloyd, Guy; Moody, William; Ring, Liam; Sandoval, Julie; Senior, Roxy; Sheikh, Nabeel; Stout, Martin; Utomi, Victor; Willis, James; Zaidi, Abbas; Steeds, Richard
2014-09-01
The aim of the study is to establish the impact of 2D echocardiographic methods on absolute values for aortic root dimensions and to describe any allometric relationship to body size. We adopted a nationwide cross-sectional prospective multicentre design using images obtained from studies utilising control groups or where specific normality was being assessed. A total of 248 participants were enrolled with no history of cardiovascular disease, diabetes, hypertension or abnormal findings on echocardiography. Aortic root dimensions were measured at the annulus, the sinus of Valsalva, the sinotubular junction, the proximal ascending aorta and the aortic arch using the inner edge and leading edge methods in both diastole and systole by 2D echocardiography. All dimensions were scaled allometrically to body surface area (BSA), height and pulmonary artery diameter. For all parameters with the exception of the aortic annulus, dimensions were significantly larger in systole (P<0.05). All aortic root and arch measurements were significantly larger when measured using the leading edge method compared with the inner edge method (P<0.05). Allometric scaling provided a b exponent of BSA(0.6) in order to achieve size independence. Similarly, ratio scaling to height in subjects under the age of 40 years also produced size independence. In conclusion, the largest aortic dimensions occur in systole while using the leading edge method. Reproducibility of measurement, however, is better when assessing aortic dimensions in diastole. There is an allometric relationship to BSA and, therefore, allometric scaling in the order of BSA(0.6) provides a size-independent index that is not influenced by the age or gender. PMID:26693286
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
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.
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
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 Astrophysics Data System (ADS)
Karamperidou, C.; Booth, J. F.; Lall, U.
2013-12-01
Zonal and meridional surface temperature gradients are associated with mean zonal circulation and storm-track variability. We investigate the projected changes in the equator-to-pole gradient and the ocean-land contrast in the suite of models participating in the Coupled Model Intercomparison Project 5 (CMIP5). The projected decrease in the gradients is in accordance with the poleward amplification of temperature increases and the faster warming of land compared to the ocean. However, we note differences in the projections between the Northern and the Southern Hemisphere, and among ocean basins in the Northern Hemisphere, that are indicative of competing mechanisms that underlie the projected shifts in the mean zonal circulation and storm tracks. As an additional indicator of the position and strength of midlatitude mean and transient atmospheric circulation, as well as the expansion of the tropics, we study the projected changes in the latitude of maximum meridional surface temperature gradient.
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,…
Spin field equations and Heun's equations
NASA Astrophysics Data System (ADS)
Jiang, Min; Wang, Xuejing; Li, Zhongheng
2015-06-01
The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino ( s=1/2), electromagnetic ( s=1), Rarita-Schwinger ( s=3/2), and gravitational ( s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun's equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.
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.
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)
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.
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.
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…
NASA Astrophysics Data System (ADS)
Ambili, K. M.; Choudhary, R. K.; St.-Maurice, J.-P.
2014-07-01
A sunrise undulation (SU) is observed by ionosondes when new ionization is produced at sunrise in the upper F region at the geomagnetic equator. It creates a very quick upward transition in the F region peak altitude (hmF2), which subsequently undergoes a sharp descent at a rate far in excess of any electrodynamic drift. The peak density also increases rapidly during the descent. However, the detection of the new plasma with ionosondes is possible only if plasma from the night before has undergone enough recombination, which, on average, can vary from one location to another and one season to the next. With this in mind, we have studied seasonal variations in the SU occurrence in 2010 at two widely separated geomagnetic equatorial stations in longitude, at Jicamarca in Peru and Trivandrum in India. Noticeable differences were found in the characteristics of undulation observed at the two locations. While full undulation (both ascend and descend in hmF2) was observed throughout the year at Trivandrum, only the descending part of undulation was visible at Jicamarca. Plasma density just before sunrise, on average, was 2 times larger at Jicamarca than at Trivandrum. The average hmF2, which peaks during night, was also higher at Jicamarca by as much as 100 km compared to Trivandrum. We traced the origin of these differences to the evolution of zonal electric field between sunset and local midnight at the two locations. The downward drift during this period was steeper at Trivandrum compared to Jicamarca, particularly during equinox. In addition, the strength of the downward drifts at Jicamarca decreased and even underwent a sign reversal prior to sunrise during equinox and winter months. In comparison, the downward motion at Trivandrum only became stronger during early morning hours. The contrast between the vertical drift at the two stations provides a very reasonable qualitative explanation for the differences in the characteristics of SU observed at the two stations.
Higher spin versus renormalization group equations
NASA Astrophysics Data System (ADS)
Sachs, Ivo
2014-10-01
We present a variation of earlier attempts to relate renormalization group equations to higher spin equations. We work with a scalar field theory in 3 dimensions. In this case we show that the classical renormalization group equation is a variant of the Vasiliev higher spin equations with Kleinians on AdS4 for a certain subset of couplings. In the large N limit this equivalence extends to the quantum theory away from the conformal fixed points.
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)
NASA Technical Reports Server (NTRS)
1977-01-01
Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.
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
NASA Astrophysics Data System (ADS)
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.
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
Evolutions equations in computational anatomy.
Younes, Laurent; Arrate, Felipe; Miller, Michael I
2009-03-01
One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shape evolution equations that are now used routinely in applications have emerged over time. Our goal in this paper is to provide an overview of these equations, placing them in their theoretical context, and giving examples of applications in which they can be used. We introduce the required theoretical background before discussing several classes of equations of increasingly complexity. These equations include energy minimizing evolutions deriving from Riemannian gradient descent, geodesics, parallel transport and Jacobi fields. PMID:19059343
New scale-relativistic derivations of Pauli and Dirac equations
NASA Astrophysics Data System (ADS)
Hammad, F.
2008-02-01
In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schrödinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation.
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.
Bernacchi, Carl J; Thompson, Jennifer N; Coleman, James S; McConnaughay, Kelly D M
2007-10-01
Nitrogen concentrations in plant tissues can vary as a function of resource availability. Altered rates of plant growth and development under varying resource availabilities were examined to determine their effects on changes in whole-plant N use efficiency (NUE). Three species of old-field annuals were grown at broadly varying light, nutrient and water levels, and four species at varying atmospheric concentrations of CO2. Study results show highly variable N accrual rates when expressed as a function of plant age or size, but similar patterns of whole-plant N versus non-N biomass accrual over a wide range of environmental conditions. However, severely light-limited plants showed increased N versus biomass accrual for two of three species, and severely nutrient-limited plants had decreased N versus biomass accrual for all species. Whole-plant N accrual versus age and N versus biomass accrual increased under saturating water for two of three species. A marginally significant, modest decrease in N versus biomass accrual was found at high CO2 levels for two of four species. Physiological adjustments in NUE, expressed as N versus biomass accrual, were limited to environments with severely limited or overabundant resources. PMID:17727413
Single wall penetration equations
NASA Technical Reports Server (NTRS)
Hayashida, K. B.; Robinson, J. H.
1991-01-01
Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.
NASA Astrophysics Data System (ADS)
Zhuravlev, V. M.
2016-03-01
We discuss an extension of the theory of multidimensional second-order equations of the elliptic and hyperbolic types related to multidimensional quasilinear autonomous first-order partial differential equations. Calculating the general integrals of these equations allows constructing exact solutions in the form of implicit functions. We establish a connection with hydrodynamic equations. We calculate the number of free functional parameters of the constructed solutions. We especially construct and analyze implicit solutions of the Laplace and d'Alembert equations in a coordinate space of arbitrary finite dimension. In particular, we construct generalized Penrose-Rindler solutions of the d'Alembert equation in 3+1 dimensions.
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)
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)
ERIC Educational Resources Information Center
Fay, Temple H.
2002-01-01
We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2015-01-01
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 structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789
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.
VanderVeen, Nathan; Raja, Nicholas; Yi, Elizabeth; Appelman, Henry; Ng, Philip; Palmer, Donna; Zamler, Daniel; Dzaman, Marta; Lowenstein, Pedro R; Castro, Maria G
2016-06-01
Glioblastoma multiforme (GBM) is the most commonly occurring primary brain cancer in adults, in whom its highly infiltrative cells prevent total surgical resection, often leading to tumor recurrence and patient death. Our group has discovered a gene therapy approach for GBM that utilizes high-capacity "gutless" adenoviral vectors encoding regulatable therapeutic transgenes. The herpes simplex type 1-thymidine kinase (TK) actively kills dividing tumor cells in the brain when in the presence of the prodrug, ganciclovir (GCV), whereas the FMS-like tyrosine kinase 3 ligand (Flt3L) is an immune-stimulatory molecule under tight regulation by a tetracycline-inducible "Tet-On" activation system that induces anti-GBM immunity. As a prelude to a phase I clinical trial, we evaluated the safety and efficacy of Food and Drug Administration (FDA)-approved doses of the tetracycline doxycycline (DOX) allometrically scaled for rats. DOX initiates the expression of Flt3L, which has been shown to recruit dendritic cells to the brain tumor microenvironment-an integral first step in the development of antitumor immunity. The data revealed a highly safe profile surrounding these human-equivalent doses of DOX under an identical therapeutic window as proposed in the clinical trial. This was confirmed through a neuropathological analysis, liver and kidney histopathology, detection of neutralizing antibodies, and systemic toxicities in the blood. Interestingly, we observed a significant survival advantage in rats with GBM receiving the 300 mg/day equivalent dosage of DOX versus the 200 mg/day equivalent. Additionally, rats rejected "recurrent" brain tumor threats implanted 90 days after their primary brain tumors. We also show that DOX detection within the plasma can be an indicator of optimal dosing of DOX to attain therapeutic levels. This work has significant clinical relevance for an ongoing phase I clinical trial in humans with primary GBM and for other therapeutic approaches using
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
Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation
NASA Astrophysics Data System (ADS)
Kazakov, A. Ya.; Slavyanov, S. Yu.
2008-05-01
Euler integral transformations relate solutions of ordinary linear differential equations and generate integral representations of the solutions in a number of cases or relations between solutions of constrained equations (Euler symmetries) in some other cases. These relations lead to the corresponding symmetries of the monodromy matrices. We discuss Euler symmetries in the case of the simplest Fuchsian system that is equivalent to a deformed Heun equation, which is in turn related to the Painlevé PVI equation. The existence of integral symmetries of the deformed Heun equation leads to the corresponding symmetries of the PVI equation.
Parabolized stability equations
NASA Astrophysics Data System (ADS)
Herbert, Thorwald
1994-04-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
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.
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).
What Makes a Chemical Equation an Equation?
ERIC Educational Resources Information Center
Fensham, Peter J.; Lui, Julia
2001-01-01
Explores how well chemistry graduates preparing for teaching can recognize the similarities and differences between the uses of the word "equation" in mathematics and in chemistry. Reports that the conservation similarities were much less frequently recognized than those involved in the creation of new entities. (Author/MM)
Octonic Gravitational Field Equations
NASA Astrophysics Data System (ADS)
Demir, Süleyman; Tanişli, Murat; Tolan, Tülay
2013-08-01
Generalized field equations of linear gravity are formulated on the basis of octons. When compared to the other eight-component noncommutative hypercomplex number systems, it is demonstrated that associative octons with scalar, pseudoscalar, pseudovector and vector values present a convenient and capable tool to describe the Maxwell-Proca-like field equations of gravitoelectromagnetism in a compact and simple way. Introducing massive graviton and gravitomagnetic monopole terms, the generalized gravitational wave equation and Klein-Gordon equation for linear gravity are also developed.
Octonic massless field equations
NASA Astrophysics Data System (ADS)
Demir, Süleyman; Tanişli, Murat; Kansu, Mustafa Emre
2015-05-01
In this paper, it is proven that the associative octons including scalar, pseudoscalar, pseudovector and vector values are convenient and capable tools to generalize the Maxwell-Dirac like field equations of electromagnetism and linear gravity in a compact and simple way. Although an attempt to describe the massless field equations of electromagnetism and linear gravity needs the sixteen real component mathematical structures, it is proved that these equations can be formulated in terms of eight components of octons. Furthermore, the generalized wave equation in terms of potentials is derived in the presence of electromagnetic and gravitational charges (masses). Finally, conservation of energy concept has also been investigated for massless fields.
NASA Astrophysics Data System (ADS)
Ge, M. L.; et al.
1996-09-01
The Table of Contents for the full book PDF is as follows: * Preface * Part I: Satellite Meeting of STATPHYS-19 * Boundary Yang-Baxter in the RSOS/SOS Representation * Quantum Domains in Ferromagnetic Anisotropic Heisenberg Chains * The Generalized Chiral Clock Model and its Phase Diagram * Algebraic Solution of the Coincidence Problem for Crystals and Quasicrystals * Reflection Equations and Surface Critical Phenomena * Fully Packed Loop Models * Quantum Field Theories in terms of Group-Valued Local Fields: An Overview * C-Statiscal Transition Transforms of the Heisenberg Spin Chain and Braided Symmetry * U(1)-Invariant Local and Integrable Lattice Formulation of the Massive Thirring Model * Corner Transfer Matrices and Novel Polynomials * Rigorous and Numerical Results on Two-Dimensional Oriented Self-Avoiding Walks * The Price for Quantum Group Symmetry: Chiral Versus 2D WZNW Model * Integrable Zn-Chiral Potts Model : The Missing Rapidity-Momentum Relation * Dilute Algebras and Solvable Lattice Models * Falicov-Kimball Model: Ground States and Flux Phase Problem * Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition * Quantum Group and the Hofstadter Problem * Domain Walls in the Spin-S Quantum Ising Chain * Quantization of Nonultralocal Models - Generalization of the Theorem for the Multiple Coproduct * Multipoint Functions(Form-factors) of Quantum sine-Gordon Field with Boundary * Three-Dimensional Vertex Model * Probability of Phase Separation and Two Point Temperature Correlation Functions for the Bose Gas with Delta Interaction * On the Fundamental Invariant of the Hecke Algebra Hn(q) * Ternary Z3-Graded Algebras and New Gauge Theories * Thermodynamics of Integrable Quantum Chains : Free Energy and Correlation Lengths * Quantum Integrable Systems and Classical Discrete Nonlinear Dynamics * Quantum Jacobi-Trudi Formula and Analytic Bethe Ansatz * On Boundary Condition of Single Particle and the Spectrum of Many
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)
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.
NASA Astrophysics Data System (ADS)
Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.
2013-04-01
This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.
NASA Astrophysics Data System (ADS)
Molesini, Giuseppe
2005-02-01
Problems in the general validity of the lens equations are reported, requiring an assessment of the conditions for correct use. A discussion is given on critical behaviour of the lens equation, and a sign and meaning scheme is provided so that apparent inconsistencies are avoided.
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.
Linear Equations: Equivalence = Success
ERIC Educational Resources Information Center
Baratta, Wendy
2011-01-01
The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…
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.
Chirinos, Julio A; Rietzschel, Ernst R; De Buyzere, Marc L; De Bacquer, Dirk; Gillebert, Thierry C; Gupta, Amit K; Segers, Patrick
2009-09-01
Accurate quantification of arterial function is crucial to distinguishing disease states from normal variants. However, there are little data regarding methods to scale arterial load to body size in humans. We studied 2365 adults aged 35 to 55 years free of overt cardiovascular disease. We assessed arterial hemodynamics and ventricular-vascular coupling with carotid tonometry and Doppler echocardiography. To define normal (physiological) relationships between hemodynamic indices and body size, we used nonlinear regression to analyze a selected reference subsample (n=612) with normal weight (body mass index 18 to 25 kg/m(2)), waist circumference, and metabolic parameters. Most arterial hemodynamic indices demonstrated important relationships with body size, which were frequently allometric (nonlinear). Allometric indexation using appropriate powers (but not ratiometric indexation) effectively eliminated the relationships between indices of arterial load and body size in normal subjects. In the entire sample (n=2365), the adverse effects of obesity on arterial load and end-systolic ventricular stiffening were clearly demonstrated only after appropriate indexation to account for the expected normal relationship to body size. After adjustment for age and sex, a progressive increase in indexed systemic vascular resistance, effective arterial and ventricular end-systolic elastance, and a decrease in total arterial compliance were seen from normal weight to obesity (P<0.0001). Arterial load relates to body size in an allometric fashion, calling for scaling with the use of appropriate powers. Obesity exerts adverse effects on arterial load and ventricular stiffening that go beyond the normal relationship with body size. Allometric normalization should allow more accurate quantification of arterial load in future studies. PMID:19581507
Weber, Olaf; Willmann, Stefan; Bischoff, Hilmar; Li, Volkhart; Vakalopoulos, Alexandros; Lustig, Klemens; Hafner, Frank-Thorsten; Heinig, Roland; Schmeck, Carsten; Buehner, Klaus
2012-01-01
AIMS The purpose of this work was to support the prediction of a potentially effective dose for the CETP-inhibitor, BAY 60–5521, in humans. METHODS A combination of allometric scaling of the pharmacokinetics of the CETP-inhibitor BAY 60–5521 with pharmacodynamic studies in CETP-transgenic mice and in human plasma with physiologically-based pharmacokinetic (PBPK) modelling was used to support the selection of the first-in-man dose. RESULTS The PBPK approach predicts a greater extent of distribution for BAY 60–5521 in humans compared with the allometric scaling method as reflected by a larger predicted volume of distribution and longer elimination half-life. The combined approach led to an estimate of a potentially effective dose for BAY 60–5521 of 51 mg in humans. CONCLUSION The approach described in this paper supported the prediction of a potentially effective dose for the CETP-inhibitor BAY 60–5521 in humans. Confirmation of the dose estimate was obtained in a first-in-man study. PMID:21762205
NASA Astrophysics Data System (ADS)
Shin, Philip
Number relativity 1.Every equation of the relativity is just the way to understand through to solve one question of the math problem. We just add the hypothesis into the number. 2. Sequence of number is the machine physics for software(computer) as the number order is program equation as calculator. 3. When zero is denominator, it is not existing as it is doing something by nothing. So nothing means time as we put zero denominator into time. My personal physics imagine.
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. PMID:25973605
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.
Efficient High-Pressure State Equations
NASA Technical Reports Server (NTRS)
Harstad, Kenneth G.; Miller, Richard S.; Bellan, Josette
1997-01-01
A method is presented for a relatively accurate, noniterative, computationally efficient calculation of high-pressure fluid-mixture equations of state, especially targeted to gas turbines and rocket engines. Pressures above I bar and temperatures above 100 K are addressed The method is based on curve fitting an effective reference state relative to departure functions formed using the Peng-Robinson cubic state equation Fit parameters for H2, O2, N2, propane, methane, n-heptane, and methanol are given.
NASA Astrophysics Data System (ADS)
Sultana, Nasrin
This dissertation consists of five papers in which discrete Volterra equations of different types and orders are studied and results regarding the behavior of their solutions are established. The first paper presents some fundamental results about subexponential sequences. It also illustrates the subexponential solutions of scalar linear Volterra sum-difference equations are asymptotically stable. The exact value of the rate of convergence of asymptotically stable solutions is found by determining the asymptotic behavior of the transient renewal equations. The study of subexponential solutions is also continued in the second and third articles. The second paper investigates the same equation using the same process as considered in the first paper. The discussion focuses on a positive lower bound of the rate of convergence of the asymptotically stable solutions. The third paper addresses the rate of convergence of the solutions of scalar linear Volterra sum-difference equations with delay. The result is proved by developing the rate of convergence of transient renewal delay difference equations. The fourth paper discusses the existence of bounded solutions on an unbounded domain of more general nonlinear Volterra sum-difference equations using the Schaefer fixed point theorem and the Lyapunov direct method. The fifth paper examines the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations and establishes some new criteria based on so-called time scales, which unifies and extends both discrete and continuous mathematical analysis. Beside these five research papers that focus on discrete Volterra equations, this dissertation also contains an introduction, a section on difference calculus, a section on time scales calculus, and a conclusion.
Time-reversal and the Bessel equation
NASA Astrophysics Data System (ADS)
Alfinito, Eleonora; Vitiello, Giuseppe
2015-07-01
The system of two damped/amplified oscillator equations is of widespread interest in the study of many physical problems and phenomena, from inflationary models of the Universe to thermal field theories, in condensed matter physics as well in high energy physics, and also in neuroscience. In this report we review the equivalence, in a suitable parametrization, between such a system of equations and the Bessel equations. In this connection, we discuss the breakdown of loop-antiloop symmetry, its relation with time-reversal symmetry and the mechanism of group contraction. Euclidean algebras such as e(2) and e(3) are also discussed in relation with Virasoro-like algebra.
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.
A Comparison of IRT Equating and Beta 4 Equating.
ERIC Educational Resources Information Center
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
Diophantine Equations and Computation
NASA Astrophysics Data System (ADS)
Davis, Martin
Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{
Regularized Structural Equation Modeling
Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.
2016-01-01
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019
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.
Equations For Rotary Transformers
NASA Technical Reports Server (NTRS)
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well. PMID:21643384
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
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
Almost periodic solutions to difference equations
NASA Technical Reports Server (NTRS)
Bayliss, A.
1975-01-01
The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.
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.
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
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
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
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)
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)
Equating designs and procedures used in Rasch scaling.
Skaggs, Gary; Wolfe, Edward W
2010-01-01
The development of alternate forms of tests requires a statistical score adjustment called equating that permits the interchanging of scores from different test forms. Equating makes possible several important measurement applications, including removing practice effects in pretest-posttest research designs, improving test security, comparing scores between new and old forms, and supporting item bank development for computerized adaptive testing. This article summarizes equating methods from a Rasch measurement perspective. The four sections of this article present an introduction and definition of equating and related linking methods, data collection designs, equating procedures, and evaluating equated measures. The methods are illustrated with worked examples. PMID:20693702
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…
Generalized diffusion equation and analytical expressions to neutron scattering experiments
NASA Astrophysics Data System (ADS)
Fa, Kwok Sau
2014-12-01
An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations. Analytical expressions related to neutron scattering experiments are presented and analyzed, which can be used to describe, for instance, biological systems.
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.
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.
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.
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.
Difference equation for superradiance
NASA Technical Reports Server (NTRS)
Lee, C. T.
1974-01-01
The evolution of a completely excited system of N two-level atoms, distributed over a large region and interacting with all modes of radiation field, is studied. The distinction between r-conserving (RC) and r-nonconserving (RNC) processes is emphasized. Considering the number of photons emitted as the discrete independent variable, the evolution is described by a partial difference equation. Numerical solution of this equation shows the transition from RNC dominance at the beginning to RC dominance later. This is also a transition from incoherent to coherent emission of radiation.
Obtaining Maxwell's equations heuristically
NASA Astrophysics Data System (ADS)
Diener, Gerhard; Weissbarth, Jürgen; Grossmann, Frank; Schmidt, Rüdiger
2013-02-01
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.
NASA Astrophysics Data System (ADS)
Biagetti, Matteo; Desjacques, Vincent; Kehagias, Alex; Racco, Davide; Riotto, Antonio
2016-04-01
Dark matter halos are the building blocks of the universe as they host galaxies and clusters. The knowledge of the clustering properties of halos is therefore essential for the understanding of the galaxy statistical properties. We derive an effective halo Boltzmann equation which can be used to describe the halo clustering statistics. In particular, we show how the halo Boltzmann equation encodes a statistically biased gravitational force which generates a bias in the peculiar velocities of virialized halos with respect to the underlying dark matter, as recently observed in N-body simulations.
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…
Dynamics of the Kuramoto equation with spatially distributed control
NASA Astrophysics Data System (ADS)
Kashchenko, Ilia; Kaschenko, Sergey
2016-05-01
We consider the scalar complex equation with spatially distributed control. Its dynamical properties are studied by asymptotic methods when the control coefficient is either sufficiently large or sufficiently small and the function of distribution is either almost symmetric or significantly nonsymmetric relative to zero. In all cases we reduce original equation to quasinormal form - the family of special parabolic equations, which do not contain big and small parameters, which nonlocal dynamics determines the behaviour of solutions of the original equation.
The Camassa-Holm equation: A loop group approach
NASA Astrophysics Data System (ADS)
Schiff, Jeremy
1998-10-01
A map is presented that associates with each element of a loop group a solution of an equation related by a simple change of coordinates to the Camassa-Holm (CH) equation. Certain simple automorphisms of the loop group give rise to Bäcklund transformations of the equation. These are used to find 2-soliton solutions of the CH equation, as well as some novel singular solutions.
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.
Derivation of the high field semiconductor equations
Hagan, P.S. ); Cox, R.W. ); Wagner, B.A. . Dept. of Mathematics)
1991-01-01
Electron and hole densities evolve in x-z phase space according to Boltzmann equations. When the mean free path of the particles is short and electric force on the particles is weak, a well-known expansion can be used to solve the Boltzmann equation. This asymptotic solution shows that the spatial density of electrons and holes evolves according to diffusion-drift equations. As devices become smaller, electric fields become stronger, which renders the Basic Semiconductor Equations increasingly inaccurate. To remedy this problem, we use singular perturbation techniques to obtain a new asymptotic expansion for the Boltzmann equation. Like the Hilbert expansion, the new expansion requires the mean free path to be short compared to all macroscopic length scales. However, it does not require the electric forces to be weak. The new expansion shows that spatial densities obey diffusion-drift equations as before, but the diffusivity D and mobility {mu} turn out to be nonlinear functions of the electric field. In particular, our analysis determines the field-dependent mobilities {mu}(E) and diffusivities D(E) directly from the scattering operator. By carrying out this asymptotic expansion to higher order, we obtain the high frequency corrections to the drift velocity and diffusivity, and also the corrections due to gradients in the electric field. Remarkably, we find that Einsteins's relation is still satisfied, even with these corrections. The new diffusion-drift equations, together with Poissons' equation for the electric field, form the high-field semiconductor equations, which can be expected to be accurate regardless of the strength of the electric fields within the semiconductor. In addition, our analysis determines the entire momentum distribution of the particles, so we derive a very accurate first moment model for semi-conductors by substituting the asymptotically-correct distribution back into the Boltzmann equation and taking moments.
ERIC Educational Resources Information Center
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
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.
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.
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…
Logistic equation of arbitrary order
NASA Astrophysics Data System (ADS)
Grabowski, Franciszek
2010-08-01
The paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems X vs. number of tasks N, operating at limited resources K, at non-extensive, heterogeneous self-organization processes characterized by parameter f. In contrast to the classical logistic equation which exclusively relates to the special case of sub-extensive homogeneous self-organization processes at f=1, the proposed model concerns both homogeneous and heterogeneous processes in sub-extensive and super-extensive areas. The parameter of arbitrary order f, where -∞
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.
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.
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.
Biaxial constitutive equation development
NASA Technical Reports Server (NTRS)
Jordan, E. H.; Walker, K. P.
1984-01-01
In developing the constitutive equations an interdisciplinary approach is being pursued. Specifically, both metallurgical and continuum mechanics considerations are recognized in the formulation. Experiments will be utilized to both explore general qualitative features of the material behavior that needs to be modeled and to provide a means of assessing the validity of the equations being developed. The model under development explicitly recognizes crystallographic slip on the individual slip systems. This makes possible direct representation of specific slip system phenomena. The present constitutive formulation takes the anisotropic creep theory and incorporates two state variables into the model to account for the effect of prior inelastic deformation history on the current rate-dependent response of the material.
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
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.
Singularities for PRANDTL'S Equations
NASA Astrophysics Data System (ADS)
Lo Bosco, G.; Sammartino, M.; Sciacca, V.
2006-03-01
We use a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our tool is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformly bounded in H1.
Multinomial diffusion equation
NASA Astrophysics Data System (ADS)
Balter, Ariel; Tartakovsky, Alexandre M.
2011-06-01
We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N→∞, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.
Multinomial diffusion equation
Balter, Ariel I.; Tartakovsky, Alexandre M.
2011-06-24
We describe a new, microscopic model for diffusion that captures diffusion induced uctuations at scales where the concept of concentration gives way to discrete par- ticles. We show that in the limit as the number of particles N ! 1, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.
ERIC Educational Resources Information Center
Vasile, Daniela
2012-01-01
We are frequently told that Hong Kong has a model system for learning mathematics. In this article Daniela Vasile notes one short-coming in that the pupils are not taught to problem-solve. She begins with a new class by asking them to write down the craziest equation they can come up with and bases her whole lesson, and the following homework,…
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.
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.
Onsager's-principle-consistent 13-moment transport equations
NASA Astrophysics Data System (ADS)
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.
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…
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.
Flow equation of functional renormalization group for three-body scattering problems
NASA Astrophysics Data System (ADS)
Tanizaki, Yuya
2013-11-01
Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish an exact flow equation on the basis of FRG and show that our flow equation is consistent with integral equations obtained from the Dyson-Schwinger equation. In particular, the relation of our flow equation and the Skornyakov and Ter-Martirosyan equation for the atom-dimer scattering is made clear.
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).…
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
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.
Consistent lattice Boltzmann equations for phase transitions.
Siebert, D N; Philippi, P C; Mattila, K K
2014-11-01
Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling. PMID:25493907
Noncommutativity and the Friedmann Equations
NASA Astrophysics Data System (ADS)
Sabido, M.; Guzmán, W.; Socorro, J.
2010-07-01
In this paper we study noncommutative scalar field cosmology, we find the noncommutative Friedmann equations as well as the noncommutative Klein-Gordon equation, interestingly the noncommutative contributions are only present up to second order in the noncommutitive parameter.
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.
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
NASA Technical Reports Server (NTRS)
Nelson, Clayton C.; Nguyen, Dung T.
1987-01-01
The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs' equation, assumes the friction factor is a function of Reynolds number only. The second, Moody's equation, approximates Moody's diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs' constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals (e/2 H sub 0 = 0.05) Moody's equation predicts 44% greater direct stiffness, 35% greater cross-coupled stiffness, 19% smaller cross-coupled damping, 59% smaller cross-coupled inertia, and nominally the same direct damping and direct inertia.
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.
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics.
Inequivalence between the Schroedinger equation and the Madelung hydrodynamic equations
Wallstrom, T.C.
1994-03-01
By differentiating the Schroedinger equation and separating the real amd imaginary parts, one obtains the Madelung hydrodynamic equations, which have inspired numerous classical interpretations of quantum mechanics. Such interpretations frequently assume that these equations are equivalent to the Schroedinger equation, and thus provide an alternative basis for quantum mechanics. This paper proves that this is incorrect: to recover the Schroedinger equation, one must add by hand a quantization condition, as in the old quantum theory. The implications for various alternative interpretations of quantum mechanics are discussed.
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…
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…
Evaluating Cross-Lingual Equating.
ERIC Educational Resources Information Center
Rapp, Joel; Allalouf, Avi
This study examined the cross-lingual equating process adopted by a large scale testing system in which target language (TL) forms are equated to the source language (SL) forms using a set of translated items. The focus was on evaluating the degree of error inherent in the routine cross-lingual equating of the Verbal Reasoning subtest of the…
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.
Gravitationally coupled Dirac equation for antimatter
NASA Astrophysics Data System (ADS)
Jentschura, U. D.
2013-03-01
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences (“surprises”) related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys.RMPHAT0034-686110.1103/RevModPhys.29.465 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called “East-Coast” to the “West-Coast” convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes antiparticles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a “fifth force” (“quintessence”).
'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.
Alternative formulation of the monokinetic transport equation
Coppa, G.; Ravetto, P.; Sumini, M.
1985-03-01
After recalling a technique already exploited in stationary neutron transport, the dynamic linear monokinetic equation for general geometry is cast into an integro-differential form where a second order space Laplace operator and both a second and first time derivatives appear. The introduced unknowns are given a physical interpretation for plane geometry and their relations with the total flux and current are derived.
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…
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…
Causality, Confirmation, Credulity, and Structural Equation Modeling.
ERIC Educational Resources Information Center
Biddle, Bruce J.; Marlin, Marjorie M.
1987-01-01
Defines structural equation modeling (SEM) and points out its relation to other more familiar data-analytic techniques, as well as some of the potentials and pitfalls of SEM in the analysis of developmental data. Discussion focuses on causal modeling, path diagrams, ordinary least-squares regression analysis, and powerful methods for model…
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.
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.
NASA Astrophysics Data System (ADS)
Gomez, Humberto
2016-06-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
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.
A Note on the Relationship Between Solutions of Einstein, Ramanujan and Chazy Equations
NASA Astrophysics Data System (ADS)
Esmakhanova, Kuralay; Myrzakulov, Yerlan; Nugmanova, Gulgasyl; Myrzakulov, Ratbay
2012-04-01
The Einstein equation for the Friedmann-Robertson-Walker metric plays a fundamental role in cosmology. The direct search of the exact solutions of the Einstein equation even in this simple metric case is sometime a hard job. Therefore, it is useful to construct solutions of the Einstein equation using a known solutions of some other equations which are equivalent or related to the Einstein equation. In this work, we establish the relationship the Einstein equation with two other famous equations namely the Ramanujan equation and the Chazy equation. Both these two equations play an important role in the number theory. Using the known solutions of the Ramanujan and Chazy equations, we find the corresponding solutions of the Einstein equation.
Painlevé equations--nonlinear special functions
NASA Astrophysics Data System (ADS)
Clarkson, Peter A.
2003-04-01
The six Painlevé equations (PI-PVI) were first discovered about a hundred years ago by Painlevé and his colleagues in an investigation of nonlinear second-order ordinary differential equations. Recently, there has been considerable interest in the Painlevé equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering. Consequently, the Painlevé equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations, despite being nonlinear equations. Although first discovered from strictly mathematical considerations, the Painlevé equations have arisen in a variety of important physical applications including statistical mechanics, plasma physics, nonlinear waves, quantum gravity, quantum field theory, general relativity, nonlinear optics and fibre optics. The Painlevé equations may be thought of a nonlinear analogues of the classical special functions. They possess hierarchies of rational solutions and one-parameter families of solutions expressible in terms of the classical special functions, for special values of the parameters. Further the Painlevé equations admit symmetries under affine Weyl groups which are related to the associated Bäcklund transformations. In this paper, I discuss some of the remarkable properties which the Painlevé equations possess including connection formulae, Bäcklund transformations associated discrete equations, and hierarchies of exact solutions. In particular, the second Painlevé equation PII is used to illustrate these properties and some of the applications of PII are also discussed.
Lagrangian aspects of the axisymmetric Euler equation
NASA Astrophysics Data System (ADS)
Preston, Stephen C.; Sarria, Alejandro
2016-03-01
In this paper we are interested in geometric aspects of blowup in the axisymmetric three-dimensional (3D) Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flow derivative along either the axis or the boundary and imposing oddness on the vertical component of the flow, we extend some blowup criteria due to Chae, Constantin and Wu related to assumptions on the sign of the pressure Hessian. In addition. we give a geometric interpretation of the results, both in terms of the local geometry along trajectories and in terms of the Riemannian geometry of the volume-preserving diffeomorphism group.
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.
Wigner-Lindblad Equations for Quantum Friction.
Bondar, Denys I; Cabrera, Renan; Campos, Andre; Mukamel, Shaul; Rabitz, Herschel A
2016-05-01
Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena. PMID:27078510
ERIC Educational Resources Information Center
Miller, G. Edward; Fitzpatrick, Steven J.
2009-01-01
Incorrect handling of item parameter drift during the equating process can result in equating error. If the item parameter drift is due to construct-irrelevant factors, then inclusion of these items in the estimation of the equating constants can be expected to result in equating error. On the other hand, if the item parameter drift is related to…
Magnetic monopoles, Galilean invariance, and Maxwell's equations
NASA Astrophysics Data System (ADS)
Crawford, Frank S.
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 v<
Non-autonomous discrete Boussinesq equation: Solutions and consistency
NASA Astrophysics Data System (ADS)
Nong, Li-Juan; Zhang, Da-Juan
2014-07-01
A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed.
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.
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.
An algorithm for solving the perturbed gas dynamic equations
NASA Technical Reports Server (NTRS)
Davis, Sanford
1993-01-01
The present application of a compact, higher-order central-difference approximation to the linearized Euler equations illustrates the multimodal character of these equations by means of computations for acoustic, vortical, and entropy waves. Such dissipationless central-difference methods are shown to propagate waves exhibiting excellent phase and amplitude resolution on the basis of relatively large time-steps; they can be applied to wave problems governed by systems of first-order partial differential equations.
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.
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
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.
On the Position Measurement Equation of XNAV
NASA Astrophysics Data System (ADS)
Yao, G. Z.; Fei, B. J.; Xiao, Y.
2012-03-01
The position measurement equation of XNAV (X-ray pulsar-based autonomous navigation) reveals the relation between the TOA and receiving position of X-ray signal . For navigation , TOA is often rewritten in the form of difference between TOA and some preset ``time reference''. The ``time reference'' may be the true TOA at SSB, or some ``equivalent TOA'' at SSB. Because the true TOA at SSB is difficult to obtain, the ``equivalent TOA'' is more convenient for navigation. From the expression of ``true TOA'', the expression of the ``equivalent TOA'' is derived, and the physical origin of each item is analyzed. The ``equivalent TOA'' consists of those items irrelevant to the craft, but relevant to the background. Then in the new measurement equation, the time difference concentrates on the items directly relevant to the position of the craft. The new equations has the time accuracy of 0.1 ns.
Absorbing layers for the Dirac equation
NASA Astrophysics Data System (ADS)
Pinaud, Olivier
2015-05-01
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.
Evolution equation for geometric quantum correlation measures
NASA Astrophysics Data System (ADS)
Hu, Ming-Liang; Fan, Heng
2015-05-01
A simple relation is established for the evolution equation of quantum-information-processing protocols such as quantum teleportation, remote state preparation, Bell-inequality violation, and particularly the dynamics of geometric quantum correlation measures. This relation shows that when the system traverses the local quantum channel, various figures of merit of the quantum correlations for different protocols demonstrate a factorization decay behavior for dynamics. We identified the family of quantum states for different kinds of quantum channels under the action of which the relation holds. This relation simplifies the assessment of many quantum tasks.
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.
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
Langevin equation approach to reactor noise analysis: stochastic transport equation
Akcasu, A.Z. ); Stolle, A.M. )
1993-01-01
The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.
A spinor representation of Maxwell equations and Dirac equation
Vaz, J. Jr.; Rodrigues, W.A. Jr.
1993-02-01
Using the Clifford bundle formalism and starting from the free Maxwell equations dF = {delta}F = 0 we show by writing F = b{psi}{gamma}{sup 1}{gamma}{sup 2}{psi}{sup *}, where {psi} is a Dirac-Hestenes spinor field, that the Dirac-Hestenes equation (which is the representative of the standard Dirac equation in the Clifford bundle over Minkowski spacetime) is equivalent under general assumptions to those free Maxwell equations. We briefly discuss the implications of our findings for the interpretation of quantum mechanics. 15 refs.
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.