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
2015-11-24
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.
NASA Astrophysics Data System (ADS)
Duncanson, L.; Dubayah, R.
2015-12-01
Lidar remote sensing is widely applied for mapping forest carbon stocks, and technological advances have improved our ability to capture structural details from forests, even resolving individual trees. Despite these advancements, the accuracy of forest aboveground biomass models remains limited by the quality of field estimates of biomass. The accuracies of field estimates are inherently dependent on the accuracy of the allometric equations used to relate measurable attributes to biomass. These equations are calibrated with relatively small samples of often spatially clustered trees. This research focuses on one of many issues involving allometric equations - understanding how sensitive allometric parameters are to the sample sizes used to fit them. We capitalize on recent advances in lidar remote sensing to extract individual tree structural information from six high-resolution airborne lidar datasets in the United States. We remotely measure millions of tree heights and crown radii, and fit allometric equations to the relationship between tree height and radius at a 'population' level, in each site. We then extract samples from our tree database, and build allometries on these smaller samples of trees, with varying sample sizes. We show that for the allometric relationship between tree height and crown radius, small sample sizes produce biased allometric equations that overestimate height for a given crown radius. We extend this analysis using translations from the literature to address potential implications for biomass, showing that site-level biomass may be greatly overestimated when applying allometric equations developed with the typically small sample sizes used in popular allometric equations for biomass.
NASA Astrophysics Data System (ADS)
Mahmood, H.; Siddique, M. R. H.; Akhter, M.
2016-08-01
Estimations of biomass, volume and carbon stock are important in the decision making process for the sustainable management of a forest. These estimations can be conducted by using available allometric equations of biomass and volume. Present study aims to: i. develop a compilation with verified allometric equations of biomass, volume, and carbon for trees and shrubs of Bangladesh, ii. find out the gaps and scope for further development of allometric equations for different trees and shrubs of Bangladesh. Key stakeholders (government departments, research organizations, academic institutions, and potential individual researchers) were identified considering their involvement in use and development of allometric equations. A list of documents containing allometric equations was prepared from secondary sources. The documents were collected, examined, and sorted to avoid repetition, yielding 50 documents. These equations were tested through a quality control scheme involving operational verification, conceptual verification, applicability, and statistical credibility. A total of 517 allometric equations for 80 species of trees, shrubs, palm, and bamboo were recorded. In addition, 222 allometric equations for 39 species were validated through the quality control scheme. Among the verified equations, 20%, 12% and 62% of equations were for green-biomass, oven-dried biomass, and volume respectively and 4 tree species contributed 37% of the total verified equations. Five gaps have been pinpointed for the existing allometric equations of Bangladesh: a. little work on allometric equation of common tree and shrub species, b. most of the works were concentrated on certain species, c. very little proportion of allometric equations for biomass estimation, d. no allometric equation for belowground biomass and carbon estimation, and d. lower proportion of valid allometric equations. It is recommended that site and species specific allometric equations should be developed and
Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests.
Ishihara, Masae I; Utsugi, Hajime; Tanouchi, Hiroyuki; Aiba, Masahiro; Kurokawa, Hiroko; Onoda, Yusuke; Nagano, Masahiro; Umehara, Toru; Ando, Makoto; Miyata, Rie; Hiura, Tsutom
2015-07-01
Accurate estimation of tree and forest biomass is key to evaluating forest ecosystem functions and the global carbon cycle. Allometric equations that estimate tree biomass from a set of predictors, such as stem diameter and tree height, are commonly used. Most allometric equations are site specific, usually developed from a small number of trees harvested in a small area, and are either species specific or ignore interspecific differences in allometry. Due to lack of site-specific allometries, local equations are often applied to sites for which they were not originally developed (foreign sites), sometimes leading to large errors in biomass estimates. In this study, we developed generic allometric equations for aboveground biomass and component (stem, branch, leaf, and root) biomass using large, compiled data sets of 1203 harvested trees belonging to 102 species (60 deciduous angiosperm, 32 evergreen angiosperm, and 10 evergreen gymnosperm species) from 70 boreal, temperate, and subtropical natural forests in Japan. The best generic equations provided better biomass estimates than did local equations that were applied to foreign sites. The best generic equations included explanatory variables that represent interspecific differences in allometry in addition to stem diameter, reducing error by 4-12% compared to the generic equations that did not include the interspecific difference. Different explanatory variables were selected for different components. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable. For branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area), suggesting importance of other traits in addition to these traits, such as canopy and root architecture. Inclusion of tree height in addition to stem diameter improved
Allometric equations for integrating remote sensing imagery into forest monitoring programmes.
Jucker, Tommaso; Caspersen, John; Chave, Jérôme; Antin, Cécile; Barbier, Nicolas; Bongers, Frans; Dalponte, Michele; van Ewijk, Karin Y; Forrester, David I; Haeni, Matthias; Higgins, Steven I; Holdaway, Robert J; Iida, Yoshiko; Lorimer, Craig; Marshall, Peter L; Momo, Stéphane; Moncrieff, Glenn R; Ploton, Pierre; Poorter, Lourens; Rahman, Kassim Abd; Schlund, Michael; Sonké, Bonaventure; Sterck, Frank J; Trugman, Anna T; Usoltsev, Vladimir A; Vanderwel, Mark C; Waldner, Peter; Wedeux, Beatrice M M; Wirth, Christian; Wöll, Hannsjörg; Woods, Murray; Xiang, Wenhua; Zimmermann, Niklaus E; Coomes, David A
2017-01-01
Remote sensing is revolutionizing the way we study forests, and recent technological advances mean we are now able - for the first time - to identify and measure the crown dimensions of individual trees from airborne imagery. Yet to make full use of these data for quantifying forest carbon stocks and dynamics, a new generation of allometric tools which have tree height and crown size at their centre are needed. Here, we compile a global database of 108753 trees for which stem diameter, height and crown diameter have all been measured, including 2395 trees harvested to measure aboveground biomass. Using this database, we develop general allometric models for estimating both the diameter and aboveground biomass of trees from attributes which can be remotely sensed - specifically height and crown diameter. We show that tree height and crown diameter jointly quantify the aboveground biomass of individual trees and find that a single equation predicts stem diameter from these two variables across the world's forests. These new allometric models provide an intuitive way of integrating remote sensing imagery into large-scale forest monitoring programmes and will be of key importance for parameterizing the next generation of dynamic vegetation models.
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
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.
Allometric comparison of skulls from two closely related weasels, Mustela itatsi and M. sibirica.
Suzuki, Satoshi; Abe, Mikiko; Motokawa, Masaharu
2011-09-01
We conducted an interspecific comparison of skulls from two closely related but differently sized mustelid species, Mustela itatsi and M. sibirica (Mammalia, Carnivora, Mustelidae); a sexual comparison within the latter species showed remarkable size dimorphism. We clarified several differences in skull proportion related to size using allometric analyses and qualitative comparisons. Allometric analysis revealed that the skulls of male M. itatsi (the smaller species) have a relatively long palate; a slender viscerocranium and postorbital constriction; a broad, short, and low neurocranium; small carnassials; and a short mandible with a thin body and small ramus compared to the skulls of male M. sibirica (the larger species). Similar results were obtained when male M. itatsi were compared to female M. sibirica, although the male M. itatsi had a broader viscerocranium than female M. sibirica. A sexual comparison in M. sibirica revealed a larger skull size among the males with a relatively wide viscerocranium; wide postorbital constriction; a slender, long, and high neurocranium; short and wide auditory bullae; short carnassials; and a long and high mandible compared to females. Qualitative comparisons revealed changes in a few characters depending on skull size or with respect to some cranial components in each species. The interspecific differences observed were clearly larger than the intraspecific differences for three qualitative characters. The allometric and qualitative differences detected between these species suggest that each species is not simply the dwarf and/or giant morph of the other, and complicated differences were clarified.
Osland, Michael J; Day, Richard H; Larriviere, Jack C; From, Andrew S
2014-01-01
Across the globe, species distributions are changing in response to climate change and land use change. In parts of the southeastern United States, climate change is expected to result in the poleward range expansion of black mangroves (Avicennia germinans) at the expense of some salt marsh vegetation. The morphology of A. germinans at its northern range limit is more shrub-like than in tropical climes in part due to the aboveground structural damage and vigorous multi-stem regrowth triggered by extreme winter temperatures. In this study, we developed aboveground allometric equations for freeze-affected black mangroves which can be used to quantify: (1) total aboveground biomass; (2) leaf biomass; (3) stem plus branch biomass; and (4) leaf area. Plant volume (i.e., a combination of crown area and plant height) was selected as the optimal predictor of the four response variables. We expect that our simple measurements and equations can be adapted for use in other mangrove ecosystems located in abiotic settings that result in mangrove individuals with dwarf or shrub-like morphologies including oligotrophic and arid environments. Many important ecological functions and services are affected by changes in coastal wetland plant community structure and productivity including carbon storage, nutrient cycling, coastal protection, recreation, fish and avian habitat, and ecosystem response to sea level rise and extreme climatic events. Coastal scientists in the southeastern United States can use the identified allometric equations, in combination with easily obtained and non-destructive plant volume measurements, to better quantify and monitor ecological change within the dynamic, climate sensitive, and highly-productive mangrove-marsh ecotone.
Osland, Michael J.; Day, Richard H.; Larriviere, Jack C.; From, Andrew S.
2014-01-01
Across the globe, species distributions are changing in response to climate change and land use change. In parts of the southeastern United States, climate change is expected to result in the poleward range expansion of black mangroves (Avicennia germinans) at the expense of some salt marsh vegetation. The morphology of A. germinans at its northern range limit is more shrub-like than in tropical climes in part due to the aboveground structural damage and vigorous multi-stem regrowth triggered by extreme winter temperatures. In this study, we developed aboveground allometric equations for freeze-affected black mangroves which can be used to quantify: (1) total aboveground biomass; (2) leaf biomass; (3) stem plus branch biomass; and (4) leaf area. Plant volume (i.e., a combination of crown area and plant height) was selected as the optimal predictor of the four response variables. We expect that our simple measurements and equations can be adapted for use in other mangrove ecosystems located in abiotic settings that result in mangrove individuals with dwarf or shrub-like morphologies including oligotrophic and arid environments. Many important ecological functions and services are affected by changes in coastal wetland plant community structure and productivity including carbon storage, nutrient cycling, coastal protection, recreation, fish and avian habitat, and ecosystem response to sea level rise and extreme climatic events. Coastal scientists in the southeastern United States can use the identified allometric equations, in combination with easily obtained and non-destructive plant volume measurements, to better quantify and monitor ecological change within the dynamic, climate sensitive, and highly-productive mangrove-marsh ecotone.
Multi-scaling allometric analysis for urban and regional development
NASA Astrophysics Data System (ADS)
Chen, Yanguang
2017-01-01
The concept of allometric growth is based on scaling relations, and it has been applied to urban and regional analysis for a long time. However, most allometric analyses were devoted to the single proportional relation between two elements of a geographical system. Few researches focus on the allometric scaling of multielements. In this paper, a process of multiscaling allometric analysis is developed for the studies on spatio-temporal evolution of complex systems. By means of linear algebra, general system theory, and by analogy with the analytical hierarchy process, the concepts of allometric growth can be integrated with the ideas from fractal dimension. Thus a new methodology of geo-spatial analysis and the related theoretical models emerge. Based on the least squares regression and matrix operations, a simple algorithm is proposed to solve the multiscaling allometric equation. Applying the analytical method of multielement allometry to Chinese cities and regions yields satisfying results. A conclusion is reached that the multiscaling allometric analysis can be employed to make a comprehensive evaluation for the relative levels of urban and regional development, and explain spatial heterogeneity. The notion of multiscaling allometry may enrich the current theory and methodology of spatial analyses of urban and regional evolution.
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.
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.
Ruijter, J M; Wendelaar Bonga, S E
1987-09-01
An analysis of the allometric relations of the total volumes occupied by prolactin (PRL) and corticotropic (ACTH) cells (PRL volume and ACTH volume, respectively) to body length and a study of the immunocytochemical staining intensity of PRL and ACTH cells were used to determine the differences in activity of PRL and ACTH cells in freshwater-reared and in saltwater-reared Cynolebias whitei during the entire lifespan of this annual cyprinodont fish. An inflection in the allometric relation of PRL volume to body length was observed in fish of one-week old. The relatively large PRL volume in younger fish may be related to PRL cell activity before hatching. No inflections were observed in the allometric relations of PRL volume and ACTH volume to body length at the onset of maturation and the onset of ageing, indicating that the increased pituitary growth in maturing and ageing C. whitei is not the result of changes in PRL or ACTH cells. The slope of the allometric relation of PRL volume to body length in freshwater-reared fish was significantly steeper than the slope in saltwater-reared fish. The PRL volume in adult freshwater-reared fish was eight times larger than that in saltwater-reared fish of the same length. The intensity of immunocytochemical staining of saltwater PRL cells was significantly reduced. These volumetric and staining differences correspond to the low functional demand put upon PRL cells in saltwater-adapted fish. In contrast, the slope of the allometric relation of ACTH volume to body length and the intensity of immunocytochemical staining of ACTH cells were similar in freshwater-reared and in saltwater-reared fish.(ABSTRACT TRUNCATED AT 250 WORDS)
Ghazi, S M; Ranjbar, R; Khaksary Mahabady, M
2016-01-01
Total and regional allometric growth rates and termination sites of the spinal cord related to the respective vertebra were studied in 36 goat fetuses, from the Ahvaz slaughterhouse. These specimens were assigned to 3 groups, group 1 (CRL 10-20 cm), group 2 (CRL 21-30 cm), and group 3 (CRL 31-40 cm), each consisting of 6 male and 6 female fetuses. Observations in all 3 groups revealed that although the growth of the vertebral column was greater than that of the spinal cord, the difference in growth was not constant throughout the spine. While in cervical and thoracic regions the growth rate of the spinal cord in relation to the vertebral column was almost isometric, in the caudal part of the spine there was marked decline in growth of the spinal cord compared to the respective regions of the vertebral column. Craniocaudally, the allometric growth rate became drastically negative. There was no significant difference (P>0.05) between males and females. Except in thoracic region, all other regions showed significant differences (P<0.01) between similar regions in all 3 groups. In the lumbar region of group 2 no significant difference was found (P>0.05). As a consequence of the negative allometric growth of the spinal cord in relation to the vertebral column in the caudal part of the spine, the conus medullaris was displaced from S4-S5 in group 1 to S2 in group 3. No significant difference (P>0.05) between male and female fetuses concerning the termination of the spinal cord was found.
Ghazi, S. M.; Ranjbar, R.; Khaksary Mahabady, M.
2016-01-01
Total and regional allometric growth rates and termination sites of the spinal cord related to the respective vertebra were studied in 36 goat fetuses, from the Ahvaz slaughterhouse. These specimens were assigned to 3 groups, group 1 (CRL 10-20 cm), group 2 (CRL 21-30 cm), and group 3 (CRL 31-40 cm), each consisting of 6 male and 6 female fetuses. Observations in all 3 groups revealed that although the growth of the vertebral column was greater than that of the spinal cord, the difference in growth was not constant throughout the spine. While in cervical and thoracic regions the growth rate of the spinal cord in relation to the vertebral column was almost isometric, in the caudal part of the spine there was marked decline in growth of the spinal cord compared to the respective regions of the vertebral column. Craniocaudally, the allometric growth rate became drastically negative. There was no significant difference (P>0.05) between males and females. Except in thoracic region, all other regions showed significant differences (P<0.01) between similar regions in all 3 groups. In the lumbar region of group 2 no significant difference was found (P>0.05). As a consequence of the negative allometric growth of the spinal cord in relation to the vertebral column in the caudal part of the spine, the conus medullaris was displaced from S4-S5 in group 1 to S2 in group 3. No significant difference (P>0.05) between male and female fetuses concerning the termination of the spinal cord was found. PMID:28224007
Gerber, Sylvain; Eble, Gunther J; Neige, Pascal
2008-06-01
Here, we advance novel uses of allometric spaces--multidimensional spaces specifically defined by allometric coefficients--with the goal of investigating the focal role of development in shaping the evolution of morphological disparity. From their examination, operational measures of allometric disparity can be derived, complementing standard signals of morphological disparity through an intuitive and process-oriented refinement of established analytical protocols used in disparity studies. Allometric spaces thereby become a promising context to reveal different patterns of evolutionary developmental changes and to assess their relative prevalence and importance. Such spaces offer a novel domain of investigation of phenotypic variation and should help in detecting large-scale trends, thus placing various macroevolutionary phenomena in an explicitly developmental context. Ammonoidea (Cephalopoda) at the Lower-Middle Jurassic transition were chosen as a case study to illustrate this methodological approach. We constructed two phenotypic spaces: a static, adult one (adult morphospace) and a dynamic, developmental one (allometric space). Comparative disparity analyses show a strikingly stable occupation in both spaces, despite extensive change in taxonomic composition. In contrast, disparity analyses of subclades reveal clearly distinct morphological and allometric disparity dynamics. Allometric approaches allow developmental insights into morphological diversification otherwise intractable from the analysis of adult morphospace alone.
Allometric scaling of pegylated liposomal anticancer drugs.
Caron, Whitney P; Clewell, Harvey; Dedrick, Robert; Ramanathan, Ramesh K; Davis, Whitney L; Yu, Ning; Tonda, Margaret; Schellens, Jan H; Beijnen, Jos H; Zamboni, William C
2011-10-01
Pegylated liposomal formulations contain lipid conjugated to polyethylene glycol. The disposition of encapsulated drug is dictated by the composition of the liposome, thus altering the pharmacokinetic (PK) profile of the drug. Allometric scaling is based on a power-log relationship between body weight (W) and drug clearance (CL) among mammals and has been used to compare the disposition of nonliposomal drugs across species. The objectives of this study were to use allometric scaling to: (1) compare the disposition of pegylated liposomal drugs across speciesand determine the best scaling model and (2) predict PK parameters of pegylated liposomal drugs in humans. The PK of pegylated liposomal CKD-602 (S-CKD602), doxorubicin (Doxil®), and cisplatin (SPI-077) were compared. PK studies ofS-CKD602, Doxil®, and SPI-077 were performed at the maximum tolerated dose (MTD) in male and female mice, rats, dogs and patients with refractory solid tumors. The allometric equation used to evaluate the relationship between W and CL in each species was CL = a(W)(m) (a = empirical coefficient; m = allometric exponent). Substitution of physiological variables other than body weight, such as factors representative of the mononuclear phagocyte system (MPS) were evaluated. Dedrick Plots and Maximum Life-Span Potential (MLP) were used to determine scaling feasibility. Standard allometry demonstrated a relationship between clearance of S-CKD602, Doxil®, and SPI-077 and body, spleen, liver, and kidney weights, total monocyte count, and spleen and liver blood flow. However, using scaling to predict CL of these agents in humans often resulted in differences >30%. Despite a strong correlation between body weight and MPS-associated variables with CL among preclinical species, the use of the equations did not predict CL. Thus, new methods of allometric scaling and measures of MPS function need to be developed.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
ERIC Educational Resources Information Center
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
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
Allometric disparity in rodent evolution
Wilson, Laura A B
2013-01-01
In this study, allometric trajectories for 51 rodent species, comprising equal representatives from each of the major clades (Ctenohystrica, Muroidea, Sciuridae), are compared in a multivariate morphospace (=allometric space) to quantify magnitudes of disparity in cranial growth. Variability in allometric trajectory patterns was compared to measures of adult disparity in each clade, and dietary habit among the examined species, which together encapsulated an ecomorphological breadth. Results indicate that the evolution of allometric trajectories in rodents is characterized by different features in sciurids compared with muroids and Ctenohystrica. Sciuridae was found to have a reduced magnitude of inter-trajectory change and growth patterns with less variation in allometric coefficient values among members. In contrast, a greater magnitude of difference between trajectories and an increased variation in allometric coefficient values was evident for both Ctenohystrica and muroids. Ctenohystrica and muroids achieved considerably higher adult disparities than sciurids, suggesting that conservatism in allometric trajectory modification may constrain morphological diversity in rodents. The results provide support for a role of ecology (dietary habit) in the evolution of allometric trajectories in rodents. PMID:23610638
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.
Wold, Per-Arvid; Bardal, Tora; Øie, Gunvor; Kjørsvik, Elin
2016-01-01
ABSTRACT Small fish larvae grow allometrically, but little is known about how this growth pattern may be affected by different growth rates and early diet quality. The present study investigates how different growth rates, caused by start-feeding with copepods or rotifers the first 30 days post-hatch (dph), affect allometric growth and development of nine major organs in ballan wrasse (Labrus bergylta) larvae up to experimental end at 60 dph. Feeding with cultivated copepod nauplii led to both increased larval somatic growth and faster development and growth of organ systems than feeding with rotifers. Of the organs studied, the digestive and respiratory organs increased the most in size between 4 and 8 dph, having a daily specific growth rate (SGR) between 30 and 40% in larvae fed copepods compared with 20% or less for rotifer-fed larvae. Muscle growth was prioritised from flexion stage and onwards, with a daily SGR close to 30% between 21 and 33 dph regardless of treatment. All larvae demonstrated a positive linear correlation between larval standard length (SL) and increase in total tissue volume, and no difference in allometric growth pattern was found between the larval treatments. A change from positive allometric to isometric growth was observed at a SL close to 6.0 mm, a sign associated with the start of metamorphosis. This was also where the larvae reached postflexion stage, and was accompanied by a change in growth pattern for most of the major organ systems. The first sign of a developing hepatopancreas was, however, first observed in the largest larva (17.4 mm SL, 55 dph), indicating that the metamorphosis in ballan wrasse is a gradual process lasting from 6.0 to at least 15-17 mm SL. PMID:27422903
Gagnat, Maren Ranheim; Wold, Per-Arvid; Bardal, Tora; Øie, Gunvor; Kjørsvik, Elin
2016-09-15
Small fish larvae grow allometrically, but little is known about how this growth pattern may be affected by different growth rates and early diet quality. The present study investigates how different growth rates, caused by start-feeding with copepods or rotifers the first 30 days post-hatch (dph), affect allometric growth and development of nine major organs in ballan wrasse (Labrus bergylta) larvae up to experimental end at 60 dph. Feeding with cultivated copepod nauplii led to both increased larval somatic growth and faster development and growth of organ systems than feeding with rotifers. Of the organs studied, the digestive and respiratory organs increased the most in size between 4 and 8 dph, having a daily specific growth rate (SGR) between 30 and 40% in larvae fed copepods compared with 20% or less for rotifer-fed larvae. Muscle growth was prioritised from flexion stage and onwards, with a daily SGR close to 30% between 21 and 33 dph regardless of treatment. All larvae demonstrated a positive linear correlation between larval standard length (SL) and increase in total tissue volume, and no difference in allometric growth pattern was found between the larval treatments. A change from positive allometric to isometric growth was observed at a SL close to 6.0 mm, a sign associated with the start of metamorphosis. This was also where the larvae reached postflexion stage, and was accompanied by a change in growth pattern for most of the major organ systems. The first sign of a developing hepatopancreas was, however, first observed in the largest larva (17.4 mm SL, 55 dph), indicating that the metamorphosis in ballan wrasse is a gradual process lasting from 6.0 to at least 15-17 mm SL.
Ibáñez, Inés; Zak, Donald R; Burton, Andrew J; Pregitzer, Kurt S
2016-04-01
As increasing levels of nitrogen (N) deposition impact many terrestrial ecosystems, understanding the potential effects of higher N availability is critical for forecasting tree carbon allocation patterns and thus future forest productivity. Most regional estimates of forest biomass apply allometric equations, with parameters estimated from a limited number of studies, to forest inventory data (i.e., tree diameter). However most of these allometric equations cannot account for potential effects of increased N availability on biomass allocation patterns. Using 18 yr of tree diameter, height, and mortality data collected for a dominant tree species (Acer saccharum) in an atmospheric N deposition experiment, we evaluated how greater N availability affects allometric relationships in this species. After taking into account site and individual variability, our results reveal significant differences in allometric parameters between ambient and experimental N deposition treatments. Large trees under experimental N deposition reached greater heights at a given diameter; moreover, their estimated maximum height (mean ± standard deviation: 33.7 ± 0.38 m) was significantly higher than that estimated under the ambient condition (31.3 ± 0.31 m). Within small tree sizes (5-10 cm diameter) there was greater mortality under experimental N deposition, whereas the relative growth rates of small trees were greater under experimental N deposition. Calculations of stemwood biomass using our parameter estimates for the diameter-height relationship indicated the potential for significant biases in these estimates (~2.5%), with under predictions of stemwood biomass averaging 4 Mg/ha lower if ambient parameters were to be used to estimate stem biomass of trees in the experimental N deposition treatment. As atmospheric N deposition continues to increase into the future, ignoring changes in tree allometry will contribute to the uncertainty associated with aboveground carbon storage
Diophantine equations related to quasicrystals: A note
NASA Astrophysics Data System (ADS)
Pelantová, E.; Perelomov, A. M.
1998-06-01
We give the general solution of three Diophantine equations in the ring of integer of the algebraic number field ${\\bf Q}[{\\sqr 5}]$. These equations are related to the problem of determination of the minimum distance in quasicrystals with fivefold symmetry.
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.
An allometric analysis of the giraffe cardiovascular system.
Mitchell, G; Skinner, J D
2009-12-01
There has been co-evolution of a long neck and high blood pressure in giraffes. How the cardiovascular system (CVS) has adapted to produce a high blood pressure, and how it compares with other similar sized mammals largely is unknown. We have measured body mass and heart structure in 56 giraffes of both genders ranging in body mass from 18 kg to 1500 kg, and developed allometric equations that relate changes in heart dimensions to growth and to cardiovascular function. Predictions made from these equations match measurements made in giraffes. We have found that heart mass increases as body mass increases but it has a relative mass of 0.51+/-0.7% of body mass which is the same as that in other mammals. The left ventricular and interventricular walls are hypertrophied and their thicknesses are linearly related to neck length. Systemic blood pressure increases as body mass and neck length increase and is twice that of mammals of the same body mass. Cardiac output is the same as, but peripheral resistance double that predicted for similar sized mammals. We have concluded that increasing hydrostatic pressure of the column of blood during neck elongation results in cardiac hypertrophy and concurrent hypertrophy of arteriole walls raising peripheral resistance, with an increase in blood pressure following.
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.…
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.
Interspecies allometric scaling.
Hunter, Robert P
2010-01-01
Lack of approved pharmaceutical agents and very limited pharmacokinetic data in the scientific literature for exotic, wildlife, and zoo species are a major issue for veterinarians treating these species. There are fewer than 15 compounds approved in the United States for zoo and wildlife species compared to nearly 300 drugs licensed for cattle. Zoo veterinarians are therefore required to extrapolate the use of approved agents (veterinary or human) to nonapproved species, often with little or no scientific basis to support drug or dose schedule selection. In general, species differences in drug absorption, metabolism, distribution, and excretion have been well documented for domestic species. However, there has been limited research to provide similar data for nondomestic species. Consequently, with the possible exception of pet bird species, there is little published information on the pharmacokinetic parameters of drugs in nondomestic species. Additionally, because of the commercial value of many zoo species, the traditional method of "trial and error" for drug and dose selection and related compliance issues is often inappropriate. There is an understandable concern, whereby the zoo veterinarian does not wish to be the first to administer an agent or formulation in an untested species. "One medicine" is a central concept in treating zoo species, in that vertebrate species are generally more similar than dissimilar. However, drug absorption can vary within as well as between species. Considering the anatomical differences between true monogastrics (canine and feline species), hind-gut fermentors (rodents, rabbits, horses, and elephants), fore-gut fermentors (Colobus monkeys and kangaroos), and ruminants (cattle, goats, sheep, and antelope), the potential for differences in pharmacokinetic profiles are marked. Moreover, there are potential differences between organisms in a single class. An example is the ability of several snake species to up- and down
Ahluwalia, Arti
2017-01-01
About two decades ago, West and coworkers established a model which predicts that metabolic rate follows a three quarter power relationship with the mass of an organism, based on the premise that tissues are supplied nutrients through a fractal distribution network. Quarter power scaling is widely considered a universal law of biology and it is generally accepted that were in-vitro cultures to obey allometric metabolic scaling, they would have more predictive potential and could, for instance, provide a viable substitute for animals in research. This paper outlines a theoretical and computational framework for establishing quarter power scaling in three-dimensional spherical constructs in-vitro, starting where fractal distribution ends. Allometric scaling in non-vascular spherical tissue constructs was assessed using models of Michaelis Menten oxygen consumption and diffusion. The models demonstrate that physiological scaling is maintained when about 5 to 60% of the construct is exposed to oxygen concentrations less than the Michaelis Menten constant, with a significant concentration gradient in the sphere. The results have important implications for the design of downscaled in-vitro systems with physiological relevance. PMID:28169362
NASA Astrophysics Data System (ADS)
Ahluwalia, Arti
2017-02-01
About two decades ago, West and coworkers established a model which predicts that metabolic rate follows a three quarter power relationship with the mass of an organism, based on the premise that tissues are supplied nutrients through a fractal distribution network. Quarter power scaling is widely considered a universal law of biology and it is generally accepted that were in-vitro cultures to obey allometric metabolic scaling, they would have more predictive potential and could, for instance, provide a viable substitute for animals in research. This paper outlines a theoretical and computational framework for establishing quarter power scaling in three-dimensional spherical constructs in-vitro, starting where fractal distribution ends. Allometric scaling in non-vascular spherical tissue constructs was assessed using models of Michaelis Menten oxygen consumption and diffusion. The models demonstrate that physiological scaling is maintained when about 5 to 60% of the construct is exposed to oxygen concentrations less than the Michaelis Menten constant, with a significant concentration gradient in the sphere. The results have important implications for the design of downscaled in-vitro systems with physiological relevance.
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
Related Operators and Exact Solutions of SCHRÖDINGER Equations
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Marmo, G.; Perelomov, A. M.; Rañada, M. F.
We consider the Schrödinger equation just as a differential equation, disregarding the physical interpretation associated with solutions. By introducing the notion of A-related equations, A being a differential operator, we associate with it a Riccati equation and study the solutions when the potential is a meromorphic function.
Quantum metabolism explains the allometric scaling of metabolic rates
Demetrius, Lloyd; Tuszynski, J. A.
2010-01-01
A general model explaining the origin of allometric laws of physiology is proposed based on coupled energy-transducing oscillator networks embedded in a physical d-dimensional space (d = 1, 2, 3). This approach integrates Mitchell's theory of chemi-osmosis with the Debye model of the thermal properties of solids. We derive a scaling rule that relates the energy generated by redox reactions in cells, the dimensionality of the physical space and the mean cycle time. Two major regimes are found corresponding to classical and quantum behaviour. The classical behaviour leads to allometric isometry while the quantum regime leads to scaling laws relating metabolic rate and body size that cover a broad range of exponents that depend on dimensionality and specific parameter values. The regimes are consistent with a range of behaviours encountered in micelles, plants and animals and provide a conceptual framework for a theory of the metabolic function of living systems. PMID:19734187
Quantum metabolism explains the allometric scaling of metabolic rates.
Demetrius, Lloyd; Tuszynski, J A
2010-03-06
A general model explaining the origin of allometric laws of physiology is proposed based on coupled energy-transducing oscillator networks embedded in a physical d-dimensional space (d = 1, 2, 3). This approach integrates Mitchell's theory of chemi-osmosis with the Debye model of the thermal properties of solids. We derive a scaling rule that relates the energy generated by redox reactions in cells, the dimensionality of the physical space and the mean cycle time. Two major regimes are found corresponding to classical and quantum behaviour. The classical behaviour leads to allometric isometry while the quantum regime leads to scaling laws relating metabolic rate and body size that cover a broad range of exponents that depend on dimensionality and specific parameter values. The regimes are consistent with a range of behaviours encountered in micelles, plants and animals and provide a conceptual framework for a theory of the metabolic function of living systems.
Conservative form of Boltzmann's equation in general relativity
NASA Astrophysics Data System (ADS)
Shibata, Masaru; Nagakura, Hiroki; Sekiguchi, Yuichiro; Yamada, Shoichi
2014-04-01
We derive a conservative form of Boltzmann's equation in general relativity, which is concisely written. Several explicit forms of this equation are written for black-hole spacetime with several coordinate conditions in real spacetime and momentum-space coordinates.
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 relationships between the length of pregnancy and body parameters in mammals
NASA Astrophysics Data System (ADS)
Atanasov, A. T.; Todorova, M.; Valev, D. T.; Todorova, R.
2014-10-01
In this manuscript we investigated the presence of allometric relationships between the length of pregnancy and the body parameters in mammals. The relationships between the length of pregnancy T (d) and the square of body length H2 (m2), body surface S (m2), body mass to surface ratio M/S (kg/m2) and body-mass index (BMI) (M/H2) were investigated in mammals: Metatheria and Placentalia, including animals with body mass ranging from 8g in Common shrew to 15t in Killer whale. In result, the found power equations are: T = 114.3 (H2)0.352; T= 120.4 S0.38; T = 9.147 (M/S)0.757 and T = 17.6 BMI0.605. The study showed that the M/S ratio and BMI are nearly equivalent characteristics in relation to length of pregnancy.
Quantum statistics and allometric scaling of organisms
NASA Astrophysics Data System (ADS)
Demetrius, Lloyd
2003-05-01
This article proposes a mechanism to explain allometric relations between basal metabolic rate and the body size of organisms. The model postulates that energy transduction in biological organisms is constrained by two classes of dynamical processes: The first process has its origin in quantum mechanics and the constraints which the coupling of electron transport and proton translocation impose on metabolic activity. The second derives from evolutionary dynamics and the constraints which ecological and demographic forces impose on metabolic rate. These two processes are invoked to show that the scaling exponent between basal metabolic rate and body size follows a {3}/{4} rule, in the case of organisms subject to ecological constraints defined by scarce but dependable resources, and a {2}/{3} rule when constraints are defined by ample but only temporarily available resources. Our conclusions are based on general arguments incorporating the molecular mechanisms that determine metabolic activity at all levels of biological organization. Hence the model applies to uni-cellular organisms, plants and animals.
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
Probability of ventricular fibrillation: allometric model based on the ST deviation
2011-01-01
Background Allometry, in general biology, measures the relative growth of a part in relation to the whole living organism. Using reported clinical data, we apply this concept for evaluating the probability of ventricular fibrillation based on the electrocardiographic ST-segment deviation values. Methods Data collected by previous reports were used to fit an allometric model in order to estimate ventricular fibrillation probability. Patients presenting either with death, myocardial infarction or unstable angina were included to calculate such probability as, VFp = δ + β (ST), for three different ST deviations. The coefficients δ and β were obtained as the best fit to the clinical data extended over observational periods of 1, 6, 12 and 48 months from occurrence of the first reported chest pain accompanied by ST deviation. Results By application of the above equation in log-log representation, the fitting procedure produced the following overall coefficients: Average β = 0.46, with a maximum = 0.62 and a minimum = 0.42; Average δ = 1.28, with a maximum = 1.79 and a minimum = 0.92. For a 2 mm ST-deviation, the full range of predicted ventricular fibrillation probability extended from about 13% at 1 month up to 86% at 4 years after the original cardiac event. Conclusions These results, at least preliminarily, appear acceptable and still call for full clinical test. The model seems promising, especially if other parameters were taken into account, such as blood cardiac enzyme concentrations, ischemic or infarcted epicardial areas or ejection fraction. It is concluded, considering these results and a few references found in the literature, that the allometric model shows good predictive practical value to aid medical decisions. PMID:21226961
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
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
Dispersion relation equation preserving FDTD method for nonlinear cubic Schrödinger equation
NASA Astrophysics Data System (ADS)
Sheu, Tony W. H.; Le Lin
2015-10-01
In this study we aim to solve the cubic nonlinear Schrödinger (CNLS) equation by the method of fractional steps. Over a time step from tn to tn+1, the linear part of the Schrödinger equation is solved firstly through four time integration steps. In this part of the simulation, the explicit symplectic scheme of fourth order accuracy is adopted to approximate the time derivative term. The second-order spatial derivative term in the linear Schrödinger equation is approximated by centered scheme. The resulting symplectic and space centered difference scheme renders an optimized numerical dispersion relation equation. In the second part of the simulation, the solution of the nonlinear equation is computed exactly thanks to the embedded invariant nature within each time increment. The proposed semi-discretized difference scheme underlying the modified equation analysis of second kind and the method of dispersion error minimization has been assessed in terms of the spatial modified wavenumber or the temporal angular frequency resolution. Several problems have been solved to show that application of this new finite difference scheme for the calculation of one- and two-dimensional Schrödinger equations can deemed conserve Hamiltonian quantities and preserve dispersion relation equation (DRE).
NASA Astrophysics Data System (ADS)
Hofhansl, Florian; Schnecker, Jörg; Singer, Gabriel; Wanek, Wolfgang
2014-05-01
Tropical forest ecosystems play a major role in global water and carbon cycles. However, mechanisms of C allocation in tropical forests and their response to environmental variation are largely unresolved as, due to the scarcity of data, they are underrepresented in global syntheses of forest C allocation. Allocation of gross primary production to wood production exerts a key control on forest C residence time and biomass C turnover, and therefore is of special interest for terrestrial ecosystem research and earth system science. Here, we synthesize pantropical data from 105 old-growth rainforests to investigate relationships between climate (mean annual precipitation, mean annual temperature, dry season length and cloud cover), soil nutrient relations (soil N:P) and the partitioning of aboveground net primary production (ANPP) to wood production (WPart) using structural equation modelling. Our results show a strong increase of WPart with ANPP, pointing towards allometric scaling controls on WPart, with increasing light competition in more productive forests triggering greater ANPP allocation to wood production. ANPP itself was positively affected by mean annual temperature and soil N:P. Beyond these allometric controls on WPart we found direct environmental controls. WPart increased with dry season length in tropical montane rainforests and with mean annual precipitation in lowland tropical rainforests. We discuss different trade-offs between plant traits, such as community-wide changes along the wood economics spectrum, the leaf economics spectrum and the plant resource economics spectrum, as underlying mechanisms for direct climatic controls on WPart. We thereby provide new insights into mechanisms driving carbon allocation to WPart in tropical rainforests and show that low and high productive tropical rainforests may respond differently to projected global changes.
Allometric growth in reef-building corals.
Dornelas, Maria; Madin, Joshua S; Baird, Andrew H; Connolly, Sean R
2017-03-29
Predicting demographic rates is a critical part of forecasting the future of ecosystems under global change. Here, we test if growth rates can be predicted from morphological traits for a highly diverse group of colonial symbiotic organisms: scleractinian corals. We ask whether growth is isometric or allometric among corals, and whether most variation in coral growth rates occurs at the level of the species or morphological group. We estimate growth as change in planar area for 11 species, across five morphological groups and over 5 years. We show that coral growth rates are best predicted from colony size and morphology rather than species. Coral size follows a power scaling law with a constant exponent of 0.91. Despite being colonial organisms, corals have consistent allometric scaling in growth. This consistency simplifies the task of projecting community responses to disturbance and climate change.
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.
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
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.
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
Time-dependent closure relations for relativistic collisionless fluid equations
Bendib-Kalache, K.; Bendib, A.; El Hadj, K. Mohammed
2010-11-15
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space ({omega},k), where {omega} and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter {omega}/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc{sup 2}/T, where m is the particle rest mass and T, the plasma temperature in energy units.
Vector order parameter in general relativity: Covariant equations
NASA Astrophysics Data System (ADS)
Meierovich, Boris E.
2010-07-01
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.
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.
The ratio and allometric scaling of speed, power, and strength in elite male rugby union players.
Crewther, Blair T; McGuigan, Mike R; Gill, Nicholas D
2011-07-01
This study compared the effectiveness of ratio and allometric scaling for normalizing speed, power, and strength in elite male rugby union players. Thirty rugby players (body mass [BM] 107.1 ± 10.1 kg, body height [BH] 187.8 ± 7.1 cm) were assessed for sprinting speed, peak power during countermovement jumps and squat jumps, and horizontal jumping distance. One-repetition maximum strength was assessed during a bench press, chin-up, and back squat. Performance was normalized using ratio and allometric scaling (Y/X), where Y is the performance, X, the body size variable (i.e., BM or BH), and b is the power exponent. An exponent of 1.0 was used during ratio scaling. Allometric scaling was applied using proposed exponents and derived exponents for each data set. The BM and BH variables were significantly related, or close to, performance during the speed, power and/or strength tests (p < 0.001-0.066). Ratio scaling and allometric scaling using proposed exponents were effective in normalizing performance (i.e., no significant correlations) for some of these tests. Allometric scaling with derived exponents normalized performance across all the tests undertaken, thereby removing the confounding effects of BM and BH. In terms of practical applications, allometric scaling with derived exponents may be used to normalize performance between larger rugby forwards and smaller rugby backs, and could provide additional information on rugby players of similar body size. Ratio scaling may provide the best predictive measure of performance (i.e., strongest correlations).
Testing the cranial evolutionary allometric 'rule' in Galliformes.
Linde-Medina, M
2016-09-01
Recent comparative studies have indicated the existence of a common cranial evolutionary allometric (CREA) pattern in mammals and birds, in which smaller species have relatively smaller faces and bigger braincases than larger species. In these studies, cranial allometry was tested using a multivariate regression between shape (described using landmarks coordinates) and size (i.e. centroid size), after accounting for phylogenetic relatedness. Alternatively, cranial allometry can be determined by comparing the sizes of two anatomical parts using a bivariate regression analysis. In this analysis, a slope higher or lower than one indicates the existence of positive or negative allometry, respectively. Thus, in those species that support the CREA 'rule', positive allometry is expected for the association between face size and braincase size, which would indicate that larger species have disproportionally larger faces. In this study, I applied these two approaches to explore cranial allometry in 83 Galliformes (Aves, Galloanserae), ranging in mean body weight from 30 g to 2.5 kg. The multivariate regression between shape and centroid size revealed the existence of a significant allometric pattern resembling CREA, whereas the second analysis revealed a negative allometry for beak size and braincase size (i.e. contrary to the CREA 'rule', larger galliform species have disproportionally shorter beaks than smaller galliform species). This study suggests that the presence of CREA may be overestimated when using cranium size as the standard measurement.
Quantum Fluctuation Relations for the Lindblad Master Equation
NASA Astrophysics Data System (ADS)
Chetrite, R.; Mallick, K.
2012-08-01
An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.
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)…
Size structuring and allometric scaling relationships in coral reef fishes.
Dunic, Jillian C; Baum, Julia K
2017-05-01
Temperate marine fish communities are often size-structured, with predators consuming increasingly larger prey and feeding at higher trophic levels as they grow. Gape limitation and ontogenetic diet shifts are key mechanisms by which size structuring arises in these communities. Little is known, however, about size structuring in coral reef fishes. Here, we aimed to advance understanding of size structuring in coral reef food webs by examining the evidence for these mechanisms in two groups of reef predators. Given the diversity of feeding modes amongst coral reef fishes, we also compared gape size-body size allometric relationships across functional groups to determine whether they are reliable indicators of size structuring. We used gut content analysis and quantile regressions of predator size-prey size relationships to test for evidence of gape limitation and ontogenetic niche shifts in reef piscivores (n = 13 species) and benthic invertivores (n = 3 species). We then estimated gape size-body size allometric scaling coefficients for 21 different species from four functional groups, including herbivores/detritivores, which are not expected to be gape-limited. We found evidence of both mechanisms for size structuring in coral reef piscivores, with maximum prey size scaling positively with predator body size, and ontogenetic diet shifts including prey type and expansion of prey size. There was, however, little evidence of size structuring in benthic invertivores. Across species and functional groups, absolute and relative gape sizes were largest in piscivores as expected, but gape size-body size scaling relationships were not indicative of size structuring. Instead, relative gape sizes and mouth morphologies may be better indicators. Our results provide evidence that coral reef piscivores are size-structured and that gape limitation and ontogenetic niche shifts are the mechanisms from which this structure arises. Although gape allometry was not indicative of
Allometric scaling of plant life history.
Marbà, Núria; Duarte, Carlos M; Agustí, Susana
2007-10-02
Plant mortality and birth rates are critical components of plant life history affecting the stability of plant populations and the ecosystems they form. Although allometric theory predicts that both plant birth and mortality rates should be size-dependent, this prediction has not yet been tested across plants ranging the full size spectrum. Here we show that both population mortality and population birth rates scale as the -(1/4) power and plant lifespan as the (1/4) power of plant mass across plant species spanning from the tiniest phototrophs to the largest trees. Whereas the controls on plant lifespans are as yet poorly understood, our findings suggest that plant mortality rates have evolved to match population birth rates, thereby helping to maintain plant communities in equilibrium and optimizing plant life histories.
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.
SESAME Equations of State for Stress Cushion and Related Materials
Coe, Joshua Damon
2015-02-12
I examine LANL equations of state (EOS) for stress cushion and related materials, namely S5370, SX358, and Sylgard 184. In the the rst two cases, the SESAME library contains entries for both the inert (unreacted) and decomposition products. I compare inert EOS results with ambient property measurements to the extent possible, then I check the compositions used to build the products tables. I plot the predicted Hugoniots alongside the available shock data, then draw some conclusions.
Equation-of-state-independent relations in neutron stars
NASA Astrophysics Data System (ADS)
Maselli, Andrea; Cardoso, Vitor; Ferrari, Valeria; Gualtieri, Leonardo; Pani, Paolo
2013-07-01
Neutron stars are extremely relativistic objects which abound in our universe and yet are poorly understood, due to the high uncertainty on how matter behaves in the extreme conditions which prevail in the stellar core. It has recently been pointed out that the moment of inertia I, the Love number λ, and the spin-induced quadrupole moment Q of an isolated neutron star, are related through functions which are practically independent of the equation of state. These surprising universal I-λ-Q relations pave the way for a better understanding of neutron stars, most notably via gravitational-wave emission. Gravitational-wave observations will probe highly dynamical binaries and it is important to understand whether the universality of the I-λ-Q relations survives strong-field and finite-size effects. We apply a post-Newtonian-affine approach to model tidal deformations in compact binaries and show that the I-λ relation depends on the inspiral frequency, but is insensitive to the equation of state. We provide a fit for the universal relation, which is valid up to a gravitational wave frequency of ˜900Hz and accurate to within a few percent. Our results strengthen the universality of I-λ-Q relations, and are relevant for gravitational-wave observations with advanced ground-based interferometers. We also discuss the possibility of using the Love-compactness relation to measure the neutron-star radius with an uncertainty ≲10% from gravitational-wave observations.
Allometric scaling of Wingate anaerobic powertest scores in women.
Hetzler, Ronald K; Stickley, Christopher D; Kimura, Iris E
2011-03-01
In this study, we developed allometric exponents for scaling Wingate anaerobic test (WAnT) power data that are effective 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) and mean power (MP) were established. Allometric exponents were applied to WAnT scores for an independent sample (n=31) to assess external validity. PP and MP were 477.0 W (SD = 80.0) and 372.6 W (SD = 61.5), respectively. Allometrice exponents for PP and MP scaled for BM were b = 0.92 and b = 0.76, respectively, and for LBM they were b = 0.93 and b = 0.91, respectively. In the independent sample, these exponents produced correlations between allometrically scaled PP and MP and BM of r = -.02 and r = .02, respectively. Correlations between allometrically scaled PP and MP and LBM were r = .004 and r = -.02, respectively. The allometric exponents were effective in partialing out the effect of BM for PP and MP and demonstrated acceptable levels of external validity when applied to an independent sample. The allometric exponents and normative values provide a useful tool for comparing WAnT scores in college-age women without the confounding effects of BM or LBM.
Allometric method to estimate leaf area index for row crops
Technology Transfer Automated Retrieval System (TEKTRAN)
Leaf area index (LAI) is critical for predicting plant metabolism, biomass production, evapotranspiration, and greenhouse gas sequestration, but direct LAI measurements are difficult and labor intensive. Several methods are available to measure LAI indirectly or calculate LAI using allometric method...
BOOK REVIEW: Partial Differential Equations in General Relativity
NASA Astrophysics Data System (ADS)
Choquet-Bruhat, Yvonne
2008-09-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory.
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
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
NASA Astrophysics Data System (ADS)
Chen, Hua; Sasakura, Naoki; Sato, Yuki
2017-03-01
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the Arnowitt-Deser-Misner formalism of general relativity, and it is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor of CTM up to the fourth order, and we show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal symmetry, while the time evolution of the scale factor is a power law in dimensions below six.
Allometric scaling and predicting cycling performance in (well-) trained female cyclists.
Lamberts, R P; Davidowitz, K J
2014-03-01
As female cycling attains greater professionalism, a larger emphasis is placed on the ability to predict and monitor changes in their cycling performance. The main aim of this study was to determine if peak power output (PPO) adjusted for body mass (W · kg-0.32) accurately predicts flat 40-km time trial performance (40 km TT) in female cyclists as found in men. 20 (well-) trained female cyclists completed a PPO test including maximal oxygen consumption (VO2max) and a flat 40 km TT test. Relationships between cycling performance parameters were also compared to the cycling performance of 45 male cyclists. Allometrically scaled PPW (W · kg(-0.32)) most accurately predicted 40 km TT performance in the female cyclists (r = -0.87, p<0.0001) compared to any other method, however different slopes between the parameters were found in the female and male cyclists (p=0.000115). In addition gender differences were also found between the relationship between relative PPO (W · kg-1) and relative VO2max (ml · min-1 · kg(-1))(p<0.0001), while no gender differences were found between actual and predicted cycling performance based on the Lamberts and Lambert Submaximal Cycle Test (LSCT), which was used a standardized warm-up. In conclusion, relationships between relative cycling parameters seem to differ between genders, while relationships between absolute cycling parameters seem to be similar. Therefore gender specific regression equations should be used when predicting relative cycling performance parameters.
Huang, Q; Gehring, R; Tell, L A; Li, M; Riviere, J E
2015-06-01
Allometric scaling is widely used for the determination of first dosage regimen and the interpolation or extrapolation of pharmacokinetic parameters across many animal species during drug development. In this article, 85 drugs used in veterinary medicine obtained from the Food Animal Residue Avoidance Databank database were selected for allometric scaling analysis. Outlier species were identified by statistical methods. The results showed that 77% and 88% of drugs displayed significant correlations between total systemic clearance (CL) and volume of distribution at steady status (Vss) vs. body weight (P < 0.05) on a log-log scale, respectively. The distribution of the allometric exponent b for CL and Vss displays approximate normal distribution, with means (0.87 and 0.99) and standard deviations (0.143 and 0.157) for CL and Vss, respectively. Twelve drugs were identified to have at least one outlier species for CL and ten drugs for Vss. The human CL and Vss were predicted for selected drugs by the obtained allometric equations. The predicted CL and Vss were within a threefold error compared to observed values, except the predicted CL values for antipyrine, warfarin and diazepam. The results can be used to estimate cross-species pharmacokinetic profiles for predicting drug dosages in veterinary species, and to identify those species for which interpolation or extrapolation of pharmacokinetics properties may be problematic.
On the Klein-Gordon equation using the dispersion relation of Doubly Special Relativity
NASA Astrophysics Data System (ADS)
Felipe, Yese J.
2017-01-01
The theory of Doubly Special Relativity or Deformed Special Relativity (DSR), proposes that there is a maximum energy scale and a minimum length scale that is invariant for all observers. These maximum energy and minimum length correspond to the Planck energy and the Planck length, respectively. As a consequence, the dispersion relation is modified to be E2 =p2c2 +m2c4 + λE3 + ... Previous work has been done to express Quantum Mechanics using the dispersion relation of DSR. Solutions of the free particle, the harmonic oscillator, and the Hydrogen atom have been obtained from the DSR Schrodinger equation. We explore how the DSR Klein-Gordon equation can be consistently approximated in the non-relativistic limit in order to derive the DSR Schrodinger equation.
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
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
Expression of VO2peak in Children and Youth, with Special Reference to Allometric Scaling.
Loftin, Mark; Sothern, Melinda; Abe, Takashi; Bonis, Marc
2016-10-01
The aim of this review was to highlight research that has focused on examining expressions of peak oxygen uptake (VO2peak) in children and youth, with special reference to allometric scaling. VO2peak is considered the highest VO2 during an increasing workload treadmill or bicycle ergometer test until volitional termination. We have reviewed scholarly works identified from PubMed, One Search, EBSCOhost and Google Scholar that examined VO2peak in absolute units (L·min(-1)), relative units [body mass, fat-free mass (FFM)], and allometric expressions [mass, height, lean body mass (LBM) or LBM of the legs raised to a power function] through July 2015. Often, the objective of measuring VO2peak is to evaluate cardiorespiratory function and fitness level. Since body size (body mass and height) frequently vary greatly in children and youth, expressing VO2peak in dimensionless units is often inappropriate for comparative or explanatory purposes. Consequently, expressing VO2peak in allometric units has gained increased research attention over the past 2 decades. In our review, scaling mass was the most frequent variable employed, with coefficients ranging from approximately 0.30 to over 1.0. The wide variance is probably due to several factors, including mass, height, LBM, sex, age, physical training, and small sample size. In summary, we recommend that since skeletal muscle is paramount for human locomotion, an allometric expression of VO2peak relative to LBM is the best expression of VO2peak in children and youth.
A potential mechanism for allometric trabecular bone scaling in terrestrial mammals
Christen, Patrik; Ito, Keita; van Rietbergen, Bert
2015-01-01
Trabecular bone microstructural parameters, including trabecular thickness, spacing, and number, have been reported to scale with animal size with negative allometry, whereas bone volume fraction is animal size-invariant in terrestrial mammals. As for the majority of scaling patterns described in animals, its underlying mechanism is unknown. However, it has also been found that osteocyte density is inversely related to animal size, possibly adapted to metabolic rate, which shows a negative relationship as well. In addition, the signalling reach of osteocytes is limited by the extent of the lacuno-canalicular network, depending on trabecular dimensions and thus also on animal size. Here we propose animal size-dependent variations in osteocyte density and their signalling influence distance as a potential mechanism for negative allometric trabecular bone scaling in terrestrial mammals. Using an established and tested computational model of bone modelling and remodelling, we run simulations with different osteocyte densities and influence distances mimicking six terrestrial mammals covering a large range of body masses. Simulated trabecular structures revealed negative allometric scaling for trabecular thickness, spacing, and number, constant bone volume fraction, and bone turnover rates inversely related to animal size. These results are in agreement with previous observations supporting our proposal of osteocyte density and influence distance variation as a potential mechanism for negative allometric trabecular bone scaling in terrestrial mammals. The inverse relationship between bone turnover rates and animal size further indicates that trabecular bone scaling may be linked to metabolic rather than mechanical adaptations. PMID:25655770
A potential mechanism for allometric trabecular bone scaling in terrestrial mammals.
Christen, Patrik; Ito, Keita; van Rietbergen, Bert
2015-03-01
Trabecular bone microstructural parameters, including trabecular thickness, spacing, and number, have been reported to scale with animal size with negative allometry, whereas bone volume fraction is animal size-invariant in terrestrial mammals. As for the majority of scaling patterns described in animals, its underlying mechanism is unknown. However, it has also been found that osteocyte density is inversely related to animal size, possibly adapted to metabolic rate, which shows a negative relationship as well. In addition, the signalling reach of osteocytes is limited by the extent of the lacuno-canalicular network, depending on trabecular dimensions and thus also on animal size. Here we propose animal size-dependent variations in osteocyte density and their signalling influence distance as a potential mechanism for negative allometric trabecular bone scaling in terrestrial mammals. Using an established and tested computational model of bone modelling and remodelling, we run simulations with different osteocyte densities and influence distances mimicking six terrestrial mammals covering a large range of body masses. Simulated trabecular structures revealed negative allometric scaling for trabecular thickness, spacing, and number, constant bone volume fraction, and bone turnover rates inversely related to animal size. These results are in agreement with previous observations supporting our proposal of osteocyte density and influence distance variation as a potential mechanism for negative allometric trabecular bone scaling in terrestrial mammals. The inverse relationship between bone turnover rates and animal size further indicates that trabecular bone scaling may be linked to metabolic rather than mechanical adaptations.
Relations between nonlinear Riccati equations and other equations in fundamental physics
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2014-10-01
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.
Allometric scaling of Wingate anaerobic power test scores in men.
Stickley, Christopher D; Hetzler, Ronald K; Wages, Jennifer J; Freemyer, Bret G; Kimura, Iris F
2013-09-01
This study examined the appropriate magnitude of allometric scaling of the Wingate anaerobic test (WAnT) power data for body mass (BM) and established normative data for the WAnT for adult men. Eighty-three men completed a standard WAnT using 0.1 kg·kg(-1) BM resistance. Allometric exponents and percentile ranks for 1-second peak power (PP), 5-second PP, and mean power (MP) were established. The Predicted Residual Sum of Squares (PRESS) procedure was used to assess external validity while avoiding data splitting. The mean 1-second PP, 5-second PP, and MP were 1,049.1 ± 168.8 W, 1,013.4 ± 158.6 W, and 777.9 ± 105.0 W, respectively. Allometric exponents for 1-second PP, 5-second PP, and MP scaled for BM were b = 0.89, 0.88, and 0.86, respectively. Correlations between allometrically scaled 1-second PP, 5-second PP, and MP, and BM were r = -0.03, -0.03, and -0.02, respectively, suggesting that the allometric exponents derived were effective in partialling out the effect of BM on WAnT values. The PRESS procedure values resulted in small decreases in R² (0.03, 0.04, and 0.02 for 1-second PP, 5-second PP, and MP, respectively) suggesting acceptable levels of external validity when applied to independent samples. The allometric exponents and normative values provide a useful tool for comparing WAnT scores in college-aged females without the confounding effect of BM. It is suggested that exponents of b = 0.89 (1-second PP), b = 0.88 (5-second PP), and b = 0.86 (MP) be used for allometrically scaling WAnT power values in healthy adult men and that the confidence limits for these allometric exponents be considered as 0.66-1.0 for PP and 0.69-1.0 for MP. The use of these exponents in allometric scaling of male WAnT power values provide coaches and practitioners with valid means for comparing power production between individuals without the confounding influence of BM.
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.
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
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.
Richards' Equation and its Constitutive Relations as a System of Differential-Algebraic Equations
NASA Astrophysics Data System (ADS)
Murray, S. K.; Mead, J. L.
2007-12-01
Richards' Equation is commonly used to understand how water flows in unsaturated soils. We present a new formulation of Richards' Equation which will allow us to incorporate model and observation errors. In addition, we can address spatial and temporal inconsistencies existing between the model and observations. There are two basic formulations for Richards' Equation: the pressure head form and the mixed form, the latter of which explicitly incorporates soil moisture content. The mixed form is typically solved using HYDRUS, a freely available program that uses finite elements with Picard iteration to handle the nonlinearities. However, recent results suggest considering Richards' Equation as a differential-algebraic equation (DAE), where the algebraic models for soil moisture content (van Genuchten's equation) is solved simultaneously with Richards' Equation (Kees, et. al., 2002). This formulation can give more accurate forward model solutions, however, we note that it also allows us to consider the uncertainties in the pressure head ψ and the soil moister content θ during the inversion process. We extend the DAE formulation to include the algebraic constraint for hydraulic conductivity K, so that its uncertainty can also be considered in an inversion. This poster focuses on the efficiency and accuracy of the forward numerical solution of this particular DAE formulation of Richards' Equation and how it compares to other forward solutions, such as HYDRUS.
Nonlinear partial differential equations: Integrability, geometry and related topics
NASA Astrophysics Data System (ADS)
Krasil'shchik, Joseph; Rubtsov, Volodya
2017-03-01
Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.
Appropriate interpretation of aerobic capacity: allometric scaling in adult and young soccer players
Chamari, K; Moussa-Chamari, I; Boussaidi, L; Hachana, Y; Kaouech, F; Wisloff, U
2005-01-01
Objective: To compare aerobic capacity of young and adult elite soccer players using appropriate scaling procedures. Methods: Twenty four male adult (mean (SD) age 24 (2) years, weight 75.7 (7.2) kg, VO2MAX 66.6 (5.2) ml/lbm/min, where lbm is lean body mass in kg) and 21 youth (14 (0.4) years, 60.2 (7.3) kg, 66.5 (5.9) ml/lbm/min) elite soccer players took part in the study. Allometric equations were used to determine the relation between maximal and submaximal oxygen cost of running (running economy) and body mass. Results: Maximal and submaximal oxygen uptake increased in proportion to body mass raised to the power of 0.72 (0.04) and 0.60 (0.06) respectively. The VO2MAX of adult players was similar to that of the youth players when expressed in direct proportion to body mass—that is, ml/kg/min—but 5% higher (p<0.05) when expressed using appropriate procedures for scaling. Conversely, compared with seniors, youth players had 13% higher (p<0.001) energy cost of running—that is, poorer running economy—when expressed as ml/kg/min but not when expressed according to the scaling procedures. Conclusions: Compared with the youth soccer players, VO2MAX in the seniors was underestimated and running economy overestimated when expressed traditionally as ml/lbm/min. The study clearly shows the pitfalls in previous studies when aerobic capacity was evaluated in subjects with different body mass. It further shows that the use of scaling procedures can affect the evaluation of, and the resultant training programme to improve, aerobic capacity. PMID:15665205
NASA Astrophysics Data System (ADS)
Gourgoulhon, Eric
2011-04-01
Numerical relativity is one of the major fields of contemporary general relativity and is developing continually. Yet three years ago, no textbook was available on this subject. The first textbook devoted to numerical relativity, by Alcubierre, appeared in 2008 [1] (cf the CQG review [2]). Now comes the second book, by Baumgarte and Shapiro, two well known players in the field. Inevitably, the two books have some common aspects (otherwise they would not deal with the same topic!). For instance the titles of the first four chapters of Baumgarte and Shapiro are very similar to those of Alcubierre. This arises from some logic inherent to the subject: chapter 1 recaps basic GR, chapter 2 introduces the 3+1 formalism, chapter 3 focuses on the initial data and chapter 4 on the choice of coordinates for the evolution. But there are also many differences between the two books, which actually make them complementary. At first glance the differences are the size (720 pages for Baumgarte and Shapiro vs 464 pages for Alcubierre) and the colour figures in Baumgarte and Shapiro. Regarding the content, Baumgarte and Shapiro address many topics which are not present in Alcubierre's book, such as magnetohydrodynamics, radiative transfer, collisionless matter, spectral methods, rotating stars and post-Newtonian approximation. The main difference regards binary systems: virtually absent from Alcubierre's book (except for binary black hole initial data), they occupy not less than five chapters in Baumgarte and Shapiro's book. In contrast, gravitational wave extraction, various hyperbolic formulations of Einstein's equations and the high-resolution shock-capturing schemes are treated in more depth by Alcubierre. In the first four chapters mentioned above, some distinctive features of Baumgarte and Shapiro's book are the beautiful treatment of Oppenheimer-Snyder collapse in chapter 1, the analogy with Maxwell's equations when discussing the constraints and the evolution equations in
Probabilistic delay differential equation modeling of event-related potentials.
Ostwald, Dirk; Starke, Ludger
2016-08-01
"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach.
QPO observations related to neutron star equations of state
NASA Astrophysics Data System (ADS)
Stuchlik, Zdenek; Urbanec, Martin; Török, Gabriel; Bakala, Pavel; Cermak, Petr
We apply a genetic algorithm method for selection of neutron star models relating them to the resonant models of the twin peak quasiperiodic oscillations observed in the X-ray neutron star binary systems. It was suggested that pairs of kilo-hertz peaks in the X-ray Fourier power density spectra of some neutron stars reflect a non-linear resonance between two modes of accretion disk oscillations. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density ρc . These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR,ρc , Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR,ρc , Ω, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have most chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR,ρ, Ω, EOS) into chromosome we used Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.
An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans
Clasen, Liv; Giedd, Jay N.; Blumenthal, Jonathan; Lerch, Jason P.; Chakravarty, M. Mallar; Raznahan, Armin
2016-01-01
Structural neuroimaging of humans with typical and atypical sex-chromosome complements has established the marked influence of both Yand X-/Y-chromosome dosage on total brain volume (TBV) and identified potential cortical substrates for the psychiatric phenotypes associated with sex-chromosome aneuploidy (SCA). Here, in a cohort of 354 humans with varying karyotypes (XX, XY, XXX, XXY, XYY, XXYY, XXXXY), we investigate sex and SCA effects on subcortical size and shape; focusing on the striatum, pallidum and thalamus. We find large effect-size differences in the volume and shape of all three structures as a function of sex and SCA. We correct for TBV effects with a novel allometric method harnessing normative scaling rules for subcortical size and shape in humans, which we derive here for the first time. We show that all three subcortical volumes scale sublinearly with TBV among healthy humans, mirroring known relationships between subcortical volume and TBV among species. Traditional TBV correction methods assume linear scaling and can therefore invert or exaggerate sex and SCA effects on subcortical anatomy. Allometric analysis restricts sex-differences to: (1) greater pallidal volume (PV) in males, and (2) relative caudate head expansion and ventral striatum contraction in females. Allometric analysis of SCA reveals that supernumerary X- and Y-chromosomes both cause disproportionate reductions in PV, and coordinated deformations of striatopallidal shape. Our study provides a novel understanding of sex and sex-chromosome dosage effects on subcortical organization, using an allometric approach that can be generalized to other basic and clinical structural neuroimaging settings. SIGNIFICANCE STATEMENT Sex and sex-chromosome dosage (SCD) are known to modulate human brain size and cortical anatomy, but very little is known regarding their impact on subcortical structures that work with the cortex to subserve a range of behaviors in health and disease. Moreover
Dynamical system related to quasiperiodic Schroedinger equations in one dimension
Kohmoto, Mahito )
1992-02-01
A dynamical map is obtained from a class of quasiperiodic discrete Schroedinger equations in one dimension which include the Fibonacci system. The potentials are constant except for steps at special points.
Heterogeneity of cells may explain allometric scaling of metabolic rate.
Takemoto, Kazuhiro
2015-04-01
The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only demonstrate either two important observations for the allometric scaling: the variability of scaling exponents and predominance of 3/4-power law. Thus, these models have a dispute over their validity. In this study, we propose a simple geometry model, and show that a hypothesis that total surface area of cells determines metabolic rate can reproduce these two observations by combining two concepts: the impact of cell sizes on metabolic rate and fractal-like (hierarchical) organization. The proposed model both theoretically and numerically demonstrates the approximately 3/4-power law although several different biological strategies are considered. The model validity is confirmed using empirical data. Furthermore, the model suggests the importance of heterogeneity of cell size for the emergence of the allometric scaling. The proposed model provides intuitive and unique insights into the origin of allometric scaling laws in biology, despite several limitations of the model.
Allometric scaling for predicting human clearance of bisphenol A
Collet, Séverine H. Picard-Hagen, Nicole Lacroix, Marlène Z. Puel, Sylvie Viguié, Catherine Bousquet-Melou, Alain Toutain, Pierre-Louis Gayrard, Véronique
2015-05-01
The investigation of interspecies differences in bisphenol A (BPA) pharmacokinetics (PK) may be useful for translating findings from animal studies to humans, identifying major processes involved in BPA clearance mechanisms, and predicting BPA PK parameters in man. For the first time, a large range of species in terms of body weight, from 0.02 kg (mice) to 495 kg (horses) was used to predict BPA clearance in man by an allometric approach. BPA PK was evaluated after intravenous administration of BPA in horses, sheep, pigs, dogs, rats and mice. A non-compartmental analysis was used to estimate plasma clearance and steady state volume of distribution and predict BPA PK parameters in humans from allometric scaling. In all the species investigated, BPA plasma clearance was high and of the same order of magnitude as their respective hepatic blood flow. By an allometric scaling, the human clearance was estimated to be 1.79 L/min (equivalent to 25.6 mL/kg.min) with a 95% prediction interval of 0.36 to 8.83 L/min. Our results support the hypothesis that there are highly efficient and hepatic mechanisms of BPA clearance in man. - Highlights: • Allometric scaling was used to predict BPA pharmacokinetic parameters in humans. • In all species, BPA plasma clearance approached hepatic blood flow. • Human BPA clearance was estimated to be 1.79 L/min.
General relativity as the equation of state of spin foam
NASA Astrophysics Data System (ADS)
Smolin, Lee
2014-10-01
Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson's argument that the Einstein equations emerge as the equation of state of a quantum gravitational system. I give three criteria a quantum theory of gravity must satisfy if it is to allow Jacobson's argument to be run. I then show that the results of FGP and Bianchi provide evidence that loop quantum gravity satisfies two of these criteria, and argue that the third should also be satisfied in loop quantum gravity. I also show that the energy defined by FGP is the canonical energy associated with the boundary term of the Holst action.
Phytoplankton productivity in relation to light intensity: A simple equation
Peterson, D.H.; Perry, M.J.; Bencala, K.E.; Talbot, M.C.
1987-01-01
A simple exponential equation is used to describe photosynthetic rate as a function of light intensity for a variety of unicellular algae and higher plants where photosynthesis is proportional to (1-e-??1). The parameter ?? (=Ik-1) is derived by a simultaneous curve-fitting method, where I is incident quantum-flux density. The exponential equation is tested against a wide range of data and is found to adequately describe P vs. I curves. The errors associated with photosynthetic parameters are calculated. A simplified statistical model (Poisson) of photon capture provides a biophysical basis for the equation and for its ability to fit a range of light intensities. The exponential equation provides a non-subjective simultaneous curve fitting estimate for photosynthetic efficiency (a) which is less ambiguous than subjective methods: subjective methods assume that a linear region of the P vs. I curve is readily identifiable. Photosynthetic parameters ?? and a are used widely in aquatic studies to define photosynthesis at low quantum flux. These parameters are particularly important in estuarine environments where high suspended-material concentrations and high diffuse-light extinction coefficients are commonly encountered. ?? 1987.
Rovira, S; Muñoz, A; Rodilla, V
2009-04-01
Scaling in biology is usually allometric, and therefore, the size of the heart may be expressed as a power function of body weight (BW). The present research analyses the echocardiographic measurements in 68 healthy Spanish foals weighed between 70 and 347kg in order to determine the correct scaling exponent for the allometric equation. The echocardiographic parameters measured were: left ventricular internal dimensions (LVID), free wall thickness (LVFWT), interventricular septum thickness (IVST) at systole (s) and diastole (d), EPSS (distance between the point E of the mitral valve and the interventricular septum), and aorta diameters at the level of the aortic valve (AOD), base of valve leaflets (ABS), sinus of Valsalva (ASV) and sino-tubular junction (AJT). Indices of left ventricular performance were calculated. It was found that LVIDd, IVSTs, AOD, and ASV have a relationship to BW raised to 0.300-0.368 power, whereas left ventricular end-diastolic volume and stroke volume scaled to BW raised to 0.731-0.712 power. With these data, appropriate values can be calculated for normal Spanish foals.
Allometric scaling laws for water uptake by plant roots.
Biondini, Mario
2008-03-07
This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as r approximately volume(2/(8+a))(0allometric scaling for root radius branches (r(i+1)=beta*r(i)) is of the form beta=f(N)((2*epsilon(N))/(8+a)), where f(N)=A(N)/(n(b)*(1+A(N))), n(b) is the number of branches, and A(N) and epsilon(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, beta converges to the beta from the WBE model. For small N, the beta's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.
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.
Differential Equations, Related Problems of Pade Approximations and Computer Applications
1988-01-01
geometric sense, like the Picard-Fuchs equations satisfied by the variation of periods, possess strong arithmetic properties (global nilpotence ...result, and the (G, C)-function conditions, one needs the definition of the p-curvature. We consider a system of matrix first order linear differential...the system (1.1) in the matrix form df f /dx = Aff ; A E M (Q(x)), one can introduce the p-curvature operators Ip, associated with the system (1.1). The
Kodama, Sakie; Fujimori, Hiroka; Hakoyama, Hiroshi
2017-01-01
Costly anti-predator traits tend to be expressed only in high-predation conditions. For the cyprinid fish genus Carassius, deeper body depth is more adaptive to avoid predation by gape-limited piscivorous fish, but it raises swimming costs. It is therefore predicted that the relative body depth will decrease when the prey fish has reached a size larger than the predator gape-size. This prediction was tested by allometric analysis of the relation between body depth and standard length of triploid asexual females of the Japanese crucian carp (Carassius auratus sspp.) sampled from 13 geographic populations. The overall allometric relation was not significantly different from isometry. The estimate of the common major-axis slope was close to 1 (near-isometry). The mean relative body depth differed significantly among populations. A significant positive correlation was found with the mean annual air temperature. The geographic variation suggests that local selection pressures vary. In conclusion, the hypothesis that larger fish will have lower body depth was not supported, perhaps indicating that deep body depth in large fish is adaptive for some reason other than defense against piscivorous fish. PMID:28150742
The effect of quantitative feed restriction on allometric growth in broilers.
van der Klein, S A S; Silva, F A; Kwakkel, R P; Zuidhof, M J
2017-01-01
Feed restriction in broilers is aimed at preventing metabolic disorders, increasing feed efficiency, or manipulating carcass conformation. The purpose of the current study was to investigate the effects of modest graded levels feed restriction during the second and third wk of life. Mixed-sex chickens were raised in pens with 4 replications per treatment to 35 d of age. Chickens were fed ad libitum throughout the trial, or 90, 80, or 70% of expected ad libitum feed intake during the second wk of life, or 95, 90, 85, or 80% of expected ad libitum feed intake during the third wk of life. Feed intake, BW, ADG, and feed conversion ratio (FCR) were measured and weekly dissections were conducted to characterize allometric growth of the breast muscle, legs, abdominal fat pad, liver, gastro-intestinal tract (GIT), and heart. Feeding 70% of ad libitum during wk 2 and 80% during wk 3 reduced ADG during the restriction period and reduced BW at the end of the restriction period, but chickens exhibited complete compensatory growth within one wk after the restriction period. No significant effects of restriction treatment were found on BW, FCR, fat pad, empty GIT, breast muscle, heart, legs, and liver weight at d 35, but allometric growth curve for breast muscle was lower in birds fed 80 and 85% of ad libitum during wk 3, and for birds fed 70% of ad libitum in wk 2. Allometric growth curves for all body parts were different between males and females, except for the liver. Females had higher relative fat pad, breast muscle, and liver weight and a lower GIT and heart and leg weight compared with males at d 35. Feed restriction could differentially affect males and females. This study showed that feeding 70% of ad libitum in wk 2 might be beneficial to reduce fat pad, but later feed restriction in wk 3 may reduce breast muscle weight at broiler processing age.
Symmetry reduction related with nonlocal symmetry for Gardner equation
NASA Astrophysics Data System (ADS)
Ren, Bo
2017-01-01
Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.
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.
Conformally related Einstein-Langevin equations for metric fluctuations in stochastic gravity
NASA Astrophysics Data System (ADS)
Satin, Seema; Cho, H. T.; Hu, Bei Lok
2016-09-01
For a conformally coupled scalar field we obtain the conformally related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally related spacetime is known. For example, from the Minkowski solution of Martín and Verdaguer, those of the Einstein-Langevin equations in conformally flat spacetimes, especially for spatially flat Friedmann-Robertson-Walker models, can be readily obtained.
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.
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
University-Industry-Government Relations. A "Complexes" Equation.
ERIC Educational Resources Information Center
Marceau, Jane
1996-01-01
The triple helix image of university-industry-government relations should be reconsidered with a focus on knowledge production systems. Public policies aimed at improving relationships should recognize the contributions made in this new mode of production and take into account users as the fourth player. (SK)
Voje, Kjetil L; Hansen, Thomas F
2013-02-01
Julian Huxley showed that within-species (static) allometric (power-law) relations can arise from proportional growth regulation with the exponent in the power law equaling the factor of proportionality. Allometric exponents may therefore be hard to change and act as constraints on the independent evolution of traits. In apparent contradiction to this, many empirical studies have concluded that static allometries are evolvable. Many of these studies have been based, however, on a broad definition of allometry that includes any monotonic shape change with size, and do not falsify the hypothesis of constrained narrow-sense allometry. Here, we present the first phylogenetic comparative study of narrow-sense allometric exponents based on a reanalysis of data on eye span and body size in stalk-eyed flies (Diopsidae). Consistent with a role in sexual selection, we found strong evidence that male slopes were tracking "optima" based on sexual dimorphism and relative male trait size. This tracking was slow, however, with estimated times of 2-3 million years for adaptation to exceed ancestral influence on the trait. Our results are therefore consistent with adaptive evolution on million-year time scales, but cannot rule out that static allometry may act as a constraint on eye-span adaptation at shorter time scales.
A new method to compute standard-weight equations that reduces length-related bias
Gerow, K.G.; Anderson-Sprecher, R. C.; Hubert, W.A.
2005-01-01
We propose a new method for developing standard-weight (Ws) equations for use in the computation of relative weight (Wr) because the regression line-percentile (RLP) method often leads to length-related biases in Ws equations. We studied the structural properties of W s equations developed by the RLP method through simulations, identified reasons for biases, and compared Ws equations computed by the RLP method and the new method. The new method is similar to the RLP method but is based on means of measured weights rather than on means of weights predicted from regression models. The new method also models curvilinear W s relationships not accounted for by the RLP method. For some length-classes in some species, the relative weights computed from Ws equations developed by the new method were more than 20 Wr units different from those using Ws equations developed by the RLP method. We recommend assessment of published Ws equations developed by the RLP method for length-related bias and use of the new method for computing new Ws equations when bias is identified. ?? Copyright by the American Fisheries Society 2005.
Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation
Cicogna, G.; Pegoraro, F.; Ceccherini, F.
2010-10-15
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.
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
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
Dececchi, T Alexander; Larsson, Hans C E
2013-09-01
The origin of birds and powered flight is a classic major evolutionary transition. Research on their origin often focuses on the evolution of the wing with trends of forelimb elongation traced back through many nonavian maniraptoran dinosaurs. We present evidence that the relative forelimb elongation within avian antecedents is primarily due to allometry and is instead driven by a reduction in body size. Once body size is factored out, there is no trend of increasing forelimb length until the origin of birds. We report that early birds and nonavian theropods have significantly different scaling relationships within the forelimb and hindlimb skeleton. Ancestral forelimb and hindlimb allometric scaling to body size is rapidly decoupled at the origin of birds, when wings significantly elongate, by evolving a positive allometric relationship with body size from an ancestrally negative allometric pattern and legs significantly shorten by keeping a similar, near isometric relationship but with a reduced intercept. These results have implications for the evolution of powered flight and early diversification of birds. They suggest that their limb lengths first had to be dissociated from general body size scaling before expanding to the wide range of fore and hindlimb shapes and sizes present in today's birds.
Allometric scaling of mortality rates with body mass in abalones.
Rossetto, Marisa; De Leo, Giulio A; Bevacqua, Daniele; Micheli, Fiorenza
2012-04-01
The existence of an allometric relationship between mortality rates and body mass has been theorized and extensively documented across taxa. Within species, however, the allometry between mortality rates and body mass has received substantially less attention and the consistency of such scaling patterns at the intra-specific level is controversial. We reviewed 73 experimental studies to examine the relationship between mortality rates and body size among seven species of abalone (Haliotis spp.), a marine herbivorous mollusk. Both in the field and in the laboratory, log-transformed mortality rates were negatively correlated with log-transformed individual body mass for all species considered, with allometric exponents remarkably similar among species. This regular pattern confirms previous findings that juvenile abalones suffer higher mortality rates than adult individuals. Field mortality rates were higher overall than those measured in the laboratory, and the relationship between mortality and body mass tended to be steeper in field than in laboratory conditions for all species considered. These results suggest that in the natural environment, additional mortality factors, especially linked to predation, could significantly contribute to mortality, particularly at small body sizes. On the other hand, the consistent allometry of mortality rates versus body mass in laboratory conditions suggests that other sources of mortality, beside predation, are size-dependent in abalone.
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.
Hulbert, A J; Else, P L; Manolis, S C; Brand, M D
2002-07-01
It has previously been shown that mitochondrial proton conductance decreases with increasing body mass in mammals and is lower in a 250-g lizard than the laboratory rat. To examine whether mitochondrial proton conductance is extremely low in very large reptiles, hepatocytes and mitochondria were prepared from saltwater crocodiles ( Crocodylus porosus) and freshwater crocodiles ( Crocodylus johnstoni). Respiration rates of hepatocytes and liver mitochondria were measured at 37 degrees C and compared with values obtained for rat or previously measured for other species. Respiration rates of hepatocytes from either species of crocodile were similar to those reported for lizards and approximately one fifth of the rates measured using cells from mammals (rat and sheep). Ten-to-thirty percent of crocodile hepatocyte respiration was used to drive mitochondrial proton leak, similar to the proportion in other species. Respiration rates of crocodile liver mitochondria were similar to those of mammalian species. Proton leak rate in isolated liver mitochondria was measured as a function of membrane potential. Contrary to our prediction, the mitochondrial proton conductance of liver mitochondria from crocodiles was greater than that of liver mitochondria from lizards and was similar to that of rats. The acyl composition of liver mitochondrial phospholipids from the crocodiles was more similar to that in mitochondria from rats than in mitochondria from lizards. The relatively high mitochondrial proton conductance was associated with a relatively small liver, which seems to be characteristic of crocodilians. Comparison of data from a number of diverse ectothermic species suggested that hepatocyte respiration rate may decrease with body mass, with an allometric exponent of about -0.2, similar to the exponent in mammalian hepatocytes. However, unlike mammals, liver mitochondrial proton conductance in ectotherms showed no allometric relationship with body size.
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
2015-09-15
Coelacanths are lobe-finned fishes known from the Devonian to Recent that were long considered extinct, until the discovery of two living species in deep marine waters of the Mozambique Channel and Sulawesi. Despite extensive studies, the pulmonary system of extant coelacanths has not been fully investigated. Here we confirm the presence of a lung and discuss its allometric growth in Latimeria chalumnae, based on a unique ontogenetic series. Our results demonstrate the presence of a potentially functional, well-developed lung in the earliest known coelacanth embryo, and its arrested growth at later ontogenetic stages, when the lung is clearly vestigial. The parallel development of a fatty organ for buoyancy control suggests a unique adaptation to deep-water environments. Furthermore, we provide the first evidence for the presence of small, hard, flexible plates around the lung in L. chalumnae, and consider them homologous to the plates of the 'calcified lung' of fossil coelacanths.
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.
Novel Expressions of Equations of Relative Motion and Control in Keplerian Orbits
2009-04-01
spacecraft , and thus prediction and control of relative motion is significantly sensitive to relative orbit modeling errors [9...proposed a continuous feedback controller for rendezvous navigation in elliptical orbit . In this work, the full equations of relative motion (see [9... Rendezvous in Elliptical Orbits ,” Acta Astronautica, Vol. 41, No. 2, July 1997, pp. 95–101. doi:10.1016/S0094-5765(97)00204-X [19] Yu, S., “ Control
NASA Astrophysics Data System (ADS)
Zhao, Wenwen; Jiang, Zhongzheng; Chen, Weifang
2016-11-01
The moment methods in rarefied gas dynamics could be divided into generalized hydrodynamic equations (GHE) and extended hydrodynamic equations (EHE), e.g., Burnett equations, Grad equations and R-13 equations, theoretically. Eu firstly developed the GHE based on a non-equilibrium canonical distribution function and demonstrated the thermodynamically consistent of this model. Subsequently, nonlinear coupled constitutive relations (NCCR) was proposed by Myong by omitting the product of heat flux and velocity gradient in GHE to reduce the computational complexity. According to the successful application in 1-D shock wave structure and 2-D flat plate flow, the capability of NCCR has already been demonstrated successfully. The motivation of this study was to investigate the different behavior of NCCR and GHE for monatomic and diatomic gases in one-dimensional shock structure problems. Therefore, argon and nitrogen shock structure was calculated using both GHE and NCCR model up to Ma=50. The 3rd order MUSCL scheme for inviscid term and the 2nd order central difference scheme for viscid scheme were employed to carry out the computations. Finally, the present results including shock wave profile and its qualitative properties by NCCR and GHE are compared with that of DSMC and NS equations. The results showed that the GHE yield 1-D shock wave in much closer agreement with DSMC results than do the NCCR model without considering the computational complexity and efficiency in present cases.
NASA Astrophysics Data System (ADS)
Immink, G. K.
1994-10-01
This paper is concerned with applications of the Mellin transformation in the study of homogeneous linear differential and difference equations with polynomial coefficients. We begin by considering a differential equation (D) with regular singularities at O and ∞ and arbitrary singularities in the rest of the complex plane, and the difference equation (Δ‧) obtained from (D) by a variant of the formal Mellin transformation. We define fundamental systems of solutions of (Δ‧), analytic in either a right or a left half plane. by the use of Mellin transforms of microsolutions of (D). The relations between these fundamental systems are expressed in terms of central connection matrices of (D). Second, we study the differential equation (D1) obtained from (D) by means of a formal Laplace transformation and the difference equation (Δ1) obtained from (D1) by a formal Mellin transformation. We use Mellin transforms of "ordinary" solutions of (D1) with moderate growth at ∞ to construct fundamental systems of solutions of (Δ1). The relation between these fundamental systems involves certain Stokes multipliers and a formal monodromy matrix of (D1).
An estimator for the relative entropy rate of path measures for stochastic differential equations
NASA Astrophysics Data System (ADS)
Opper, Manfred
2017-02-01
We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.
Filobello-Nino, Uriel; Vazquez-Leal, Hector; Benhammouda, Brahim; Hernandez-Martinez, Luis; Khan, Yasir; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustin Leobardo; Castaneda-Sheissa, Roberto; Pereyra-Diaz, Domitilo; Cervantes-Perez, Juan; Agustin Perez-Sesma, Jose Antonio; Hernandez-Machuca, Sergio Francisco; Cuellar-Hernandez, Leticia
2014-01-01
In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.
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,…
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.
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.
NASA Astrophysics Data System (ADS)
Fahlman, Andreas
2017-02-01
A probabilistic model was used to predict decompression sickness (DCS) outcome in pig (70 and 20 kg), hamster (100 g), rat (220 g) and mouse (20 g) following air saturation dives. The data set included 179 pig, 200 hamster, 360 rat, and 224 mouse exposures to saturation pressures ranging from 1.9–15.2 ATA and with varying decompression rates (0.9–156 ATA • min‑1). Single exponential kinetics described the tissue partial pressures (Ptiss) of N2: Ptiss = ∫(Pamb – Ptiss) • τ‑1 dt, where Pamb is ambient N2 pressure and τ is a time constant. The probability of DCS [P(DCS)] was predicted from the risk function: P(DCS) = 1‑e‑r, where r = ∫(PtissN2 ‑ Thr ‑ Pamb) • Pamb–1 dt, and Thr is a threshold parameter. An equation that scaled τ with body mass included a constant (c) and an allometric scaling parameter (n), and the best model included n, Thr, and two c. The final model provided accurate predictions for 58 out of 61 dive profiles for pig, hamster, rat, and mouse. Thus, body mass helped improve the prediction of DCS risk in four mammalian species over a body mass range covering 3 orders of magnitude.
Fahlman, Andreas
2017-01-01
A probabilistic model was used to predict decompression sickness (DCS) outcome in pig (70 and 20 kg), hamster (100 g), rat (220 g) and mouse (20 g) following air saturation dives. The data set included 179 pig, 200 hamster, 360 rat, and 224 mouse exposures to saturation pressures ranging from 1.9–15.2 ATA and with varying decompression rates (0.9–156 ATA • min−1). Single exponential kinetics described the tissue partial pressures (Ptiss) of N2: Ptiss = ∫(Pamb – Ptiss) • τ−1 dt, where Pamb is ambient N2 pressure and τ is a time constant. The probability of DCS [P(DCS)] was predicted from the risk function: P(DCS) = 1−e−r, where r = ∫(PtissN2 − Thr − Pamb) • Pamb–1 dt, and Thr is a threshold parameter. An equation that scaled τ with body mass included a constant (c) and an allometric scaling parameter (n), and the best model included n, Thr, and two c. The final model provided accurate predictions for 58 out of 61 dive profiles for pig, hamster, rat, and mouse. Thus, body mass helped improve the prediction of DCS risk in four mammalian species over a body mass range covering 3 orders of magnitude. PMID:28150725
Fahlman, Andreas
2017-02-02
A probabilistic model was used to predict decompression sickness (DCS) outcome in pig (70 and 20 kg), hamster (100 g), rat (220 g) and mouse (20 g) following air saturation dives. The data set included 179 pig, 200 hamster, 360 rat, and 224 mouse exposures to saturation pressures ranging from 1.9-15.2 ATA and with varying decompression rates (0.9-156 ATA • min(-1)). Single exponential kinetics described the tissue partial pressures (Ptiss) of N2: Ptiss = ∫(Pamb - Ptiss) • τ(-1) dt, where Pamb is ambient N2 pressure and τ is a time constant. The probability of DCS [P(DCS)] was predicted from the risk function: P(DCS) = 1-e(-r), where r = ∫(PtissN2 - Thr - Pamb) • Pamb(-1) dt, and Thr is a threshold parameter. An equation that scaled τ with body mass included a constant (c) and an allometric scaling parameter (n), and the best model included n, Thr, and two c. The final model provided accurate predictions for 58 out of 61 dive profiles for pig, hamster, rat, and mouse. Thus, body mass helped improve the prediction of DCS risk in four mammalian species over a body mass range covering 3 orders of magnitude.
McVittie's mass particle in an expanding universe and related solutions of Einstein's equations
Hogan, P.A. )
1990-09-01
Three alternative forms are presented for the Robertson-Walker line element of the k = -1 Riemannian curvature isotropic cosmological models, as well as two alternative forms for the k = 0 model and one form for the k = +1 model; these forms are directly derived by solving Einstein's field equations. It is then noted that McVittie's (1933) embedding of a Schwarzschild field in the Robertson-Walker spacetimes fits naturally into one each of the alternative line elements. Related solutions of Einstein's equations are derived with a perfect fluid source which fit naturally in the remaining two forms of the k = -1 universe and the one remaining form of the k = 0 universe. Three additional perfect fluid solutions of Einstein's equations that are in a different sense analogous to McVittie's original solutions are also presented. 12 refs.
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.
A new dispersion-relation preserving method for integrating the classical Boussinesq equation
NASA Astrophysics Data System (ADS)
Jang, T. S.
2017-02-01
In this paper, a dispersion-relation preserving method is proposed for nonlinear dispersive waves, starting from the oldest weakly nonlinear dispersive wave mathematical model in shallow water waves, i.e., the classical Boussinesq equation. It is a semi-analytic procedure, however, which preserves, as a distinctive feature, the dispersion-relation imbedded in the model equation without adding (unwelcome) numerical effects, i.e., the proposed method has the same dispersion-relation as the original classical Boussinesq equation. This remarkable (dispersion-relation) preserving property is proved mathematically for small wave motion in present study. The property is also numerically examined by observing both the local wave number and the local frequency of a slowly varying water-wave group. The dispersion-relation preserving method proposed here is powerful as well for observing nonlinear wave phenomena such as solitary waves and their collision. In fact, the main features of nonlinear wave characteristics are clearly seen through not only a single propagating solitary wave but counter-propagating (head-on) solitary wave collisions. They are compared with known (exact) nonlinear solutions, the results of which represent a major improvement over existing solution formulations in the literature.
Verdade, L M
2000-08-01
In the present study, regression equations between body and head length measurements for the broad-snouted caiman (Caiman latirostris) are presented. Age and sex are discussed as sources of variation for allometric models. Four body-length, fourteen head-length, and ten ratio variables were taken from wild and captive animals. With the exception of body mass, log-transformation did not improve the regression equations. Besides helping to estimate body-size from head dimensions, the regression equations stressed skull shape changes during the ontogenetic process. All age-dependent variables are also size-dependent (and consequently dependent on growth rate), which is possibly related to the difficulty in predicting age of crocodilians based on single variable growth curves. Sexual dimorphism was detected in the allometric growth of cranium but not in the mandible, which may be evolutionarily related to the visual recognition of gender when individuals exhibit only the top of their heads above the surface of the water, a usual crocodilian behavior.
A new type of massive spin-one boson: And its relation with Maxwell equations
Ahluwalia, D.V.
1995-10-01
First, the author showed that in the (1, 0) {circle_plus} (0, 1) representation space there exist not one but two theories for charged particles. In the Weinberg construct, the boson and its antiboson carry same relative intrinsic parity, whereas in the author`s construct the relative intrinsic parities of the boson and its antiboson are opposite. These results originate from the commutativity of the operations of Charge conjugation and Parity in Weinberg`s theory, and from the anti-commutativity of the operations of Charge conjugation and Parity in the author`s theory. The author thus claims that he has constructed a first non-trivial quantum theory of fields for the Wigner-type particles. Second, the massless limit of both theories seems formally identical and suggests a fundamental modification of Maxwell equations. At its simplest level, the modification to Maxwell equations enters via additional boundary condition(s).
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
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
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.
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
Thermodynamics constrains allometric scaling of optimal development time in insects.
Dillon, Michael E; Frazier, Melanie R
2013-01-01
Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the "hotter is better" hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes. The
Thermodynamics Constrains Allometric Scaling of Optimal Development Time in Insects
Dillon, Michael E.; Frazier, Melanie R.
2013-01-01
Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the “hotter is better” hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes
Ivanov, Ivan Tanev
2007-08-01
Thermal stability of erythrocyte membrane is a measure for its ability to maintain permeability barrier at deleterious conditions. Hence, it could impact the resistance of erythrocytes against detrimental factors in circulation. In this study the thermostability of erythrocyte membranes was expressed by the temperature, T(go), at which the transmembrane gradient of ion concentration rapidly dissipated during transient heating. T(go) is the inducing temperature of the membrane transition that activated passive ion permeability at hyperthermia causing thermal hemolysis. A good allometric correlation of T(go) to the resistance against thermal hemolysis and the life span of erythrocytes were found for 13 mammals; sheep, cow, goat, dog, horse, man, rabbit, pig, cat, hamster, guinea pig, rat, and mouse. For the same group, the values of T(go) were strictly related to the sphingomyelin content of erythrocyte membranes. The residual ion permeability, P, was temperature activated from 38 to 57 degrees C with activation energy of 250+/-15 kJ/mol that strongly differed from that below 37 degrees C. The projected value of P at 37 degrees C was about half that of residual physiological permeability for Na+ and K+ that build ground for possible explanation of the life span vs membrane thermostability allometric correlation.
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.
Pressure-velocity relations in reservoir rocks: Modified MacBeth's equation
NASA Astrophysics Data System (ADS)
Grana, Dario
2016-09-01
The knowledge of the saturation and pressure effects on elastic properties is a key factor in reservoir monitoring. The relation between saturation changes and velocity variations is well known in rock physics and at seismic frequency it can be satisfactorily described by Gassmann's equations. The pressure effect still requires deeper investigations in order to be included in rock physics models for 4D studies. Theoretical models of velocity-pressure relations often do not match lab measurements, or contain empirical constants or theoretical parameters that are difficult to calibrate or do not have a precise physical meaning. In this work, I present a new model to describe the pressure sensitivity of elastic moduli for clastic rocks. The proposed model is an extension of MacBeth's relations. These equations are then integrated within a complete rock physics model to describe the relation between rock properties (porosity and clay content), dynamic attributes (saturation and pressure) and elastic properties. The proposed model is calibrated with laboratory measurements of dry samples over a wide range of pressure variations and then applied to well data to simulate different production scenarios. The complete rock physics model can then be used in time-lapse inversion to predict the distribution of dynamic property changes in the reservoir within an inversion workflow for reservoir monitoring.
Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity.
Urošević, A; Ljubisavljević, K; Ivanović, A
2013-02-01
We explored the ontogenetic dynamics of the morphological and allometric disparity in the cranium shapes of twelve lacertid lizard species. The analysed species (Darevskia praticola, Dinarolacerta mosorensis, Iberolacerta horvathi, Lacerta agilis, L. trilineata, L. viridis, Podarcis erhardii, P. melisellensis, P. muralis, P. sicula, P. taurica and Zootoca vivipara) can be classified into different ecomorphs: terrestrial lizards that inhabit vegetated habitats (habitats with lush or sparse vegetation), saxicolous and shrub-climbing lizards. We observed that there was an overall increase in the morphological disparity (MD) during the ontogeny of the lacertid lizards. The ventral cranium, which is involved in the mechanics of jaw movement and feeding, showed higher levels of MD, an ontogenetic shift in the morphospace planes and more variable allometric patterns than more conserved dorsal crania. With respect to ecology, the allometric trajectories of the shrub-climbing species tended to cluster together, whereas the allometric trajectories of the saxicolous species were highly dispersed. Our results indicate that the ontogenetic patterns of morphological and allometric disparity in the lacertid lizards are modified by ecology and functional constraints and that the identical mechanisms that lead to intraspecific morphological variation also produce morphological divergence at higher taxonomic levels.
Relation of the Cyclotomic Equation with the Harmonic and Derived Series
Boya, Luis J.; Rivera, Cristian
2015-01-01
We associate some (old) convergent series related to definite integrals with the cyclotomic equation xm − 1 = 0, for several natural numbers m; for example, for m = 3, x3 − 1 = (x − 1)(1 + x + x2) leads to ∫01dx(1/(1+x+x2))=π/(33)=(1-1/2)+(1/4-1/5)+(1/7-1/8)+⋯. In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary m are well defined but do imply integrals and/or series summations rather involved. PMID:25688380
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
NASA Astrophysics Data System (ADS)
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-02-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
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.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
NASA Astrophysics Data System (ADS)
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
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.
A Structural Equation Model of HIV-related Symptoms, Depressive Symptoms, and Medication Adherence
Yoo-Jeong, Moka; Waldrop-Valverde, Drenna; McCoy, Katryna; Ownby, Raymond L
2016-01-01
Adherence to combined antiretroviral therapy (cART) remains critical in management of HIV infection. This study evaluated depression as a potential mechanism by which HIV-related symptoms affect medication adherence and explored if particular clusters of HIV symptoms are susceptible to this mechanism. Baseline data from a multi-visit intervention study were analyzed among 124 persons living with HIV (PLWH). A bifactor model showed two clusters of HIV-related symptom distress: general HIV-related symptoms and gastrointestinal (GI) symptoms. Structural equation modeling showed that both general HIV-related symptoms and GI symptoms were related to higher levels of depressive symptoms, and higher levels of depressive symptoms were related to lower levels of medication adherence. Although general HIV-related symptoms and GI symptoms were not directly related to adherence, they were indirectly associated with adherence via depression. The findings highlight the importance of early recognition and evaluation of symptoms of depression, as well as the underlying physical symptoms that might cause depression, to improve medication adherence. PMID:27695710
Allometric scaling of chemical restraint associated with inhalant anesthesia in giant anteaters.
Carregaro, Adriano Bonfim; Gerardi, Patrícia Molina; Honsho, Daniel Kan
2009-04-01
This study describes the use of allometric scaling in five giant anteaters (Myrmecophaga tridactyla) submitted for osteosynthesis, gastrostomy, or treatment of burns. Chemical restraint was performed by allometric scaling using the dog as a reference; acepromazine (0.06 mg/kg), diazepam (0.3 mg/kg), ketamine (8.8 mg/kg), and buprenorphine (5.9 microg/kg) were combined, and the animals were maintained under isoflurane anesthesia. Heart rate, respiratory rate, hemoglobin oxygen saturation, temperature, and anesthetic depth were measured. Postoperative treatment consisted of ketoprofen, buprenorphine, and ceftiofur. Anesthetic induction was obtained in 10-15 min, achieving muscle relaxation and absence of excitement. Physiologic parameters were stable during the procedures, and postoperative treatment was effective. Allometric scaling was effective for chemical restraint and postoperative treatment.
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
Allometric scaling of strength scores in NCAA division I-A football athletes.
Oba, Yukiya; Hetzler, Ronald K; Stickley, Christopher D; Tamura, Kaori; Kimura, Iris F; Heffernan, Thomas P
2014-12-01
This study examined population-specific allometric exponents to control for the effect of body mass (BM) on bench press, clean, and squat strength measures among Division I-A collegiate football athletes. One repetition maximum data were obtained from a university pre-season football strength assessment (bench press, n = 207; clean, n = 88; and squat n = 86) and categorized into 3 groups by positions (line, linebacker, and skill). Regression diagnostics and correlations of scaled strength data to BM were used to assess the efficacy of the allometric scaling model and contrasted with that of ratio scaling and theoretically based allometric exponents of 0.67 and 0.33. The log-linear regression models yielded the following exponents (b): b = 0.559, 0.287, and 0.496 for bench press, clean, and squat, respectively. Correlations between bench press, clean, and squat to BM were r = -0.024, -0.047, and -0.018, respectively, suggesting that the derived allometric exponents were effective in partialling out the effect of BM on these lifts and removing between-group differences. Conversely, unscaled, ratio-scaled, and allometrically scaled (b = 0.67 or 0.33) data resulted in significant differences between groups. It is suggested that the exponents derived in the present study be used for allometrically scaling strength measures in National Collegiate Athletic Association Division I-A football athletes. Use of the normative percentile rank scores provide coaches and trainers with a valid means of judging the effectiveness of their training programs by allowing comparisons between individuals without the confounding influence of BM.
Allometric scaling of brain regions to intra-cranial volume: An epidemiological MRI study.
de Jong, Laura W; Vidal, Jean-Sébastien; Forsberg, Lars E; Zijdenbos, Alex P; Haight, Thaddeus; Sigurdsson, Sigurdur; Gudnason, Vilmundur; van Buchem, Mark A; Launer, Lenore J
2017-01-01
There is growing evidence that sub-structures of the brain scale allometrically to total brain size, that is, in a non-proportional and non-linear way. Here, scaling of different volumes of interest (VOI) to intra-cranial volume (ICV) was examined. It was assessed whether scaling was allometric or isometric and whether scaling coefficients significantly differed from each other. We also tested to what extent allometric scaling of VOI was introduced by the automated segmentation technique. Furthermore, reproducibility of allometric scaling was studied different age groups and study populations. Study samples included samples of cognitively healthy adults from the community-based Age Gene/Environment Susceptibility-Reykjavik Study (AGES-Reykjavik Study) (N = 3,883), the Coronary Artery Risk Development in Young Adults Study (CARDIA) (N =709), and the Alzheimer's Disease Neuroimaging Initiative (ADNI) (N = 180). Data encompassed participants with different age, ethnicity, risk factor profile, and ICV and VOI obtained with different automated MRI segmentation techniques. Our analysis showed that (1) allometric scaling is a trait of all parts of the brain, (2) scaling of neo-cortical white matter, neo-cortical gray matter, and deep gray matter structures including the cerebellum are significantly different from each other, and (3) allometric scaling of brain structures cannot solely be explained by age-associated atrophy, sex, ethnicity, or a systematic bias from study-specific segmentation algorithm, but appears to be a true feature of brain geometry. Hum Brain Mapp 38:151-164, 2017. © 2016 Wiley Periodicals, Inc.
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.
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.
NASA Astrophysics Data System (ADS)
Ohara, Atsumi; Wada, Tatsuaki
2010-01-01
This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss thermostatistical structure with information geometry on a manifold of generalized exponential densities. A dualistic relation between the two existing formalisms is elucidated. Next by equipping the manifold of q-Gaussian densities with such a structure, we derive several physically and geometrically interesting properties of the solutions. The manifold is proved invariant and attracting for the evolving solutions, which play crucial roles in our analysis. We demonstrate that the moment-conserving projection of a solution coincides with a geodesic curve on the manifold. Further, the evolutional velocities of the second moments and the convergence rate to the manifold are evaluated in terms of the Bregman divergence. Finally we show that the self-similar solution is geometrically special in the sense that it is simultaneously geodesic with respect to the mutually dual two affine connections. Preliminary forms of several results in this paper will appear in [50] without proofs.
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
NASA Astrophysics Data System (ADS)
Canoglu, Ahmet; Güldogan, Bahri; Salihoglu, Selâmi
We obtain new integrable coupled nonlinear partial differential equations by assuming the soliton connection having values in orthogonal-symplectic Lie superalgebras [B(m, n), C(n), D(m, n)]. These equations are coupled Nonlinear Schrödinger equations on various super symmetric spaces.
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.
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
The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory
NASA Astrophysics Data System (ADS)
Novello, M.; Bittencourt, E.; Salim, J. M.
2014-12-01
A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.
Republication of: Exact solutions of the field equations of the general theory of relativity
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Ehlers, Jürgen; Kundt, Wolfgang
2009-09-01
This is an English translation of a paper by Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, first published in 1960. The original paper was part 1 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (The other parts of the series will be printed as Golden Oldies in the future.) The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. It is accompanied by an editorial note written by G. F. R. Ellis, and by the biographies of the authors: P. Jordan (written by A. Krasiński) and W. Kundt (written by himself). The biography of J. Ehlers is contained elsewhere in the same issue of GRG, which is devoted to his memory.
Numerical study of a parametric parabolic equation and a related inverse boundary value problem
NASA Astrophysics Data System (ADS)
Mustonen, Lauri
2016-10-01
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the nonhomogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In the case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any linearized subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.
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.
We developed models to estimate the soft tissue content of benthic marine invertebrates that are prey for aquatic wildlife. Allometric regression models of tissue wet weight with shell length for 10 species of benthic invertebrates had r2 values ranging from 0.29 for hermit crabs...
Allometric scaling of UK urban emissions: interpretation and implications for air quality management
NASA Astrophysics Data System (ADS)
MacKenzie, Rob; Barnes, Matt; Whyatt, Duncan; Hewitt, Nick
2016-04-01
Allometry uncovers structures and patterns by relating the characteristics of complex systems to a measure of scale. We present an allometric analysis of air quality for UK urban settlements, beginning with emissions and moving on to consider air concentrations. We consider both airshed-average 'urban background' concentrations (cf. those derived from satellites for NO2) and local pollution 'hotspots'. We show that there is a strong and robust scaling (with respect to population) of the non-point-source emissions of the greenhouse gases carbon dioxide and methane, as well as the toxic pollutants nitrogen dioxide, PM2.5, and 1,3-butadiene. The scaling of traffic-related emissions is not simply a reflection of road length, but rather results from the socio-economic patterning of road-use. The recent controversy regarding diesel vehicle emissions is germane to our study but does not affect our overall conclusions. We next develop an hypothesis for the population-scaling of airshed-average air concentrations, with which we demonstrate that, although average air quality is expected to be worse in large urban centres compared to small urban centres, the overall effect is an economy of scale (i.e., large cities reduce the overall burden of emissions compared to the same population spread over many smaller urban settlements). Our hypothesis explains satellite-derived observations of airshed-average urban NO2 concentrations. The theory derived also explains which properties of nature-based solutions (urban greening) can make a significant contribution at city scale, and points to a hitherto unforeseen opportunity to make large cities cleaner than smaller cities in absolute terms with respect to their airshed-average pollutant concentration.
Washout allometric reference method (WARM) for parametric analysis of [(11)C]PIB in human brains.
Rodell, Anders; Aanerud, Joel; Braendgaard, Hans; Gjedde, Albert
2013-01-01
Rapid clearance and disappearance of a tracer from the circulation challenges the determination of the tracer's binding potentials in brain (BP ND) by positron emission tomography (PET). This is the case for the analysis of the binding of radiolabeled [(11)C]Pittsburgh Compound B ([(11)C]PIB) to amyloid-β (Aβ) plaques in brain of patients with Alzheimer's disease (AD). To resolve the issue of rapid clearance from the circulation, we here introduce the flow-independent Washout Allometric Reference Method (WARM) for the analysis of washout and binding of [(11)C]PIB in two groups of human subjects, healthy aged control subjects (HC), and patients suffering from AD, and we compare the results to the outcome of two conventional analysis methods. We also use the rapid initial clearance to obtain a surrogate measure of the rate of cerebral blood flow (CBF), as well as a method of identifying a suitable reference region directly from the [(11)C]PIB signal. The difference of average absolute CBF values between the AD and HC groups was highly significant (P < 0.003). The CBF measures were not significantly different between the groups when normalized to cerebellar gray matter flow. Thus, when flow differences confound conventional measures of [(11)C]PIB binding, the separate estimates of CBF and BP ND provide additional information about possible AD. The results demonstrate the importance of data-driven estimation of CBF and BP ND, as well as reference region detection from the [(11)C]PIB signal. We conclude that the WARM method yields stable measures of BP ND with relative ease, using only integration for noise reduction and no model regression. The method accounts for relative flow differences in the brain tissue and yields a calibrated measure of absolute CBF directly from the [(11)C]PIB signal. Compared to conventional methods, WARM optimizes the Aβ plaque load discrimination between patients with AD and healthy controls (P = 0.009).
Mechanical Work and Long-Distance Performance Prediction: the Influence of Allometric Scaling
Tartaruga, Marcus Peikriszwili; Brisswalter, Jeanick; Mota, Carlos Bolli; Alberton, Cristine Lima; Gomeñuka, Natalia Andrea; Peyré-Tartaruga, Leonardo Alexandre
2013-01-01
The purpose of this study was to examine the effect of allometric scaling on the relationship between mechanical work and long-distance running performance in recreational runners. Fourteen recreational long-distance runners (male, mean ± SD - age: 29 ± 7 years; body mass: 70.0 ± 10.2 kg; body height: 1.71 ± 0.07 m; maximal oxygen uptake: VO2max 52.0 ± 4.9 ml·kg−1·min−1) performed two tests: a continuous incremental test to volitional exhaustion in order to determine VO2max, and a 6-minute running submaximal test at 3.1 m·s−1, during which segments in the sagittal plane were recorded using a digital camera and the internal (Wint), external (Wext) and total (Wtot) mechanic work, in J·kg−1·m−1, was subsequently calculated. The results indicated a significant correlation between mechanical work and performance, however, the strongest correlations were observed when allometric exponents were used (respectively for Wint, Wext and Wtot; non allometric vs. allometric scaling defined by literature (0.75) or determined mathematically (0.49): r = 0.38 vs. r = 0.44 and r = 0.50; r = 0.80 vs. r = 0.83 and r = 0.82; r = 0.70 vs. r = 0.77 and r = 0.78). These results indicate that mechanical work could be used as a predictor of recreational long-distance performance and an allometric model may improve this prediction. PMID:24235986
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
Brustein, Ram; Hadad, Merav
2009-09-04
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.
On the balance equations for a dilute binary mixture in special relativity
Moratto, Valdemar; Garcia-Perciante, A. L.; Garcia-Colin, L. S.
2010-12-14
In this work we study the properties of a relativistic mixture of two non-reacting species in thermal local equilibrium. We use the full Boltzmann equation (BE) to find the general balance equations. Following conventional ideas in kinetic theory, we use the concept of chaotic velocity. This is a novel approach to the problem. The resulting equations will be the starting point of the calculation exhibiting the correct thermodynamic forces and the corresponding fluxes; these results will be published elsewhere.
2016-01-01
Feeding adaptation, social behaviour, and interspecific interactions related to sexual dimorphism and allometric growth are particularly challenging to be investigated in the high sexual monomorphic Delphinidae. We used geometric morphometrics to extensively explore sexual dimorphism and ontogenetic allometry of different projections of the skull and the mandible of the bottlenose dolphin Tursiops truncatus. Two-dimensional landmarks were recorded on the dorsal, ventral, lateral, and occipital views of the skull, and on the lateral view of the left and the right mandible of 104 specimens from the Mediterranean and the North Seas, differing environmental condition and degree of interspecific associations. Landmark configurations were transformed, standardized and superimposed through a Generalized Procrustes Analysis. Size and shape differences between adult males and females were respectively evaluated through ANOVA on centroid size, Procrustes ANOVA on Procrustes distances, and MANOVA on Procrustes coordinates. Ontogenetic allometry was investigated by multivariate regression of shape coordinates on centroid size in the largest homogenous sample from the North Sea. Results evidenced sexual dimorphic asymmetric traits only detected in the adults of the North Sea bottlenose dolphins living in monospecific associations, with females bearing a marked incision of the cavity hosting the left tympanic bulla. These differences were related to a more refined echolocalization system that likely enhances the exploitation of local resources by philopatric females. Distinct shape in immature versus mature stages and asymmetric changes in postnatal allometry of dorsal and occipital traits, suggest that differences between males and females are established early during growth. Allometric growth trajectories differed between males and females for the ventral view of the skull. Allometric trajectories differed among projections of skull and mandible, and were related to dietary
de Francesco, Maria Carla; Loy, Anna
2016-01-01
Feeding adaptation, social behaviour, and interspecific interactions related to sexual dimorphism and allometric growth are particularly challenging to be investigated in the high sexual monomorphic Delphinidae. We used geometric morphometrics to extensively explore sexual dimorphism and ontogenetic allometry of different projections of the skull and the mandible of the bottlenose dolphin Tursiops truncatus. Two-dimensional landmarks were recorded on the dorsal, ventral, lateral, and occipital views of the skull, and on the lateral view of the left and the right mandible of 104 specimens from the Mediterranean and the North Seas, differing environmental condition and degree of interspecific associations. Landmark configurations were transformed, standardized and superimposed through a Generalized Procrustes Analysis. Size and shape differences between adult males and females were respectively evaluated through ANOVA on centroid size, Procrustes ANOVA on Procrustes distances, and MANOVA on Procrustes coordinates. Ontogenetic allometry was investigated by multivariate regression of shape coordinates on centroid size in the largest homogenous sample from the North Sea. Results evidenced sexual dimorphic asymmetric traits only detected in the adults of the North Sea bottlenose dolphins living in monospecific associations, with females bearing a marked incision of the cavity hosting the left tympanic bulla. These differences were related to a more refined echolocalization system that likely enhances the exploitation of local resources by philopatric females. Distinct shape in immature versus mature stages and asymmetric changes in postnatal allometry of dorsal and occipital traits, suggest that differences between males and females are established early during growth. Allometric growth trajectories differed between males and females for the ventral view of the skull. Allometric trajectories differed among projections of skull and mandible, and were related to dietary
ERIC Educational Resources Information Center
Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P.
2015-01-01
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…
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.
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.
NASA Astrophysics Data System (ADS)
Myrzakulov, R.; Mamyrbekova, G. K.; Nugmanova, G. N.; Yesmakhanova, K. R.; Lakshmanan, M.
2014-06-01
Motion of curves and surfaces in R3 lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota-Maxwell-Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability.
Wu, Junru; Layman, Christopher; Liu, Jun
2004-02-01
A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.
NASA Astrophysics Data System (ADS)
Wu, Junru; Layman, Christopher; Liu, Jun
2004-02-01
A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.
Allometric scaling of electrical excitation and propagation in the mammalian heart.
Bassil, Guillaume; Zarzoso, Manuel; Noujaim, Sami F
2016-09-26
Variations in body mass impose constraints on the structure and function of mammalian species, including those of the cardiovascular system. Numerous biological processes, including cardiovascular parameters, have been shown to scale with body mass (BM) according to the law of allometric scaling: Y=Y =a∙BM(b) (Y, biological process; a, normalization constant; b, scaling exponent, which in many instances is a multiple of ¼). These parameters include heart and breathing rates, intervals and subintervals of the electrocardiogram (ECG), action potential duration (APD), metabolic rate, and temporal properties of ventricular fibrillation. For instance, the hierarchical branching networks of the vascular system, and of the specialized conduction system in the heart have been proposed to be important determinants of allometric scaling. A global and unifying molecular mechanism of allometric scaling has not been put forth, but changes in gene expression have been proposed to play an important role. Even though it is accepted that differences in body size have cardiovascular effects, the use of scaling in the clinical setting is limited. An increase in the clinical utilization of scaling is thought to lead to improved cardiovascular disease diagnosis and management in patients.
Mahmood, Iftekhar
2013-09-01
Allometric scaling is a useful tool in early drug development and can be used for the prediction of human pharmacokinetic (PK) parameters from animal PK parameters. The main objective of this work was to predict concentration-time profiles of coagulation factors in humans in a multi-compartment system using animal PK parameters. The prediction of concentration-time profiles in humans in a multi-compartment system was based on the predicted values of clearance and volumes of distribution (V(c), V(ss) and V(β)) from animals. Five coagulation factors from the literature were chosen that were described by two-compartment model in both humans and animals. Clearance and volumes of distribution from animals were allometrically scaled to humans and then were used to predict concentration-time profiles in humans. The predicted concentration-time profile for a given coagulation factor was accurate for most of the time points. Percent prediction error range varied across coagulation factors. The prediction error >50% was observed either at 1 or a maximum of two time points for a given drug. The study indicated that the allometric scaling can be useful in the prediction of concentration-time profiles of coagulation factors in humans from animals and may be helpful in designing a first-in-human study.
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.
Which electromagnetic equations apply in rotating coordinates. [frame transformations in relativity
NASA Technical Reports Server (NTRS)
Webster, D. L.; Whitten, R. C.
1973-01-01
It was discovered some years ago by Schiff that two equations for fields in vacuum do not carry over without change from an inertial frame to a frame with rotating axes of space coordinates, even for a region with all velocities much lower than the speed of light. However, the belief that all four of the field equations are invariant under such conditions is still prevalent and causes misconceptions in physical applications, including astrophysical and geophysical ones. The purpose of the present paper is therefore to call attention to Schiff's discovery, discussing its basis and its extension to fields in material media, and to interpret the additional terms that must be added to the equations in order to obtain valid transformations to rotating axes of coordinates.
Daly, Edoardo; Porporato, Amilcare
2004-11-01
Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.
Lochmiller, R L; Hellgren, E C; Grant, W E
1986-01-01
Selected morphological features of 8 adult male and 8 adult female collared peccaries (Tayassu tajacu) shot from southern Texas during March 1983 are described. A total of 16 adult peccaries with an average body mass of 18.68 +/- 0.61 (SE) Kg was examined. Significant differences between males and females were observed for absolute and relative mass of liver and lungs, and relative heart mass. These visceral organs were heavier among females than males. Significant sex effects were also found for absolute and relative mass of the dorsal scent gland. The dorsal scent gland contributed twice as much to total body mass in males as in females. No sexual dimorphisms of the gastrointestinal tract were noted. Females had a significantly greater portion of total visceral fat deposited around the kidneys than did males. Relative mass of the mandible was significantly greater in males than in females. Adult males had extremely large accessory sex glands. The bulbourethral and seminal vesicle glands comprised 0.27 per cent of the total body mass. Allometric growth coefficients (b) varied among the various organs and glands examined, ranging from below (eyes, b = 0.34) to well above (seminal vesicles, b = 1.87) unity. Growth coefficients of lungs, kidneys, pituitary gland, and thyroid gland during adulthood greatly exceeded respective values in developing nurslings.
Properties of Linear Integral Equations Related to the Six-Vertex Model with Disorder Parameter
NASA Astrophysics Data System (ADS)
Boos, Hermann; Göhmann, Frank
2011-10-01
One of the key steps in recent work on the correlation functions of the XXZ chain was to regularize the underlying six-vertex model by a disorder parameter α. For the regularized model it was shown that all static correlation functions are polynomials in only two functions. It was further shown that these two functions can be written as contour integrals involving the solutions of a certain type of linear and non-linear integral equations. The linear integral equations depend parametrically on α and generalize linear integral equations known from the study of the bulk thermodynamic properties of the model. In this note we consider the generalized dressed charge and a generalized magnetization density. We express the generalized dressed charge as a linear combination of two quotients of Q-functions, the solutions of Baxter's t-Q-equation. With this result we give a new proof of a lemma on the asymptotics of the generalized magnetization density as a function of the spectral parameter.
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
Enders, Craig K.; Bandalos, Deborah L.
2001-01-01
Used Monte Carlo simulation to examine the performance of four missing data methods in structural equation models: (1)full information maximum likelihood (FIML); (2) listwise deletion; (3) pairwise deletion; and (4) similar response pattern imputation. Results show that FIML estimation is superior across all conditions of the design. (SLD)
ERIC Educational Resources Information Center
Sahin, Elvan; Ertepinar, Hamide; Teksoz, Gaye
2012-01-01
The purpose of this study is to construct a structural equation model to examine the links among attitudes, values, and behaviors pertaining to sustainability, participation in outdoor recreation as well as gender and tendency to follow mass media for university students. The data were collected by on-line administration of a survey to 958…
Student Interpretations of Equations Related to the First Law of Thermodynamics
ERIC Educational Resources Information Center
Hadfield, Linda C.; Wieman, Carl E.
2010-01-01
Student interpretations of the equation for the first law of thermodynamics, [delta]U = q + w, an expression defining work done on or by a gas, w = -[image omitted]PdV, and an expression defining heat, q = [image omitted]C[subscript v]dT were investigated through a multiple-choice survey, a free-response written survey, and interviews. The…
Allometric scaling of the optic tectum in cartilaginous fishes.
Yopak, Kara E; Lisney, Thomas J
2012-01-01
In cartilaginous fishes (Chondrichthyes; sharks, skates and rays (batoids), and holocephalans), the midbrain or mesencephalon can be divided into two parts, the dorsal tectum mesencephali or optic tectum (analogous to the superior colliculus of mammals) and the ventral tegmentum mesencephali. Very little is known about interspecific variation in the relative size and organization of the components of the mesencephalon in these fishes. This study examined the relative development of the optic tectum and the tegmentum in 75 chondrichthyan species representing 32 families. This study also provided a critical assessment of attempts to quantify the size of the optic tectum in these fishes volumetrically using an idealized half-ellipsoid approach (method E), by comparing this method to measurements of the tectum from coronal cross sections (method S). Using species as independent data points and phylogenetically independent contrasts, relationships between the two midbrain structures and both brain and mesencephalon volume were assessed and the relative volume of each brain area (expressed as phylogenetically corrected residuals) was compared among species with different ecological niches (as defined by primary habitat and lifestyle). The relatively largest tecta and tegmenta were found in pelagic coastal/oceanic and oceanic sharks, benthopelagic reef sharks, and benthopelagic coastal sharks. The smallest tecta were found in all benthic sharks and batoids and the majority of bathyal (deep-sea) species. These results were consistent regardless of which method of estimating tectum volume was used. We found a highly significant correlation between optic tectum volume estimates calculated using method E and method S. Taxon-specific variation in the difference between tectum volumes calculated using the two methods appears to reflect variation in both the shape of the optic tectum relative to an idealized half-ellipsoid and the volume of the ventricular cavity. Because the
Huang, Yingxin; Lechowicz, Martin J; Zhou, Daowei; Price, Charles A
2016-03-01
The ability of general scaling models to capture the central tendency or dispersion in biological data has been questioned. In fact, the appropriate domain of such models has never been clearly articulated and they have been supported and challenged using both interspecific and/or intraspecific data. Here, we evaluate several simplifying assumptions and predictions of two prominent scaling models: West, Brown and Enquist's fractal model (WBE) and a null model of geometric similarity (GEOM). Using data for 53 herbaceous angiosperm species from the Songnen Grasslands of Northern China, we compared both the interspecific and intraspecific scaling relationships for plant geometry and biomass partitioning. Specifically, we considered biomass investment in shoots and leaves as well as related several traits not commonly collected in plant allometric analyses: shoot volume, leaf number, and mean leaf mass. At the interspecific level, we find substantial variation in regression slopes, and the simplifying assumptions of WBE and predictions of both the WBE and GEOM models do not hold. In contrast, we find substantial support for the WBE model at the intraspecific level, and to a lesser extent for GEOM. The differences between our results at interspecific and intraspecific levels are due to the fact that leaf size and stem tissue density vary considerably across species in contrast to the simplifying assumptions of WBE. These results highlight the domain within which simplifying model assumptions might be most appropriate, and suggest allometric models may be useful points of departure within some species, growth forms or taxonomic groups.
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.
NASA Technical Reports Server (NTRS)
Holst, T. L.
1976-01-01
Four explicit finite difference techniques designed to solve the time-dependent, compressible Navier Stokes equations are compared. These techniques are: (1) MacCormack, (2) modified Du Fort-Frankel, (3) modified hopscotch, and (4) Brailovskaya. The comparison was made numerically by solving the quasi-one dimensional Navier Stokes equations for the flow in a converging-diverging nozzle. Solutions with and without standing normal shock waves were computed for unit Reynolds numbers (based on total conditions) ranging from 45374 to 2269. The results indicate that all four techniques are comparable in accuracy; however, the modified hopscotch scheme is two to three times faster than the Brailovskaya and MacCormack schemes and three to six times faster than the modified Du Fort-Frankel scheme.
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.
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.
NASA Astrophysics Data System (ADS)
Hamano, Katsumi; Hirotsu, Shunsuke
1980-01-01
Phenomenological equations are derived which interrelate the anomalies in various thermodynamic quantities above the transition point of a cubic-to-tetragonal phase transition caused by an instability of a triply degenerate soft mode. The anomalous part of the Gibbs free energy is assumed to be a simple sum of the three parts which represent the contributions from the three fluctuation components. A cylindrical approximation is adopted to each of the three contributions by taking into account the symmetry of the fluctuations. The theory predicts that the adiabatic elastic compliances, s11s, s12s, and also s11s-s12s should exhibit anomalies proportional to the anomaly in the specific heat at constant pressure. This is in marked contrast with the result of the generalized Pippard equations derived by Garland, and by Janovec. The new equations are successfully tested for KMnF3, CsPbCl3, and CsPbBr3. The β-γ transition of NH4Br is also discussed.
The origin of allometric scaling laws in biology.
Demetrius, Lloyd
2006-12-21
The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon-specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.
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
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.
Crewther, Blair T; Gill, Nicholas; Weatherby, Robert P; Lowe, Tim
2009-12-01
In this study, we compared the effectiveness of ratio and allometric scaling for normalizing power and strength in elite male rugby union players. Rugby union forwards (n = 18) and backs (n = 20) were assessed for squat jump and bench throw peak power, and box squat and bench press one-repetition maximum strength. The performance data for the forwards and backs were compared using ratio (P/BM) and allometric scaling (P/BM(b)), where P represents performance, BM is body mass in kilograms, and b is a power exponent. A proposed allometric exponent (0.67) and exponents (+/-95% confidence intervals) derived for the box squat (0.33 +/- 0.31), bench press (0.45 +/- 0.30), bench throw (0.46 +/- 0.36), and squat jump (0.64 +/- 0.31) exercises were used. In general, the absolute expression of power and strength was superior for the heavier forwards, but after ratio scaling these performance measures then favoured the lighter backs. There were no performance differences between the forwards and backs after allometric scaling using either the proposed or the derived exponents. Thus, allometric scaling may provide a more effective method for normalizing power and strength in elite athletes when body size is a confounding variable.
NASA Astrophysics Data System (ADS)
Dinh, Khanh N.; Sidje, Roger B.
2016-06-01
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP.
Dinh, Khanh N; Sidje, Roger B
2016-05-13
The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP.
NASA Astrophysics Data System (ADS)
Frank, T. D.
The Lotka-Volterra-Haken equations have been frequently used in ecology and pattern formation. Recently, the equations have been proposed by several research groups as amplitude equations for task-related patterns of brain activity. In this theoretical study, the focus is on the circular causality aspect of pattern formation systems as formulated within the framework of synergetics. Accordingly, the stable modes of a pattern formation system inhibit the unstable modes, whereas the unstable modes excite the stable modes. Using this circular causality principle it is shown that under certain conditions the Lotka-Volterra-Haken amplitude equations can be derived from a general model of brain activity akin to the Wilson-Cowan model. The model captures the amplitude dynamics for brain activity patterns in experiments involving several consecutively performed multiple-choice tasks. This is explicitly demonstrated for two-choice tasks involving grasping and walking. A comment on the relevance of the theoretical framework for clinical psychology and schizophrenia is given as well.
NASA Astrophysics Data System (ADS)
Singh, K. N.; Pant, N.
2016-07-01
In this paper, we present generalization of anisotropic analogue of charged Heintzmann's solution of the general relativistic field equations in curvature coordinates. These exact solutions are stable and well behaved in all respect for a wide range of anisotropy parameter and charge parameter. We have found that these new solutions are suitable for the modeling of super dense stars like neutron stars and quark stars because they yield a wide range of masses and radii with simple mathematical expressions. By tuning different values of the few parameters, we can model various neutron stars and quark stars which are compatible with the experimentally observed values of masses and radii. Therefore, we have synchronized our solution with the observed values of some of the compact stars XTE J1739 - 217, EXO 0748 - 676, PSR J1614 - 2230, PSR J0348 + 0432 and PSR B0943 + 10.
Vispoel, Walter P; Morris, Carrie A; Kilinc, Murat
2017-01-23
Although widely recognized as a comprehensive framework for representing score reliability, generalizability theory (G-theory), despite its potential benefits, has been used sparingly in reporting of results for measures of individual differences. In this article, we highlight many valuable ways that G-theory can be used to quantify, evaluate, and improve psychometric properties of scores. Our illustrations encompass assessment of overall reliability, percentages of score variation accounted for by individual sources of measurement error, dependability of cut-scores for decision making, estimation of reliability and dependability for changes made to measurement procedures, disattenuation of validity coefficients for measurement error, and linkages of G-theory with classical test theory and structural equation modeling. We also identify computer packages for performing G-theory analyses, most of which can be obtained free of charge, and describe how they compare with regard to data input requirements, ease of use, complexity of designs supported, and output produced. (PsycINFO Database Record
NASA Astrophysics Data System (ADS)
Gomes, Rodney; Deienno, Rogerio; Morbidelli, Alessandro
2017-01-01
We evaluate the effects of a distant planet, commonly known as planet 9, on the dynamics of the giant planets of the solar system. We find that the dynamics of the giant planets can be decomposed into a classic Lagrange–Laplace dynamics relative to their own invariant plane and a slow precession of said plane relative to the total angular momentum vector of the solar system, including planet 9. Under specific configurations for planet 9, this precession can explain the current tilt of ∼6° between the invariant plane of the giant planets and the solar equator. An analytical model is developed to map the evolution of the inclination of the inner giant planets’ invariant plane as a function of the planet 9's mass and orbital elements, and numerical simulations of the equations of motion are performed to validate our analytical approach. The longitude of the ascending node of planet 9 is found to be linked to the longitude of the ascending node of the giant planets’ invariant plane, which also constrains the longitude of the node of planet 9 on the ecliptic. Some of the planet 9 configurations that allow the explanation of the current solar tilt are compatible with those proposed to explain the orbital confinement of distant Kuiper Belt objects. This work gives an elegant explanation for the current tilt between the invariant plane of the inner giant planets and the solar equator and also adds new constraints to the orbital elements of planet 9.
Khodarahmi, Iman; Shakeri, Mostafa; Sharp, M; Amini, Amir A
2010-01-01
Pressure gradient across a Gaussian-shaped 87% area stenosis phantom was estimated by solving the pressure Poisson equation (PPE) for a steady flow mimicking the blood flow through the human iliac artery. The velocity field needed to solve the pressure equation was obtained using particle image velocimetry (PIV). A steady flow rate of 46.9 ml/s was used, which corresponds to a Reynolds number of 188 and 595 at the inlet and stenosis throat, respectively (in the range of mean Reynolds number encountered in-vivo). In addition, computational fluid dynamics (CFD) simulation of the same flow was performed. Pressure drops across the stenosis predicted by PPE/PIV and CFD were compared with those measured by a pressure catheter transducer. RMS errors relative to the measurements were 17% and 10% for PPE/PIV and CFD, respectively.
NASA Astrophysics Data System (ADS)
Meza-Fajardo, Kristel C.; Lai, Carlo G.
2007-12-01
The theory of linear viscoelasticity is the simplest constitutive model that can be adopted to accurately predict the small-strain mechanical response of materials exhibiting the ability to both store and dissipate strain energy. An important result implied by this theory is the relationship existing between material attenuation and the velocity of propagation of a mechanical disturbance. The functional dependence of these important parameters is represented by the Kramers-Kronig (KK) equations, also known as dispersion equations, which are nothing but a statement of the necessary and sufficient conditions to satisfy physical causality. This paper illustrates the derivation of exact solutions of the KK equations to provide explicit relations between frequency-dependent phase velocity and material damping ratio (or equivalently, quality factor). The assumptions that form the basis of the derivation are not beyond those established by the standard theory of viscoelasticity for a viscoelastic solid. The explicit expression for phase velocity as a function of damping ratio was derived by means of the theory of linear singular integral equations, and in particular by the solution of the associated Homogeneous Riemann Boundary Value Problem. It is shown that the same solution may be obtained also by using the implications of physical causality on the Fourier Transform. On the other hand, the explicit solution for damping ratio as a function of phase velocity was found through the components of the complex wavenumber. The exact solutions make it possible to obtain frequency-dependent material damping ratio solely from phase velocity measurements, and conversely. Hence, these relations provide an innovative and inexpensive tool to determine the small-strain dynamic properties of geomaterials. It is shown that the obtained rigorous solutions are in good agreement with well-known solutions based on simplifying assumptions that have been developed in the fields of seismology
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.
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.
Latitude-related changes in the amplitude of annual mortality rhythm. The biological equator in man.
Douglas, S; Rawles, J
1999-03-01
There is extensive literature describing the effect of season on mortality rates, especially in cardiovascular and respiratory disease. This study compares latitude with the extent of seasonal variation of monthly deaths from all causes. In developed countries, there is a peak of deaths in winter and a trough in summer. Monthly numbers of deaths were established in 89 countries in the Northern and Southern Hemisphere. Using cosinor analysis, the extent of seasonal variation (amplitude) was established and correlated with latitude. The amplitude of seasonality was greatest in mid-latitude around 35 degrees, but low or absent near the equator and subpolar regions. The amplitude can differ at the same latitude. The weather in equatorial regions and in habitations near the Arctic Circle is very different, but death has a similar seasonal rhythm. The purpose is to record this epidemiological finding even though no simple explanation is provided. Weather alone cannot explain it, and it is possible that day length (photoperiod) has an important, but complex, underlying role.
NASA Astrophysics Data System (ADS)
Murad, Mohammad Hassan; Pant, Neeraj
2014-03-01
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/ c 2 R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538-52, LMC X-4, SAX J1808.4-3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
Young, C.W.
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
NASA Astrophysics Data System (ADS)
Raychaudhuri, Debasree
2013-12-01
There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following question. Who succeeds at making the leap and can we describe the attributes that set them apart from the ones that do not? In this article, we offer a framework to categorize students as learners based on their individual approaches towards learning concepts in differential equations and related concepts - as demonstrated by their efforts to resolve a conflict, conserve and rebuild their cognitive structures.
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
Vlad, Marcel Ovidiu; Ross, John
2002-12-01
We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.
Verification of capillary pressure functions and relative permeability equations for gas production
Jang, Jaewon
2016-10-25
The understanding of multiphase fluid flow in porous media is of great importance in many fields such as enhanced oil recovery, hydrology, CO_{2} sequestration, contaminants cleanup and natural gas production from hydrate bearing sediments. However, there are many unanswered questions about the key parameters that characterize gas and water flows in porous media. The characteristics of multiphase fluid flow in porous media such as water retention curve, relative permeability, preferential fluid flow patterns and fluid-particle interaction should be taken into consideration for a fundamental understanding of the behavior of pore scale systems.
NASA Astrophysics Data System (ADS)
Szybisz, Leszek
1990-06-01
The self-consistency of solutions obtained from a recently proposed numerical relaxation method of solving the Euler-Lagrange equations for the ground state of inhomogeneous Bose systems at zero temperature is investigated. For this kind of system at least three different dispersion relations can be formulated, all of them providing information about the same eigenstates. The quality of our optimization scheme is studied by analyzing the convergence of the low-lying eigenvalues and eigenfunctions of these dispersion relations. Numerical results for the spectrum and spatial shape of elementary excitations of a thin film of liquid 4He supported by an external potential are reported. The optimal lowest-lying eigenvalues are compared with estimations based on simple theoretical approaches and with calculations performed by other authors.
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
NASA Astrophysics Data System (ADS)
Steinhoff, John; Chitta, Subhashini
2012-08-01
The linear wave equation represents the basis of many linear electromagnetic and acoustic propagation problems. Features that a computational model must have, to capture large scale realistic effects (for over the horizon or "OTH" radar communication, for example), include propagation of short waves with scattering and partial absorption by complex topography. For these reasons, it is not feasible to use Green's Function or any simple integral method, which neglects these intermediate effects and requires a known propagation function between source and observer. In this paper, we describe a new method for propagating such short waves over long distances, including intersecting scattered waves. The new method appears to be much simpler than conventional high frequency schemes: Lagrangian "particle" based approaches, such as "ray tracing" become very complex in 3-D, especially for waves that may be expanding, or even intersecting. The other high frequency scheme in common use, the Eikonal, also has difficulty with intersecting waves. Our approach, based on nonlinear solitary waves concentrated about centroid surfaces of physical wave features, is related to that of Whitham [1], which involves solving wave fronts propagating on characteristics. Then, the evolving electromagnetic (or acoustic) field can be approximated as a collection of propagating co-dimension one surfaces (for example, 2-D surfaces in three dimensions). This approach involves solving propagation equations discretely on an Eulerian grid to approximate the linear wave equation. However, to propagate short waves over long distances, conventional Eulerian numerical methods, which attempt to resolve the structure of each wave, require far too many grid cells and are not feasible on current or foreseeable computers. Instead, we employ an "extended" wave equation that captures the important features of the propagating waves. This method is first formulated at the partial differential equation (PDE) level
Fifth dimension of life and the 4/5 allometric scaling law for human brain.
He, Ji-Huan; Zhang, Juan
2004-01-01
Brain cells are not spherical. The basal metabolic rate (B) of a spherical cell scales as B approximately r2, where r is the radius of the cell; that of a brain cell scales as B approximately r(d), where r is the characteristic radius of the cell and d is the fractal dimensionality of its contour. The fractal geometry of the cell leads to a 4/5 allometric scaling law for human brain, uniquely endowing humans with a 5th dimension and successfully explains why the scaling exponent varies during rest and exercise. A striking analogy between Kleiber's 3/4 law and Newton's second law is heuristically illustrated. A physical explanation is given for the 4th dimension of life for three-dimensional organisms and the 5th dimension for human brain.
New allometric scaling relationships and applications for dose and toxicity extrapolation.
Cao, Qiming; Yu, Jimmy; Connell, Des
2014-01-01
Allometric scaling between metabolic rate, size, body temperature, and other biological traits has found broad applications in ecology, physiology, and particularly in toxicology and pharmacology. Basal metabolic rate (BMR) was observed to scale with body size and temperature. However, the mass scaling exponent was increasingly debated whether it should be 2/3, 3/4, or neither, and scaling with body temperature also attracted recent attention. Based on thermodynamic principles, this work reports 2 new scaling relationships between BMR, size, temperature, and biological time. Good correlations were found with the new scaling relationships, and no universal scaling exponent can be obtained. The new scaling relationships were successfully validated with external toxicological and pharmacological studies. Results also demonstrated that individual extrapolation models can be built to obtain scaling exponent specific to the interested group, which can be practically applied for dose and toxicity extrapolations.
Bentley, Lisa Patrick; Stegen, James C; Savage, Van M; Smith, Duncan D; von Allmen, Erica I; Sperry, John S; Reich, Peter B; Enquist, Brian J
2013-08-01
Several theories predict whole-tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self-similar within trees. However, differences among scaling exponents calculated at node- and whole-tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.
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.
Abad, Cesar C. C.; Barros, Ronaldo V.; Bertuzzi, Romulo; Gagliardi, João F. L.; Lima-Silva, Adriano E.; Lambert, Mike I.
2016-01-01
Abstract The aim of this study was to verify the power of VO2max, peak treadmill running velocity (PTV), and running economy (RE), unadjusted or allometrically adjusted, in predicting 10 km running performance. Eighteen male endurance runners performed: 1) an incremental test to exhaustion to determine VO2max and PTV; 2) a constant submaximal run at 12 km·h−1 on an outdoor track for RE determination; and 3) a 10 km running race. Unadjusted (VO2max, PTV and RE) and adjusted variables (VO2max0.72, PTV0.72 and RE0.60) were investigated through independent multiple regression models to predict 10 km running race time. There were no significant correlations between 10 km running time and either the adjusted or unadjusted VO2max. Significant correlations (p < 0.01) were found between 10 km running time and adjusted and unadjusted RE and PTV, providing models with effect size > 0.84 and power > 0.88. The allometrically adjusted predictive model was composed of PTV0.72 and RE0.60 and explained 83% of the variance in 10 km running time with a standard error of the estimate (SEE) of 1.5 min. The unadjusted model composed of a single PVT accounted for 72% of the variance in 10 km running time (SEE of 1.9 min). Both regression models provided powerful estimates of 10 km running time; however, the unadjusted PTV may provide an uncomplicated estimation. PMID:28149382
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.
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.
Chen, Guangshui; Yang, Yusheng; Robinson, David
2014-05-01
To fully understand how soil respiration is partitioned among its component fluxes and responds to climate, it is essential to relate it to belowground carbon allocation, the ultimate carbon source for soil respiration. This remains one of the largest gaps in knowledge of terrestrial carbon cycling. Here, we synthesize data on gross and net primary production and their components, and soil respiration and its components, from a global forest database, to determine mechanisms governing belowground carbon allocation and their relationship with soil respiration partitioning and soil respiration responses to climatic factors across global forest ecosystems. Our results revealed that there are three independent mechanisms controlling belowground carbon allocation and which influence soil respiration and its partitioning: an allometric constraint; a fine-root production vs. root respiration trade-off; and an above- vs. belowground trade-off in plant carbon. Global patterns in soil respiration and its partitioning are constrained primarily by the allometric allocation, which explains some of the previously ambiguous results reported in the literature. Responses of soil respiration and its components to mean annual temperature, precipitation, and nitrogen deposition can be mediated by changes in belowground carbon allocation. Soil respiration responds to mean annual temperature overwhelmingly through an increasing belowground carbon input as a result of extending total day length of growing season, but not by temperature-driven acceleration of soil carbon decomposition, which argues against the possibility of a strong positive feedback between global warming and soil carbon loss. Different nitrogen loads can trigger distinct belowground carbon allocation mechanisms, which are responsible for different responses of soil respiration to nitrogen addition that have been observed. These results provide new insights into belowground carbon allocation, partitioning of soil
Pretzsch, Hans
2006-01-01
Experimental plots covering a 120 years' observation period in unthinned, even-aged pure stands of common beech (Fagus sylvatica), Norway spruce (Picea abies), Scots pine (Pinus sylvestris), and common oak (Quercus Petraea) are used to scrutinize Reineke's (1933) empirically derived stand density rule [see text], N=tree number per unit area, [see text]=mean stem diameter), Yoda's (1963) self-thinning law based on Euclidian geometry ([see text] [see text]=mean biomass per tree), and basic assumptions of West, Brown and Enquist's (1997, 1999) fractal scaling rules ([see text] [see text] w=biomass per tree, d=stem diameter). RMA and OLS regression provides observed allometric exponents, which are tested against the exponents, expected by the considered rules. Hope for a consistent scaling law fades away, as observed exponents significantly correspond with the considered rules only in a minority of cases: (1) exponent r of [see text] varies around Reineke's constant -1.605, but is significantly different from r=-2, supposed by Euclidian or fractal scaling, (2) Exponent c of the self-thinning line [see text] roams roughly about the Euclidian scaling constant -3/2, (3) Exponent a of [see text] tends to follow fractal scaling 8/3. The unique dataset's evaluation displays that (4) scaling exponents and their oscillation are species-specific, (5) Euclidian scaling of one relation and fractal scaling of another are coupled, depending on species. Ecological implications of the results in respect to self-tolerance (common oak>Norway spruce>Scots pine>common beech) and efficiency of space occupation (common beech>Scots pine>Norway spruce>common oak) are stressed and severe consequences for assessing, regulating and scheduling stand density are discussed.
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.
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
2015-02-23
(3) JC'C' and (3) JHNHα couplings are related to the intervening backbone torsion angle ${\\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\\varphi }$, 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, yields 50-60 % better Karplus equation agreement between ${\\varphi }$ angles and experimental (3) JC'C' and (3) JHNHα values than does the high-resolution X-ray structure. In intrinsically disordered proteins, (3) JC'C' and (3) JHNHα couplings can be measured at even higher accuracy, and the impact of factors other than the intervening torsion angle on (3) J will be smaller than in folded proteins, making these couplings exceptionally valuable reporters on the ensemble of ${\\varphi }$ angles sampled by each residue.
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.
Allometry data and equations for coastal marsh plants.
Lu, Meng; Caplan, Joshua S; Bakker, Jonathan D; Adam Langley, J; Mozdzer, Thomas J; Drake, Bert G; Patrick Megonigal, J
2016-12-01
Coastal marshes are highly valued for ecosystem services such as protecting inland habitats from storms, sequestering carbon, removing nutrients and other pollutants from surface water, and providing habitat for fish, shellfish, and birds. Because plants largely determine the structure and function of coastal marshes, quantifying plant biomass is essential for evaluating these ecosystem services, understanding the biogeochemical processes that regulate ecosystem function, and forecasting tidal wetland responses to accelerated sea level rise. Allometry is a convenient and efficient technique for nondestructive estimation of plant biomass, and it is commonly used in studies of carbon and nitrogen cycles, energy flows, and marsh surface elevation change. We present plant allometry data and models developed for three long-term experiments at the Smithsonian Global Change Research Wetland, a brackish marsh in the Rhode River subestuary of the Chesapeake Bay. The dataset contains 9,771 measurements of stem height, dry mass, and (in 9638 cases) stem width across 11 plant species. The vast majority of observations are for Schoenoplectus americanus (8430) and Phragmites australis (311), with fewer observations for other common species: Amaranthus cannabinus, Atriplex patula, Iva frutescens, Kosteletzkya virginica, Polygonum hydropiper, Solidago sempervirens, Spartina alterniflora, Spartina cynosuroides, and Typha angustifolia. Allometric relationships take the form of linear regressions of biomass (transformed using the Box-Cox procedure) on either stem height and width, or on stem height alone. Allometric relationships for Schoenoplectus americanus were not meaningfully altered by elevated CO2 , N enrichment, the community context, interannual variation in climate, or year, showing that a single equation can be used across a broad range of conditions for this species. Archived files include: (1) raw data used to derive allometric equations for each species, (2) reports and
Fueki, K; Yoshida, E; Igarashi, Y
2011-02-01
The aim of this study was to investigate the relationships between objective masticatory function with respect to masticatory performance and food mixing ability, patients' perception of chewing ability and oral health-related quality of life (OHRQoL). Partially dentate patients with removable partial dentures (n = 131, mean age 67·1 year) participated in the study. Four tests were performed to evaluate objective and subjective masticatory function and OHRQoL. Masticatory performance and food mixing ability were assessed using peanuts or a two-coloured wax cube as test items. Patients' perception of chewing ability was rated using a food intake questionnaire. OHRQoL was measured using the Japanese version of the oral health impact profile. A structural equation model was constructed based on hypothesis in which objective masticatory function would be related to OHRQoL via perceived chewing ability as a mediator. Structural equation modelling analysis found a statistically significant medium effect of perceived chewing ability on OHRQoL and statistically significant medium or small effects of masticatory performance on perceived chewing ability and OHRQoL (P < 0·05); however, the effect of food mixing ability on perceived chewing ability or OHRQoL was not statistically significant (P > 0·05). A fit index indicated that the model fitted well to the data (Goodness-of-fit index = 0·99). These results suggest that perceived chewing ability is a critical factor for OHRQoL and that masticatory performance rather than food mixing ability is important for perceived chewing ability and OHRQoL in patients with removable partial dentures.
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.
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.
Franceschini, T.; Martin-Ducup, O.; Schneider, R.
2016-01-01
Background and Aims Trees invest in both primary (e.g. height) and secondary (e.g. diameter) growth. The trade-off between these investments varies between species and changes with the tree growing environment. To better establish this trade-off, readily available allometric exponents relating height to diameter at breast height (γh,dbh) and stem volume to diameter at breast height (αv,dbh) were simultaneously studied. Methods Allometric exponents αv,dbh and γh,dbh were obtained from 8893 individual tree stem analyses from two broadleaved species (Betula papyrifera, Populus tremuloides) and four conifers (Picea glauca, Picea mariana, Pinus banksiana, Abies balsamea) in the temperate and boreal forests of the province of Quebec, Canada. αv,dbh and γh,dbh were related to tree age, stand density index (SDI), and mean temperature (TGS) and total precipitation (PGS) of the growing season. Key Results αv,dbh and γh,dbh were found to be invariant with PGS and positively related to SDI and TGS for all species except Pinus banksiana . The parameter values associated with SDI and TGS were of higher value for conifers than for broadleaved species. Conclusions This suggests that conifers and broadleaved species have different growth patterns. This could be explained by their different mode of development, the conifer species having a stronger apical dominance than broadleaved species. Such results could be further considered in allocation studies to quantify future carbon stocks in managed forests. PMID:26975315
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.
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.
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
McGregor, B A; Butler, K L
2016-12-01
The mean fibre diameter (MFD) of wool is the primary determinant of price, processing performance and textile quality. This study determines the primary influences on MFD as Saxon Merino sheep age, by allometrically relating MFD to fleece-free liveweight (FFLwt). In total, 79 sheep were grazed in combinations of three stocking rates and two grazing systems (GS: sheep only; mixed with Angora goats) and studied over 3 years. Measurements were made over 14 consecutive periods (Segments), including segments of FFLwt gain or FFLwt loss. Using shearing and liveweight records and dye-bands on wool, the FFLwt and average daily gain (ADG) of each sheep were determined for each segment. The mean and range in key measurements were as follows: FFLwt, 40.1 (23.1 to 64.1) kg; MFD, 18.8 (12.7 to 25.8) μm. A random coefficient restricted maximum likelihood (REML) regression mixed model was developed to relate the logarithm of MFD to the logarithm of FFLwt and other effects. The model can be written in the form of ${\\rm MFD}\\,{\\equals}\\,\\rkappa \\left( {{\\rm GS,}\\,{\\rm A}{\\rm ,}\\,{\\rm Segment}{\\rm .Plot,}\\,{\\rm Segment,}\\,{\\rm ADG}} \\right){\\times}{\\rm FFLwt}^{{\\left( {\\ralpha \\left( {{\\rm GS}} \\right){\\plus}\\rbeta \\left(\\rm A \\right){\\plus}\\rgamma \\left( {{\\rm Segment}{\\rm .Plot}} \\right)} \\right)}} $ , where $\\ralpha \\left( {{\\rm GS}} \\right)\\,{\\equals}\\,\\;\\left\\{ {\\matrix{\\!\\! {0.32\\left( {{\\rm SE}\\,{\\equals}\\,{\\rm 0}{\\rm .038}} \\right)\\,{\\rm when}\\,{\\rm sheep}\\,{\\rm are}\\,{\\rm grazed}\\,{\\rm alone}} \\hfill \\cr \\!\\!\\!\\!{0.49\\left( {{\\rm SE}\\,{\\equals}\\,{\\rm 0}{\\rm .049}} \\right)\\,{\\rm when}\\,{\\rm sheep}\\,{\\rm are}\\,{\\rm mixed}\\,{\\rm with}\\,{\\rm goats}} \\hfill \\cr } } \\right.$ β(A) is a random animal effect, γ(Segment.Plot) a random effect associated with Segment.plot combinations, and κ a constant that depends on GS, random animal effects, random Segment.plot combination effects
Mankiw, Catherine; Park, Min Tae M; Reardon, P K; Fish, Ari M; Clasen, Liv S; Greenstein, Deanna; Giedd, Jay N; Blumenthal, Jonathan D; Lerch, Jason P; Chakravarty, M Mallar; Raznahan, Armin
2017-03-17
The cerebellum is a large hindbrain structure that is increasingly recognized for its contribution to diverse domains of cognitive and affective processing in human health and disease. Although several of these domains are sex-biased, our fundamental understanding of cerebellar sex differences - including their spatial distribution, potential biological determinants, and independence from brain volume variation - lags far behind that for the cerebrum. Here, we harness automated neuroimaging methods for cerebellar morphometrics in 417 individuals to (i) localize normative male-female differences in raw cerebellar volume, (ii) compare these to sex chromosome effects estimated across five rare X-/Y-chromosome aneuploidy (SCA) syndromes, and (iii) clarify brain size-independent effects of sex and SCA on cerebellar anatomy using a generalizable allometric approach which considers scaling relationships between regional cerebellar volume and brain volume in health. Integration of these approaches shows that (i) sex and SCA effects on raw cerebellar volume are large and distributed, but regionally heterogeneous, (ii) human cerebellar volume scales with brain volume in a highly non-linear and regionally heterogeneous fashion that departs from documented patterns of cerebellar scaling in phylogeny, and (iii) cerebellar organization is modified in a brain size-independent manner by sex (relative expansion of total cerebellum, flocculus, and Crus II-lobule VIIIB volumes in males) and SCA (contraction of total cerebellar, lobule IV and Crus I volumes with additional X- or Y-chromosomes; X-specific contraction of Crus II-lobule VIIIB). Our methods and results clarify the shifts in human cerebellar organization that accompany interwoven variations in sex, sex chromosome complement, and brain size.SIGNIFICANCE STATEMENTCerebellar systems are implicated in diverse domains of sex-biased behavior and pathology, but we lack a basic understanding of how sex differences in the human
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.
Naliboff, Bruce D.; Kim, Sharon E.; Bolus, Roger; Bernstein, Charles N.; Mayer, Emeran A.; Chang, Lin
2013-01-01
Objective Inflammatory bowel disease (IBD) and irritable bowel syndrome (IBS) are chronic gastrointestinal (GI) syndromes in which both GI and psychological symptoms have been shown to negatively impact health-related quality of life (HRQOL). The objective of this study was to use structural equation modeling (SEM) to characterize the interrelationships among HRQOL, GI, and psychological symptoms to improve our understanding of the illness processes in both conditions. Methods Study participants included 564 Rome positive IBS patients and 126 IBD patients diagnosed via endoscopic and / or tissue confirmation. All patients completed questionnaires to assess bowel symptoms, psychological symptoms (SCL-90R), and HRQOL (SF-36). SEM with its two components of confirmatory analyses and structural modeling were applied to determine the relationships between GI and psychological symptoms and HRQOL within the IBS and IBD groups. Results For both IBD and IBS, psychological distress was found to have a stronger direct effect on HRQOL(−0.51 and −0.48 for IBS and IBD, respectively) than GI symptoms (−0.25 and −0.28). The impact of GI symptoms on psychological distress was stronger in IBD compared with IBS (0.43 vs. 0.22; P <0.05). The indirect effect of GI symptoms on HRQOL operating through psychological distress was significantly higher in IBD than IBS (−0.21 vs. −0.11; P <0.05). Conclusions Psychological distress is less dependent on GI symptom severity in IBS compared with IBD even though the degree that psychological distress impacts HRQOL is similar. The findings emphasize the importance of addressing psychological symptoms in both syndromes. PMID:22085819
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
Cheng, Dongliang; Ma, Yuzhu; Zhong, Quanling; Xu, Weifeng
2014-10-01
Allometric biomass allocation theory predicts that leaf biomass (M L ) scaled isometrically with stem (M S ) and root (M R ) biomass, and thus above-ground biomass (leaf and stem) (M A ) and root (M R ) 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 M L and M S scaled in an isometric or a nearly isometric manner with M R , as well as M A to M R 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 M L versus M S and M L versus M R , but not for M S versus M R and M A versus M R . We conclude, therefore, that a nearly isometric scaling relationship of M A versus M R holds true within each of the studied woody species and across them irrespective the negative scaling relationship between leaf and stem.
Jayasundara, Nishad; Kozal, Jordan S.; Arnold, Mariah C.; Chan, Sherine S. L.; Di Giulio, Richard T.
2015-01-01
Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO2), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO2 scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO2) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism’s vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate—a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in
Jayasundara, Nishad; Kozal, Jordan S; Arnold, Mariah C; Chan, Sherine S L; Di Giulio, Richard T
2015-01-01
Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO2), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO2 scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO2) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism's vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate-a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in
Duconge, Jorge; Castillo, Rubén; Crombet, Tania; Alvarez, Daniel; Matheu, Janet; Vecino, Gloria; Alonso, Katia; Beausoleil, Irene; Valenzuela, Carmen; Becquer, Maria A; Fernández-Sánchez, Eduardo
2004-02-01
The multiple-dose strategy with the monoclonal ior EGF/r3 antibody, in xenograft bearing nude mice, was supported upon the basis of its integrated pharmacokinetic-pharmacodynamic relationship, according to both the temporal (K(e0)=0.0015+/-0.000035h(-1)) and the time-independent sensitivity (C(50%)(ss), 9.23+/-0.17microg/ml; C(max,eff)(ss), 12.5microg/ml) components of its tumor growth delay action. This relationship was consistent with a sigmoidal E(max) pharmacodynamic model postulating a hypothetical effect compartment that permits us to estimate an effective steady-state concentration range (7.5-12microg/ml). Using this information we calculated both the cumulative and non-cumulative dosage regimens to compare their response patterns with respect to the control group. It follows that the differences in the estimated tumor growth inhibition ratio were statistically significant between the control group and either of the treated ones (P<0.05). The median survival time in treated mice under non-cumulative regimen (72+/-10 days), predicted an increase in this parameter as compared to the control one (55+/-6 days). Finally, using the allometric paradigm, the empiric power equation for dose scaling across mammalian species allowed the calculation of the dosage schedule for further clinical trial. The estimated maintenance dose in human (70kg) was 200mg/m(2) to be given weekly, and the corresponding loading dose was 600mg/m(2).
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.
Schaeper, Nina D; Prpic, Nikola-Michael; Wimmer, Ernst A
2009-08-01
The genes encoding the closely related zinc finger transcription factors Buttonhead (Btd) and D-Sp1 are expressed in the developing limb primordia of Drosophila melanogaster and are required for normal growth of the legs. The D-Sp1 homolog of the red flour beetle Tribolium castaneum, Sp8 (appropriately termed Sp8/9), is also required for the proper growth of the leg segments. Here we report on the isolation and functional study of the Sp8/9 gene from the milkweed bug Oncopeltus fasciatus. We show that Sp8/9 is expressed in the developing appendages throughout development and that the downregulation of Sp8/9 via RNAi leads to antennae, rostrum, and legs with shortened and fused segments. This supports a conserved role of Sp8/9 in allometric leg segment growth. However, all leg segments including the claws are present and the expression of the leg genes Distal-less, dachshund, and homothorax are proportionally normal, thus providing no evidence for a role of Sp8/9 in appendage specification.
Parametrically defined differential equations
NASA Astrophysics Data System (ADS)
Polyanin, A. D.; Zhurov, A. I.
2017-01-01
The paper deals with nonlinear ordinary differential equations defined parametrically by two relations. It proposes techniques to reduce such equations, of the first or second order, to standard systems of ordinary differential equations. It obtains the general solution to some classes of nonlinear parametrically defined ODEs dependent on arbitrary functions. It outlines procedures for the numerical solution of the Cauchy problem for parametrically defined differential equations.
Alexander, K.S.; Dollimore, D.; Tata, S.S.; Uppala, V. )
1991-01-01
Steinour and Richardson and Zaki proposed relationships to explain the hindered settling phenomena from their independent experiments about 10 years apart. An attempt has been made to compare the coefficients and derive a relationship between Steinour's parameter A and Richardson and Zaki's parameter n. It is possible to express this relationship in the form of an equation involving parameters for which values can be assigned. Theoretically, this derived relationship should be applicable to any sedimenting suspension which obeys both Steinour's and Richardson and Zaki's equations. This derived expression has been evaluated for various experimentally determined values of A and n. The experimental systems which have been tested include calcium carbonate suspensions in water, sucrose-water, and glycerin-water solutions, and ethyl alcohol and magnesium hydroxide suspensions in glycerin-water, sucrose-water and sorbitol-water solutions. The calculated values have been shown to agree well with experimentally predicted values.
Urošević, Aleksandar; Ljubisavljević, Katarina; Jelić, Dušan; Ivanović, Ana
2012-08-01
We used geometric morphometrics to explore the influence of phylogenetic and allometric constraints as well as ecology on variation in cranium shape in five species of monophyletic, morphologically similar Podarcis lizards (Podarcis erhardii, Podarcis melisellensis, Podarcis muralis, Podarcis sicula and Podarcis taurica). These species belong to different clades, they differ in their habitat preferences and can be classified into two distinct morphotypes: saxicolous and terrestrial. We found (i) no phylogenetic signal in cranium shape, (ii) diverging allometric slopes among species, and (iii) a significant effect of habitat on cranium shape. The saxicolous species (P. erhardii and P. muralis) had crania with elongated parietals, elongated cranium bases, shortened anterior parts of the dorsal cranium, reduced chambers of the jaw adductor muscles and larger subocular foramina. These cranial features are adaptations that compensate for a flattened cranium, dwelling on vertical surfaces and seeking refuge in crevices. The crania of the terrestrial species (P. melisellensis, P. sicula and P. taurica) tended to be more elongate and robust, with enlarged chambers of the jaw adductor muscle, reduced skull bases and shortened parietals. Terrestrial species exhibited more variation in cranium shape than saxicolous species. Our study suggests that shape variation in Podarcis sp. lizards is largely influenced by ecology, which likely affects species-specific patterns of static allometry.
Gingerich, P D; Smith, B H; Rosenberg, K
1982-05-01
Tooth size varies exponentially with body weight in primates. Logarithmic transformation of tooth crown area and body weight yields a linear model of slope 0.67 as an isometric (geometric) baseline for study of dental allometry. This model is compared with that predicted by metabolic scaling (slope = 0.75). Tarsius and other insectivores have larger teeth for their body size than generalized primates do and they are not included in this analysis. Among generalized primates, tooth size is highly correlated with body size. Correlations of upper and lower cheek teeth with body size range from 0.90-0.97, depending on tooth position. Central cheek teeth (P44 and M11) have allometric coefficients ranging from 0.57-0.65, falling well below geometric scaling. Anterior and posterior cheek teeth scale at or above metabolic scaling. Considered individually or as a group, upper cheek teeth scale allometrically with lower coefficients than corresponding lower cheek teeth; the reverse is true for incisors. The sum of crown areas for all upper cheek teeth scales significantly below geometric scaling, while the sum of crown areas for all lower cheek teeth approximates geometric scaling. Tooth size can be used to predict the body weight of generalized fossil primates. This is illustrated for Aegyptopithecus and other Eocene, Oligocene, and miocene primates. Regressions based on tooth size in generalized primates yield reasonable estimates of body weight, but much remains to be learned about tooth size and body size scaling in more restricted systematic groups and dietary guilds.
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.
Duncan, Michael J.; Mota, Jorge; Carvalho, Joana; Nevill, Alan M.
2015-01-01
Objective This study compared actual 6 minute walk test (6MWT) performance with predicted 6MWT using previously validated equations and then determined whether allometric modelling offers a sounder alternative to estimating 6MWT in adults aged 50–80 years. Methods We compared actual 6MWT performance against predicted 6MWT in 125 adults aged 50–85 years (62 male, 63 female). In a second sample of 246 adults aged 50–85 years (74 male, 172 female), a new prediction equation for 6MWT performance was developed using allometric modelling. This equation was then cross validated using the same sample that the other prediction equations were compared with. Results Significant relationships were evident between 6MWT actual and 6MWT predicted using all of the commonly available prediction equations (all P<0.05 or better) with the exception of the Alameri et al prediction equation (P>0.05). A series of paired t-tests indicated significant differences between 6MWT actual and 6MWT predicted for all available prediction equations (all P<0.05 or better) with the exception of the Iwama et al equation (P = .540). The Iwama et al equation also had similar bias (79.8m) and a coefficient of variation of over 15%. Using sample 2, a log-linear model significantly predicted 6MWT from the log of body mass and height and age (P = 0.001, adjusted R2 = .526), predicting 52.6% of the variance in actual 6MWT. When this allometric equation was applied to the original sample, the relationship between 6MWT actual and 6MWT predicted was in excess of values reported for the other previously validated prediction equations (r = .706, P = 0.001). There was a significant difference between actual 6MWT and 6MWT predicted using this new equation (P = 0.001) but the bias, standard deviation of differences and coefficient of variation were all less than for the other equations. Conclusions Where actual assessment of the 6MWT is not possible, the allometrically derived equation presented in the current
NASA Astrophysics Data System (ADS)
Boubaker, K.; Bhrawy, A. H.
2012-03-01
In this paper, Bonnor-Ebert gas sphere model of polytropic stars has been investigated through an analytical approach. Two confirmed and well-established methods have been used: the Enhanced Lagrangian Formulation Method ELFM and the Boubaker Polynomials Expansion Scheme BPES. Solutions to the related generalized Lane-Emden equation of the second kind have been expressed and plotted. Results have given evidence to the relevance of the dimensionless Bonnor-Ebert radius, in good agreement with some recently proposed profiles.
NASA Astrophysics Data System (ADS)
Kawakami, Hajime; Tsuchiya, Masaaki
2010-12-01
The paper deals with an inverse problem determining the shape of a time-varying Lipschitz domain by boundary measurements of the temperature; such a domain is treated as a non-cylindrical domain in the time-space. Here we focus on the uniqueness of the shape identification. As a general treatment to show the uniqueness, a comparability condition on a pair of domains is introduced; the condition holds automatically in the time-independent case. Based on the condition, we provide several classes of domains in which the uniqueness of the shape identification holds under an appropriate initial shape condition or initial temperature condition. Each of such classes is characterized by a certain geometric condition on its each single element; in particular, it is verified that the class of polyhedral domains and any class of domains with C1 smoothness and with a common initial shape fulfil the uniqueness property. The inverse problem is studied via a parabolic equation with a mixed boundary condition. Then the unique continuation property of weak solutions and the uniqueness of weak solutions to an induced parabolic equation with the homogeneous Dirichlet boundary condition on a non-cylindrical non-Lipschitz domain play key roles. This work was partially supported by JSPS Grant-in-Aid for Scientific Research 21540160.
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.
Nonlinear equations of 'variable type'
NASA Astrophysics Data System (ADS)
Larkin, N. A.; Novikov, V. A.; Ianenko, N. N.
In this monograph, new scientific results related to the theory of equations of 'variable type' are presented. Equations of 'variable type' are equations for which the original type is not preserved within the entire domain of coefficient definition. This part of the theory of differential equations with partial derivatives has been developed intensively in connection with the requirements of mechanics. The relations between equations of the considered type and the problems of mathematical physics are explored, taking into account quasi-linear equations, and models of mathematical physics which lead to equations of 'variable type'. Such models are related to transonic flows, problems involving a separation of the boundary layer, gasdynamics and the van der Waals equation, shock wave phenomena, and a combustion model with a turbulent diffusion flame. Attention is also given to nonlinear parabolic equations, and nonlinear partial differential equations of the third order.
NASA Astrophysics Data System (ADS)
Cartailler, J.; Schuss, Z.; Holcman, D.
2017-01-01
The electro-diffusion of ions is often described by the Poisson-Nernst-Planck (PNP) equations, which couple nonlinearly the charge concentration and the electric potential. This model is used, among others, to describe the motion of ions in neuronal micro-compartments. It remains at this time an open question how to determine the relaxation and the steady state distribution of voltage when an initial charge of ions is injected into a domain bounded by an impermeable dielectric membrane. The purpose of this paper is to construct an asymptotic approximation to the solution of the stationary PNP equations in a d-dimensional ball (d = 1 , 2 , 3) in the limit of large total charge. In this geometry the PNP system reduces to the Liouville-Gelfand-Bratú (LGB) equation, with the difference that the boundary condition is Neumann, not Dirichlet, and there is a minus sign in the exponent of the exponential term. The entire boundary is impermeable to ions and the electric field satisfies the compatibility condition of Poisson's equation. These differences replace attraction by repulsion in the LGB equation, thus completely changing the solution. We find that the voltage is maximal in the center and decreases toward the boundary. We also find that the potential drop between the center and the surface increases logarithmically in the total number of charges and not linearly, as in classical capacitance theory. This logarithmic singularity is obtained for d = 3 from an asymptotic argument and cannot be derived from the analysis of the phase portrait. These results are used to derive the relation between the outward current and the voltage in a dendritic spine, which is idealized as a dielectric sphere connected smoothly to the nerve axon by a narrow neck. This is a fundamental microdomain involved in neuronal communication. We compute the escape rate of an ion from the steady density in a ball, which models a neuronal spine head, to a small absorbing window in the sphere. We
Uthman, Olalekan A.; Moradi, Tahereh; Lawoko, Stephen
2011-01-01
Background Intimate partner violence against women (IPVAW) is a serious and widespread problem worldwide. Much of the research on IPVAW focused on individual-level factors and attention has been paid to the contextual factors. The aim of this study was to develop and test a model of individual- and community-level factors associated with IPVAW. Methods and Findings We conducted a (multivariate) multilevel structural equation analysis on 8731 couples nested within 883 communities in Nigerian Demographic and Health Survey 2008. Variables included in the model were derived from respondents' answers to the experience of IPVAW, attitudes towards wife beating and witnessing physical violence in childhood. We found that women that witnessed physical violence were more likely to have tolerant attitudes towards IPVAW and women with tolerant attitudes were more likely to have reported spousal IPVAW abuse. Women with husbands with tolerant attitudes towards IPVAW were more likely to have reported spousal abuse. We found that an increasing proportion of women in the community with tolerant attitudes was significantly positively associated with spousal sexual and emotional abuse, but not significantly associated with spousal physical abuse. In addition, we found that an increasing proportion of men in the community with tolerant attitudes and an increasing proportion of women who had witnessed physical violence in the community was significantly positively associated with spousal physical abuse, but not significantly associated with spousal sexual and emotional abuse. There was a positive correlation between all three types of IPVAW at individual- and community-level. Conclusions We found that community tolerant attitudes context in which people live is associated with exposure to IPVAW even after taking into account individual tolerant attitudes. Public health interventions designed to reduce IPVAW must address people and the communities in which they live in order to be
Benítez, Hugo A.; Bravi, Raffaella; Parra, Luis E.; Sanzana, Maria-Jose; Sepúlveda-Zúñiga, Einer
2013-01-01
Bees and wasps could exhibit shape and size sexual dimorphism, and most of their morphological variation could depend on phenotypic responses due to environmental pressure during ontogenetic development. More complex measurement techniques related to size and shape rather than simply to mass and length should be required to analyze such a complex sexual dimorphism. In this study, differences related to wing shape and size of males and females of Ophion intricatus Brullé (Hymenoptera: Ichneumonidae) were evaluated using geometric morphometrics. Right and left wings of specimens were used, and a photographic matrix was constructed in which 18 morphological landmarks based on shape and vein patterns of the wings were digitalized. A multivariate analysis of wing shape showed significant differences between sexes and sites. The geometric variation demonstrated that the points at the intersection of radial and cubital-anal veins might be key characters to differentiate between sexes. This study also showed the presence of two clearly different male morphotypes coexisting in the same study site. However, it should be noted that the results of this study showed that the variation in wing shape is an analytical character in the determination of sexual differences in the family Ichneumonidae. These differences raise the question of whether sexual dimorphism of wing shape may be modulated by natural selection. PMID:24766555
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)
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
NASA Astrophysics Data System (ADS)
Guan, Jian; Liu, Zhengyu; Wen, Xinyu; Brady, Esther; Noone, David; Zhu, Jiang; Han, Jing
2016-09-01
The temporal and spatial slopes of water isotope-temperature relations are studied for the last 21,000 years over the middle and high latitudes using a series of snapshot simulations of global climate and water isotopes in the isotope-enabled atmospheric model isoCAM3. Our model simulation suggests that both the temporal slope and spatial slope remain largely stable throughout the last deglaciation. Furthermore, the temporal slope can vary substantially across regions. Nevertheless, on average, and most likely, the temporal slope is about 0.3‰ °C-1 and is about half of the spatial slope. Finally, the relation between temporal and spatial slopes is understood using a semiempirical equation that is derived based on both the Rayleigh distillation and a fixed spatial slope. The slope equation quantifies the Boyle's mechanism and suggests that the temporal slope is usually smaller than the spatial slope in the extratropics mainly because of the polar amplification feature in global climate change, such that the response in local temperature at middle and high latitudes is usually greater than that in the total equivalent source temperature.
NASA Technical Reports Server (NTRS)
Eades, J. B., Jr.
1974-01-01
The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.
Craig, Jaquelyn M.; 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.
Vatsalya, Vatsalya; Arora, Kashmiri L
2012-01-01
The Japanese quail is a very valuable animal model for research in a variety of biological disciplines. The purpose of this study was to characterize and interrelate age-dependent testicular parameters with various blood constituents: blood glucose, plasma proteins and packed cell volume that are developing concurrently in the growing bird. Another objective of the study was to identify selective physioanatomical markers for predicting the testicular growth and the onset of sexual maturity. Male Japanese quail hatchlings were raised in temperature controlled brooders for up to 3 weeks of age under a constant light and then shifted to hanging cages in an air conditioned room set at ~73° F under a 14L: 10D lighting system and ad libitum access to feed and water. Starting d8, a group of 8-10 birds of uniform size and weight were selected randomly at 4-day intervals up to d52 of age for the project. The birds were weighed and blood sampled using the brachial vein and Blood Glucose (BGL), Total Plasma Proteins (PP) and Packed Cell Volume (PCV) levels were measured prior to euthanization. The testes were removed and measured for weight, length, width and Volume (VOL). All the testicular measurements were then correlated with age and body weight. The left testes were larger than the right testes and their differences were evident at d36 of age. Testicular measurements also reflected two distinct growth surges at d28, d32 and d36 of age. Combined Testes Weight (CTW) and Combined Testes Volume (CTV) revealed a strong positive correlation with PCV and PP and a negative correlation with Blood Glucose Level (BGL). Accordingly, these measurements could serve as reliable markers of growth rate and sexual maturation in male Japanese quail.
NASA Astrophysics Data System (ADS)
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
NASA Astrophysics Data System (ADS)
Ndeda, J. O. H.; Rabiu, A. B.; Ngoo, L. H. M.; Ouma, G. O.
2006-11-01
This paper investigates the inter-relationship between solar radiation intensity RD and relative humidity RH in Kenya using daily data obtained at five meteorological stations; Nairobi (1.3°S, 36.75°E), Kericho (0.37˚S, 35.72˚E), Kisumu (0.10˚S, 34.75˚E), Mombasa (4.03˚S, 39.65˚E) and Garissa (0.48˚S, 39.63˚E) during the solar minimum year 1986. Statistical methods were employed and the coefficients of correlation, r obtained range from 0.16094 to -0.6758618 between the two variables for the five stations. The linear equation relating the solar radiation intensity RD to relative humidity RH is obtained using linear regression analysis as RH = 109.1091-1.5997RD for the Nairobi station. Jandel scientific and Megastat software analyses gave fairly similar trends of results for Nairobi and other stations, and for all the seasons except for those of Garissa station. Obviously there exists a negative interdependence between solar radiation intensity and relative humidity such that the relative humidity decreases as solar radiation increases and vice versa. This observation is explicable in terms of the dynamics of atmospheric heating and advection traceable to solar activity.
Nooe, Allison; Edwards, Meghan K; Addoh, Ovuokerie; Loprinzi, Paul D
2017-01-01
Background: The potential convergent validity of the pooled cohort risk (PCR) equations in predicting health-related quality of life (HRQOL) has yet to be evaluated, which was this study's purpose. Methods: Data from the 2001-2011 National Health and Nutrition Examination Survey (NHANES) were used (N = 8978 adults, 40-79 years, free of cardiovascular disease at baseline). Calculation of an individual's 10-year risk of a first atherosclerotic cardiovascular disease (ASCVD) event was determined via the PCR equation. The Centers for Disease Control and Prevention (CDC) HRQOL measure was assessed utilizing 4 questions regarding participants' perceived mental and physical health status from the past 30 days. Results: When adjusting for moderate-to-vigorous physical activity (MVPA), obesity, age, gender and race-ethnicity, an ASCVD score of >20% (vs. <20%) was associated with a 0.53-unit (95% CI: 0.34-0.71) higher HRQOL score. A higher HRQOL score indicates a poorer patient perception of their mental and physical health. Conclusion: The observed association between PCR-determined ASCVD-risk scores and HRQOL provides evidence for the convergent validity of the PCR algorithms, indicating that individuals with a higher risk for a first time ASCVD-event may also have an overall worse HRQOL. As such, employing ASCVD risk reduction efforts may be an important strategy in improving an individual's HRQOL.
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.
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)
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)
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.
NASA Astrophysics Data System (ADS)
Rasmussen, Mads Olander; Göttsche, Frank-M.; Diop, Doudou; Mbow, Cheikh; Olesen, Folke-S.; Fensholt, Rasmus; Sandholt, Inge
2011-08-01
A tree survey and an analysis of high resolution satellite data were performed to characterise the woody vegetation within a 10 × 10 km 2 area around a site located close to the town of Dahra in the semi-arid northern part of Senegal. The surveyed parameters were tree species, height, tree crown radius, and diameter at breast height (DBH), for which allometric models were determined. An object-based classification method was used to determine tree crown cover (TCC) from Quickbird data. The average TCC from the tree survey and the respective TCC from remote sensing were both about 3.0%. For areas beyond the surveyed areas TCC varied between 3.0% and 4.5%. Furthermore, an empirical correction factor for tree clumping was obtained, which considerably improved the estimated number of trees and the estimated average tree crown area and radius. An allometric model linking TCC to tree stem crosssectional area (CSA) was developed, which allows to estimate tree biomass from remote sensing. The allometric models for the three main tree species found performed well and had r2-values of about 0.7-0.8.
Bergland, Alan O.; Genissel, Anne; Nuzhdin, Sergey V.; Tatar, Marc
2008-01-01
Environmental factors during juvenile growth such as temperature and nutrition have major effects on adult morphology and life-history traits. In Drosophila melanogaster, ovary size, measured as ovariole number, and body size, measured as thorax length, are developmentally plastic traits with respect to larval nutrition. Herein we investigated the genetic basis for plasticity of ovariole number and body size, as well the genetic basis for their allometric relationship using recombinant inbred lines (RILs) derived from a natural population in Winters, California. We reared 196 RILs in four yeast concentrations and measured ovariole number and body size. The genetic correlation between ovariole number and thorax length was positive, but the strength of this correlation decreased with increasing yeast concentration. Genetic variation and genotype-by-environment (G × E) interactions were observed for both traits. We identified quantitative trait loci (QTL), epistatic, QTL-by-environment, and epistatic-by-environment interactions for both traits and their scaling relationships. The results are discussed in the context of multivariate trait evolution. PMID:18716336
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.
Logie, Carmen H.; Jenkinson, Jesse I. R.; Earnshaw, Valerie; Tharao, Wangari; Loutfy, Mona R.
2016-01-01
African and Caribbean Black women in Canada have new HIV infection rates 7 times higher than their white counterparts. This overrepresentation is situated in structural contexts of inequities that result in social, economic and health disparities among African and Caribbean Black populations. Economic insecurity is a distal driver of HIV vulnerability, reducing access to HIV testing, prevention and care. Less is known about how economic insecurity indicators, such as housing security, continue to influence the lives of women living with HIV following HIV-positive diagnoses. The aim of this study was to test a conceptual model of the pathways linking HIV-related stigma, racial discrimination, housing insecurity, and wellbeing (depression, social support, self-rated health). We implemented a cross-sectional survey with African and Caribbean Black women living with HIV in 5 Ontario cities, and included 157 participants with complete data in the analyses. We conducted structural equation modeling using maximum likelihood estimation to evaluate the hypothesized conceptual model. One-fifth (22.5%; n = 39) of participants reported housing insecurity. As hypothesized, racial discrimination had significant direct effects on: HIV-related stigma, depression and social support, and an indirect effect on self-rated health via HIV-related stigma. HIV-related stigma and housing insecurity had direct effects on depression and social support, and HIV-related stigma had a direct effect on self-rated health. The model fit the data well: χ2 (45, n = 154) = 54.28, p = 0.387; CFI = 0.997; TLI = 0.996; RMSEA = 0.016. Findings highlight the need to address housing insecurity and intersecting forms of stigma and discrimination among African and Caribbean Black women living with HIV. Understanding the complex relationships between housing insecurity, HIV-related stigma, racial discrimination, and wellbeing can inform multi-level interventions to reduce stigma and enhance health. PMID
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.
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
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.
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.
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
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.
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
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
2013-05-07
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.
Driving forces from soil invertebrates to ecosystem functioning: the allometric perspective
NASA Astrophysics Data System (ADS)
Mulder, Christian
2006-10-01
The European soil policy is being focussed towards a more conscious and sustainable use of the soil, taking into account ecological, economical and societal dimensions. Living soil organisms are reliable bioindicators, as they provide the best reflection of the soil system, ecological services and ecosystem functioning therein. These most complex (bio)physical systems indicate, among others, the energy flow. Such processes can be described by rather simple power law relationships. In fact, the average body mass (dry weight) can be seen as an inherent species property, while population density is a much more flexible parameter reflecting ecosystem state. In this study, I review the interactions between these items in relation to feedbacks and conjectured relationships which can be seen as ecological networks. From this novel perspective, allometry can be used as an integrated measure for the anthropogenic influence on landscapes and related food webs. Allometry is, therefore, a perfect surrogate for land use intensity in modelling of field effects for restoration ecology and conservation biology. Robust correlations will be addressed between the density dependence of invertebrates and the ability of soil systems themselves to recover after disturbance. Quantitative indicators of soil community composition and related ecological services are proposed and their application for ecological risk assessment is illustrated.
Driving forces from soil invertebrates to ecosystem functioning: the allometric perspective.
Mulder, Christian
2006-10-01
The European soil policy is being focussed towards a more conscious and sustainable use of the soil, taking into account ecological, economical and societal dimensions. Living soil organisms are reliable bioindicators, as they provide the best reflection of the soil system, ecological services and ecosystem functioning therein. These most complex (bio)physical systems indicate, among others, the energy flow. Such processes can be described by rather simple power law relationships. In fact, the average body mass (dry weight) can be seen as an inherent species property, while population density is a much more flexible parameter reflecting ecosystem state. In this study, I review the interactions between these items in relation to feedbacks and conjectured relationships which can be seen as ecological networks. From this novel perspective, allometry can be used as an integrated measure for the anthropogenic influence on landscapes and related food webs. Allometry is, therefore, a perfect surrogate for land use intensity in modelling of field effects for restoration ecology and conservation biology. Robust correlations will be addressed between the density dependence of invertebrates and the ability of soil systems themselves to recover after disturbance. Quantitative indicators of soil community composition and related ecological services are proposed and their application for ecological risk assessment is illustrated.
Poźniak, B; Pawłowski, P; Pasławska, U; Grabowski, T; Suszko, A; Lis, M; Świtała, M
2017-04-01
1. The aim of this study was to determine if the pharmacokinetics (PK) of florfenicol (FF) undergo age-dependent changes in broilers. Since drug elimination depends on cardiovascular functions, a haemodynamic study was performed in parallel. 2. Broilers of 0.68, 1.27, 2.45 and 5.13 kg were administered FF in a single intravenous dose of 30 mg/kg body weight. Plasma drug concentrations were determined using high-performance liquid chromatography and PK parameters were calculated using a non-compartmental model. Echocardiography was used to measure haemodynamic functions. 3. During growth, the area under the drug concentration-time curve (AUCinf) increased from 25.7 ± 2.9 to 39.0 ± 8.0 mg h/l. Total body clearance (ClB) gradually decreased from 1.19 ± 0.14 to 0.80 ± 0.15 l/h/kg. Elimination half-life increased from 0.73 ± 0.08 to 1.07 ± 0.07 h, whereas volume of distribution (Vss) remained unchanged. Haemodynamic measurements revealed an increase in cardiac output, from 495 ± 65 to 1303 ± 306 ml/min, in the respective body weight groups. 4. Allometric models for PK and haemodynamic parameters were developed and validated. All models proved to be statistically significant; however, only models for ClB and Vss met stringent validation criteria. Model for ClB was used to calculate an optimal dose for a given age group that provides uniform AUCinf. 5. Age-dependent change in FF kinetics may cause variability in therapeutic response under clinical conditions. A novel approach to the dosing protocol was proposed as a means of optimising therapeutic efficacy.
Cunha, Giovani; Lorenzi, Thiago; Sapata, Katiuce; Lopes, Andre Luiz; Gaya, Adroaldo Cezar; Oliveira, Álvaro
2011-07-01
In this study, we investigated the effect of biological maturation on maximal oxygen uptake ([Vdot]O(2max)) and ventilatory thresholds (VT(1) and VT(2)) in 110 young soccer players separated into pubescent and post-pubescent groups.. Maximal oxygen uptake and [Vdot]O(2) corresponding to VT(1) and VT(2) were expressed as absolute values, ratio standards, theoretical exponents, and experimentally observed exponents. Absolute [Vdot]O(2) (ml · min(-1)) was different between groups for VT(1), VT(2), and [Vdot]O(2max). Ratio standards (ml · kg(-1) · min(-1)) were not significantly different between groups for VT(1), VT(2), and [Vdot]O(2max). Theoretical exponents (ml · kg(-0.67) · min(-1) and ml · kg(-0.75) · min(-1)) were not properly adjusted for the body mass effects on VT(1), VT(2), and [Vdot]O(2max). When the data were correctly adjusted using experimentally observed exponents, VT(1) (ml · kg(-0.94) · min(-1)) and VT(2) (ml · kg(-0.95) · min(-1)) were not different between groups. The experimentally observed exponent for [Vdot]O(2max) (ml · kg(-0.90) · min(-1)) was different between groups (P = 0.048); however, this difference could not be attributed to biological maturation. In conclusion, biological maturation had no effect on VT(1), VT(2) or [Vdot]O(2max) when the effect of body mass was adjusted by experimentally observed exponents. Thus, when evaluating the physiological performance of young soccer players, allometric scaling needs to be taken into account instead of using theoretical approaches.
NASA Astrophysics Data System (ADS)
Zhang, D. H.; Li, F. W.
2011-05-01
An analytic solution for the problem of Williams-Brinkmann axisymmetric steady flow in the vicinity of a stagnation point at a blunt body is proposed. The boundary conditions are embedded in the main system of equations by means of the Boubaker polynomials expansion scheme (BPES). These differential equations are solved analytically and yield continuous and differentiable solutions compared to some published ones.
The Complexity of One-Step Equations
ERIC Educational Resources Information Center
Ngu, Bing
2014-01-01
An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…
Soil acidity, ecological stoichiometry and allometric scaling in grassland food webs
MULDER, CHRISTIAN; ELSER, JAMES J
2009-01-01
The factors regulating the structure of food webs are a central focus of community and ecosystem ecology, as trophic interactions among species have important impacts on nutrient storage and cycling in many ecosystems. For soil invertebrates in grassland ecosystems in the Netherlands, the site-specific slopes of the faunal biomass to organism body mass relationships reflected basic biochemical and biogeochemical processes associated with soil acidity and soil C : N : P stoichiometry. That is, the higher the phosphorus availability in the soil, the higher, on average, the slope of the faunal biomass size spectrum (i.e., the higher the biomass of large-bodied invertebrates relative to the biomass of small invertebrates). While other factors may also be involved, these results are consistent with the growth rate hypothesis from biological stoichiometry that relates phosphorus demands to ribosomal RNA and protein production. Thus our data represent the first time that ecosystem phosphorus availability has been associated with allometry in soil food webs (supporting information available online). Our results have broad implications, as soil invertebrates of different size have different effects on soil processes.
Allometric scaling of production and life-history variation in vascular plants
NASA Astrophysics Data System (ADS)
Enquist, Brian J.; West, Geoffrey B.; Charnov, Eric L.; Brown, James H.
1999-10-01
A prominent feature of comparative life histories is the well documented negative correlation between growth rate and life span. Patterns of resource allocation during growth and reproduction reflect life-history differences between species. This is particularly striking in tropical forests, where tree species can differ greatly in their rates of growth and ages of maturity but still attain similar canopy sizes. Here we provide a theoretical framework for relating life-history variables to rates of production, dM/dt, where M is above-ground mass and t is time. As metabolic rate limits production as an individual grows, dM/dt ~ M3/4. Incorporating interspecific variation in resource allocation to wood density, we derive a universal growth law that quantitatively fits data for a large sample of tropical tree species with diverse life histories. Combined with evolutionary life-history theory, the growth law also predicts several qualitative features of tree demography and reproduction. This framework also provides a general quantitative answer to why relative growth rate (1/M)(dM/df) decreases with increasing plant size (~M-1/4) and how it varies with differing allocation strategies.
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.
Ladd, Fernando V Lobo; Ladd, Aliny A B Lobo; da Silva, Andrea A P; Coppi, A Augusto
2014-01-01
The superior cervical ganglion (SCG) plays an important role in neuropathies including Horner's syndrome, stroke, and epilepsy. While mammalian SCGs seem to share certain organizational features, they display natural differences related to the animal size and side and the complexity and synaptic coverage of their dendritic arborizations. However, apart from the rat SCG, there is little information concerning the number of SCG neurons and synapses, and the nature of relationships between body weight and the numbers and sizes of neurons and synapses remain uncertain. In the recognition of this gap in the literature, in this chapter, we reviewed the current knowledge on the SCG structure and its remodeling during postnatal development across a plethora of large mammalian species, focusing on exotic rodents and domestic animals. Instrumentally, we present stereology as a state-of-the-art 3D technology to assess the SCG 3D structure unbiasedly and suggest future research directions on this topic.
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
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
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.
Allometric scaling of long-distance seed dispersal by migratory birds.
Viana, Duarte S; Santamaría, Luis; Michot, Thomas C; Figuerola, Jordi
2013-05-01
Migratory birds are often suggested to be important vectors for long-distance dispersal (LDD) of plant and animal propagules. The scale of such dispersal events (hundreds to thousands of kilometers) can influence landscape-level biological processes and species distributions. However, the few vector species studied and the lack of proper integration of their migratory movement in models of LDD has precluded the study of their potential as long-distance biotic dispersers. By means of a mechanistic model parameterized with empirical data, we first investigated the properties of seed dispersal curves generated by migratory birds and then analyzed the effect of bird size on model parameters and consequent seed dispersal patterns. Seed dispersal curves showed in most cases large and heavy tails, resulting in relatively frequent LDD (up to 3.5% of dispersal distances longer than 100 km). Bird size mediated trade-offs between bird movement and seed retention time that, in turn, determined seed dispersal patterns and the potential of each bird species as an LDD vector. Our modeling framework builds on a mechanistic understanding of seed dispersal by migratory birds and may thus be a useful tool to estimate the scale and frequency of bird-mediated, large-scale transport of native, invasive, and pathogenic organisms.
Stochastic differential equations
Sobczyk, K. )
1990-01-01
This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.
NASA Astrophysics Data System (ADS)
Sławianowski, J. J.; Kovalchuk, V.
2010-01-01
Considered is the Schrödinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting example of "mechanics" with singular Lagrangians, effectively treatable within the framework of Dirac formalism. We discuss also some modified "Schrödinger" equations involving second-order time derivatives and introduce a kind of nondirect, nonperturbative, geometrically-motivated nonlinearity based on making the scalar product a dynamical quantity. There are some reasons to expect that this might be a new way of describing open dynamical systems and explaining some quantum "paradoxes".
Phillips, Darci; Covian, Raul; Aponte, Angel M; Glancy, Brian; Taylor, Joni F; Chess, David; Balaban, Robert S
2012-05-01
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
Waters, James S; Ochs, Alison; Fewell, Jennifer H; Harrison, Jon F
2017-02-22
Metabolic rates of individual animals and social insect colonies generally scale hypometrically, with mass-specific metabolic rates decreasing with increasing size. Although this allometry has wide ranging effects on social behaviour, ecology and evolution, its causes remain controversial. Because it is difficult to experimentally manipulate body size of organisms, most studies of metabolic scaling depend on correlative data, limiting their ability to determine causation. To overcome this limitation, we experimentally reduced the size of harvester ant colonies (Pogonomyrmex californicus) and quantified the consequent increase in mass-specific metabolic rates. Our results clearly demonstrate a causal relationship between colony size and hypometric changes in metabolic rate that could not be explained by changes in physical density. These findings provide evidence against prominent models arguing that the hypometric scaling of metabolic rate is primarily driven by constraints on resource delivery or surface area/volume ratios, because colonies were provided with excess food and colony size does not affect individual oxygen or nutrient transport. We found that larger colonies had lower median walking speeds and relatively more stationary ants and including walking speed as a variable in the mass-scaling allometry greatly reduced the amount of residual variation in the model, reinforcing the role of behaviour in metabolic allometry. Following the experimental size reduction, however, the proportion of stationary ants increased, demonstrating that variation in locomotory activity cannot solely explain hypometric scaling of metabolic rates in these colonies. Based on prior studies of this species, the increase in metabolic rate in size-reduced colonies could be due to increased anabolic processes associated with brood care and colony growth.
Behavioral and phylogenetic implications of a narrow allometric study of Ardipithecus ramidus.
Sarmiento, E E; Meldrum, D J
2011-04-01
Narrow allometry is used to compare Ardipithecus ramidus molar and body segment lengths and proportions to those of living primates, with the goal of reconstructing fossil behavior and exploring how lengths and proportions bear on phylogeny. Comparatively short hands and upper limbs suggest Ardipithecus was less adept at forelimb suspension and vertical climbing than are great apes. Its tibial and tarsal lengths, suggest bonobo-like leaping ability. Its short lower limbs, but long toes relative to humans, are not conducive to habitual bipedality. When terrestrial, Ardipithecus would have engaged in palmigrade quadrupedality. Compared to the semi-digitigrade baboon its long fingers and toes suggest a less marked terrestrial commitment and agree with carpal anatomy reflecting full palmigrady. Molar dimensions and surface areas are similar to those of baboons and drills, but greater than in chimpanzees, indicating a diet with less fruit and more roughage than that of chimpanzees. Ardipithecus dimensions reflect a generalized ape, able to move in trees and on the ground, and exploit food sources in woodlands, grasslands and/or flooded terrain. These abilities are well-suited to the mosaic habitats that characterize Africa at 11°N. Parsimonious reconstruction of the common human/African ape ancestor suggests the short upper limbs and metacarpals of Ardipithecus are too derived to belong to an exclusive human ancestor. Because parsimony is a theoretical construct and not an evolutionary reality, derived segment lengths alone do not prove conclusively Ardipithecus is not such an ancestor. Description in Ardipithecus of complex anatomy uniquely shared by humans and African apes, that leaves a record of reversals or parallelisms, would be a first step in showing whether this fossil qualifies as such an ancestor.
Wu Shuangqing
2008-09-15
The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations. The general solution is expressed as a superposition of solutions derived from these two decoupled ordinary differential equations. By separating variables for the massive Klein-Gordon equation in the same spacetime background, I derive a simple and elegant form for the Staeckel-Killing tensor, which can be easily written as the square of a rank-three Killing-Yano tensor. I have also explicitly constructed a symmetry operator that commutes with the scalar Laplacian by using the Staeckel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.
``Riemann equations'' in bidifferential calculus
NASA Astrophysics Data System (ADS)
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
Modelling by Differential Equations
ERIC Educational Resources Information Center
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Structural Equation Model Trees
ERIC Educational Resources Information Center
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
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.
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)
Jamal, Sameerah; Shabbir, Ghulam
2017-02-01
We study the geometric properties of generators for the Klein-Gordon equation in Kantowski-Sachs and certain Bianchi-type spaces. Several versions of the Klein-Gordon equation are derived from its dependence on a potential function. The criteria for different versions of the (1+3) Klein-Gordon equation originates from analyzing three sources, viz. through generators that are identically the Killing algebra, or with the Killing vector fields that are recast into linear combinations and thirdly, real sub-algebras within the conformal algebra. In turn, these equations admit a catalogue of infinitesimal symmetries that are equivalent to the corresponding Killing vector fields in Kantowski-Sachs, Bianchi type III, IX, VIII, VI0 and VII0 space-times, with the exception of a linear vector W=upartialu in every case. The sheer number of results are displayed in appropriate tables. Subsequently, in application, we derive some Noetherian conservation laws and identify some exact solutions by quadratures.
The Bessel Equation and Dissipation
NASA Astrophysics Data System (ADS)
Alfinito, Eleonora; Vitiello, Giuseppe
The Bessel equation can be cast, by means of suitable transformations, into a system of two damped/amplified parametric oscillator equations. The role of group contraction and the breakdown of loop-antiloop symmetry is discussed. The relation between the Virasoro algebra and the Euclidean algebras e(2) and e(3) is also presented.
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.
Investigation of the kinetic model equations.
Liu, Sha; Zhong, Chengwen
2014-03-01
Currently the Boltzmann equation and its model equations are widely used in numerical predictions for dilute gas flows. The nonlinear integro-differential Boltzmann equation is the fundamental equation in the kinetic theory of dilute monatomic gases. By replacing the nonlinear fivefold collision integral term by a nonlinear relaxation term, its model equations such as the famous Bhatnagar-Gross-Krook (BGK) equation are mathematically simple. Since the computational cost of solving model equations is much less than that of solving the full Boltzmann equation, the model equations are widely used in predicting rarefied flows, multiphase flows, chemical flows, and turbulent flows although their predictions are only qualitatively right for highly nonequilibrium flows in transitional regime. In this paper the differences between the Boltzmann equation and its model equations are investigated aiming at giving guidelines for the further development of kinetic models. By comparing the Boltzmann equation and its model equations using test cases with different nonequilibrium types, two factors (the information held by nonequilibrium moments and the different relaxation rates of high- and low-speed molecules) are found useful for adjusting the behaviors of modeled collision terms in kinetic regime. The usefulness of these two factors are confirmed by a generalized model collision term derived from a mathematical relation between the Boltzmann equation and BGK equation that is also derived in this paper. After the analysis of the difference between the Boltzmann equation and the BGK equation, an attempt at approximating the collision term is proposed.
Noh, Keumhan; Kang, Wonku
2017-03-10
7-O-succinyl macrolactin A (SMA) exerts several pharmacological effects including anti-bacterial, anti-inflammation, and anticancer activities. Recently, SMA has been extensively evaluated as an anti-cancer drug. Thus, the objectives of the present study were to characterise the pharmacokinetics of SMA via both non-compartmental and compartmental analysis in mice, rats, and dogs, and to derive an appropriate first-in-man dose based on allometric scaling of the animal data. The time courses of plasma SMA concentrations after intravenous administration to rats and dogs were analysed retrospectively, as were data collected after intraperitoneal SMA injection in mice. Pharmacokinetic parameters were estimated via both noncompartmental and compartmental analysis, and were correlated with body weight and/or the potential maximum life-span. The clearance and distribution volume of SMA in humans were predicted, and a first-in-man dose proposed. A two-compartment model best described the time courses of SMA plasma concentrations after a saturation elimination process was applied to fit the dataset obtained from rats. Incorporation of the maximum potential life-span during allometric scaling was required to improve the estimation of human clearance. The SMA clearance and the distribution volume in the steady state, in a 70-kg adult male, were estimated to be 30.6 L/h and 19.5 L, respectively. To meet the area under the curve (AUC) required for anti-tumour activity, a dose of 100 mg (~1.5 mg/kg) was finally proposed as the first dose for a 70-kg human. Although toxicological profiles derived from non-clinical studies must be considered before any final decision is made, our work will facilitate clinical studies on SMA.
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.
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
Makowitz, H.
1992-10-01
We have studied various formulations of the concept of pressure, in the context of the usual Six-Equation Model of thermal-hydraulics. A different concept of pressure, than the usual one, has been used. This new pressure concept is Galilean Invariant, and results for the One-Pressure Model with the same complex characteristic roots as the ``Basic III-Posed Model,`` discussed in the literature for the cases we have investigated. We have also examined several Two-Pressure formulations and shown that two pressures are a necessary but not sufficient condition for obtaining a Well-Posed system. Several counter examples are presented. We have shown that the standard theory is not Galilean Invariant and suggested that the origin of III-Posedness is due to our closure relationships. We also question whether the current theory can satisfy conservation principles for mass, energy, and momentum.
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1981-01-01
Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.
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…
Students' Equation Understanding and Solving in Iran
ERIC Educational Resources Information Center
Barahmand, Ali; Shahvarani, Ahmad
2014-01-01
The purpose of the present article is to investigate how 15-year-old Iranian students interpret the concept of equation, its solution, and studying the relation between the students' equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between…
Variational Derivation of Dissipative Equations
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2017-03-01
A new variational principle is formulated to derive various dissipative equations. Model equations considered are the damping equation, Bloch equation, diffusion equation, Fokker-Planck equation, Kramers equation and Smoluchowski equation. Each equation and its time reversal equation are simultaneously obtained in our variational principle.
NASA Astrophysics Data System (ADS)
Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem
2016-05-01
``The nature has two magnitudes and two elongations, one is gradual being (wavy-like motion) which belongs to the time and dividable to the former and the next times in mind, and the other one is jerky-like motion which belongs to the space and dividable to the former and the next places'' [Asfar, Mulla Sadra, (1571/2-1640)]. These two separated natures of space-time are matched on wave-particle duality. Therefore, the nature of time can be wavy-like and the nature of space can be jerky-like. So, there are two independent variable sources of particle(s)' flow while they are match exactly with each other. These two sources are potential of flow and potential of time (relative time) which vary with respect to both space and time. Here, we propose two additional parts to Schrodinger's equation with respect to relative time: HΨ + ∇t' = EΨ + ∂t' / ∂t , where t is time and t' is relative time: t' = t +/- Δt [Gholibeigian et al., APS March Meeting 2016], which for each atom becomes: tatom = ∑mnucleons + ∑melectrons where m is momentum [Gholibeigian, APS March Meeting 2015, abstract #V1.023]. Using time's relativity in Schrodinger equation will give us more precious results. AmirKabir University of Technology,Tehran, Iran.
ERIC Educational Resources Information Center
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,…
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''.
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)
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.
ERIC Educational Resources Information Center
Chen, Haiwen
2012-01-01
In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…
CROFT, MARY ANN; HEATLEY, GREGG; MCDONALD, JARED P.; KATZ, ALEXANDER; KAUFMAN, PAUL L.
2016-01-01
Purpose To elucidate the dynamic accommodative movements of the lens capsule, posterior lens and the strand that attaches to the posterior vitreous zonule insertion zone and posterior lens equator (PVZ INS-LE), and their age-related changes. Methods Twelve human subjects (ages 19–65 years) and twelve rhesus monkeys (ages 6–27 years) were studied. Accommodation was induced pharmacologically (humans) or by central electrical stimulation (monkeys). Ultrasound biomicroscopy was used to image intraocular structures in both species. Surgical procedures and contrast agents were utilized in the monkey eyes to elucidate function and allow visualization of the intraocular accommodative structures. Results Human: The posterior pole of the lens moves posteriorly during accommodation in proportion to accommodative amplitude and ciliary muscle movement. Monkey: Similar accommodative movements of the posterior lens pole were seen in the monkey eyes. Following extracapsular lens extraction (ECLE), the central capsule bows backward during accommodation in proportion to accommodative amplitude and ciliary muscle movement, while the peripheral capsule moves forward. During accommodation the ciliary muscle moved forward by ~1.0 mm, pulling forward the vitreous zonule and the PVZ INS-LE structure. During the accommodative response the PVZ INS-LE structure moved forward when the lens was intact and when the lens substance and capsule were removed. In both the monkey and the human eyes these movements declined with age. Conclusions The accommodative shape change of the central capsule may be due to the elastic properties of the capsule itself. For these capsule/lens accommodative posterior movements to occur, the vitreous face must either allow for it or facilitate it. The PVZ INS-LE structure may act as a “strut” to the posterior lens equator (pushing the lens equator forward) and thereby facilitate accommodative forward lens equator movement and lens thickening. The age-related
Fredholm's equations for subwavelength focusing
NASA Astrophysics Data System (ADS)
Velázquez-Arcos, J. M.
2012-10-01
Subwavelength focusing (SF) is a very useful tool that can be carried out with the use of left hand materials for optics that involve the range of the microwaves. Many recent works have described a successful alternative procedure using time reversal methods. The advantage is that we do not need devices which require the complicated manufacture of left-hand materials; nevertheless, the theoretical mathematical bases are far from complete because before now we lacked an adequate easy-to-apply frame. In this work we give, for a broad class of discrete systems, a solid support for the theory of electromagnetic SF that can be applied to communications and nanotechnology. The very central procedure is the development of vector-matrix formalism (VMF) based on exploiting both the inhomogeneous and homogeneous Fredholm's integral equations in cases where the last two kinds of integral equations are applied to some selected discrete systems. To this end, we first establish a generalized Newmann series for the Fourier transform of the Green's function in the inhomogeneous Fredholm's equation of the problem. Then we go from an integral operator equation to a vector-matrix algebraic one. In this way we explore the inhomogeneous case and later on also the very interesting one about the homogeneous equation. Thus, on the one hand we can relate in a simple manner the arriving electromagnetic signals with those at their sources and we can use them to perform a SF. On the other hand, we analyze the homogeneous version of the equations, finding resonant solutions that have analogous properties to their counterparts in quantum mechanical scattering, that can be used in a proposed very powerful way in communications. Also we recover quantum mechanical operator relations that are identical for classical electromagnetics. Finally, we prove two theorems that formalize the relation between the theory of Fredholm's integral equations and the VMF we present here.
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)
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.
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…
Bending equation for a quasianisotropic plate
NASA Astrophysics Data System (ADS)
Shachnev, V. A.
2010-10-01
In the framework of the linear theory of elasticity, an exact bending equation is obtained for the median plane of a plate whose material is a monoclinic system with the axis of symmetry perpendicular to the plate plane. As an example, the equation of the median plane of an isotropic plate is considered; the operator of this equation coincides with the operator of Sophie Germain's approximate equation. As the plate thickness tends to zero, the right-hand side of the equation is asymptotically equivalent to the right-hand side of the approximate equation. In addition, equations relating the median plane transverse stresses and the total stresses in the plate boundary planes to the median plane deflexions are obtained.
Álvarez-Dávila, Esteban; Cayuela, Luis; González-Caro, Sebastián; Aldana, Ana M; Stevenson, Pablo R; Phillips, Oliver; Cogollo, Álvaro; Peñuela, Maria C; von Hildebrand, Patricio; Jiménez, Eliana; Melo, Omar; Londoño-Vega, Ana Catalina; Mendoza, Irina; Velásquez, Oswaldo; Fernández, Fernando; Serna, Marcela; Velázquez-Rua, Cesar; Benítez, Doris; Rey-Benayas, José M
2017-01-01
Understanding and predicting the likely response of ecosystems to climate change are crucial challenges for ecology and for conservation biology. Nowhere is this challenge greater than in the tropics as these forests store more than half the total atmospheric carbon stock in their biomass. Biomass is determined by the balance between biomass inputs (i.e., growth) and outputs (mortality). We can expect therefore that conditions that favor high growth rates, such as abundant water supply, warmth, and nutrient-rich soils will tend to correlate with high biomass stocks. Our main objective is to describe the patterns of above ground biomass (AGB) stocks across major tropical forests across climatic gradients in Northwestern South America. We gathered data from 200 plots across the region, at elevations ranging between 0 to 3400 m. We estimated AGB based on allometric equations and values for stem density, basal area, and wood density weighted by basal area at the plot-level. We used two groups of climatic variables, namely mean annual temperature and actual evapotranspiration as surrogates of environmental energy, and annual precipitation, precipitation seasonality, and water availability as surrogates of water availability. We found that AGB is more closely related to water availability variables than to energy variables. In northwest South America, water availability influences carbon stocks principally by determining stand structure, i.e. basal area. When water deficits increase in tropical forests we can expect negative impact on biomass and hence carbon storage.
Cayuela, Luis; González-Caro, Sebastián; Aldana, Ana M.; Stevenson, Pablo R.; Phillips, Oliver; Cogollo, Álvaro; Peñuela, Maria C.; von Hildebrand, Patricio; Jiménez, Eliana; Melo, Omar; Londoño-Vega, Ana Catalina; Mendoza, Irina; Velásquez, Oswaldo; Fernández, Fernando; Serna, Marcela; Velázquez-Rua, Cesar; Benítez, Doris; Rey-Benayas, José M.
2017-01-01
Understanding and predicting the likely response of ecosystems to climate change are crucial challenges for ecology and for conservation biology. Nowhere is this challenge greater than in the tropics as these forests store more than half the total atmospheric carbon stock in their biomass. Biomass is determined by the balance between biomass inputs (i.e., growth) and outputs (mortality). We can expect therefore that conditions that favor high growth rates, such as abundant water supply, warmth, and nutrient-rich soils will tend to correlate with high biomass stocks. Our main objective is to describe the patterns of above ground biomass (AGB) stocks across major tropical forests across climatic gradients in Northwestern South America. We gathered data from 200 plots across the region, at elevations ranging between 0 to 3400 m. We estimated AGB based on allometric equations and values for stem density, basal area, and wood density weighted by basal area at the plot-level. We used two groups of climatic variables, namely mean annual temperature and actual evapotranspiration as surrogates of environmental energy, and annual precipitation, precipitation seasonality, and water availability as surrogates of water availability. We found that AGB is more closely related to water availability variables than to energy variables. In northwest South America, water availability influences carbon stocks principally by determining stand structure, i.e. basal area. When water deficits increase in tropical forests we can expect negative impact on biomass and hence carbon storage. PMID:28301482
SCREENED COULOMB FORMULATION OF THE IONIZATION EQUILIBRIUM EQUATION OF STATE,
The ionization equilibrium equation of state (IEEOS) is formulated relative to the numerical solutions of the Schrodinger equation with the complete...for hydrogen and iron, where pressures at high densities and temperature are compared with pressures from the equation of state based upon the Thomas...IEEOS represents a significant improvement over the TFD equation of state . (Author)
NASA Astrophysics Data System (ADS)
Sullivan, F. B.; Palace, M. W.; Ducey, M.; Czarnecki, C.; Zanin Shimbo, J.; Mota e Silva, J.
2012-12-01
Tropical forests are considered to be some of the most structurally complex forests in the world. Understanding vegetation height structure in these forests can aid in understanding the spatial temporal components of disturbance, from blowdowns to gap dynamics. Vegetation profiles can be used to better estimate carbon storage and flux across the landscape. Using light detection and ranging (lidar) data collected at La Selva, Costa Rica from four instruments (three airborne, one terrestrial) at four times since 2005, and field data collected in January 2012, we generated relative vegetation profiles for twenty plots in La Selva. Relative vegetation profiles were derived from lidar data by accounting for obscured plant material through a log transformation of the cumulative proportion of observations (percent canopy closure). Profiles were derived from field data using two different sets of allometric equations describing crown shape and tree height. We conducted a cluster analysis on similarity matrices developed in R (version 2.14.1) using three different metrics (sum of squares, Kullback-Leibler divergence, Kolmogorov-Smirnov D statistic) and identified general similarity between lidar profiles. Results were consistent across each of the three similarity metrics. Three distinct clusters were found, with profiles from three airborne lidar instruments, two profiles from a terrestrial lidar instrument, and profiles derived from field data forming the clusters. Our results indicate that although estimating lidar relative vegetation profiles from field data was not possible, terrestrial lidar relative vegetation profiles are generally similar to airborne relative vegetation profiles. Given the rapidity and repeatability of terrestrial lidar measurements, these results show promise for terrestrial lidar instruments to collect plot-specific data on forest structure and vertical distribution of plant material. Furthermore, identifying relationships between terrestrial and
The Husimi representation and the Vlasov equation
LEplattenier, P.; Suraud, E.; Reinhard, P.G.
1995-12-01
We investigate the {ital h} expansion of the Time-Dependent Hartree Fock equation in the Wigner and Husimi representations. Both lead formally to the Vlasov equation in lowest order. The Husimi representation delivers a more stable expansion in particular when the self-interaction in the mean field is considered. The test particle solution of the Vlasov equation turns out to be closely related to the Husimi representation. Copyright {copyright} 1995 Academic Press, Inc.
Integration rules for scattering equations
NASA Astrophysics Data System (ADS)
Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-09-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints fo any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
2011-01-01
Background The Drosophila wing represents a particularly appropriate model to investigate the developmental control of phenotypic variation. Previous studies which aimed to identify candidate genes for wing morphology demonstrated that the genetic basis of wing shape variation in D. melanogaster is composed of numerous genetic factors causing small, additive effects. In this study, we analyzed wing shape in males and females from 191 lines of D. melanogaster, homozygous for a single P-element insertion, using geometric morphometrics techniques. The analysis allowed us to identify known and novel candidate genes that may contribute to the expression of wing shape in each sex separately and to compare them to candidate genes affecting wing size which have been identified previously using the same lines. Results Our results indicate that more than 63% of induced mutations affected wing shape in one or both sexes, although only 33% showed significant differences in both males and females. The joint analysis of wing size and shape revealed that only 19% of the P-element insertions caused coincident effects on both components of wing form in one or both sexes. Further morphometrical analyses revealed that the intersection between veins showed the smallest displacements in the proximal region of the wing. Finally, we observed that mutations causing general deformations were more common than expected in both sexes whereas the opposite occurred with those generating local changes. For most of the 94 candidate genes identified, this seems to be the first record relating them with wing shape variation. Conclusions Our results support the idea that the genetic architecture of wing shape is complex with many different genes contributing to the trait in a sexually dimorphic manner. This polygenic basis, which is relatively independent from that of wing size, is composed of genes generally involved in development and/or metabolic functions, especially related to the regulation of
NASA Astrophysics Data System (ADS)
Kostov, Ivan; Serban, Didina; Volin, Dmytro
2008-08-01
We give a realization of the Beisert, Eden and Staudacher equation for the planar Script N = 4 supersymetric gauge theory which seems to be particularly useful to study the strong coupling limit. We are using a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotański. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.
Fractional chemotaxis diffusion equations.
Langlands, T A M; Henry, B I
2010-05-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.
Euler's Amazing Way to Solve Equations.
ERIC Educational Resources Information Center
Flusser, Peter
1992-01-01
Presented is a series of examples that illustrate a method of solving equations developed by Leonhard Euler based on an unsubstantiated assumption. The method integrates aspects of recursion relations and sequences of converging ratios and can be extended to polynomial equation with infinite exponents. (MDH)
How Should Equation Balancing Be Taught?
ERIC Educational Resources Information Center
Porter, Spencer K.
1985-01-01
Matrix methods and oxidation-number methods are currently advocated and used for balancing equations. This article shows how balancing equations can be introduced by a third method which is related to a fundamental principle, is easy to learn, and is powerful in its application. (JN)
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.
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.
Prolongation structures of nonlinear evolution equations
NASA Technical Reports Server (NTRS)
Wahlquist, H. D.; Estabrook, F. B.
1975-01-01
A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.
Stochastic differential equation model to Prendiville processes
NASA Astrophysics Data System (ADS)
Granita, Bahar, Arifah
2015-10-01
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.
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)
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
Explicit integration of Friedmann's equation with nonlinear equations of state
Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong E-mail: gwg1@damtp.cam.ac.uk
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.
Uniqueness of Maxwell's Equations.
ERIC Educational Resources Information Center
Cohn, Jack
1978-01-01
Shows that, as a consequence of two feasible assumptions and when due attention is given to the definition of charge and the fields E and B, the lowest-order equations that these two fields must satisfy are Maxwell's equations. (Author/GA)
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…
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.
On the Solution of the Rational Matrix Equation[InlineEquation not available: see fulltext.
NASA Astrophysics Data System (ADS)
Benner, Peter; Faßbender, Heike
2007-12-01
We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation[InlineEquation not available: see fulltext.], where[InlineEquation not available: see fulltext.] is symmetric positive definite and[InlineEquation not available: see fulltext.] is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE). We discuss how to use the butterfly[InlineEquation not available: see fulltext.] algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.
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.
AN APPROXIMATE EQUATION OF STATE OF SOLIDS.
research. By generalizing experimental data and obtaining unified relations describing the thermodynamic properties of solids, and approximate equation of state is derived which can be applied to a wide class of materials. (Author)
NASA Astrophysics Data System (ADS)
Sivron, Ran
2006-12-01
With the introduction of "Ranking Tests" some quantitative ideas were added to a large body of successful techniques for teaching conceptual astronomy. We incorporated those methods into our classes, and added a new ingredient: On a biweekly basis we included a quantitative excercise: Students working in groups of 2-3 draw geometrical figures, say: a circle, and use some trivial geometry equations, such as circumference = 2 x pi x r, in solving astronomy problems on 3'x4' white boards. A few examples included: Finding the distance to the moon with the Aristarchus method, finding the Solar Constant with the inverse square law, etc. Our methodolgy was similar to problem solving techniques in introductory physics. We were therefore worried that the students may be intimidated. To our surprize, not only did most students succeed in solving the problems, but they were not intimidated at all (that is: after the first class...) As a matter of fact, their test results improved, and the students interviewed expressed great enthusiasm for the new method. Warning: Our classes were relatively small <40 studets). For larger classes TA help is needed.
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.
Next-order structure-function equations
NASA Astrophysics Data System (ADS)
Hill, Reginald J.; Boratav, Olus N.
2001-01-01
Kolmogorov's equation [Dokl. Akad. Nauk SSSR 32, 16 (1941)] relates the two-point second- and third-order velocity structure functions and the energy dissipation rate. The analogous next higher-order two-point equation relates the third- and fourth-order velocity structure functions and the structure function of the product of pressure-gradient difference and two factors of velocity difference, denoted Tijk. The equation is simplified on the basis of local isotropy. Laboratory and numerical simulation data are used to evaluate and compare terms in the equation, examine the balance of the equation, and evaluate components of Tijk. Atmospheric surface-layer data are used to evaluate Tijk in the inertial range. Combined with the random sweeping hypothesis, the equation relates components of the fourth-order velocity structure function. Data show the resultant error of this application of random sweeping. The next-order equation constrains the relationships that have been suggested among components of the fourth-order velocity structure function. The pressure structure function, pressure-gradient correlation, and mean-squared pressure gradient are related to Tijk. Inertial range formulas are discussed.
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.
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.
The Quadrature Master Equations
NASA Astrophysics Data System (ADS)
Hassan, N. J.; Pourdarvish, A.; Sadeghi, J.; Olaomi, J. O.
2017-04-01
In this paper, we derive the non-Markovian stochastic equation of motion (SEM) and master equations (MEs) for the open quantum system by using the non-Markovian stochastic Schrödinger equations (SSEs) for the quadrature unraveling in linear and nonlinear cases. The SSEs for quadrature unraveling arise as a special case of a quantum system. Also we derive the Markovian SEM and ME by using linear and nonlinear Itô SSEs for the measurement probabilities. In linear non-Markovian case, we calculate the convolutionless linear quadrature non-Markovian SEM and ME. We take advantage from example and show that corresponding theory.
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.
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.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
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.
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.
ERIC Educational Resources Information Center
Shumway, Richard J.
1989-01-01
Illustrated is the problem of solving equations and some different strategies students might employ when using available technology. Gives illustrations for: exact solutions, approximate solutions, and approximate solutions which are graphically generated. (RT)
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.
Discrete wave equation upscaling
NASA Astrophysics Data System (ADS)
Fichtner, Andreas; Hanasoge, Shravan M.
2017-01-01
We present homogenisation technique for the uniformly discretised wave equation, based on the derivation of an effective equation for the low-wavenumber component of the solution. The method produces a down-sampled, effective medium, thus making the solution of the effective equation less computationally expensive. Advantages of the method include its conceptual simplicity and ease of implementation, the applicability to any uniformly discretised wave equation in one, two or three dimensions, and the absence of any constraints on the medium properties. We illustrate our method with a numerical example of wave propagation through a one-dimensional multiscale medium, and demonstrate the accurate reproduction of the original wavefield for sufficiently low frequencies.
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.
NASA Astrophysics Data System (ADS)
Gel'fgat, V. I.
2014-11-01
Formulas for inverting regularized systems of linear equations whose coefficient matrices are complex, Toeplitz, and singular or nearly singular are derived. They make it possible to develop economical algorithms for solving such systems in mass calculations.
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.
Deformed cohomologies of symmetry pseudo-groups and coverings of differential equations
NASA Astrophysics Data System (ADS)
Morozov, Oleg I.
2017-03-01
The work establishes a relation between deformed cohomologies of symmetry pseudo-groups and coverings of differential equations. Examples include the potential Khokhlov-Zabolotskaya equation and the Boyer-Finley equation.
Constitutive equations for discrete electromagnetic problems over polyhedral grids
Codecasa, Lorenzo . E-mail: codecasa@elet.polimi.it; Trevisan, Francesco . E-mail: trevisan@uniud.it
2007-08-10
In this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field problem. The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations. In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual grid. Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations of the electromagnetic field.
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)
Spatial equation for water waves
NASA Astrophysics Data System (ADS)
Dyachenko, A. I.; Zakharov, V. E.
2016-02-01
A compact spatial Hamiltonian equation for gravity waves on deep water has been derived. The equation is dynamical and can describe extreme waves. The equation for the envelope of a wave train has also been obtained.
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)
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…
Shock wave equation of state of muscovite
NASA Technical Reports Server (NTRS)
Sekine, Toshimori; Rubin, Allan M.; Ahrens, Thomas J.
1991-01-01
Shock wave data were obtained between 20 and 140 GPa for natural muscovite obtained from Methuen Township (Ontario), in order to provide a shock-wave equation of state for this crustal hydrous mineral. The shock equation of state data could be fit by a linear shock velocity (Us) versus particle velocity (Up) relation Us = 4.62 + 1.27 Up (km/s). Third-order Birch-Murnaghan equation of state parameters were found to be K(OS) = 52 +/-4 GPa and K-prime(OS) = 3.2 +/-0.3 GPa. These parameters are comparable to those of other hydrous minerals such as brucite, serpentine, and tremolite.
Budini, Adrian A.
2006-11-15
In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develop strong nonlocal effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantee the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of nontrivial structured dephasing and depolarizing reservoirs over a single qubit.
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.
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.
Comparison of Kernel Equating and Item Response Theory Equating Methods
ERIC Educational Resources Information Center
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Accumulative Equating Error after a Chain of Linear Equatings
ERIC Educational Resources Information Center
Guo, Hongwen
2010-01-01
After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…
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
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
NASA Astrophysics Data System (ADS)
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
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…
NASA Astrophysics Data System (ADS)
Mejjaoli, Hatem
2008-12-01
We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
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]…
Parallel Multigrid Equation Solver
Adams, Mark
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.
Quenching equation for scintillation
NASA Astrophysics Data System (ADS)
Kato, Takahisa
1980-06-01
A mathematical expression is postulated showing the relationship between counting rate and quenching agent concentration in a liquid scintillation solution. The expression is more suited to a wider range of quenching agent concentrations than the Stern-Volmer equation. An estimation of the quenched correction is demonstrated using the expression.
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
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Numerical bifurcation for the capillary Whitham equation
NASA Astrophysics Data System (ADS)
Remonato, Filippo; Kalisch, Henrik
2017-03-01
The so-called Whitham equation arises in the modeling of free surface water waves, and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid with finite depth. In this work, the effect of incorporating capillarity into the Whitham equation is in focus. The capillary Whitham equation is a nonlocal equation similar to the usual Whitham equation, but containing an additional term with a coefficient depending on the Bond number which measures the relative strength of capillary and gravity effects on the wave motion. A spectral collocation scheme for computing approximations to periodic traveling waves for the capillary Whitham equation is put forward. Numerical approximations of periodic traveling waves are computed using a bifurcation approach, and a number of bifurcation curves are found. Our analysis uncovers a rich structure of bifurcation patterns, including subharmonic bifurcations, as well as connecting and crossing branches. Indeed, for some values of the Bond number, the bifurcation diagram features distinct branches of solutions which intersect at a secondary bifurcation point. The same branches may also cross without connecting, and some bifurcation curves feature self-crossings without self-connections.
Relativistic Langevin equation for runaway electrons
NASA Astrophysics Data System (ADS)
Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.
2016-10-01
The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.
Exact Pressure Evolution Equation for Incompressible Fluids
NASA Astrophysics Data System (ADS)
Tessarotto, M.; Ellero, M.; Aslan, N.; Mond, M.; Nicolini, P.
2008-12-01
An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid pressure which replaces the Poisson equation and yields an algorithm which is a Poisson solver, i.e., it permits to time-advance exactly the same fluid pressure without solving the Poisson equation. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. This amounts to transform an elliptic type fluid equation into a suitable hyperbolic equation, a result which usually is reached only by means of an asymptotic formulation. Besides being a still unsolved mathematical problem, the issue is relevant for at least two reasons: a) the proliferation of numerical algorithms in computational fluid dynamics which reproduce the behavior of incompressible fluids only in an asymptotic sense (see below); b) the possible verification of conjectures involving the validity of appropriate equations of state for the fluid pressure. Another possible motivation is, of course, the ongoing quest for efficient numerical solution methods to be applied for the construction of the fluid fields {ρ,V,p}, solutions of the initial and boundary-value problem associated to the incompressible N-S equations (INSE). In this paper we intend to show that an exact solution to this problem can be achieved adopting the approach based on inverse kinetic theory (IKT) recently developed for incompressible fluids by Tessarotto et al. [7, 6, 7, 8, 9]. In particular we intend to prove that the evolution of the fluid fields can be achieved by means of a suitable dynamical system, to be identified with the so-called Navier-Stokes (N-S) dynamical system. As a consequence it is found that the fluid pressure obeys a well-defined evolution equation. The result appears
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…
Flavored quantum Boltzmann equations
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-05-15
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
An equation for behavioral contrast.
Williams, B A; Wixted, J T
1986-01-01
Pigeons were trained on a three-component multiple schedule in which the rates of reinforcement in the various components were systematically varied. Response rates were described by an equation that posits that the response-strengthening effects of reinforcement are inversely related to the context of reinforcement in which it occurs, and that the context is calculated as the weighted average of the various sources of reinforcement in the situation. The quality of fits was comparable to that found with previous quantitative analyses of concurrent schedules, especially for relative response rates, with over 90% of the variance accounted for in every case. As with previous research, reinforcements in the component that was to follow received greater weights in determining the context than did reinforcements in the preceding component. PMID:3950534
Entropic corrections to Friedmann equations
Sheykhi, Ahmad
2010-05-15
Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In Verlinde's argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton's law of gravitation as well as modified Friedmann equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde's model.
NASA Astrophysics Data System (ADS)
Trzetrzelewski, Maciej
2016-11-01
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1974-01-01
For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.
Quantum molecular master equations
NASA Astrophysics Data System (ADS)
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
Double-Plate Penetration Equations
NASA Technical Reports Server (NTRS)
Hayashida, K. B.; Robinson, J. H.
2000-01-01
This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.
Classification of five-point differential-difference equations
NASA Astrophysics Data System (ADS)
Garifullin, R. N.; Yamilov, R. I.; Levi, D.
2017-03-01
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes such well-known examples as the Itoh–Narita–Bogoyavlensky and the discrete Sawada–Kotera equations. The resulting list contains 17 equations, some of which seem to be new. We have found non-point transformations relating most of the resulting equations among themselves and their generalized symmetries.
Five-wave classical scattering matrix and integrable equations
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Odesskii, A. V.; Cisternino, M.; Onorato, M.
2014-07-01
We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type u∂u/∂x. Our aim is to find the most general nontrivial form of the dispersion relation ω(k) for which the five-wave interaction scattering matrix is identically zero on the resonance manifold. As could be expected, the matrix in one dimension is zero for the Korteweg-de Vries equation, the Benjamin-Ono equation, and the intermediate long-wave equation. In two dimensions, we find a new equation that satisfies our requirement.
[Dosing adjustment and renal function: Which equation(s)?].
Delanaye, Pierre; Flamant, Martin; Cavalier, Étienne; Guerber, Fabrice; Vallotton, Thomas; Moranne, Olivier; Pottel, Hans; Boffa, Jean-Jacques; Mariat, Christophe
2016-02-01
While the CKD-EPI (for Chronic Kidney Disease Epidemiology) equation is now implemented worldwide, utilization of the Cockcroft formula is still advocated by some physicians for drug dosage adjustment. Justifications for this recommendation are that the Cockcroft formula was preferentially used to determine dose adjustments according to renal function during the development of many drugs, better predicts drugs-related adverse events and decreases the risk of drug overexposure in the elderly. In this opinion paper, we discuss the weaknesses of the rationale supporting the Cockcroft formula and endorse the French HAS (Haute Autorité de santé) recommendation regarding the preferential use of the CKD-EPI equation. When glomerular filtration rate (GFR) is estimated in order to adjust drug dosage, the CKD-EPI value should be re-expressed for the individual body surface area (BSA). Given the difficulty to accurately estimate GFR in the elderly and in individuals with extra-normal BSA, we recommend to prescribe in priority monitorable drugs in those populations or to determine their "true" GFR using a direct measurement method.
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
Reduction operators of Burgers equation
Pocheketa, Oleksandr A.; Popovych, Roman O.
2013-01-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special “no-go” case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf–Cole transformation to a parameterized family of Lie reductions of the linear heat equation. PMID:23576819
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.
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.
Consistent lattice Boltzmann equations for phase transitions
NASA Astrophysics Data System (ADS)
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.
Non-markovian boltzmann equation
Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.
1997-08-01
A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov{endash}Born{endash}Green{endash}Kirkwood{endash}Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. {copyright} 1997 Academic Press, Inc.
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.
Problems, Perspectives, and Practical Issues in Equating.
ERIC Educational Resources Information Center
Weiss, David J., Ed.
1987-01-01
Issues concerning equating test scores are discussed in an introduction, four papers, and two commentaries. Equating methods research, sampling errors, linear equating, population differences, sources of equating errors, and a circular equating paradigm are considered. (SLD)
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1972-01-01
The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.
Noncommutativity and the Friedmann Equations
Sabido, M.; Socorro, J.; Guzman, W.
2010-07-12
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.
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
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…
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…
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.
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…
Structural Equation Modeling with Interchangeable Dyads
ERIC Educational Resources Information Center
Olsen, Joseph A.; Kenny, David A.
2006-01-01
Structural equation modeling (SEM) can be adapted in a relatively straightforward fashion to analyze data from interchangeable dyads (i.e., dyads in which the 2 members cannot be differentiated). The authors describe a general strategy for SEM model estimation, comparison, and fit assessment that can be used with either dyad-level or pairwise…
Wavelet=Galerkin discretization of hyperbolic equations
Restrepo, J.M.; Leaf, G.K.
1994-12-31
The relative merits of the wavelet-Galerkin solution of hyperbolic partial differential equations, typical of geophysical problems, are quantitatively and qualitatively compared to traditional finite difference and Fourier-pseudo-spectral methods. The wavelet-Galerkin solution presented here is found to be a viable alternative to the two conventional techniques.
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…
Duality properties of Gorringe Leach equations
NASA Astrophysics Data System (ADS)
Grandati, Yves; Bérard, Alain; Mohrbach, Hervé
2009-02-01
In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold Vassiliev type. The specific associated conserved quantities (Laplace Runge Lenz vector and Fradkin Jauch Hill tensor) are then dual reflections of each other.
'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.
Generalized Klein-Kramers equations.
Fa, Kwok Sau
2012-12-21
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)]. 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.
On the Derivation of the Equations of Motion
NASA Astrophysics Data System (ADS)
Kaniel, S.; Itin, Y.
General Relativity is unique, among the class of field theories, in the treatment of the equations of motion. The equations of motion of massive particles are completely determined by the field equation 1-5. Einstein's field equations, as well as most field equations in gravity theory, have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order, with coefficients that depend on the variables. We propose for the N-body problem of equations that are Lorentz invariant a novel algorithm for the derivation of the equations of motion from the field equations. It is: (1) Compute a static, spherically symmetric solution of the field equation. It will be singular at the origin. This will be taken to be the field generated by a single particle. (2) Move the solution on a trajectory P and apply the instantaneous Lorentz transformation based on instantaneous velocity. (3) Take, as first approximation, the field generated by N particles to be the superposition of the fields generated by the single particles. (4) Compute the leading part of the equation. Hopefully, only terms that involve the acceleration will be dominant. This is the ``inertial'' part. (5) Compute the quadratic part of the equation. This is the agent of the ``force''. (6) Equate for each singularity, the highest order terms of the singularities that came from the linear part and the quadratic parts, respectively. This is an equation between the inertial part and the force. The algorithm was applied to Einstein's equations. The approximate evolution of the scalar curvature leads, in turn, to an invariant scalar equation. The algorithm for it did produce Newton's law of gravitation. This is, also, the starting point for the embedding of the trajectories in a common field.
ERIC Educational Resources Information Center
Powers, Sonya Jean
2010-01-01
When test forms are administered to examinee groups that differ in proficiency, equating procedures are used to disentangle group differences from form differences. This dissertation investigates the extent to which equating results are population invariant, the impact of group differences on equating results, the impact of group differences on…
Asymptotic stability of singularly perturbed differential equations
NASA Astrophysics Data System (ADS)
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Efficient High Pressure MixtureState Equations
NASA Technical Reports Server (NTRS)
Harstad, K. G.; Miller, R. S.; Bellan, J.
1996-01-01
A method is presented for an accurate noniterative, computationally efficient calculation of high pressure fluid mixture equations of state, especially targeted to gas turbines and rocket engines. Pressures above 1 bar and temperatures above 100 K are addressed. The method is based on curve fitting an effective reference state relative to departure funcitons formed using the Peng-Robinson cubic state equation. Fit parameters for H(sub 2), O(sub 2), N(sub 2), propane, n-heptane and methanol are given.
Thermoelastic constitutive equations for chemically hardening materials
NASA Technical Reports Server (NTRS)
Shaffer, B. W.; Levitsky, M.
1974-01-01
Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.
Constitutive equations of ageing polymeric materials
NASA Technical Reports Server (NTRS)
Peng, S. T. J.
1985-01-01
The constitutive equation for the relaxation behavior of time-dependent, chemically unstable materials developed by Valanis and Peng (1983), which used the irreversible thermodynamics of internal variables in Eyring's absolute reaction theory and yielded a theoretical expression for the effect of chemical crosslink density on the relaxation rate, is presently applied to the creep behavior of a network polymer which is undergoing a scission process. In particular, two equations are derived which may for the first time show the relations between mechanical models and internal variables in the creep expressions, using a three-element model with a Maxwell element.
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.
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.
NASA Astrophysics Data System (ADS)
Frimmer, Martin; Novotny, Lukas
2014-10-01
Coherent control of a quantum mechanical two-level system is at the heart of magnetic resonance imaging, quantum information processing, and quantum optics. Among the most prominent phenomena in quantum coherent control are Rabi oscillations, Ramsey fringes, and Hahn echoes. We demonstrate that these phenomena can be derived classically by use of a simple coupled-harmonic-oscillator model. The classical problem can be cast in a form that is formally equivalent to the quantum mechanical Bloch equations with the exception that the longitudinal and the transverse relaxation times (T1 and T2) are equal. The classical analysis is intuitive and well suited for familiarizing students with the basic concepts of quantum coherent control, while at the same time highlighting the fundamental differences between classical and quantum theories.
Modeling some real phenomena by fractional differential equations
NASA Astrophysics Data System (ADS)
Almeida, Ricardo; Bastos, Nuno R. O.; Monteiro, M. Teresa T.
2016-11-01
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data, as well as other related parameters.
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.
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.
Stability of drift waves with the integral eigenmode equation
Chen, L.; Ke, F.J.; Xu, M.J.; Tsai, S.T.; Lee, Y.C.; Antonsen, T.M. Jr.
1981-11-01
An analytical theory on the stability properties of drift-wave eigenmodes in a slab plasma with finite magnetic shear is presented. The corresponding eigenmode equation is the integral equation first given by Coppi, Rosenbluth, and Sagdeev (1967) and rederived here, in a relatively simpler fashion, via the gyrokinetic equation. It is then proved that the universal drift-wave eigenmodes remain absolutely stable and finite electron temperature gradients do not alter the stability.
On Modifications of the Zakharov Equation for Surface Gravity Waves.
1983-07-01
finite water depth (in section 2) and show its relations to the cubic Schr - dinger equation and to Hasselmann’s nonlinear interaction model (in section 3...on a modification of the nonlinear Schr { dinger equation for waves moving over an uneven bottom. Progress Report, Department of Civil Eng. Technion...7th Conf. of Coastal Engineering, Vol. 1, 184-196. Stiassnie, M. 1983 Note on the modified nonlinear Schr ~ dinger equation for deep water waves. Wave
Evaluation of a Predictive Equation for Runup
NASA Astrophysics Data System (ADS)
Stockdon, H. F.; Stockdon, H. F.; Holman, R. A.; Sallenger, A. H.
2001-12-01
Extreme runup occurring during storms and hurricanes is likely to be responsible for the most dramatic erosional events, impacting both the beach and dunes and forming an important design criterion for coastal structures and set back. Yet one of the most commonly used predictive equations for runup (Holman, 1986) is based on data from a single site and has not been broadly tested. We will examine the consequences of the extension of Holman's equation to other beach and wave conditions by comprehensive testing using data from seven field experiments: Duck, NC (1982, 1990, 1997); Scripps Beach, CA (1989); San Onofre, CA (1993); Gleneden, OR (1994); and Agate Beach, OR (1996). Special attention will be given to data collected during high tides and large wave events as they represent times of highest runup and most significant erosion. Holman's equation shows a relationship between extreme runup and the Iribarren number, which includes a linear dependence on beach slope. However, on more complex topographies, it is unclear whether runup is more dependent upon the foreshore or surf zone slope. Our analysis will investigate the most appropriate definition of beach slope by testing both in the single horizontal dimension equation. We will then expand the one-dimensional equation to examine beaches with longshore variable topographies. Here, the equation predicts significant variations in runup with possible consequences to short scale variability in beach erosion. Using the improved equation and data from sites with multiple longshore locations, we will examine the longshore variability of beach slope and how it relates to both predicted and observed runup statistics.
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<
NASA Astrophysics Data System (ADS)
Alolyan, Ibraheem; Simos, T. E.
2016-12-01
A family of implicit symmetric linear six-step methods for the numerical solution of second order periodic initial or boundary-value problems is investigated in this paper. The construction of the new family of methods is based on: • the vanishing phase-lag and • the vanished of its derivatives.For the produced methods of the new family of methods, we investigate their local truncation error and its application to a test problem. We compare the results of the above mentioned application in order to extract summaries about the efficiency of each method of the family. We also studied the stability for the developed methods of the new family of methods. Finally, we applied the new produced family of methods to the resonance problem of the radial time independent Schrödinger equation in order to show their efficiency.
2013-01-01
Background The extent to which psychosocial and diet behavior factors affect dietary self-report remains unclear. We examine the contribution of these factors to measurement error of self-report. Methods In 450 postmenopausal women in the Women’s Health Initiative Observational Study doubly labeled water and urinary nitrogen were used as biomarkers of objective measures of total energy expenditure and protein. Self-report was captured from food frequency questionnaire (FFQ), four day food record (4DFR) and 24 hr. dietary recall (24HR). Using regression calibration we estimated bias of self-reported dietary instruments including psychosocial factors from the Stunkard-Sorenson Body Silhouettes for body image perception, the Crowne-Marlowe Social Desirability Scale, and the Three Factor Eating Questionnaire (R-18) for cognitive restraint for eating, uncontrolled eating, and emotional eating. We included a diet behavior factor on number of meals eaten at home using the 4DFR. Results Three categories were defined for each of the six psychosocial and diet behavior variables (low, medium, high). Participants with high social desirability scores were more likely to under-report on the FFQ for energy (β = -0.174, SE = 0.054, p < 0.05) and protein intake (β = -0.142, SE = 0.062, p < 0.05) compared to participants with low social desirability scores. Participants consuming a high percentage of meals at home were less likely to under-report on the FFQ for energy (β = 0.181, SE = 0.053, p < 0.05) and protein (β = 0.127, SE = 0.06, p < 0.05) compared to participants consuming a low percentage of meals at home. In the calibration equations combining FFQ, 4DFR, 24HR with age, body mass index, race, and the psychosocial and diet behavior variables, the six psychosocial and diet variables explained 1.98%, 2.24%, and 2.15% of biomarker variation for energy, protein, and protein density respectively. The variations explained are
NASA Astrophysics Data System (ADS)
Sokolova, Tatiana S.; Dorogokupets, Peter I.; Dymshits, Anna M.; Danilov, Boris S.; Litasov, Konstantin D.
2016-09-01
We present Microsoft Excel spreadsheets for calculation of thermodynamic functions and P-V-T properties of MgO, diamond and 9 metals, Al, Cu, Ag, Au, Pt, Nb, Ta, Mo, and W, depending on temperature and volume or temperature and pressure. The spreadsheets include the most common pressure markers used in in situ experiments with diamond anvil cell and multianvil techniques. The calculations are based on the equation of state formalism via the Helmholtz free energy. The program was developed using Visual Basic for Applications in Microsoft Excel and is a time-efficient tool to evaluate volume, pressure and other thermodynamic functions using T-P and T-V data only as input parameters. This application is aimed to solve practical issues of high pressure experiments in geosciences and mineral physics.
Multiscale equations for strongly stratified turbulent flows
NASA Astrophysics Data System (ADS)
Chini, Greg; Rocha, Cesar; Julien, Keith; Caulfield, Colm-Cille
2016-11-01
Strongly stratified turbulent shear flows are of fundamental importance owing to their widespread occurrence and their impact on diabatic mixing, yet direct numerical simulations of such flows remain challenging. Here, a reduced, multiscale description of turbulent shear flows in the presence of strong stable density stratification is derived via asymptotic analysis of the governing Boussinesq equations. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemoporal scales, and yields simplified partial differential equations governing the coupled evolution of slowly-evolving small aspect-ratio ('pancake') modes and isotropic, strongly non-hydrostatic stratified-shear (e.g. Kelvin-Helmholtz) instability modes. The reduced model is formally valid in the physically-relevant regime in which the aspect-ratio of the pancake structures tends to zero in direct proportion to the horizontal Froude number. Relative to the full Boussinesq equations, the model offers both computational and conceptual advantages.
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.
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.
Master equation analysis of deterministic chemical chaos
NASA Astrophysics Data System (ADS)
Wang, Hongli; Li, Qianshu
1998-05-01
The underlying microscopic dynamics of deterministic chemical chaos was investigated in this paper. We analyzed the master equation for the Williamowski-Rössler model by direct stochastic simulation as well as in the generating function representation. Simulation within an ensemble revealed that in the chaotic regime the deterministic mass action kinetics is related neither to the ensemble mean nor to the most probable value within the ensemble. Cumulant expansion analysis of the master equation also showed that the molecular fluctuations do not admit bounded values but increase linearly in time infinitely, indicating the meaninglessness of the chaotic trajectories predicted by the phenomenological equations. These results proposed that the macroscopic description is no longer useful in the chaotic regime and a more microscopic description is necessary in this circumstance.
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.
Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation
NASA Astrophysics Data System (ADS)
Li, Xiang-Zheng; Zhang, Jin-Liang; Wang, Ming-Liang
2017-02-01
Three (2+1)-dimensional equations–KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully. Supported by the National Natural Science Foundation of China under Grant No. 11301153 and the Doctoral Foundation of Henan University of Science and Technology under Grant No. 09001562, and the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No. 2015XPT001
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.
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
Squared eigenfunctions for the Sasa-Satsuma equation
NASA Astrophysics Data System (ADS)
Yang, Jianke; Kaup, D. J.
2009-02-01
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.
A reciprocal transformation for the Geng-Xue equation
Li, Nianhua Niu, Xiaoxing
2014-05-15
In this paper, we construct a reciprocal transformation for the Geng-Xue equation and show that, with help of this transformation, we relate the first negative flow of the modified Boussinesq hierarchy to the Geng-Xue equation. Furthermore, we analyze the construction of conserved quantities and present new ones.
Representing Rate Equations for Enzyme-Catalyzed Reactions
ERIC Educational Resources Information Center
Ault, Addison
2011-01-01
Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…
Hamiltonian structures for the Ostrovsky-Vakhnenko equation
NASA Astrophysics Data System (ADS)
Brunelli, J. C.; Sakovich, S.
2013-01-01
We obtain a bi-Hamiltonian formulation for the Ostrovsky-Vakhnenko (OV) equation using its higher order symmetry and a new transformation to the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Central to this derivation is the relation between Hamiltonian structures when dependent and independent variables are transformed.
Observed-Score Equating with a Heterogeneous Target Population
ERIC Educational Resources Information Center
Duong, Minh Q.; von Davier, Alina A.
2012-01-01
Test equating is a statistical procedure for adjusting for test form differences in difficulty in a standardized assessment. Equating results are supposed to hold for a specified target population (Kolen & Brennan, 2004; von Davier, Holland, & Thayer, 2004) and to be (relatively) independent of the subpopulations from the target population (see…
Menikoff, Ralph
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
A note on "Kepler's equation".
NASA Astrophysics Data System (ADS)
Dutka, J.
1997-07-01
This note briefly points out the formal similarity between Kepler's equation and equations developed in Hindu and Islamic astronomy for describing the lunar parallax. Specifically, an iterative method for calculating the lunar parallax has been developed by the astronomer Habash al-Hasib al-Marwazi (about 850 A.D., Turkestan), which is surprisingly similar to the iterative method for solving Kepler's equation invented by Leonhard Euler (1707 - 1783).
Factorization of the Compressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.
2005-01-01
The Navier-Stokes equations for a Newtonian ideal gas are examined to determine the factorizable form of the equations relevant to the construction of a factorizable relaxation scheme. The principal linearization of the equations is found by examining the relative magnitude of the terms for short-wavelength errors. The principal part of the operator is then found. Comparison of the factors of the Navier-Stokes and Euler equations differ qualitatively because of the coupling of entropy and pressure through thermal diffusion. Special cases of the factorization are considered.
The intrinsic periodic fluctuation of forest: a theoretical model based on diffusion equation
NASA Astrophysics Data System (ADS)
Zhou, J.; Lin, G., Sr.
2015-12-01
Most forest dynamic models predict the stable state of size structure as well as the total basal area and biomass in mature forest, the variation of forest stands are mainly driven by environmental factors after the equilibrium has been reached. However, although the predicted power-law size-frequency distribution does exist in analysis of many forest inventory data sets, the estimated distribution exponents are always shifting between -2 and -4, and has a positive correlation with the mean value of DBH. This regular pattern can not be explained by the effects of stochastic disturbances on forest stands. Here, we adopted the partial differential equation (PDE) approach to deduce the systematic behavior of an ideal forest, by solving the diffusion equation under the restricted condition of invariable resource occupation, a periodic solution was gotten to meet the variable performance of forest size structure while the former models with stable performance were just a special case of the periodic solution when the fluctuation frequency equals zero. In our results, the number of individuals in each size class was the function of individual growth rate(G), mortality(M), size(D) and time(T), by borrowing the conclusion of allometric theory on these parameters, the results perfectly reflected the observed "exponent-mean DBH" relationship and also gave a logically complete description to the time varying form of forest size-frequency distribution. Our model implies that the total biomass of a forest can never reach a stable equilibrium state even in the absence of disturbances and climate regime shift, we propose the idea of intrinsic fluctuation property of forest and hope to provide a new perspective on forest dynamics and carbon cycle research.
Electronic representation of wave equation
NASA Astrophysics Data System (ADS)
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Delay equations and radiation damping
NASA Astrophysics Data System (ADS)
Chicone, C.; Kopeikin, S. M.; Mashhoon, B.; Retzloff, D. G.
2001-06-01
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we identify this invariant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not contained in the local equations of motion.
New conditions for obtaining the exact solutions of the general Riccati equation.
Bougoffa, Lazhar
2014-01-01
We propose a direct method for solving the general Riccati equation y' = f(x) + g(x)y + h(x)y(2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
Generalized Langevin theory for inhomogeneous fluids: The equations of motion
NASA Astrophysics Data System (ADS)
Grant, Martin; Desai, Rashmi C.
1982-05-01
We use the generalized Langevin approach to study the dynamical correlations in an inhomogeneous system. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor, and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamiclike quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low-density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We also indicate how the resulting general set of equations would simplify for systems in which the inhomogeneity is unidirectional, e.g., a liquid-vapor interface.
A Least-Squares Transport Equation Compatible with Voids
Hansen, Jon; Peterson, Jacob; Morel, Jim; Ragusa, Jean; Wang, Yaqi
2014-12-01
Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S_{n} formulation represents an excellent alternative to existing second-order S_{n} transport formulations
Kleinert, H; Zatloukal, V
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
NASA Astrophysics Data System (ADS)
Cintra, B. B. L.; Schietti, J.; Emillio, T.; Martins, D.; Moulatlet, G.; Souza, P.; Levis, C.; Quesada, C. A.; Schöngart, J.
2013-04-01
The ongoing demand for information on forest productivity has increased the number of permanent monitoring plots across the Amazon. Those plots, however, do not comprise the whole diversity of forest types in the Amazon. The complex effects of soil, climate and hydrology on the productivity of seasonally waterlogged interfluvial wetland forests are still poorly understood. The presented study is the first field-based estimate for tree ages and wood biomass productivity in the vast interfluvial region between the Purus and Madeira rivers. We estimate stand age and wood biomass productivity by a combination of tree-ring data and allometric equations for biomass stocks of eight plots distributed along 600 km in the Purus-Madeira interfluvial area that is crossed by the BR-319 highway. We relate stand age and wood biomass productivity to hydrological and edaphic conditions. Mean productivity and stand age were 5.6 ± 1.1 Mg ha-1 yr-1 and 102 ± 18 yr, respectively. There is a strong relationship between tree age and diameter, as well as between mean diameter increment and mean wood density within a plot. Regarding the soil hydromorphic properties we find a positive correlation with wood biomass productivity and a negative relationship with stand age. Productivity also shows a positive correlation with the superficial phosphorus concentration. In addition, superficial phosphorus concentration increases with enhanced soil hydromorphic condition. We raise three hypotheses to explain these results: (1) the reduction of iron molecules on the saturated soils with plinthite layers close to the surface releases available phosphorous for the plants; (2) the poor structure of the saturated soils creates an environmental filter selecting tree species of faster growth rates and shorter life spans and (3) plant growth on saturated soil is favored during the dry season, since there should be low restrictions for soil water availability.
A new rate equation for desorption at the solid/solution interface
NASA Astrophysics Data System (ADS)
Bashiri, Hadis; Hassani Javanmardi, Alireza
2017-03-01
In this article, a new integrated kinetics Langmuir equation for desorption from the solid surface is derived. This new equation is simple and easy to be used. Several sets of kinetic data points are generated to analyze the accuracy of the new rate equation. By applying theoretical and experimental data, the applicability of the new equation is proved. The analysis of the new equation explains its relation with the pseudo first-order rate equation, and it shows the conditions of its possible application based on Langmuir model. The accuracy of theoretical derivation of pseudo first-order rate equation is proved.
Koyama, Kohei; Kikuzawa, Kihachiro
2009-05-01
Allometric scalings and a logistic equation assume that whole-plant photosynthetic rate under resource-unlimited conditions is proportional to leaf area. We tested this proportionality for the herb Helianthus tuberosus. During growth, we repeatedly measured the percentage of leaves with high, medium, and low photosynthetic capacity to estimate the whole-plant sum of photosynthetic capacity. We found that the whole-plant sum of the light-saturated photosynthetic rate of leaves is proportional to the whole-plant leaf area, disregarding the dynamics of the leaf population. We also found that the daily photosynthesis of each leaf appeared as a linear function of the light-saturated photosynthetic rate of that leaf, as predicted by the optimization theory. Using those results, we expressed whole-plant photosynthetic rate as a product of the light-saturated whole-plant photosynthetic rate and an efficiency index that reflects resource limitation as in the logistic equation. This efficiency decreased with increasing leaf area, reflecting light limitation. Therefore, realized whole-plant photosynthetic rate is not proportional to leaf area. These "diminishing returns" are well explained by a simple saturating curve, such as the logistic equation.