Growth of the eye lens: II. Allometric studies

PubMed Central

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

Growth of the eye lens: II. Allometric studies.

PubMed

Augusteyn, Robert C

2014-01-01

The purpose of this study was to examine the ontogeny and phylogeny of lens growth in a variety of species using allometry. 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. 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. 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.

Crown ratio influences allometric scaling in trees

Treesearch

Annikki Makela; Harry T. Valentine

2006-01-01

Allometric theories suggest that the size and shape of organisms follow universal rules, with a tendency toward quarter-power scaling. In woody plants, however, structure is influenced by branch death and shedding, which leads to decreasing crown ratios, accumulation of heartwood, and stem and branch tapering. This paper examines the impacts on allometric scaling of...

Root-shoot growth responses during interspecific competition quantified using allometric modelling.

PubMed

Robinson, David; Davidson, Hazel; Trinder, Clare; Brooker, Rob

2010-12-01

Plant competition studies are restricted by the difficulty of quantifying root systems of competitors. Analyses are usually limited to above-ground traits. Here, a new approach to address this issue is reported. Root system weights of competing plants can be estimated from: shoot weights of competitors; combined root weights of competitors; and slopes (scaling exponents, α) and intercepts (allometric coefficients, β) of ln-regressions of root weight on shoot weight of isolated plants. If competition induces no change in root : shoot growth, α and β values of competing and isolated plants will be equal. Measured combined root weight of competitors will equal that estimated allometrically from measured shoot weights of each competing plant. Combined root weights can be partitioned directly among competitors. If, as will be more usual, competition changes relative root and shoot growth, the competitors' combined root weight will not equal that estimated allometrically and cannot be partitioned directly. However, if the isolated-plant α and β values are adjusted until the estimated combined root weight of competitors matches the measured combined root weight, the latter can be partitioned among competitors using their new α and β values. The approach is illustrated using two herbaceous species, Dactylis glomerata and Plantago lanceolata. Allometric modelling revealed a large and continuous increase in the root : shoot ratio by Dactylis, but not Plantago, during competition. This was associated with a superior whole-plant dry weight increase in Dactylis, which was ultimately 2·5-fold greater than that of Plantago. Whole-plant growth dominance of Dactylis over Plantago, as deduced from allometric modelling, occurred 14-24 d earlier than suggested by shoot data alone. Given reasonable assumptions, allometric modelling can analyse competitive interactions in any species mixture, and overcomes a long-standing problem in studies of competition.

Estimating geographic variation on allometric growth and body condition of Blue Suckers with quantile regression

USGS Publications Warehouse

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�

Body size and allometric variation in facial shape in children.

PubMed

Larson, Jacinda R; Manyama, Mange F; Cole, Joanne B; Gonzalez, Paula N; Percival, Christopher J; Liberton, Denise K; Ferrara, Tracey M; Riccardi, Sheri L; Kimwaga, Emmanuel A; Mathayo, Joshua; Spitzmacher, Jared A; Rolian, Campbell; Jamniczky, Heather A; Weinberg, Seth M; Roseman, Charles C; Klein, Ophir; Lukowiak, Ken; Spritz, Richard A; Hallgrimsson, Benedikt

2018-02-01

Morphological integration, or the tendency for covariation, is commonly seen in complex traits such as the human face. The effects of growth on shape, or allometry, represent a ubiquitous but poorly understood axis of integration. We address the question of to what extent age and measures of size converge on a single pattern of allometry for human facial shape. Our study is based on two large cross-sectional cohorts of children, one from Tanzania and the other from the United States (N = 7,173). We employ 3D facial imaging and geometric morphometrics to relate facial shape to age and anthropometric measures. The two populations differ significantly in facial shape, but the magnitude of this difference is small relative to the variation within each group. Allometric variation for facial shape is similar in both populations, representing a small but significant proportion of total variation in facial shape. Different measures of size are associated with overlapping but statistically distinct aspects of shape variation. Only half of the size-related variation in facial shape can be explained by the first principal component of four size measures and age while the remainder associates distinctly with individual measures. Allometric variation in the human face is complex and should not be regarded as a singular effect. This finding has important implications for how size is treated in studies of human facial shape and for the developmental basis for allometric variation more generally. © 2017 Wiley Periodicals, Inc.

Quantum metabolism explains the allometric scaling of metabolic rates.

PubMed

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.

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.

Jellyfish Body Plans Provide Allometric Advantages beyond Low Carbon Content

PubMed Central

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.

PubMed

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

Allometric Models for Predicting Aboveground Biomass and Carbon Stock of Tropical Perennial C 4 Grasses in Hawaii

DOE PAGES

Youkhana, Adel H.; Ogoshi, Richard M.; Kiniry, James R.; ...

2017-05-02

Biomass is a promising renewable energy option that provides a more environmentally sustainable alternative to fossil resources by reducing the net flux of greenhouse gasses to the atmosphere. Yet, allometric models that allow the prediction of aboveground biomass (AGB), biomass carbon (C) stock non-destructively have not yet been developed for tropical perennial C 4 grasses currently under consideration as potential bioenergy feedstock in Hawaii and other subtropical and tropical locations. The objectives of this study were to develop optimal allometric relationships and site-specific models to predict AGB, biomass C stock of napiergrass, energycane, and sugarcane under cultivation practices for renewablemore » energy and validate these site-specific models against independent data sets generated from sites with widely different environments. Several allometric models were developed for each species from data at a low elevation field on the island of Maui, Hawaii. A simple power model with stalk diameter (D) was best related to AGB and biomass C stock for napiergrass, energycane, and sugarcane, (R 2 = 0.98, 0.96, and 0.97, respectively). The models were then tested against data collected from independent fields across an environmental gradient. For all crops, the models over-predicted AGB in plants with lower stalk D, but AGB was under-predicted in plants with higher stalk D. The models using stalk D were better for biomass prediction compared to dewlap H (Height from the base cut to most recently exposed leaf dewlap) models, which showed weak validation performance. Although stalk D model performed better, however, the mean square error (MSE)-systematic was ranged from 23 to 43 % of MSE for all crops. A strong relationship between model coefficient and rainfall was existed, although these were irrigated systems; suggesting a simple site-specific coefficient modulator for rainfall to reduce systematic errors in water-limited areas. These allometric equations

Allometric scaling of echocardiographic measurements in healthy Spanish foals with different body weight.

PubMed

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 in-vitro

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.

The ratio and allometric scaling of speed, power, and strength in elite male rugby union players.

PubMed

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).

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)…

Allometric biomass estimators for aspen-dominated ecosystems in the upper Great Lakes.

Treesearch

Donald A. Perala; David Alban

1993-01-01

Presents allometric estimators relating aboveground and belowground component weights to diameter measurements of more than 2,500 trees and shrubs encompassing 35 woody species samples from 8 soil series. The estimators were only weakly related to soil character but were strongly influenced by population density variation induced by silvicultural treatment.

Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity.

PubMed

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. © 2012 The Authors. Journal of Evolutionary Biology © 2012 European Society For Evolutionary Biology.

Problems of allometric scaling analysis: examples from mammalian reproductive biology.

PubMed

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

Updated generalized biomass equations for North American tree species

Treesearch

David C. Chojnacky; Linda S. Heath; Jennifer C. Jenkins

2014-01-01

Historically, tree biomass at large scales has been estimated by applying dimensional analysis techniques and field measurements such as diameter at breast height (dbh) in allometric regression equations. Equations often have been developed using differing methods and applied only to certain species or isolated areas. We previously had compiled and combined (in meta-...

A potential mechanism for allometric trabecular bone scaling in terrestrial mammals.

PubMed

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. © 2015 Anatomical Society.

Allometric scaling of strength scores in NCAA division I-A football athletes.

PubMed

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.

Equations for estimating biomass, foliage area, and sapwood of small trees in the southern Appalachians

Treesearch

Steven T. Brantley; Morgan L. Schulte; Paul V. Bolstad; Chelcy F. Miniat

2016-01-01

Small trees and shrubs play an important role in forest diversity and regeneration and may contribute substantially to ecosystem fluxes of carbon and water; however, relatively little attention is given to quantifying the contribution of small trees to forest processes. One reason for this may be that the allometric equations developed for large trees tend to...

Allometric growth in reef-building corals.

PubMed

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. © 2017 The Author(s).

Allometric scaling for predicting human clearance of bisphenol A

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collet, Séverine H., E-mail: s.collet@envt.fr; Picard-Hagen, Nicole, E-mail: n.hagen-picard@envt.fr; Lacroix, Marlène Z., E-mail: m.lacroix@envt.fr

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 statemore » 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.« less

Pharmacokinetics, Pharmacodynamics, and Allometric Scaling of Chloroquine in a Murine Malaria Model▿

PubMed Central

Moore, Brioni R.; Page-Sharp, Madhu; Stoney, Jillian R.; Ilett, Kenneth F.; Jago, Jeffrey D.; Batty, Kevin T.

2011-01-01

Chloroquine (CQ) is an important antimalarial drug for the treatment of special patient groups and as a comparator for preclinical testing of new drugs. Pharmacokinetic data for CQ in animal models are limited; thus, we conducted a three-part investigation, comprising (i) pharmacodynamic studies of CQ and CQ plus dihydroartemisinin (DHA) in Plasmodium berghei-infected mice, (ii) pharmacokinetic studies of CQ in healthy and malaria-infected mice, and (iii) interspecies allometric scaling for CQ from 6 animal and 12 human studies. The single-dose pharmacodynamic study (10 to 50 mg CQ/kg of body weight) showed dose-related reduction in parasitemia (5- to >500-fold) and a nadir 2 days after the dose. Multiple-dose regimens (total dose, 50 mg/kg CQ) demonstrated a lower nadir and longer survival time than did the same single dose. The CQ-DHA combination provided an additive effect compared to each drug alone. The elimination half-life (t1/2), clearance (CL), and volume of distribution (V) of CQ were 46.6 h, 9.9 liters/h/kg, and 667 liters/kg, respectively, in healthy mice and 99.3 h, 7.9 liters/h/kg, and 1,122 liters/kg, respectively, in malaria-infected mice. The allometric equations for CQ in healthy mammals (CL = 3.86 × W0.56, V = 230 × W0.94, and t1/2 = 123 × W0.2) were similar to those for malaria-infected groups. CQ showed a delayed dose-response relationship in the murine malaria model and additive efficacy when combined with DHA. The biphasic pharmacokinetic profiles of CQ are similar across mammalian species, and scaling of specific parameters is plausible for preclinical investigations. PMID:21646487

[Biomass allometric equations of nine common tree species in an evergreen broadleaved forest of subtropical China].

PubMed

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.

A model for allometric scaling of mammalian metabolism with ambient heat loss.

PubMed

Kwak, Ho Sang; Im, Hong G; Shim, Eun Bo

2016-03-01

Allometric scaling, which represents the dependence of biological traits or processes on body size, is a long-standing subject in biological science. However, there has been no study to consider heat loss to the ambient and an insulation layer representing mammalian skin and fur for the derivation of the scaling law of metabolism. A simple heat transfer model is proposed to analyze the allometry of mammalian metabolism. The present model extends existing studies by incorporating various external heat transfer parameters and additional insulation layers. The model equations were solved numerically and by an analytic heat balance approach. A general observation is that the present heat transfer model predicted the 2/3 surface scaling law, which is primarily attributed to the dependence of the surface area on the body mass. External heat transfer effects introduced deviations in the scaling law, mainly due to natural convection heat transfer, which becomes more prominent at smaller mass. These deviations resulted in a slight modification of the scaling exponent to a value < 2/3. The finding that additional radiative heat loss and the consideration of an outer insulation fur layer attenuate these deviation effects and render the scaling law closer to 2/3 provides in silico evidence for a functional impact of heat transfer mode on the allometric scaling law in mammalian metabolism.

Allometric scaling law in a simple oxygen exchanging network: possible implications on the biological allometric scaling laws.

PubMed

Santillán, Moisés

2003-07-21

A simple model of an oxygen exchanging network is presented and studied. This network's task is to transfer a given oxygen rate from a source to an oxygen consuming system. It consists of a pipeline, that interconnects the oxygen consuming system and the reservoir and of a fluid, the active oxygen transporting element, moving through the pipeline. The network optimal design (total pipeline surface) and dynamics (volumetric flow of the oxygen transporting fluid), which minimize the energy rate expended in moving the fluid, are calculated in terms of the oxygen exchange rate, the pipeline length, and the pipeline cross-section. After the oxygen exchanging network is optimized, the energy converting system is shown to satisfy a 3/4-like allometric scaling law, based upon the assumption that its performance regime is scale invariant as well as on some feasible geometric scaling assumptions. Finally, the possible implications of this result on the allometric scaling properties observed elsewhere in living beings are discussed.

Biomass equations for shrub species of Tamualipan thornscrub of North-Eastern Mexico

Treesearch

J. Navar; E. Mendez; A. Najera; J. Graciano; V. Dale; B. Parresol

2004-01-01

Nine additive allometric equations for computing above-ground, standing biomass were developed for the plant community and for each of 18 single species typical of the Tamaulipan thornscrub of north-eastern Mexico. Equations developed using additive procedures in seemingly unrelated linear regression provided statistical efficiency in total biomass estimates at the...

Evolution of extreme ontogenetic allometric diversity and heterochrony in pythons, a clade of giant and dwarf snakes.

PubMed

Esquerré, Damien; Sherratt, Emma; Keogh, J Scott

2017-12-01

Ontogenetic allometry, how species change with size through their lives, and heterochony, a decoupling between shape, size, and age, are major contributors to biological diversity. However, macroevolutionary allometric and heterochronic trends remain poorly understood because previous studies have focused on small groups of closely related species. Here, we focus on testing hypotheses about the evolution of allometry and how allometry and heterochrony drive morphological diversification at the level of an entire species-rich and diverse clade. Pythons are a useful system due to their remarkably diverse and well-adapted phenotypes and extreme size disparity. We collected detailed phenotype data on 40 of the 44 species of python from 1191 specimens. We used a suite of analyses to test for shifts in allometric trajectories that modify morphological diversity. Heterochrony is the main driver of initial divergence within python clades, and shifts in the slopes of allometric trajectories make exploration of novel phenotypes possible later in divergence history. We found that allometric coefficients are highly evolvable and there is an association between ontogenetic allometry and ecology, suggesting that allometry is both labile and adaptive rather than a constraint on possible phenotypes. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Metabolic allometric scaling model: combining cellular transportation and heat dissipation constraints.

PubMed

Shestopaloff, Yuri K

2016-08-15

Living organisms need energy to be 'alive'. Energy is produced by the biochemical processing of nutrients, and the rate of energy production is called the metabolic rate. Metabolism is very important from evolutionary and ecological perspectives, and for organismal development and functioning. It depends on different parameters, of which organism mass is considered to be one of the most important. Simple relationships between the mass of organisms and their metabolic rates were empirically discovered by M. Kleiber in 1932. Such dependence is described by a power function, whose exponent is referred to as the allometric scaling coefficient. With the increase of mass, the metabolic rate usually increases more slowly; if mass increases by two times, the metabolic rate increases less than two times. This fact has far-reaching implications for the organization of life. The fundamental biological and biophysical mechanisms underlying this phenomenon are still not well understood. The present study shows that one such primary mechanism relates to transportation of substances, such as nutrients and waste, at a cellular level. Variations in cell size and associated cellular transportation costs explain the known variance of the allometric exponent. The introduced model also includes heat dissipation constraints. The model agrees with experimental observations and reconciles experimental results across different taxa. It ties metabolic scaling to organismal and environmental characteristics, helps to define perspective directions of future research and allows the prediction of allometric exponents based on characteristics of organisms and the environments they live in. © 2016. Published by The Company of Biologists Ltd.

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.

Allometric Convergence in Savanna Trees and Implications for the Use of Plant Scaling Models in Variable Ecosystems

PubMed Central

Tredennick, Andrew T.; Bentley, Lisa Patrick; Hanan, Niall P.

2013-01-01

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those

Evolution of static allometries: adaptive change in allometric slopes of eye span in stalk-eyed flies.

PubMed

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. © 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.

An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans.

PubMed

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. Copyright © 2016 the authors 0270-6474/16/362438-11$15.00/0.

Size structuring and allometric scaling relationships in coral reef fishes.

PubMed

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

An Allometric Analysis of Sex and Sex Chromosome Dosage Effects on Subcortical Anatomy in Humans

PubMed Central

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

Allometric scaling and accidents at work

PubMed Central

Cempel, Czesław; Tabaszewski, Maciej; Ordysiński, Szymon

2016-01-01

Allometry is the knowledge concerning relations between the features of some beings, like animals, or cities. For example, the daily energy rate is proportional to a mass of mammals rise of 3/4. This way of thinking has spread quickly from biology to many areas of research concerned with sociotechnical systems. It was revealed that the number of innovations, patents or heavy crimes rises as social interaction increases in a bigger city, while other urban indexes such as suicides decrease with social interaction. Enterprise is also a sociotechnical system, where social interaction and accidents at work take place. Therefore, do these interactions increase the number of accidents at work or, on the contrary, are they reduction-driving components? This article tries to catch such links and assess the allometric exponent between the number of accidents at work and the number of employees in an enterprise. PMID:26655044

Allometric relationships among body mass, MUZZLE-tail length, and tibia length during the growth of Wistar rats.

PubMed

Santiago, Hildemberg Agostinho Rocha de; De Pierro, Lucas Rodolfo; Reis, Rafael Menezes; Caluz, Antônio Gabriel Ricardo Engracia; Ribeiro, Victor Barbosa; Volpon, José Batista

2015-11-01

To investigate allometric relationships among body mass (BM), muzzle-tail length (MTL), and tibia length (TL) in Wistar rats and establish their growth rate change parameters. Eighteen male and 18 female Wistar rats were studied from the 3rd to the 21st week of age. BM, MTL, and TL were measured daily, and relative growth was compared using allometry. A positive correlation between BM and MTL (p<0.05) and BM and TL (p<0.05) was observed. Males and females showed comparable curves; however, females had turning points at a younger age. The allometric relationship between BM and MTL presented a regular increase until reaching a mass of 351 g (males) and 405 g (females). BM and TL showed an initial increase until 185 g (males) and 182 g (females), and then reached a plateau that finished at 412 g (males) and 334 g (females), to display another increase. The allometric relationship of body mass with animal length and tibia length was comparable for male and female rats, with female rats maturing earlier. Animal longitudinal growth occurred in a single stage. In contrast, tibia length depicted two stages of accelerated growth with an intermediate period of deceleration.

Allometric scaling theory applied to FIA biomass estimation

Treesearch

David C. Chojnacky

2002-01-01

Tree biomass estimates in the Forest Inventory and Analysis (FIA) database are derived from numerous methodologies whose abundance and complexity raise questions about consistent results throughout the U.S. A new model based on allometric scaling theory ("WBE") offers simplified methodology and a theoretically sound basis for improving the reliability and...

Allometric growth and development of organs in ballan wrasse (Labrus bergylta Ascanius, 1767) larvae in relation to different live prey diets and growth rates

PubMed Central

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

Allometric Scaling of the Active Hematopoietic Stem Cell Pool across Mammals

PubMed Central

Dingli, David; Pacheco, Jorge M.

2006-01-01

Background Many biological processes are characterized by allometric relations of the type Y = Y 0 Mb between an observable Y and body mass M, which pervade at multiple levels of organization. In what regards the hematopoietic stem cell pool, there is experimental evidence that the size of the hematopoietic stem cell pool is conserved in mammals. However, demands for blood cell formation vary across mammals and thus the size of the active stem cell compartment could vary across species. Methodology/Principle Findings Here we investigate the allometric scaling of the hematopoietic system in a large group of mammalian species using reticulocyte counts as a marker of the active stem cell pool. Our model predicts that the total number of active stem cells, in an adult mammal, scales with body mass with the exponent ¾. Conclusion/Significance The scaling predicted here provides an intuitive justification of the Hayflick hypothesis and supports the current view of a small active stem cell pool supported by a large, quiescent reserve. The present scaling shows excellent agreement with the available (indirect) data for smaller mammals. The small size of the active stem cell pool enhances the role of stochastic effects in the overall dynamics of the hematopoietic system. PMID:17183646

Component biomass equations for black spruce in Maine

Treesearch

M. M. Czapowskyj; D. J. Robison; R. D. Briggs; E. H. White; E. H. White

1985-01-01

Component biomass prediction equations are presented for young black spruce (Picea mariana B.S.P. (Mill,:)) in northern Maine. A weighted least squares model was used to construct the eq~iationsfo r small trees from 1 to 15 cm d.b.h., and an ordinary least squares model for trees less than 2 m in height. A linearized allometric model was also tested but was not used....

Allometric method to estimate leaf area index for row crops

USDA-ARS?s Scientific Manuscript database

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...

An allometric scaling relationship in the brain of preterm infants

PubMed Central

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

Allometric relationships predicting foliar biomass and leaf area:sapwood area ratio from tree height in five Costa Rican rain forest species.

PubMed

Calvo-Alvarado, J C; McDowell, N G; Waring, R H

2008-11-01

We developed allometric equations to predict whole-tree leaf area (A(l)), leaf biomass (M(l)) and leaf area to sapwood area ratio (A(l):A(s)) in five rain forest tree species of Costa Rica: Pentaclethra macroloba (Willd.) Kuntze (Fabaceae/Mim), Carapa guianensis Aubl. (Meliaceae), Vochysia ferru-gi-nea Mart. (Vochysiaceae), Virola koshnii Warb. (Myristicaceae) and Tetragastris panamensis (Engl.) Kuntze (Burseraceae). By destructive analyses (n = 11-14 trees per species), we observed strong nonlinear allometric relationships (r(2) > or = 0.9) for predicting A(l) or M(l) from stem diameters or A(s) measured at breast height. Linear relationships were less accurate. In general, A(l):A(s) at breast height increased linearly with tree height except for Penta-clethra, which showed a negative trend. All species, however, showed increased total A(l) with height. The observation that four of the five species increased in A(l):A(s) with height is consistent with hypotheses about trade--offs between morphological and anatomical adaptations that favor efficient water flow through variation in the amount of leaf area supported by sapwood and those imposed by the need to respond quickly to light gaps in the canopy.

Reference intervals and allometric scaling of two-dimensional echocardiographic measurements in 150 healthy cats.

PubMed

Karsten, Schober; Stephanie, Savino; Vedat, Yildiz

2017-11-10

The objective of the study was to evaluate the effects of body weight (BW), breed, and sex on two-dimensional (2D) echocardiographic measures, reference ranges, and prediction intervals using allometrically-scaled data of left atrial (LA) and left ventricular (LV) size and LV wall thickness in healthy cats. Study type was retrospective, observational, and clinical cohort. 150 healthy cats were enrolled and 2D echocardiograms analyzed. LA diameter, LV wall thickness, and LV dimension were quantified using three different imaging views. The effect of BW, breed, sex, age, and interaction (BW*sex) on echocardiographic variables was assessed using univariate and multivariate regression and linear mixed model analysis. Standard (using raw data) and allometrically scaled (Y=a × M b ) reference intervals and prediction intervals were determined. BW had a significant (P<0.05) independent effect on 2D variables whereas breed, sex, and age did not. There were clinically relevant differences between reference intervals using mean ± 2SD of raw data and mean and 95% prediction interval of allometrically-scaled variables, most prominent in larger (>6 kg) and smaller (<3 kg) cats. A clinically relevant difference between thickness of the interventricular septum (IVS) and dimension of the LV posterior wall (LVPW) was identified. In conclusion, allometric scaling and BW-based 95% prediction intervals should be preferred over conventional 2D echocardiographic reference intervals in cats, in particular in small and large cats. These results are particularly relevant to screening examinations for feline hypertrophic cardiomyopathy.

Development of LiDAR aware allometrics for Abies grandis: A Case Study

NASA Astrophysics Data System (ADS)

Stone, G. A.; Tinkham, W. T.; Smith, A. M.; Hudak, A. T.; Falkowski, M. J.; Keefe, R.

2012-12-01

Forest managers rely increasingly on accurate allometric relationships to inform decisions regarding stand rotations, silvilcultural treatments, timber harvesting, and biometric modeling. At the same time, advances in remote sensing techniques like LiDAR (light detection and ranging) have brought about opportunities to advance how we assess forest growth, and thus are contributing to the need for more accurate allometries. Past studies have attempted to relate LiDAR data to both plot and individual tree measures of forest biomass. However, many of these studies have been limited by the accuracy of their coincident observations. In this study, 24 Abies grandis were measured, felled, and dissected for the explicit objective of developing LiDAR aware allometrics. The analysis predicts spatial variables of competition, growth potential (e.g, trees per acre, aspect, elevation, etc.) and common statistical distributional metrics (e.g., mean, mode, percentiles, variance, skewness, kurtosis, etc.) derived from LiDAR point cloud returns to coincident in situ measures of Abies grandis stem biomass. The resulting allometries exemplify a new approach for predicting structural attributes of interest (biomass, basal area, volume, etc.) directly from LiDAR point cloud data, precluding the measurement errors that are propogated by indirectly predicting these structure attributes of interest from LiDAR data using traditional plot-based measurements.

Morphological changes and allometric growth in hatchery-reared Chinese loach Paramisgurnus dabryanus (Dabry de Thiersant, 1872)

NASA Astrophysics Data System (ADS)

Zhang, Yunlong; Wu, Qiaowan; Hu, Weihua; Wang, Fan; Shao, Weihan; Zhang, Chengming; Zhao, Zhongbo; He, Hui; Fan, Qixue; Gu, Zemao

2016-07-01

The length-weight relationship and allometric growth patterns of hatchery-reared Chinese loach, Paramisgurnus dabryanus (Dabry de Thiersant, 1872), were determined from hatching to 60 days after hatching. A best power model was estimated for the length-weight relationship during the early life stages. Positive allometric growth for the head segment, trunk length, tail length and eye diameter was also found in the early life stages, while body depth, tail depth, tail fin length, pectoral fin length and barbel length displayed a negative coefficient. During the subsequent early developmental stage, the growth coefficients showed a clear and common tendency towards isometry for all measured body ratios. The allometric growth changes in Chinese loach during the early stage are possibly the result of selective organogenesis directed towards survival priorities.

The effect of allometric scaling in coral thermal microenvironments

PubMed Central

Ong, Robert H.; Kaandorp, Jaap A.; Mullins, Benjamin J.; Caley, M. Julian

2017-01-01

A long-standing interest in marine science is in the degree to which environmental conditions of flow and irradiance, combined with optical, thermal and morphological characteristics of individual coral colonies, affects their sensitivity of thermal microenvironments and susceptibility to stress-induced bleaching within and/or among colonies. The physiological processes in Scleractinian corals tend to scale allometrically as a result of physical and geometric constraints on body size and shape. There is a direct relationship between scaling to thermal stress, thus, the relationship between allometric scaling and rates of heating and cooling in coral microenvironments is a subject of great interest. The primary aim of this study was to develop an approximation that predicts coral thermal microenvironments as a function of colony morphology (shape and size), light or irradiance, and flow velocity or regime. To do so, we provided intuitive interpretation of their energy budgets for both massive and branching colonies, and then quantified the heat-size exponent (b*) and allometric constant (m) using logarithmic linear regression. The data demonstrated a positive relationship between thermal rates and changes in irradiance, A/V ratio, and flow, with an interaction where turbulent regime had less influence on overall stress which may serve to ameliorate the effects of temperature rise compared to the laminar regime. These findings indicated that smaller corals have disproportionately higher stress, however they can reach thermal equilibrium quicker. Moreover, excellent agreements between the predicted and simulated microscale temperature values with no significant bias were observed for both the massive and branching colonies, indicating that the numerical approximation should be within the accuracy with which they could be measured. This study may assist in estimating the coral microscale temperature under known conditions of water flow and irradiance, in particular

Allometric constraints on Sr/Ca and Ba/Ca partitioning in terrestrial mammalian trophic chains.

PubMed

Balter, Vincent

2004-03-01

In biological systems, strontium (Sr) and barium (Ba) are two non-essential elements, in comparison to calcium (Ca) which is essential. The Sr/Ca and Ba/Ca ratios tend to decrease in biochemical pathways which include Ca as an essential element, and these processes are termed biopurification of Ca. The quantitative pathway of the biopurification of Ca in relation to Sr and Ba between two biological reservoirs ( Rn and R(n -1)) is measured with an observed ratio (OR) expressed by the (Sr/Ca) Rn /(Sr/Ca)( Rn-1) and (Ba/Ca) Rn /(Ba/Ca)( Rn-1) ratios. For a mammalian organism, during the whole biopurification of Ca starting with the diet to the ultimate reservoir of Ca which is the bone, the mean values for ORSr and ORBa are 0.25 and 0.2, respectively. In this study, published Sr/Ca and Ba/Ca ratios are used for three sets of soils, plants, and bones of herbivorous and carnivorous mammals, each comprising a trophic chain, to illustrate the biopurification of Ca at the level of trophic chains. Calculated ORSr and ORBa of herbivore bones in relation to plants and of bones of carnivores in relation to bones of herbivores give ORSr=0.30+/-0.08 and ORBa=0.16+/-0.08, thus suggesting that trophic chains reflect the Sr/Ca and Ba/Ca fluxes that are prevalent at the level of a mammalian organism. The slopes of the three regression equations of log(Sr/Ca) vs. log(Ba/Ca) are similar, indicating that the process of biopurification of Ca with respect to Sr and Ba is due to biological processes and is independent of the geological settings. Modifications of the logarithmic expression of the Sr/Ca and Ba/Ca relationship allow a new formula of the biopurification process to be deduced, leading to the general equation ORBa=ORSr(1.79+/-0.33), where the allometric coefficient is the mean of the slopes of the three regression equations. Some recent examples are used to illustrate this new analysis of predator-prey relations between mammals. This opens up new possibilities for the

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…

Body size and meta-community structure: the allometric scaling of parasitic worm communities in their mammalian hosts.

PubMed

DE Leo, Giulio A; Dobson, Andrew P; Gatto, Marino

2016-06-01

In this paper we derive from first principles the expected body sizes of the parasite communities that can coexist in a mammal of given body size. We use a mixture of mathematical models and known allometric relationships to examine whether host and parasite life histories constrain the diversity of parasite species that can coexist in the population of any host species. The model consists of one differential equation for each parasite species and a single density-dependent nonlinear equation for the affected host under the assumption of exploitation competition. We derive threshold conditions for the coexistence and competitive exclusion of parasite species using invasion criteria and stability analysis of the resulting equilibria. These results are then used to evaluate the range of parasites species that can invade and establish in a target host and identify the 'optimal' size of a parasite species for a host of a given body size; 'optimal' is defined as the body size of a parasite species that cannot be outcompeted by any other parasite species. The expected distributions of parasites body sizes in hosts of different sizes are then compared with those observed in empirical studies. Our analysis predicts the relative abundance of parasites of different size that establish in the host and suggests that increasing the ratio of parasite body size to host body size above a minimum threshold increases the persistence of the parasite population.

Allometric scaling of fatty acyl chains in fowl liver, lung and kidney, but not in brain phospholipids.

PubMed

Szabó, András; Mézes, Miklós; Romvári, Róbert; Fébel, Hedvig

2010-03-01

The phospholipid (PL) fatty acyl chain (FA) composition (mol%) was determined in the kidney, liver, lung and brain of 8 avian species ranging in body mass from 150g (Japanese quail, Coturnix coturnix japonica) to 19kg (turkey, Meleagris gallopavo). In all organs except the brain, docosahexaenoic acid (C22:6 n3, DHA) was found to show a negative allometric scaling (allometric exponent: B=-0.18; -0.20 and -0.24, for kidney, liver and lung, respectively). With minor inter-organ differences, smaller birds had more n3 FAs and longer FA chains in the renal, hepatic and pulmonary PLs. Comparing our results with literature data on avian skeletal muscle, liver mitochondria and kidney microsomes and divergent mammalian tissues, the present findings in the kidney, liver and lung PLs seem to be a part of a general relationship termed "membranes as metabolic pacemakers". Marked negative allometric scaling was found furthermore for the tissue malondialdehyde concentrations in all organs except the brain (B=-0.17; -0.13 and -0.05, respectively). In the liver and kidney a strong correlation was found between the tissue MDA and DHA levels, expressing the role of DHA in shaping the allometric properties of membrane lipids. 2009 Elsevier Inc. All rights reserved.

Allometric and temporal scaling of movement characteristics in Galapagos tortoises

USGS Publications Warehouse

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

Adding constraints to predation through allometric relation of scats to consumption.

PubMed

Chakrabarti, Stotra; Jhala, Yadvendradev V; Dutta, Sutirtha; Qureshi, Qamar; Kadivar, Riaz F; Rana, Vishwadipsinh J

2016-05-01

A thorough understanding of mechanisms of prey consumption by carnivores and the constraints on predation help us in evaluating the role of carnivores in an ecosystem. This is crucial in developing appropriate management strategies for their conservation and mitigating human-carnivore conflict. Current models on optimal foraging suggest that mammalian carnivores would profit most from killing the largest prey that they can subdue with minimal risk of injury to themselves. Wild carnivore diets are primarily estimated through analysis of their scats. Using extensive feeding experiments (n = 68) on a wide size range (4·5-130 kg) of obligate carnivores - lion, leopard, jungle cat and domestic cat, we parameterize biomass models that best relate consumption to scat production. We evaluate additional constraints of gut fill, prey digestibility and carcass utilization on carnivory that were hereto not considered in optimal foraging studies. Our results show that patterns of consumption to scat production against prey size are similar and asymptotic, contrary to established linear models, across these carnivores after accounting for the effect of carnivore size. This asymptotic, allometric relationship allowed us to develop a generalized model: biomass consumed per collectable scat/predator weight = 0·033-0·025exp(-4·284(prey weight/predator weight)) , which is applicable to all obligate carnivores to compute prey biomass consumed from scats. Our results also depict a relationship for prey digestibility which saturates at about 90% for prey larger than predator size. Carcass utilization declines exponentially with prey size. These mechanisms result in digestible biomass saturating at prey weights approximately equal to predator weight. Published literature on consumption by tropical carnivores that has relied on linear biomass models is substantially biased. We demonstrate the nature of these biases by correcting diets of tiger, lion and leopard in recent

Allometric and temporal scaling of movement characteristics in Galapagos tortoises.

PubMed

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

Inconsistency of allometric scaling for dissociative anesthesia of wild felids.

PubMed

Carregaro, Adriano B; Freitas, Gabrielle C; Bisetto, Shayne P; Xavier, Nathalia V; Sterzo, Elton V

2016-05-01

To evaluate allometric scaling for ketamine-xylazine (KX) anesthesia in wild felids using domestic cats for reference. Prospective single-phase non-blinded study. Six domestic cats and 13 wild felids (five Leopardus pardalis, five Puma concolor, one Panthera onca and two Panthera leo). Six domestic cats (4.1 ± 0.8 kg, REF1) were anesthetized by intramuscular administration of ketamine (15 mg kg(-1) ) and xylazine (1 mg kg(-1) ). Wild cats were divided into three groups based on body weight: 12.9 ± 2.4 kg (G1; n = 7), 43.0 ± 15.7 kg (G2; n = 4) and 126.0 ± 7.8 kg (G3; n = 2). Ketamine and xylazine doses were calculated based on allometric scaling of the basal metabolic rate (BMR = 70 × body mass(0.75) ). Afterwards, the six domestic cats were administered mean KX doses calculated for G1 and G2 (REF2). The heart rate, systolic arterial pressure, respiratory frequency, pH, the venous partial pressure of carbon dioxide, bicarbonate and lactate concentrations were recorded for up to 60 minutes. Additional doses were required in 12 out of the 13 wild cats. Anesthesia was not achieved in G3. Latency periods in wild felids were longer than REF1 and REF2. Anesthesia duration in REF1 was longer than that in the other groups. Recovery from anesthesia in REF1 and REF2 was longer than G1 and G2. Physiological variables remained within the range limits for the species. G1 baseline lactate concentration was higher than in the other groups. KX anesthesia established by allometric scaling of BMR from doses administered to domestic cats did not predict reliable anesthetic doses for wild cats. Dose rates calculated with this method must not be applied to these species. © 2015 Association of Veterinary Anaesthetists and the American College of Veterinary Anesthesia and Analgesia.

The allometric relationship between resting metabolic rate and body mass in wild waterfowl (Anatidae) and an application to estimation of winter habitat requirements

USGS Publications Warehouse

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.

Equations for Estimating Biomass of Herbaceous and Woody Vegetation in Early-Successional Southern Appalachian Pine-Hardwood Forests

Treesearch

Katherine J. Elliott; Barton D. Clinton

1993-01-01

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 diamet,er, height, or both, as the independent variables and dry weight as the dependent variable. Coefficients of determination for the selected total...

BOOK REVIEW: Partial Differential Equations in General Relativity

NASA Astrophysics Data System (ADS)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed

Allometric scaling of biceps strength before and after resistance training in men.

PubMed

Zoeller, Robert F; Ryan, Eric D; Gordish-Dressman, Heather; Price, Thomas B; Seip, Richard L; Angelopoulos, Theodore J; Moyna, Niall M; Gordon, Paul M; Thompson, Paul D; Hoffman, Eric P

2007-06-01

The purposes of this study were 1) derive allometric scaling models of isometric biceps muscle strength using pretraining body mass (BM) and muscle cross-sectional area (CSA) as scaling variables in adult males, 2) test model appropriateness using regression diagnostics, and 3) cross-validate the models before and after 12 wk of resistance training. A subset of FAMuSS (Functional SNP Associated with Muscle Size and Strength) study data (N=136) were randomly split into two groups (A and B). Allometric scaling models using pretraining BM and CSA were derived and tested for group A. The scaling exponents determined from these models were then applied to and tested on group B pretraining data. Finally, these scaling exponents were applied to and tested on group A and B posttraining data. BM and CSA models produced scaling exponents of 0.64 and 0.71, respectively. Regression diagnostics determined both models to be appropriate. Cross-validation of the models to group B showed that the BM model, but not the CSA model, was appropriate. Removal of the largest six subjects (CSA>30 cm) from group B resulted in an appropriate fit for the CSA model. Application of the models to group A posttraining data showed that both models were appropriate, but only the body mass model was successful for group B. These data suggest that the application of scaling exponents of 0.64 and 0.71, using BM and CSA, respectively, are appropriate for scaling isometric biceps strength in adult males. However, the scaling exponent using CSA may not be appropriate for individuals with biceps CSA>30 cm. Finally, 12 wk of resistance training does not alter the relationship between BM, CSA, and muscular strength as assessed by allometric scaling.

Allometric associations between body size, shape, and 100-m butterfly speed performance.

PubMed

Sammoud, Senda; Nevill, Alan M; Negra, Yassine; Bouguezzi, Raja; Chaabene, Helmi; Hachana, Younés

2018-05-01

This study aimed to estimate the optimal body size, limb-segment length, and girth or breadth ratios associated with 100-m butterfly speed performance in swimmers. One-hundred-sixty-seven swimmers as subjects (male: N.=103; female: N.=64). Anthropometric measurements comprised height, body-mass, skinfolds, arm-span, upper-limb-length, upper-arm, forearm, hand-lengths, lower-limb-length, thigh-length, leg-length, foot-length, arm-relaxed-girth, forearm-girth, wrist-girth, thigh-girth, calf-girth, ankle-girth, biacromial and biiliocristal-breadths. To estimate the optimal body size and body composition components associated with 100-m butterfly speed performance, we adopted a multiplicative allometric log-linear regression model, which was refined using backward elimination. Fat-mass was the singularly most important whole-body characteristic. Height and body-mass did not contribute to the model. The allometric model identified that having greater limb segment length-ratio (arm-ratio = [arm-span]/[forearm]) and limb girth-ratio (girth-ratio = [calf-girth]/[ankle-girth]) were key to butterfly speed performance. A greater arm-span to forearm-length ratio and a greater calf to ankle-girth-ratio suggest that a combination of larger arm-span and shorter forearm-length and the combination of larger calves and smaller ankles-girth may benefit butterfly swim speed performance. In addition having greater biacromial and biliocristal breadths is also a major advantage in butterfly swimming speed performance. Finally, the estimation of these ratios was made possible by adopting a multiplicative allometric model that was able to confirm, theoretically, that swim speeds are nearly independent of total body size. The 100-m butterfly speed performance was strongly negatively associated with fat mass and positively associated with the segment length ratio (arm-span/forearm-length) and girth ratio (calf-girth)/(ankle-girth), having controlled for the developmental changes in age.

Intra- and Interspecific Interactions as Proximate Determinants of Sexual Dimorphism and Allometric Trajectories in the Bottlenose Dolphin Tursiops truncatus (Cetacea, Odontoceti, Delphinidae)

PubMed Central

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

Choosing the Allometric Exponent in Covariate Model Building.

PubMed

Sinha, Jaydeep; Al-Sallami, Hesham S; Duffull, Stephen B

2018-04-27

Allometric scaling is often used to describe the covariate model linking total body weight (WT) to clearance (CL); however, there is no consensus on how to select its value. The aims of this study were to assess the influence of between-subject variability (BSV) and study design on (1) the power to correctly select the exponent from a priori choices, and (2) the power to obtain unbiased exponent estimates. The influence of WT distribution range (randomly sampled from the Third National Health and Nutrition Examination Survey, 1988-1994 [NHANES III] database), sample size (N = 10, 20, 50, 100, 200, 500, 1000 subjects), and BSV on CL (low 20%, normal 40%, high 60%) were assessed using stochastic simulation estimation. A priori exponent values used for the simulations were 0.67, 0.75, and 1, respectively. For normal to high BSV drugs, it is almost impossible to correctly select the exponent from an a priori set of exponents, i.e. 1 vs. 0.75, 1 vs. 0.67, or 0.75 vs. 0.67 in regular studies involving < 200 adult participants. On the other hand, such regular study designs are sufficient to appropriately estimate the exponent. However, regular studies with < 100 patients risk potential bias in estimating the exponent. Those study designs with limited sample size and narrow range of WT (e.g. < 100 adult participants) potentially risk either selection of a false value or yielding a biased estimate of the allometric exponent; however, such bias is only relevant in cases of extrapolating the value of CL outside the studied population, e.g. analysis of a study of adults that is used to extrapolate to children.

Differences in motor performance between children and adolescents in Mozambique and Portugal: impact of allometric scaling.

PubMed

Dos Santos, Fernanda Karina; Nevill, Allan; Gomes, Thayse Natacha Q F; Chaves, Raquel; Daca, Timóteo; Madeira, Aspacia; Katzmarzyk, Peter T; Prista, António; Maia, José A R

2016-05-01

Children from developed and developing countries have different anthropometric characteristics which may affect their motor performance (MP). To use the allometric approach to model the relationship between body size and MP in youth from two countries differing in socio-economic status-Portugal and Mozambique. A total of 2946 subjects, 1280 Mozambicans (688 girls) and 1666 Portuguese (826 girls), aged 10-15 years were sampled. Height and weight were measured and the reciprocal ponderal index (RPI) was computed. MP included handgrip strength, 1-mile run/walk, curl-ups and standing long jump tests. A multiplicative allometric model was adopted to adjust for body size differences across countries. Differences in MP between Mozambican and Portuguese children exist, invariably favouring the latter. The allometric models used to adjust MP for differences in body size identified the optimal body shape to be either the RPI or even more linear, i.e. approximately (height/mass(0.25)). Having adjusted the MP variables for differences in body size, the differences between Mozambican and Portuguese children were invariably reduced and, in the case of grip strength, reversed. These results reinforce the notion that significant differences exist in MP across countries, even after adjusting for differences in body size.

Geometric morphometric analysis of allometric variation in the mandibular morphology of the hominids of Atapuerca, Sima de los Huesos site.

PubMed

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. Copyright 2004 Wiley-Liss, Inc.

The allometric exponent for scaling clearance varies with age: a study on seven propofol datasets ranging from preterm neonates to adults.

PubMed

Wang, Chenguang; Allegaert, Karel; Peeters, Mariska Y M; Tibboel, Dick; Danhof, Meindert; Knibbe, Catherijne A J

2014-01-01

For scaling clearance between adults and children, allometric scaling with a fixed exponent of 0.75 is often applied. In this analysis, we performed a systematic study on the allometric exponent for scaling propofol clearance between two subpopulations selected from neonates, infants, toddlers, children, adolescents and adults. Seven propofol studies were included in the analysis (neonates, infants, toddlers, children, adolescents, adults1 and adults2). In a systematic manner, two out of the six study populations were selected resulting in 15 combined datasets. In addition, the data of the seven studies were regrouped into five age groups (FDA Guidance 1998), from which four combined datasets were prepared consisting of one paediatric age group and the adult group. In each of these 19 combined datasets, the allometric scaling exponent for clearance was estimated using population pharmacokinetic modelling (nonmem 7.2). The allometric exponent for propofol clearance varied between 1.11 and 2.01 in cases where the neonate dataset was included. When two paediatric datasets were analyzed, the exponent varied between 0.2 and 2.01, while it varied between 0.56 and 0.81 when the adult population and a paediatric dataset except for neonates were selected. Scaling from adults to adolescents, children, infants and neonates resulted in exponents of 0.74, 0.70, 0.60 and 1.11 respectively. For scaling clearance, ¾ allometric scaling may be of value for scaling between adults and adolescents or children, while it can neither be used for neonates nor for two paediatric populations. For scaling to neonates an exponent between 1 and 2 was identified. © 2013 The British Pharmacological Society.

Cardiovascular performance of adult breeding sows fails to obey allometric scaling laws.

PubMed

van Essen, G J; Vernooij, J C M; Heesterbeek, J A P; Anjema, D; Merkus, D; Duncker, D J

2011-02-01

In view of the remarkable decrease of the relative heart weight (HW) and the relative blood volume in growing pigs, we investigated whether HW, cardiac output (CO), and stroke volume (SV) of modern growing pigs are proportional to BW, as predicted by allometric scaling laws: HW (or CO or SV) = a·BW(b), in which a and b are constants, and constant b is a multiple of 0.25 (quarter-power scaling law). Specifically, we tested the hypothesis that both HW and CO scale with BW to the power of 0.75 (HW or CO = a·BW(0.75)) and SV scales with BW to the power of 1.00 (SV = a·BW(1.0)). For this purpose, 2 groups of pigs (group 1, consisting of 157 pigs of 50 ± 1 kg; group 2, consisting of 45 pigs of 268 ± 18 kg) were surgically instrumented with a flow probe or a thermodilution dilution catheter, under open-chest anesthetized conditions to measure CO and SV, after which HW was determined. The 95% confidence intervals of power-coefficient b for HW were 0.74 to 0.80, encompassing the predicted value of 0.75, suggesting that HW increased proportionally with BW, as predicted by the allometric scaling laws. In contrast, the 95% confidence intervals of power-coefficient b for CO and SV as measured with flow probes were 0.40 to 0.56 and 0.39 to 0.61, respectively, and values obtained with the thermodilution technique were 0.34 to 0.53 and 0.40 to 0.62, respectively. Thus, the 95% confidence limits failed to encompass the predicted values of b for CO and SV of 0.75 and 1.0, respectively. In conclusion, although adult breeding sows display normal heart growth, cardiac performance appears to be disproportionately low for BW. This raises concern regarding the health status of adult breeding sows.

Appropriate interpretation of aerobic capacity: allometric scaling in adult and young soccer players

PubMed Central

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

ALLOMETRIC LENGTH-WEIGHT RELATIONSHIPS FOR BENTHIC PREY OF AQUATIC WILDLIFE IN COASTAL MARINE HABITATS

EPA Science Inventory

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 equations for urban ash trees (Fraxinus spp.) in Oakville, Southern Ontario, Canada

Treesearch

Paula J. Peper; Claudia P. Alzate; John W. McNeil; Jalil Hashemi

2014-01-01

Tree growth equations are an important and common tool used to effectively assess the yield and determine management practices in forest plantations. Increasingly, they are being developed for urban forests, providing tools to assist urban forest managers with species selection, placement, and estimation of management costs and ecosystem services. This study describes...

An allometric approach to quantify the extinction vulnerability of birds and mammals.

PubMed

Hilbers, J P; Schipper, A M; Hendriks, A J; Verones, F; Pereira, H M; Huijbregts, M A J

2016-03-01

Methods to quantify the vulnerability of species to extinction are typically limited by the availability of species-specific input data pertaining to life-history characteristics and population dynamics. This lack of data hampers global biodiversity assessments and conservation planning. Here, we developed a new framework that systematically quantifies extinction risk based on allometric relationships between various wildlife demographic parameters and body size. These allometric relationships have a solid theoretical and ecological foundation. Extinction risk indicators included are (1) the probability of extinction, (2) the mean time to extinction, and (3) the critical patch size. We applied our framework to assess the global extinction vulnerability of terrestrial carnivorous and non-carnivorous birds and mammals. Irrespective of the indicator used, large-bodied species were found to be more vulnerable to extinction than their smaller counterparts. The patterns with body size were confirmed for all species groups by a comparison with IUCN data on the proportion of extant threatened species: the models correctly predicted a multimodal distribution with body size for carnivorous birds and a monotonic distribution for mammals and non-carnivorous birds. Carnivorous mammals were found to have higher extinction risks than non-carnivores, while birds were more prone to extinction than mammals. These results are explained by the allometric relationships, predicting the vulnerable species groups to have lower intrinsic population growth rates, smaller population sizes, lower carrying capacities, or larger dispersal distances, which, in turn, increase the importance of losses due to environmental stochastic effects and dispersal activities. Our study is the first to integrate population viability analysis and allometry into a novel, process-based framework that is able to quantify extinction risk of a large number of species without requiring data-intensive, species

An allometric pharmacokinetic/pharmacodynamics model for BI 893923, a novel IGF-1 receptor inhibitor.

PubMed

Titze, Melanie I; Schaaf, Otmar; Hofmann, Marco H; Sanderson, Michael P; Zahn, Stephan K; Quant, Jens; Lehr, Thorsten

2017-03-01

BI 893923 is a novel IGF1R/INSR inhibitor with promising anti-tumor efficacy. Dose-limiting hyperglycemia has been observed for other IGF1R/INSR inhibitors in clinical trials. To counterbalance anti-tumor efficacy with the risk of hyperglycemia and to determine the therapeutic window, we aimed to develop a translational pharmacokinetic/pharmacodynamics model for BI 893923. This aimed to translate pharmacokinetics and pharmacodynamics from animals to humans by an allometrically scaled semi-mechanistic model. Model development was based on a previously published PK/PD model for BI 893923 in mice (Titze et al., Cancer Chemother Pharmacol 77:1303-1314, 13). PK and blood glucose parameters were scaled by allometric principles using body weight as a scaling factor along with an estimation of the parameter exponents. Biomarker and tumor growth parameters were extrapolated from mouse to human using the body weight ratio as scaling factor. The allometric PK/PD model successfully described BI 893923 pharmacokinetics and blood glucose across mouse, rat, dog, minipig, and monkey. BI 893923 human exposure as well as blood glucose and tumor growth were predicted and compared for different dosing scenarios. A comprehensive risk-benefit analysis was conducted by determining the net clinical benefit for each schedule. An oral dose of 2750 mg BI 893923 divided in three evenly distributed doses was identified as the optimal human dosing regimen, predicting a tumor growth inhibition of 90.4% without associated hyperglycemia. Our model supported human therapeutic dose estimation by rationalizing the optimal efficacious dosing regimen with minimal undesired effects. This modeling approach may be useful for PK/PD scaling of other IGF1R/INSR inhibitors.

Allometric growth in juvenile marine turtles: possible role as an antipredator adaptation.

PubMed

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. Copyright © 2014 Elsevier GmbH. All rights reserved.

Controversy in the allometric application of fixed- versus varying-exponent models: a statistical and mathematical perspective.

PubMed

Tang, Huadong; Hussain, Azher; Leal, Mauricio; Fluhler, Eric; Mayersohn, Michael

2011-02-01

This commentary is a reply to a recent article by Mahmood commenting on the authors' article on the use of fixed-exponent allometry in predicting human clearance. The commentary discusses eight issues that are related to criticisms made in Mahmood's article and examines the controversies (fixed-exponent vs. varying-exponent allometry) from the perspective of statistics and mathematics. The key conclusion is that any allometric method, which is to establish a power function based on a limited number of animal species and to extrapolate the resulting power function to human values (varying-exponent allometry), is infused with fundamental statistical errors. Copyright © 2010 Wiley-Liss, Inc.

Languages cool as they expand: Allometric scaling and the decreasing need for new words

NASA Astrophysics Data System (ADS)

Petersen, Alexander M.; Tenenbaum, Joel N.; Havlin, Shlomo; Stanley, H. Eugene; Perc, Matjaž

2012-12-01

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ``cooling pattern'' forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature.

Body size and allometric shape variation in the molly Poecilia vivipara along a gradient of salinity and predation.

PubMed

Araújo, Márcio S; Perez, S Ivan; Magazoni, Maria Julia C; Petry, Ana C

2014-12-04

Phenotypic diversity among populations may result from divergent natural selection acting directly on traits or via correlated responses to changes in other traits. One of the most frequent patterns of correlated response is the proportional change in the dimensions of anatomical traits associated with changes in growth or absolute size, known as allometry. Livebearing fishes subject to predation gradients have been shown to repeatedly evolve larger caudal peduncles and smaller cranial regions under high predation regimes. Poecilia vivipara is a livebearing fish commonly found in coastal lagoons in the north of the state of Rio de Janeiro, Brazil. Similar to what is observed in other predation gradients, lagoons inhabited by P. vivipara vary in the presence of piscivorous fishes; contrary to other poeciliid systems, populations of P. vivipara vary greatly in body size, which opens the possibility of strong allometric effects on shape variation. Here we investigated body shape diversification among six populations of P. vivipara along a predation gradient and its relationship with allometric trajectories within and among populations. We found substantial body size variation and correlated shape changes among populations. Multivariate regression analysis showed that size variation among populations accounted for 66% of shape variation in females and 38% in males, suggesting that size is the most important dimension underlying shape variation among populations of P. vivipara in this system. Changes in the relative sizes of the caudal peduncle and cranial regions were only partly in line with predictions from divergent natural selection associated with predation regime. Our results suggest the possibility that adaptive shape variation among populations has been partly constrained by allometry in P. vivipara. Processes governing body size changes are therefore important in the diversification of this species. We conclude that in species characterized by substantial

Assessing allometric models to predict vegetative growth of mango (Mangifera indica; Anacardiaceae) at the current-year branch scale.

PubMed

Normand, Frédéric; Lauri, Pierre-Éric

2012-03-01

Accurate and reliable predictive models are necessary to estimate nondestructively key variables for plant growth studies such as leaf area and leaf, stem, and total biomass. Predictive models are lacking at the current-year branch scale despite the importance of this scale in plant science. We calibrated allometric models to estimate leaf area and stem and branch (leaves + stem) mass of current-year branches, i.e., branches several months old studied at the end of the vegetative growth season, of four mango cultivars on the basis of their basal cross-sectional area. The effects of year, site, and cultivar were tested. Models were validated with independent data and prediction accuracy was evaluated with the appropriate statistics. Models revealed a positive allometry between dependent and independent variables, whose y-intercept but not the slope, was affected by the cultivar. The effects of year and site were negligible. For each branch characteristic, cultivar-specific models were more accurate than common models built with pooled data from the four cultivars. Prediction quality was satisfactory but with data dispersion around the models, particularly for large values. Leaf area and stem and branch mass of mango current-year branches could be satisfactorily estimated on the basis of branch basal cross-sectional area with cultivar-specific allometric models. The results suggested that, in addition to the heteroscedastic behavior of the variables studied, model accuracy was probably related to the functional plasticity of branches in relation to the light environment and/or to the number of growth units composing the branches.

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.

Languages cool as they expand: Allometric scaling and the decreasing need for new words

PubMed Central

Petersen, Alexander M.; Tenenbaum, Joel N.; Havlin, Shlomo; Stanley, H. Eugene; Perc, Matjaž

2012-01-01

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This “cooling pattern” forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature. PMID:23230508

Comparative Allometric Growth of the Mimetic Ephippid Reef Fishes Chaetodipterus faber and Platax orbicularis.

PubMed

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.

Allometric modelling of peak oxygen uptake in male soccer players of 8-18 years of age.

PubMed

Valente-Dos-Santos, João; Coelho-E-Silva, Manuel J; Tavares, Óscar M; Brito, João; Seabra, André; Rebelo, António; Sherar, Lauren B; Elferink-Gemser, Marije T; Malina, Robert M

2015-03-01

Peak oxygen uptake (VO2peak) is routinely scaled as mL O2 per kilogram body mass despite theoretical and statistical limitations of using ratios. To examine the contribution of maturity status and body size descriptors to age-associated inter-individual variability in VO2peak and to present static allometric models to normalize VO2peak in male youth soccer players. Total body and estimates of total and regional lean mass were measured with dual energy X-ray absorptiometry in a cross-sectional sample of Portuguese male soccer players. The sample was divided into three age groups for analysis: 8-12 years, 13-15 years and 16-18 years. VO2peak was estimated using an incremental maximal exercise test on a motorized treadmill. Static allometric models were used to normalize VO2peak. The independent variables with the best statistical fit explained 72% in the younger group (lean body mass: k = 1.07), 52% in mid-adolescent players (lean body mass: k = 0.93) and 31% in the older group (body mass: k = 0.51) of variance in VO2peak. The inclusion of the exponential term pubertal status marginally increased the explained variance in VO2peak (adjusted R(2 )= 36-75%) and provided statistical adjustments to the size descriptors coefficients. The allometric coefficients and exponents evidenced the varying inter-relationship among size descriptors and maturity status with aerobic fitness from early to late-adolescence. Lean body mass, lean lower limbs mass and body mass combined with pubertal status explain most of the inter-individual variability in VO2peak among youth soccer players.

Allometric models for predicting aboveground biomass and carbon stock of tropical perennial C4 grasses in Hawaii

USDA-ARS?s Scientific Manuscript database

Biomass represents a promising renewable energy opportunity that mayprovide a more sustainable alternative to the use of fossil resources by minimizing the net production of greenhouse gases. Yet, allometric models that allow the prediction of biomass, biomass carbon (C) and nitrogen (N) stocks rap...

Allometric constraints to inversion of canopy structure from remote sensing

NASA Astrophysics Data System (ADS)

Wolf, A.; Berry, J. A.; Asner, G. P.

2008-12-01

Canopy radiative transfer models employ a large number of vegetation architectural and leaf biochemical attributes. Studies of leaf biochemistry show a wide array of chemical and spectral diversity that suggests that several leaf biochemical constituents can be independently retrieved from multi-spectral remotely sensed imagery. In contrast, attempts to exploit multi-angle imagery to retrieve canopy structure only succeed in finding two or three of the many unknown canopy arhitectural attributes. We examine a database of over 5000 destructive tree harvests from Eurasia to show that allometry - the covariation of plant form across a broad range of plant size and canopy density - restricts the architectural diversity of plant canopies into a single composite variable ranging from young canopies with many short trees with small crowns to older canopies with fewer trees and larger crowns. Moreover, these architectural attributes are closely linked to biomass via allometric constraints such as the "self-thinning law". We use the measured variance and covariance of plant canopy architecture in these stands to drive the radiative transfer model DISORD, which employs the Li-Strahler geometric optics model. This correlations introduced in the Monte Carlo study are used to determine which attributes of canopy architecture lead to important variation that can be observed by multi-angle or multi-spectral satellite observations, using the sun-view geometry characteristic of MODIS observations in different biomes located at different latitude bands. We conclude that although multi-angle/multi-spectral remote sensing is only sensitive to some of the many unknown canopy attributes that ecologists would wish to know, the strong allometric covariation between these attributes and others permits a large number of inferrences, such as forest biomass, that will be meaningful next-generation vegetation products useful for data assimilation.

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.…

Allometric variation among juvenile, adult male and female eastern bearded dragons Pogona barbata (Cuvier, 1829), with comments on the behavioural implications.

PubMed

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. Crown Copyright © 2011. Published by Elsevier GmbH. All rights reserved.

Baecklund transformation for the Ernst equation of general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harrison, B.K.

A Baecklund transformation for the Ernst equation arising in general relativity in connection with several physical problems is derived, using the pseudopotential method of Wahlquist and Estabrook. A prolongation structure is also constructed, using a method of writing the equations in terms of differential forms, and an equation in the spirit of Lax is constructed, somewhat different from that given by Maison. Possible uses of the Baecklund transformation to generate new solutions are mentioned.

[Duration of the pre-nesting period and its relation with social organization in sandpipers (Charadrii, Aves) nesting in north-east Yakutia].

PubMed

Gavrilov, V V

2013-01-01

Investigations were carried out at two stations of Ornithological Unit, IBPN FEB RAS, located in Nizhnekolymsk District, Yakutia, starting from May 18-20 in 1984, 1985, 1987, 1988 and 1990. Duration of the pre-nesting period in 11 sandpiper species with different social organization was studied and compared with each other by allometric equations. As a characteristic of bird size the body mass was selected. Sandpipers come flying to the tundra at almost critical temperatures, to begin breeding as early as possible. Tining of breeding depends on birds feeding manner and the proximity to sites of overwintering. Duration of the pre-nesting period is invariable for every bird species and sex. There are sexual distinctions in time spent for the pre-nesting period in jointly-nesting sandpipers. The exponents in allometric equations that relate duration of the pre-nesting period with body mass are constant within a particular sex and differ between males and females. In different sexes, time spent for the pre-nesting period depends on mating, parental, and territorial systems. In sandpipers' males and females, this time is determined by the type of social organization. Relatively large sandpiper species seek to shortening of the pre-nesting period calendar time, which constrains their social organization. Monogamy and pair parental care lead to a necessity for spatial population structure to be controlled more strictly and maintained for a longer time. This, in turn, causes the increasing of males' time expenditures for such a behavior.

National scale biomass estimators for United States tree species

Treesearch

Jennifer C. Jenkins; David C. Chojnacky; Linda S. Heath; Richard A. Birdsey

2003-01-01

Estimates of national-scale forest carbon (C) stocks and fluxes are typically based on allometric regression equations developed using dimensional analysis techniques. However, the literature is inconsistent and incomplete with respect to large-scale forest C estimation. We compiled all available diameter-based allometric regression equations for estimating total...

Comparative Allometric Growth of the Mimetic Ephippid Reef Fishes Chaetodipterus faber and Platax orbicularis

PubMed Central

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

Generalized Dynamic Equations Related to Condensation and Freezing Processes

NASA Astrophysics Data System (ADS)

Wang, Xingrong; Huang, Yong

2018-01-01

The generalized thermodynamic equation related to condensation and freezing processes was derived by introducing the condensation and freezing probability function into the dynamic framework based on the statistical thermodynamic fluctuation theory. As a result, the physical mechanism of some weather phenomena covered by using δ(0,1) can in turn be studied and uncovered. From the generalized dynamic equations, the tendency equation of the generalized potential vorticity (GPV) is derived. From the discussion of tendency equation of GPV, in some very thin transitional areas, GPV is found nonconserved because of the introduction of the condensation and freezing probability function, even in frictionless and moist adiabatic air motion.

Allometric scaling of infraorbital surface topography in Homo.

PubMed

Maddux, Scott D; Franciscus, Robert G

2009-02-01

Infraorbital morphology is often included in phylogenetic and functional analyses of Homo. The inclusion of distinct infraorbital configurations, such as the "canine fossa" in Homo sapiens or the "inflated" maxilla in Neandertals, is generally based on either descriptive or qualitative assessments of this morphology, or simple linear chord and subtense measurements. However, the complex curvilinear surface of the infraorbital region has proven difficult to quantify through these traditional methods. In this study, we assess infraorbital shape and its potential allometric scaling in fossil Homo (n=18) and recent humans (n=110) with a geometric morphometric method well-suited for quantifying complex surface topographies. Our results indicate that important aspects of infraorbital shape are correlated with overall infraorbital size across Homo. Specifically, individuals with larger infraorbital areas tend to exhibit relatively flatter infraorbital surface topographies, taller and narrower infraorbital areas, sloped inferior orbital rims, anteroinferiorly oriented maxillary body facies, posteroinferiorly oriented maxillary processes of the zygomatic, and non-everted lateral nasal margins. In contrast, individuals with smaller infraorbital regions generally exhibit relatively depressed surface topographies, shorter and wider infraorbital areas, projecting inferior orbital rims, posteroinferiorly oriented maxillary body facies, anteroinferiorly oriented maxillary processes, and everted lateral nasal margins. These contrasts form a continuum and only appear dichotomized at the ends of the infraorbital size spectrum. In light of these results, we question the utility of incorporating traditionally polarized infraorbital morphologies in phylogenetic and functional analyses without due consideration of continuous infraorbital and facial size variation in Homo. We conclude that the essentially flat infraorbital surface topography of Neandertals is not unique and can be

Urban tree database and allometric equations

Treesearch

E. Gregory McPherson; Natalie S. van Doorn; Paula J.  Peper

2016-01-01

Information on urban tree growth underpins models used to calculate the effects of trees on the environment and human well-being. Maximum tree size and other growth data are used by urban forest managers, landscape architects, and planners to select trees most suitable to the amount of growing space, thereby reducing costly future conflicts between trees and...

Urban forest biomass estimates: is it important to use allometric relationships developed specifically for urban trees? 

Treesearch

M.R. McHale; I.C. Burke; M.A. Lefsky; P.J. Peper; E.G. McPherson

2009-01-01

Many studies have analyzed the benefits, costs, and carbon storage capacity associated with urban trees. These studies have been limited by a lack of research on urban tree biomass, such that estimates of carbon storage in urban systems have relied upon allometric relationships developed in traditional forests. As urbanization increases globally, it is becoming...

Does living in urban or rural settings affect aspects of physical fitness in children? An allometric approach

PubMed Central

Tsimeas, P; Tsiokanos, A; Koutedakis, Y; Tsigilis, N; Kellis, S

2005-01-01

Objective: The aim of this study was to investigate physical fitness in relation to fatness in urban and rural Greek children by means of allometric scaling. Methods: The sample consisted of 360 (189 urban and 171 rural; age 12.3±0.42 years) boys and 247 (125 urban and 122 rural; age 12.3±0.43 years) girls. The sample was highly representative (32–64%) of all 12 year old children registered in the prefecture of Trikala, Greece. All volunteers were assessed for BMI and % body fat, as well as sit and reach, basketball throw (BT), vertical jump (VJ), handgrip strength (HG), 40 m sprint, agility run, and 20 m shuttle run. To correct for possible associations between fatness and fitness, a single cause allometric scaling was employed using the natural logarithms (ln) of fitness parameters that were significantly correlated with the ln body fat. Results: Independent-samples t tests revealed that VJ (p<0.05) was significantly higher in boys living in urban settings compared to their rural counterparts. Similarly, BT was found to be significantly better (p<0.05) in urban girls, whereas HG was significantly higher (p<0.05) in rural girls. Conclusion: Considering that (a) only three out of the 14 possible cases (seven fitness parameters for boys and seven for girls) were significantly different between urban and rural children, and (b) these differences were not uniformly distributed in children living in either urban or rural environments, it is concluded that the place of residence has no clear impact on physical fitness as studied herein. PMID:16118308

Musculoskeletal determinants of pelvic sucker function in Hawaiian stream gobiid fishes: interspecific comparisons and allometric scaling.

PubMed

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. Copyright © 2013 Wiley Periodicals, Inc.

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.

An allometric analysis of the number of muscle spindles in mammalian skeletal muscles

PubMed Central

Banks, R W

2006-01-01

An allometric analysis of the number of muscle spindles in relation to muscle mass in mammalian (mouse, rat, guinea-pig, cat, human) skeletal muscles is presented. It is shown that the trend to increasing number as muscle mass increases follows an isometric (length) relationship between species, whereas within a species, at least for the only essentially complete sample (human), the number of spindles scales, on average, with the square root rather than the cube root of muscle mass. An attempt is made to reconcile these apparently discrepant relationships. Use of the widely accepted spindle density (number of spindles g−1 of muscle) as a measure of relative abundance of spindles in different muscles is shown to be grossly misleading. It is replaced with the residuals of the linear regression of ln spindle number against ln muscle mass. Significant differences in relative spindle abundance as measured by residuals were found between regional groups of muscles: the greatest abundance is in axial muscles, including those concerned with head position, whereas the least is in muscles of the shoulder girdle. No differences were found between large and small muscles operating in parallel, or between antigravity and non-antigravity muscles. For proximal vs. distal muscles, spindles were significantly less abundant in the hand than the arm, but there was no difference between the foot and the leg. PMID:16761976

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.

Are tree ontogenetic structure and allometric relationship independent of vegetation formation type? A case study with Cordia oncocalyx in the Brazilian caatinga

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

Allometric shell growth in infaunal burrowing bivalves: examples of the archiheterodonts Claibornicardia paleopatagonica (Ihering, 1903) and Crassatella kokeni Ihering, 1899.

PubMed

Perez, Damián Eduardo; Santelli, María Belén

2018-01-01

We present two cases of study of ontogenetic allometry in outlines of bivalves using longitudinal data, a rarity among fossils, based on the preserved post-larval record of shells. The examples are two infaunal burrowing bivalves of the southern South America, Claibornicardia paleopatagonica (Archiheterodonta: Carditidae) (early Paleocene) and Crassatella kokeni (Archiheterodonta: Crassatellidae) (late Oligocene-late Miocene). Outline analyses were conducted using a geometric morphometric approach (Elliptic Fourier Analysis), obtaining successive outlines from shells' growth lines, which were used to reconstruct ontogenetic trajectories. In both taxa, ontogenetic changes are characterized by the presence of positive allometry in the extension of posterior end, resulting in elongated adult shells. This particular allometric growth is known in others infaunal burrowing bivalves ( Claibornicardia alticostata and some Spissatella species) and the resulting adult morphology is present in representatives of several groups (e.g., Carditidae, Crassatellidae, Veneridae, Trigoniidae). Taxonomic, ecological and evolutionary implications of this allometric growth pattern are discussed.

Comparative biology of the crab Goniopsis cruentata: geographic variation of body size, sexual maturity, and allometric growth

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.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Leon, J. J.-P.; Pempinelli, F.

1989-10-01

We define a new spectral transform r(k, l) of the potential u in the time dependent Schrödinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schrödinger equation are used to express the spectral transform f( k, l) previously introduced by Manakov and Fokas and Ablowitz in terms of r( k, l). The main advantage of the new spectral transform r( k, l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r( k, l) are also obtained.

Echocardiographic Assessment of Left Atrial Size and Function in Warmblood Horses: Reference Intervals, Allometric Scaling, and Agreement of Different Echocardiographic Variables.

PubMed

Huesler, I M; Mitchell, K J; Schwarzwald, C C

2016-07-01

Echocardiographic assessment of left atrial (LA) size and function in horses is not standardized. The aim of this study was to establish reference intervals for echocardiographic indices of LA size and function in Warmblood horses and to provide proof of concept for allometric scaling of variables and for the clinical use of area-based indices. Thirty-one healthy Warmblood horses and 91 Warmblood horses with a primary diagnosis of mitral regurgitation (MR) or aortic regurgitation (AR). Retrospective study. Echocardiographic indices of LA size and function were measured and scaled to body weight (BWT). Reference intervals were calculated, the influence of BWT, age, and valvular regurgitation on LA size and function was investigated and agreement between different measurements of LA size was assessed. Allometric scaling of variables of LA size allowed for correction of differences in BWT. Indices of LA size documented LA enlargement with moderate and severe MR and AR, whereas most indices of LA mechanical function were not significantly altered by valvular regurgitation. Different indices of LA size were in fair to good agreement but still lead to discordant conclusions with regard to assessment of LA enlargement in individual horses. Allometric scaling of echocardiographic variables of LA size is advised to correct for differences in BWT among Warmblood horses. Assessment of LA dimensions should be based on an integrative approach combining subjective evaluation and assessment of multiple measurements, including area-based variables. The clinical relevance of indices of LA mechanical function remains unclear when used in horses with mitral or aortic regurgitation. Copyright © 2016 The Authors. Journal of Veterinary Internal Medicine published by Wiley Periodicals, Inc. on behalf of the American College of Veterinary Internal Medicine.

Generalized Onsager's reciprocal relations for the master and Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-06-01

The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.

Allometric scaling enhances stability in complex food webs.

PubMed

Brose, Ulrich; Williams, Richard J; Martinez, Neo D

2006-11-01

Classic local stability theory predicts that complex ecological networks are unstable and are unlikely to persist despite empiricists' abundant documentation of such complexity in nature. This contradiction has puzzled biologists for decades. While some have explored how stability may be achieved in small modules of a few interacting species, rigorous demonstrations of how large complex and ecologically realistic networks dynamically persist remain scarce and inadequately understood. Here, we help fill this void by combining structural models of complex food webs with nonlinear bioenergetic models of population dynamics parameterized by biological rates that are allometrically scaled to populations' average body masses. Increasing predator-prey body mass ratios increase population persistence up to a saturation level that is reached by invertebrate and ectotherm vertebrate predators when being 10 or 100 times larger than their prey respectively. These values are corroborated by empirical predator-prey body mass ratios from a global data base. Moreover, negative effects of diversity (i.e. species richness) on stability (i.e. population persistence) become neutral or positive relationships at these empirical ratios. These results demonstrate that the predator-prey body mass ratios found in nature may be key to enabling persistence of populations in complex food webs and stabilizing the diversity of natural ecosystems.

Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xi; Yu, Hao-Ran; Zhang, Tong-Jie, E-mail: yangwds@mail.bnu.edu.cn, E-mail: yu@bnu.edu.cn, E-mail: tjzhang@bnu.edu.cn

2013-06-01

Our real universe is locally inhomogeneous. Dyer and Roeder introduced the smoothness parameter α to describe the influence of local inhomogeneity on angular diameter distance, and they obtained the angular diameter distance-redshift approximate relation (Dyer-Roeder equation) for locally inhomogeneous universe. Furthermore, the Distance-Duality (DD) relation, D{sub L}(z)(1+z){sup −2}/D{sub A}(z) = 1, should be valid for all cosmological models that are described by Riemannian geometry, where D{sub L} and D{sub A} are, respectively, the luminosity and angular distance distances. Therefore, it is necessary to test whether if the Dyer-Roeder approximate equation can satisfy the Distance-Duality relation. In this paper, we usemore » Union2.1 SNe Ia data to constrain the smoothness parameter α and test whether the Dyer-Roeder equation meet the DD relation. By using χ{sup 2} minimization, we get α = 0.92{sub −0.32}{sup +0.08} at 1σ and 0.92{sub −0.65}{sup +0.08} at 2σ, and our results show that the Dyer-Roeder equation is in good consistency with the DD relation at 1σ.« less

Allometric Scaling and Cell Ratios in Multi-Organ in vitro Models of Human Metabolism.

PubMed

Ucciferri, Nadia; Sbrana, Tommaso; Ahluwalia, Arti

2014-01-01

Intelligent in vitro models able to recapitulate the physiological interactions between tissues in the body have enormous potential as they enable detailed studies on specific two-way or higher order tissue communication. These models are the first step toward building an integrated picture of systemic metabolism and signaling in physiological or pathological conditions. However, the rational design of in vitro models of cell-cell or cell-tissue interaction is difficult as quite often cell culture experiments are driven by the device used, rather than by design considerations. Indeed, very little research has been carried out on in vitro models of metabolism connecting different cell or tissue types in a physiologically and metabolically relevant manner. Here, we analyze the physiological relationship between cells, cell metabolism, and exchange in the human body using allometric rules, downscaling them to an organ-on-a-plate device. In particular, in order to establish appropriate cell ratios in the system in a rational manner, two different allometric scaling models (cell number scaling model and metabolic and surface scaling model) are proposed and applied to a two compartment model of hepatic-vascular metabolic cross-talk. The theoretical scaling studies illustrate that the design and hence relevance of multi-organ models is principally determined by experimental constraints. Two experimentally feasible model configurations are then implemented in a multi-compartment organ-on-a-plate device. An analysis of the metabolic response of the two configurations demonstrates that their glucose and lipid balance is quite different, with only one of the two models recapitulating physiological-like homeostasis. In conclusion, not only do cross-talk and physical stimuli play an important role in in vitro models, but the numeric relationship between cells is also crucial to recreate in vitro interactions, which can be extrapolated to the in vivo reality.

Allometric Scaling and Cell Ratios in Multi-Organ in vitro Models of Human Metabolism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ucciferri, Nadia; Interdepartmental Research Center “E. Piaggio”, University of Pisa, Pisa; Sbrana, Tommaso

2014-12-17

Intelligent in vitro models able to recapitulate the physiological interactions between tissues in the body have enormous potential as they enable detailed studies on specific two-way or higher order tissue communication. These models are the first step toward building an integrated picture of systemic metabolism and signaling in physiological or pathological conditions. However, the rational design of in vitro models of cell–cell or cell–tissue interaction is difficult as quite often cell culture experiments are driven by the device used, rather than by design considerations. Indeed, very little research has been carried out on in vitro models of metabolism connecting differentmore » cell or tissue types in a physiologically and metabolically relevant manner. Here, we analyze the physiological relationship between cells, cell metabolism, and exchange in the human body using allometric rules, downscaling them to an organ-on-a-plate device. In particular, in order to establish appropriate cell ratios in the system in a rational manner, two different allometric scaling models (cell number scaling model and metabolic and surface scaling model) are proposed and applied to a two compartment model of hepatic-vascular metabolic cross-talk. The theoretical scaling studies illustrate that the design and hence relevance of multi-organ models is principally determined by experimental constraints. Two experimentally feasible model configurations are then implemented in a multi-compartment organ-on-a-plate device. An analysis of the metabolic response of the two configurations demonstrates that their glucose and lipid balance is quite different, with only one of the two models recapitulating physiological-like homeostasis. In conclusion, not only do cross-talk and physical stimuli play an important role in in vitro models, but the numeric relationship between cells is also crucial to recreate in vitro interactions, which can be extrapolated to the in vivo reality.« less

Allometric methodology for the assessment of radon exposures to terrestrial wildlife.

PubMed

Vives i Batlle, J; Copplestone, D; Jones, S R

2012-06-15

A practical approach to calculate (222)Rn daughter dose rates to terrestrial wildlife is presented. The method scales allometrically the relevant parameters for respiration in different species of wildlife, allowing inter-species calculation of the dose per unit radon concentration in air as simple base-and-exponent power functions of the mass. For plants, passive gas exchange through the leaf surface is assumed, also leading to specific power relationships with mass. The model generates conservative predictions in which the main contributor to the dose rate of target tissues of the respiratory system is from α radiation arising from (222)Rn daughters. Tabulated (222)Rn DPURn values are given for 69 species used by the England & Wales Environment Agency for habitats assessments. The approach is then applied to assess the authorised discharges of (222)Rn from sites in England, demonstrating that, from a whole-body dose perspective, the biota considered are protected from effects at the population level. Copyright © 2012 Elsevier B.V. All rights reserved.

Scaling tunable network model to reproduce the density-driven superlinear relation

NASA Astrophysics Data System (ADS)

Gao, Liang; Shan, Xiaoya; Qin, Yuhao; Yu, Senbin; Xu, Lida; Gao, Zi-You

2018-03-01

Previous works have shown the universality of allometric scaling under total and density values at the city level, but our understanding of the size effects of regions on the universality of allometric scaling remains inadequate. Here, we revisit the scaling relations between the gross domestic production (GDP) and the population based on the total and density values and first reveal that the allometric scaling under density values for different regions is universal. The scaling exponent β under the density value is in the range of (1.0, 2.0], which unexpectedly exceeds the range observed by Pan et al. [Nat. Commun. 4, 1961 (2013)]. For the wider range, we propose a network model based on a 2D lattice space with the spatial correlation factor α as a parameter. Numerical experiments prove that the generated scaling exponent β in our model is fully tunable by the spatial correlation factor α. Our model will furnish a general platform for extensive urban and regional studies.

A comprehensive allometric analysis of 2nd digit length to 4th digit length in humans.

PubMed

Lolli, Lorenzo; Batterham, Alan M; Kratochvíl, Lukáš; Flegr, Jaroslav; Weston, Kathryn L; Atkinson, Greg

2017-06-28

It has been widely reported that men have a lower ratio of the 2nd and 4th human finger lengths (2D : 4D). Size-scaling ratios, however, have the seldom-appreciated potential for providing biased estimates. Using an information-theoretic approach, we compared 12 candidate models, with different assumptions and error structures, for scaling untransformed 2D to 4D lengths from 154 men and 262 women. In each hand, the two-parameter power function and the straight line with intercept models, both with normal, homoscedastic error, were superior to the other models and essentially equivalent to each other for normalizing 2D to 4D lengths. The conventional 2D : 4D ratio biased relative 2D length low for the generally bigger hands of men, and vice versa for women, thereby leading to an artefactual indication that mean relative 2D length is lower in men than women. Conversely, use of the more appropriate allometric or linear regression models revealed that mean relative 2D length was, in fact, greater in men than women. We conclude that 2D does not vary in direct proportion to 4D for both men and women, rendering the use of the simple 2D : 4D ratio inappropriate for size-scaling purposes and intergroup comparisons. © 2017 The Author(s).

Generalized Bondi-Sachs equations for characteristic formalism of numerical relativity

NASA Astrophysics Data System (ADS)

Cao, Zhoujian; He, Xiaokai

2013-11-01

The Cauchy formalism of numerical relativity has been successfully applied to simulate various dynamical spacetimes without any symmetry assumption. But discovering how to set a mathematically consistent and physically realistic boundary condition is still an open problem for Cauchy formalism. In addition, the numerical truncation error and finite region ambiguity affect the accuracy of gravitational wave form calculation. As to the finite region ambiguity issue, the characteristic extraction method helps much. But it does not solve all of the above issues. Besides the above problems for Cauchy formalism, the computational efficiency is another problem. Although characteristic formalism of numerical relativity suffers the difficulty from caustics in the inner near zone, it has advantages in relation to all of the issues listed above. Cauchy-characteristic matching (CCM) is a possible way to take advantage of characteristic formalism regarding these issues and treat the inner caustics at the same time. CCM has difficulty treating the gauge difference between the Cauchy part and the characteristic part. We propose generalized Bondi-Sachs equations for characteristic formalism for the Cauchy-characteristic matching end. Our proposal gives out a possible same numerical evolution scheme for both the Cauchy part and the characteristic part. And our generalized Bondi-Sachs equations have one adjustable gauge freedom which can be used to relate the gauge used in the Cauchy part. Then these equations can make the Cauchy part and the characteristic part share a consistent gauge condition. So our proposal gives a possible new starting point for Cauchy-characteristic matching.

A note on the relations between thermodynamics, energy definitions and Friedmann equations

NASA Astrophysics Data System (ADS)

Moradpour, H.; Nunes, Rafael C.; Abreu, Everton M. C.; Neto, Jorge Ananias

2017-04-01

We investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a suitable solution for the Friedmann equations leading to the standard modeling of the universe expansion history, cannot simultaneously satisfy the thermodynamic pressure equation and those of Friedmann. Moreover, we consider various energy definitions, such as the Komar mass, and solve the Friedmann and thermodynamic pressure equations simultaneously to get some models for dark energy fluids. The cosmological consequences of obtained solutions are also addressed. Our results indicate that some of obtained solutions may unify the dominated fluid in both the primary inflationary and current accelerating eras into one model. In addition, by taking into account a cosmic fluid of a known equation of state (EoS), and combining it with the Friedmann and thermodynamic pressure equations, we obtain the corresponding energy of these cosmic fluids and face their limitations. Finally, we point out the cosmological features of this cosmic fluid and also study its observational constraints.

Allometric growth and allocation in forests: a perspective from FLUXNET.

PubMed

Wolf, Adam; Field, Christopher B; Berry, Joseph A

2011-07-01

To develop a scheme for partitioning the products of photosynthesis toward different biomass components in land-surface models, a database on component mass and net primary productivity (NPP), collected from FLUXNET sites, was examined to determine allometric patterns of allocation. We found that NPP per individual of foliage (Gfol), stem and branches (Gstem), coarse roots (Gcroot) and fine roots (Gfroot) in individual trees is largely explained (r2 = 67-91%) by the magnitude of total NPP per individual (G). Gfol scales with G isometrically, meaning it is a fixed fraction of G ( 25%). Root-shoot trade-offs were manifest as a slow decline in Gfroot, as a fraction of G, from 50% to 25% as stands increased in biomass, with Gstem and Gcroot increasing as a consequence. These results indicate that a functional trade-off between aboveground and belowground allocation is essentially captured by variations in G, which itself is largely governed by stand biomass and only secondarily by site-specific resource availability. We argue that forests are characterized by strong competition for light, observed as a race for individual trees to ascend by increasing partitioning toward wood, rather than by growing more leaves, and that this competition stronglyconstrains the allocational plasticity that trees may be capable of. The residual variation in partitioning was not related to climatic or edaphic factors, nor did plots with nutrient or water additions show a pattern of partitioning distinct from that predicted by G alone. These findings leverage short-term process studies of the terrestrial carbon cycle to improve decade-scale predictions of biomass accumulation in forests. An algorithm for calculating partitioning in land-surface models is presented.

A critical appraisal of allometric growth among alpine cirques based on multivariate statistics and spatial analysis

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.

Sexual Dimorphism and Allometric Effects Associated With the Wing Shape of Seven Moth Species of Sphingidae (Lepidoptera: Bombycoidea)

PubMed Central

de Camargo, Nícholas Ferreira; Corrêa, Danilo do Carmo Vieira; de Camargo, Amabílio J. Aires; Diniz, Ivone Rezende

2015-01-01

Sexual dimorphism is a pronounced pattern of intraspecific variation in Lepidoptera. However, moths of the family Sphingidae (Lepidoptera: Bombycoidea) are considered exceptions to this rule. We used geometric morphometric techniques to detect shape and size sexual dimorphism in the fore and hindwings of seven hawkmoth species. The shape variables produced were then subjected to a discriminant analysis. The allometric effects were measured with a simple regression between the canonical variables and the centroid size. We also used the normalized residuals to assess the nonallometric component of shape variation with a t-test. The deformations in wing shape between sexes per species were assessed with a regression between the nonreduced shape variables and the residuals. We found sexual dimorphism in both wings in all analyzed species, and that the allometric effects were responsible for much of the wing shape variation between the sexes. However, when we removed the size effects, we observed shape sexual dimorphism. It is very common for females to be larger than males in Lepidoptera, so it is expected that the shape of structures such as wings suffers deformations in order to preserve their function. However, sources of variation other than allometry could be a reflection of different reproductive flight behavior (long flights in search for sexual mates in males, and flight in search for host plants in females). PMID:26206895

Variation in the cranium shape of wall lizards (Podarcis spp.): effects of phylogenetic constraints, allometric constraints and ecology.

PubMed

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. Copyright © 2012 Elsevier GmbH. All rights reserved.

Experimental determination and allometric prediction of vitreous volume, and retina and lens weights in Göttingen minipigs.

PubMed

Shafiee, Afshin; McIntire, Greg L; Sidebotham, Lisa C; Ward, Keith W

2008-01-01

To determine the vitreous volume, and retinal and lens wet weights in male and female Göttingen minipigs of different age groups. Vitreous, lens and retina were isolated from fresh minipig eyes. Vitreous volume, lens and retina weight were measured and allometric scaling was utilized to predict these parameters. There were no gender differences in body weights or retina and lens weights in the three age groups examined in this study. For vitreous volumes, females had a significantly larger volume (approximately 10%-12%) than males in the 4-6 and 6-8 month, but not in the 8-11-month group. The mean body weight increased from 12.2 +/- 2.6 kg (4-6 months) to 19.4 +/- 4.0 kg (8-11 months). In the same period, the mean vitreous volume increased from 2.00 +/- 0.28 to 2.67 +/- 0.31 mL, while the mean retinal and lens weights increased from 114 +/- 22 to 126 +/- 17 mg, and from 298 +/- 26 to 392 +/- 15 mg, respectively. Allometric analysis between six species for vitreous volume and four species for lens weight covering a weight range of 260-fold was not able to estimate the vitreous volume, but it did predict the lens weight in 8-11 months minipigs. Overall these measurements add important context to intraocular pharmacology studies, and will help in the improved design and interpretation of such experiments.

Minimizing bias in biomass allometry: Model selection and log transformation of data

Treesearch

Joseph Mascaro; undefined undefined; Flint Hughes; Amanda Uowolo; Stefan A. Schnitzer

2011-01-01

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the raditional approach of log-transformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models....

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Fitness consequences of artificial selection on relative male genital size

PubMed Central

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

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

Sexual Dimorphism and Allometric Effects Associated With the Wing Shape of Seven Moth Species of Sphingidae (Lepidoptera: Bombycoidea).

PubMed

de Camargo, Willian Rogers Ferreira; de Camargo, Nícholas Ferreira; Corrêa, Danilo do Carmo Vieira; de Camargo, Amabílio J Aires; Diniz, Ivone Rezende

2015-01-01

Sexual dimorphism is a pronounced pattern of intraspecific variation in Lepidoptera. However, moths of the family Sphingidae (Lepidoptera: Bombycoidea) are considered exceptions to this rule. We used geometric morphometric techniques to detect shape and size sexual dimorphism in the fore and hindwings of seven hawkmoth species. The shape variables produced were then subjected to a discriminant analysis. The allometric effects were measured with a simple regression between the canonical variables and the centroid size. We also used the normalized residuals to assess the nonallometric component of shape variation with a t-test. The deformations in wing shape between sexes per species were assessed with a regression between the nonreduced shape variables and the residuals. We found sexual dimorphism in both wings in all analyzed species, and that the allometric effects were responsible for much of the wing shape variation between the sexes. However, when we removed the size effects, we observed shape sexual dimorphism. It is very common for females to be larger than males in Lepidoptera, so it is expected that the shape of structures such as wings suffers deformations in order to preserve their function. However, sources of variation other than allometry could be a reflection of different reproductive flight behavior (long flights in search for sexual mates in males, and flight in search for host plants in females). © The Author 2015. Published by Oxford University Press on behalf of the Entomological Society of America.

Allometric scaling of UK urban emissions: interpretation and implications for air quality management

NASA Astrophysics Data System (ADS)

MacKenzie, Rob; Barnes, Matt; Whyatt, Duncan; Hewitt, Nick

2016-04-01

Allometry uncovers structures and patterns by relating the characteristics of complex systems to a measure of scale. We present an allometric analysis of air quality for UK urban settlements, beginning with emissions and moving on to consider air concentrations. We consider both airshed-average 'urban background' concentrations (cf. those derived from satellites for NO2) and local pollution 'hotspots'. We show that there is a strong and robust scaling (with respect to population) of the non-point-source emissions of the greenhouse gases carbon dioxide and methane, as well as the toxic pollutants nitrogen dioxide, PM2.5, and 1,3-butadiene. The scaling of traffic-related emissions is not simply a reflection of road length, but rather results from the socio-economic patterning of road-use. The recent controversy regarding diesel vehicle emissions is germane to our study but does not affect our overall conclusions. We next develop an hypothesis for the population-scaling of airshed-average air concentrations, with which we demonstrate that, although average air quality is expected to be worse in large urban centres compared to small urban centres, the overall effect is an economy of scale (i.e., large cities reduce the overall burden of emissions compared to the same population spread over many smaller urban settlements). Our hypothesis explains satellite-derived observations of airshed-average urban NO2 concentrations. The theory derived also explains which properties of nature-based solutions (urban greening) can make a significant contribution at city scale, and points to a hitherto unforeseen opportunity to make large cities cleaner than smaller cities in absolute terms with respect to their airshed-average pollutant concentration.

Allometric scaling of microbial fuel cells and stacks: The lifeform case for scale-up

NASA Astrophysics Data System (ADS)

Greenman, John; Ieropoulos, Ioannis A.

2017-07-01

This case study reports for the first time on the comparison between allometric scaling of lifeforms and scale-up of microbial fuel cell entities; enlarging individual units in volume, footprint and electrode surface area but also multiplying a static size/footprint and electrode surface area to scale-up by stacking. A study published in 2010 by DeLong et al. showed for the first time that Kleiber's law does not apply uniformly to all lifeforms, and that in fact growth rate for prokaryotes is superlinear, for protists is linear and for metazoa is sublinear. The current study, which is utilising data from previous experiments, is showing for the first time that for individual MFC units, which are enlarged, growth rate/power is sublinear, whereas for stacks this is superlinear.

Fifth dimension of life and the 4/5 allometric scaling law for human brain.

PubMed

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.

Choice of resolution by functional trait or taxonomy affects allometric scaling in soil food webs.

PubMed

Sechi, Valentina; Brussaard, Lijbert; De Goede, Ron G M; Rutgers, Michiel; Mulder, Christian

2015-01-01

Belowground organisms often display a shift in their mass-abundance scaling relationships due to environmental factors such as soil chemistry and atmospheric deposition. Here we present new empirical data that show strong differences in allometric scaling according to whether the resolution at the local scale is based on a taxonomic or a functional classification, while only slight differences arise according to soil environmental conditions. For the first time, isometry (an inverse 1:1 proportion) is recognized in mass-abundance relationships, providing a functional signal for constant biomass distribution in soil biota regardless of discrete trophic levels. Our findings are in contrast to those from aquatic ecosystems, in that higher trophic levels in soil biota are not a direct function of increasing body mass.

Interspecies scaling of a camptothecin analogue: human predictions for intravenous topotecan using animal data.

PubMed

Ahlawat, P; Srinivas, N R

2008-11-01

As a class, camptothecin analogues via market entry of topotecan and irinotecan, have shown promise for the treatment of various solid tumours. Topotecan, in particular, was chosen as the substrate for allometric scaling and prediction of human parameter values for both total clearance (CL) and volume of distribution (V(ss)). The availability of published data in mouse, rat, dog, and monkey paved the way for interspecies scaling via allometry. Although it appeared that at a minimum mouse, rat, and dog would reasonably fit in a three-species allometry scale-up, the inclusion of monkey data enabled a better prediction of the human parameter values for total topotecan-e.g., CL: allometric equation: 1.5234W(0.7865); predicted value = 43.04 l h(-1): observed CL = 24-53 l h(-1); V(ss): allometric equation: 1.1939W(1.0208); predicted value = 91.29 litres: observed V(ss) = 66-146 litres. The proximity of the allometric exponent values of CL (0.7885) and V(ss) (1.0208) to the suggested values of 0.75 and 1.00 was not only encouraging, but also confirmed the applicability of interspecies scaling approach for topotecan. The data suggest that allometric scaling approaches with suitable correction factors could potentially be used to predict the human pharmacokinetics of novel CPT analogues prospectively.

Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

NASA Astrophysics Data System (ADS)

Zalaletdinov, R. M.

1998-04-01

The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

On the Rate of Relaxation for the Landau Kinetic Equation and Related Models

NASA Astrophysics Data System (ADS)

Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong

2017-08-01

We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.

Allometric shape change and heterochrony in the freeliving coral Trachyphyllia bilobata (Duncan)

NASA Astrophysics Data System (ADS)

Foster, Ann Budd; Johnson, Kenneth G.; Schultz, Lori L.

1988-05-01

Regression analysis has been used to study the relationship between age, size, shape, and surface area in two ancestral-descendant populations of the Neogene Caribbean coral Trachyphyllia bilobata. Analyses of the relationship between size and age show that the relationship is isometric and that little difference occurs between populations in mean corallite length or height and in their rates of growth. Onset of columella growth is significantly earlier, however, in the descendant population. Studies of the relationship between size and shape show that growth is allometric, with shape change occurring in both corallum elongation and pinching of the corallite wall during ontogeny. In the descendant population, pinching and elongation initiate earlier in the ontogeny of the coral. These results suggest that the evolutionary development of the meandroid form in freeliving corals has been accomplished by heterochrony, involving a complex set of disassociated peramorphic changes in ontogeny accompanied by paedomorphic changes in astogeny. Further analyses show that the observed heterochronic changes serve to decrease corallum surface area which may in turn enhance sediment removal and nutrition in unstable habitats.

Calculation of prevalence estimates through differential equations: application to stroke-related disability.

PubMed

Mar, Javier; Sainz-Ezkerra, María; Moler-Cuiral, Jose Antonio

2008-01-01

Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model. (c) 2008 S. Karger AG, Basel.

Measuring the neutron star tidal deformability with equation-of-state-independent relations and gravitational waves

NASA Astrophysics Data System (ADS)

Chatziioannou, Katerina; Haster, Carl-Johan; Zimmerman, Aaron

2018-05-01

Gravitational wave measurements of binary neutron star coalescences offer information about the properties of the extreme matter that comprises the stars. Despite our expectation that all neutron stars in the Universe obey the same equation of state, i.e. the properties of the matter that forms them are universal, current tidal inference analyses treat the two bodies as independent. We present a method to measure the effect of tidal interactions in the gravitational wave signal—and hence constrain the equation of state—that assumes that the two binary components obey the same equation of state. Our method makes use of a relation between the tidal deformabilities of the two stars given the ratio of their masses, a relation that has been shown to only have a weak dependence on the equation of state. We use this to link the tidal deformabilities of the two stars in a realistic parameter inference study while simultaneously marginalizing over the error in the relation. This approach incorporates more physical information into our analysis, thus leading to a better measurement of tidal effects in gravitational wave signals. Through simulated signals we estimate that uncertainties in the measured tidal parameters are reduced by a factor of at least 2—and in some cases up to 10—depending on the equation of state and mass ratio of the system.

Allometry of visceral organs in living amniotes and its implications for sauropod dinosaurs

PubMed Central

Franz, Ragna; Hummel, Jürgen; Kienzle, Ellen; Kölle, Petra; Gunga, Hanns-Christian; Clauss, Marcus

2009-01-01

Allometric equations are often used to extrapolate traits in animals for which only body mass estimates are known, such as dinosaurs. One important decision can be whether these equations should be based on mammal, bird or reptile data. To address whether this choice will have a relevant influence on reconstructions, we compared allometric equations for birds and mammals from the literature to those for reptiles derived from both published and hitherto unpublished data. Organs studied included the heart, kidneys, liver and gut, as well as gut contents. While the available data indicate that gut content mass does not differ between the clades, the organ masses for reptiles are generally lower than those for mammals and birds. In particular, gut tissue mass is significantly lower in reptiles. When applying the results in the reconstruction of a sauropod dinosaur, the estimated volume of the coelomic cavity greatly exceeds the estimated volume of the combined organ masses, irrespective of the allometric equation used. Therefore, substantial deviation of sauropod organ allometry from that of the extant vertebrates can be allowed conceptually. Extrapolations of retention times from estimated gut contents mass and food intake do not suggest digestive constraints on sauropod dinosaur body size. PMID:19324837

Performance and welfare of steers housed on concrete slatted floors at fixed and dynamic (allometric based) space allowances.

PubMed

Keane, Michael P; McGee, Mark; O'Riordan, Edward G; Kelly, Alan K; Earley, Bernadette

2018-04-03

The objectives of the study were to determine whether allometric equations are suitable for estimating the space requirements of finishing beef cattle housed on concrete slatted floors (CSF) and to examine the effect of fixed and dynamic space allowances on the performance and welfare of these cattle. Continental crossbred steers [n = 120: mean initial live weight, 590 (SD 29.8) kg] were blocked by breed, weight, and age and assigned to 1 of 5 space allowance treatments (3 fixed and 2 dynamic) on CSF: 1) 2.0 m2 per animal, 2) 2.5 m2 per animal, 3) 3.0 m2 per animal, 4) Equation 1 (E1); y = 0.033w0.667, where y = m2 per animal and w = body weight, and 5) Equation 2 (E2); y = 0.048w0.667. The length of the feed face was 3.0 m for all treatments. Steers were offered grass silage and concentrates ad libitum. DMI was recorded weekly on a pen basis. Steers were weighed and dirt scored every 14 d. Blood samples were collected every 28 d, and analyzed for complete cell counts. Behavior was recorded using closed-circuit infrared cameras. Steers' hooves were inspected for lesions at the beginning of the study and post-slaughter. Slaughter weight and ADG were lowest, and feed conversion ratio (FCR) was poorest, for steers accommodated at 2.0 m2, and slaughter weight and ADG were greatest, and FCR was the best, for steers accommodated at E2 (P < 0.05); steers accommodated at 2.5 m2 were intermediate (P > 0.05) to those accommodated at 2.0 m2 and both 3.0 m2 and E1, whereas steers accommodated at 3.0 m2 and E1 were intermediate (P > 0.05) to 2.5 m2 and E2. Carcass weight of steers housed at 2.0 m2 was lower (P < 0.05) than all other treatments. Steers housed at 2.5 m2 had lower carcass weights (P < 0.05) than those with accommodated at E1 and E2, whereas the carcass weight of steers accommodated at 3.0 m2 was intermediate. Carcass fat scores and hide weights were lower (P < 0.05) in steers accommodated at 2.0 m2 than those housed at E2 with other treatments being intermediate

Comparison of methods for estimating carbon dioxide storage by Sacramento's urban forest

Treesearch

Elena Aguaron; E. Gregory McPherson

2012-01-01

Limited open-grown urban tree species biomass equations have necessitated use of forest-derived equations with diverse conclusions on the accuracy of these equations to estimate urban biomass and carbon storage. Our goal was to determine and explain variability among estimates of CO2 storage from four sets of allometric equations for the same...

Aboveground tree biomass for Pinus ponderosa in northeastern California

Treesearch

Martin W. Ritchie; Jianwei Zhang; Todd A. Hamilton

2013-01-01

Forest managers need accurate biomass equations to plan thinning for fuel reduction or energy production. Estimates of carbon sequestration also rely upon such equations. The current allometric equations for ponderosa pine (Pinus ponderosa) commonly employed for California forests were developed elsewhere, and are often applied without consideration potential for...

`Negative of my money, positive of her money': secondary students' ways of relating equations to a debt context

NASA Astrophysics Data System (ADS)

Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P.

2015-02-01

We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways. Many students represented the situation numerically without invoking negative numbers, whereas others wrote equations involving negative numbers. When asked to interpret equations involving negative numbers in relation to the story, students did so in two ways. Their responses reflect distinct perspectives concerning the relationship between arithmetic equations and borrowing/owing. We discuss these findings and their implications regarding the role of contexts in integer instruction.

Fractal Physiology and the Fractional Calculus: A Perspective

PubMed Central

West, Bruce J.

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

Quadratic equations in Banach space, perturbation techniques and applications to Chandrasekhar's and related equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Argyros, I.K.

1984-01-01

In this dissertation perturbation techniques are developed, based on the contraction mapping principle which can be used to prove existence and uniqueness for the quadratic equation x = y + lambdaB(x,x) (1) in a Banach space X; here B: XxX..-->..X is a bounded, symmetric bilinear operator, lambda is a positive parameter and y as a subset of X is fixed. The following is the main result. Theorem. Suppose F: XxX..-->..X is a bounded, symmetric bilinear operator and that the equation z = y + lambdaF(z,z) has a solution z/sup */ of sufficiently small norm. Then equation (1) has a uniquemore » solution in a certain closed ball centered at z/sup */. Applications. The theorem is applied to the famous Chandrasekhar equation and to the Anselone-Moore system which are of the form (1) above and yields existence and uniqueness for a solution of (1) for larger values of lambda than previously known, as well as more accurate information on the location of solutions.« less

Identification, sexual dimorphism, and allometric effects of three psyllid species of the genus Psyllopsis by geometric morphometric analysis (Hemiptera, Liviidae)

PubMed Central

Gushki, Roghayeh Shamsi; Lashkari, Mohammadreza; Mirzaei, Saeid

2018-01-01

Abstract Jumping plant lice (Hemiptera: Psylloidea) are considered important vectors of plant diseases and also economically important pests in agriculture and forest ecosystems. Three psyllid species Psyllopsis repens Loginova, 1963, Psyllopsis securicola Loginova, 1963, and Psyllopsis machinosus Loginova, 1963 associated with the ash tree Fraxinus are morphologically very similar. So far, their distinction has been possible only by comparing their male and female genitalia. In this research, forewing shape and size characteristics, sexual dimorphism and their allometric effects, using geometric morphometric analysis, were examined for identification purposes. The results showed significant differences in wing shape and size between the species studied. Based on the results, two species P. machinosus and P. securicola can be differentiated with the vein M1+2, as in P. securicola the vein M1+2 is located between Rs and M3+4 veins, but the vein M1+2 is closer to the vein M3+4 in P. machinosus; also, P. repens can be differentiated from the two species P. machinosus and P. securicola by vein M. Hence, the veins M1+2, M3+4, Rs and M were the most important wing characters for discrimination of the three species, especially in the field. The analysis also showed significant differences in wing shape and size between male and female of the three species, and the allometric analysis showed that significant shape differences still remain in constant size in P. machinosus and P. repens. Geometric changes in the forewings of both sexes for the three species are illustrated. PMID:29674872

Mathematical Model for the Contribution of Individual Organs to Non-Zero Y-Intercepts in Single and Multi-Compartment Linear Models of Whole-Body Energy Expenditure

PubMed Central

Kaiyala, Karl J.

2014-01-01

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit ‘local linearity.’ Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying ‘latent’ allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses. PMID:25068692

Mathematical model for the contribution of individual organs to non-zero y-intercepts in single and multi-compartment linear models of whole-body energy expenditure.

PubMed

Kaiyala, Karl J

2014-01-01

Mathematical models for the dependence of energy expenditure (EE) on body mass and composition are essential tools in metabolic phenotyping. EE scales over broad ranges of body mass as a non-linear allometric function. When considered within restricted ranges of body mass, however, allometric EE curves exhibit 'local linearity.' Indeed, modern EE analysis makes extensive use of linear models. Such models typically involve one or two body mass compartments (e.g., fat free mass and fat mass). Importantly, linear EE models typically involve a non-zero (usually positive) y-intercept term of uncertain origin, a recurring theme in discussions of EE analysis and a source of confounding in traditional ratio-based EE normalization. Emerging linear model approaches quantify whole-body resting EE (REE) in terms of individual organ masses (e.g., liver, kidneys, heart, brain). Proponents of individual organ REE modeling hypothesize that multi-organ linear models may eliminate non-zero y-intercepts. This could have advantages in adjusting REE for body mass and composition. Studies reveal that individual organ REE is an allometric function of total body mass. I exploit first-order Taylor linearization of individual organ REEs to model the manner in which individual organs contribute to whole-body REE and to the non-zero y-intercept in linear REE models. The model predicts that REE analysis at the individual organ-tissue level will not eliminate intercept terms. I demonstrate that the parameters of a linear EE equation can be transformed into the parameters of the underlying 'latent' allometric equation. This permits estimates of the allometric scaling of EE in a diverse variety of physiological states that are not represented in the allometric EE literature but are well represented by published linear EE analyses.

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

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…

Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion

NASA Technical Reports Server (NTRS)

Lane, Christopher; Axelrad, Penina

2004-01-01

Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.

An Allometric Modelling Approach to Identify the Optimal Body Shape Associated with, and Differences between Brazilian and Peruvian Youth Motor Performance

PubMed Central

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

An Allometric Modelling Approach to Identify the Optimal Body Shape Associated with, and Differences between Brazilian and Peruvian Youth Motor Performance.

PubMed

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.

BOOK REVIEW: Numerical Relativity: Solving Einstein's Equations on the Computer Numerical Relativity: Solving Einstein's Equations on the Computer

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

The importance of body mass normalisation for ultrasound measurements of the morphology of oblique abdominis muscles: the effect of age, gender, and sport practice.

PubMed

Linek, P

2018-01-01

Some studies have not considered body mass as a confounder in analysis of oblique abdominis muscles (OAM) (including the oblique externus [OE] and oblique internus [OI]), which may have led to improper interpretation of results. To assess the differences in the effect of age, gender, and physical activity between normalised for body mass and actual values of the OAM as well as to establish the effect of age, gender, and physical activity on normalised for body mass OAM thicknesses in adolescents. A real-time ultrasound was used to obtain images of the OAM. Body mass normalisation for OAM thicknesses was performed with allometric scaling and the following equations: Allometric-scaled OE = OE thickness/body mass0.88; Allometric-scaled OI = OI thickness/body mass0.72. Analysis showed that boys have significantly thicker OAM than girls, and those who practise sports have thicker OAM than non-active individuals. For allometric-scaled OAM, there was only a significant gender effect, where boys have thicker allometric-scaled OAM than girls. There was a significant correlation between participants' age and the actual value of the OAM. The correlations between age and allometric-scaled OAM were insignificant. An analysis of OAM without body mass normalisation can lead to improper interpretation of study results. Thus, future studies should analyse OE and OI thickness measurements after normalisation rather than actual values. In the adolescent population, there is no effect of age and physical activity on allometric-scaled OAM; males have thicker allometric-scaled OAM than females. (Folia Morphol 2018; 77, 1: 123-130).

Episodic growth and relative shoot:root balance in loblolly pine seedlings

Treesearch

A.P. Drew; F. Thomas Ledig

1980-01-01

Leaf, root and stem systems of loblolly pine seedlings are characterized by a seasonal periodicity in growth, during which they alternate in spurts of activity. Despite this periodicity, the allometric coefficient describing the ratio of the relative growth rates of leaf to root remains constant for at least the first two years of development. In part, constancy...

Noncommutative differential geometry related to the Young-Baxter equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurevich, D.; Radul, A.; Rubtsov, V.

1995-11-10

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf Z`s considered in which local solutions of the Young-Baxter quantum equation are defined but there is no global section.

Reduction of lattice equations to the Painlevé equations: PIV and PV

NASA Astrophysics Data System (ADS)

Nakazono, Nobutaka

2018-02-01

In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

[Characteristics of carbon storage of Inner Mongolia forests: a review].

PubMed

Yang, Hao; Hu, Zhong-Min; Zhang, Lei-Ming; Li, Sheng-Gong

2014-11-01

Forests in Inner Mongolia account for an important part of the forests in China in terms of their large area and high living standing volume. This study reported carbon storage, carbon density, carbon sequestration rate and carbon sequestration potential of forest ecosystems in Inner Mongolia using the biomass carbon data from the related literature. Through analyzing the data of forest inventory and the generalized allometric equations between volume and biomass, previous studies had reported that biomass carbon storage of the forests in Inner Mongolia was about 920 Tg C, which was 12 percent of the national forest carbon storage, the annual average growth rate was about 1.4%, and the average of carbon density was about 43 t · hm(-2). Carbon storage and carbon density showed an increasing trend over time. Coniferous and broad-leaved mixed forest, Pinus sylvestris var. mongolica forest and Betula platyphylla forest had higher carbon sequestration capacities. Carbon storage was reduced due to human activities such as thinning and clear cutting. There were few studies on carbon storage of the forests in Inner Mongolia with focus on the soil, showing that the soil car- bon density increased with the stand age. Study on the carbon sequestration potential of forest ecosystems was still less. Further study was required to examine dynamics of carbon storage in forest ecosystems in Inner Mongolia, i. e., to assess carbon storage in the forest soils together with biomass carbon storage, to compute biomass carbon content of species organs as 45% in the allometric equations, to build more species-specific and site-specific allometric equations including root biomass for different dominant species, and to take into account the effects of climate change on carbon sequestration rate and carbon sequestration potential.

Allometric shape change of the lower pharyngeal jaw correlates with a dietary shift to piscivory in a cichlid fish.

PubMed

Hellig, Christoph J; Kerschbaumer, Michaela; Sefc, Kristina M; Koblmüller, Stephan

2010-07-01

The morphological versatility of the pharyngeal jaw of cichlid fishes is assumed to represent a key factor facilitating their unparalleled trophic diversification and explosive radiation. It is generally believed that the functional design of an organism relates to its ecology, and thus, specializations to different diets are typically associated with distinct morphological designs, especially manifested in the cichlids' pharyngeal jaw apparatus. Thereby, the lower pharyngeal jaw (LPJ) incorporates some of the most predictive features for distinct diet-related morphotypes. Thus, considering that piscivorous cichlids experience an ontogenetic dietary shift from typically various kinds of invertebrates to fish, concomitant morphological changes in the LPJ are expected. Using Lepidiolamprologus elongatus, a top predator in the shallow rocky habitat of Lake Tanganyika, as model, and applying geometric and traditional morphometric techniques, we demonstrate an allometric change in ontogenetic LPJ shape development coinciding with the completion of the dietary shift toward piscivory. The piscivorous LPJ morphotype is initiated in juvenile fish by increasing elongation and narrowing of the LPJ and--when the fish reach a size of 80-90 mm standard length--further refined by the elongation of the posterior muscular processes, which serve as insertion for the fourth musculus levator externus. The enlarged muscular processes of the fully mature piscivorous morphotype provide for the construction of a powerful lever system, which allows the large individuals to process large prey fish and rely on exclusive piscivory.

Allometric shape change of the lower pharyngeal jaw correlates with a dietary shift to piscivory in a cichlid fish

NASA Astrophysics Data System (ADS)

Hellig, Christoph J.; Kerschbaumer, Michaela; Sefc, Kristina M.; Koblmüller, Stephan

2010-07-01

The morphological versatility of the pharyngeal jaw of cichlid fishes is assumed to represent a key factor facilitating their unparalleled trophic diversification and explosive radiation. It is generally believed that the functional design of an organism relates to its ecology, and thus, specializations to different diets are typically associated with distinct morphological designs, especially manifested in the cichlids’ pharyngeal jaw apparatus. Thereby, the lower pharyngeal jaw (LPJ) incorporates some of the most predictive features for distinct diet-related morphotypes. Thus, considering that piscivorous cichlids experience an ontogenetic dietary shift from typically various kinds of invertebrates to fish, concomitant morphological changes in the LPJ are expected. Using Lepidiolamprologus elongatus, a top predator in the shallow rocky habitat of Lake Tanganyika, as model, and applying geometric and traditional morphometric techniques, we demonstrate an allometric change in ontogenetic LPJ shape development coinciding with the completion of the dietary shift toward piscivory. The piscivorous LPJ morphotype is initiated in juvenile fish by increasing elongation and narrowing of the LPJ and—when the fish reach a size of 80-90 mm standard length—further refined by the elongation of the posterior muscular processes, which serve as insertion for the fourth musculus levator externus. The enlarged muscular processes of the fully mature piscivorous morphotype provide for the construction of a powerful lever system, which allows the large individuals to process large prey fish and rely on exclusive piscivory.

Scaling relations for a functionally two-dimensional plant: Chamaesyce setiloba (Euphorbiaceae).

PubMed

Koontz, Terri L; Petroff, Alexander; West, Geoffrey B; Brown, James H

2009-05-01

Many characteristics of plants and animals scale with body size as described by allometric equations of the form Y = βM(α), where Y is an attribute of the organism, β is a coefficient that varies with attribute, M is a measure of organism size, and α is another constant, the scaling exponent. In current models, the frequently observed quarter-power scaling exponents are hypothesized to be due to fractal-like structures. However, not all plants or animals conform to the assumptions of these models. Therefore, they might be expected to have different scaling relations. We studied one such plant, Chamaesyce setiloba, a prostrate annual herb that grows to functionally fill a two-dimensional space. Number of leaves scaled slightly less than isometrically with total aboveground plant mass (α ≈ 0.9) and substantially less than isometrically with dry total stem mass (α = 0.82), showing reduced allocation to leaf as opposed to stem tissue with increasing plant size. Additionally, scalings of the lengths and radii of parent and daughter branches differed from those predicted for three-dimensional trees and shrubs. Unlike plants with typical three-dimensional architectures, C. setiloba has distinctive scaling relations associated with its particular prostrate herbaceous growth form.

Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization

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.

Allometric relationships of the dentition of the great White Shark, Carcharodon carcharias, in forensic investigations of shark attacks.

PubMed

Nambiar, P; Bridges, T E; Brown, K A

1991-06-01

As a result of a systematic morphometric study of shark dentitions, a system of notation for describing the location of shark teeth has been developed and is proposed as a standard to be adopted for use in similar studies in the future. The macroscopic morphology of White Shark teeth has been characterised in order to gain quantitative data which might assist in identification of these sharks from bite marks on victims or objects or from shark carcasses. Using these data, a nomogram has been developed which can be used to estimate the body length of a White Shark from measurements of tooth or bite mark morphology. An example of the forensic application of such allometric data is provided as it applied to a recent fatal attack on a diver by a White Shark.

Relationships between basic soils-engineering equations and basic ground-water flow equations

USGS Publications Warehouse

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.

Adaptive diversification of growth allometry in the plant Arabidopsis thaliana

PubMed Central

Vasseur, François; Ayala-Garay, Oscar J.; Wang, George; Enquist, Brian J.; Vile, Denis; Violle, Cyrille

2018-01-01

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near-constant allometric scaling exponents across species. However, the observed variation in scaling exponents calls into question the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST was correlated with relative growth rate, seed production, and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4, has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology and begin to link adaptive variation in allometric scaling to specific genes. PMID:29540570

The microcomputer scientific software series 5: the BIOMASS user's guide.

Treesearch

George E. Host; Stephen C. Westin; William G. Cole; Kurt S. Pregitzer

1989-01-01

BIOMASS is an interactive microcomputer program that uses allometric regression equations to calculate aboveground biomass of common tree species of the Lake States. The equations are species-specific and most use both diameter and height as independent variables. The program accommodates fixed area and variable radius sample designs and produces both individual tree...

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.…

Aboveground biomass and nitrogen allocation of ten deciduous southern Appalachian tree species

Treesearch

Jonathan G. Martin; Brian D. Kloeppel; Tara L. Schaefer; Darrin L. Kimbler; Steven G. McNulty

1998-01-01

Allometric equations were developed for mature trees of 10 deciduous species (Acer rubrum L.; Betula lenta L.; Carya spp.; Cornus florida L.; Liriodendron tulipifera L.; Oxydendrum arboreum (L.) DC.; Quercus alba L.; Quercus...

Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce

Treesearch

Harry T. Valentine; Annikki Makela; Edward J. Green; Ralph L. Amateis; Harri Makinen; Mark J. Ducey

2012-01-01

We derive and analyze a model that relates the growth rate of cross-sectional area ('csa') at any height on the central stem of a tree to crown-length dynamics. The derivation is based, in part, on assumptions that (a) active csa on the central stem relates allometrically to the length of crown above the cross section, and (b) inactive csa is proportional to...

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

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.

Thermodynamics constrains allometric scaling of optimal development time in insects.

PubMed

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

Non-Trivial Feature Derivation for Intensifying Feature Detection Using LIDAR Datasets Through Allometric Aggregation Data Analysis Applying Diffused Hierarchical Clustering for Discriminating Agricultural Land Cover in Portions of Northern Mindanao, Philippines

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

Allometric Scaling of Patrolling Rate and Nest Volume in Constrictotermes cyphergaster Termites: Hints on the Settlement of Inquilines

PubMed Central

DeSouza, Og; Araújo, Ana Paula Albano; Florencio, Daniela Faria; Rosa, Cassiano Sousa; Marins, Alessandra; Costa, Diogo Andrade; Rodrigues, Vinicius Barros; Cristaldo, Paulo Fellipe

2016-01-01

Structural and functional traits of organisms are known to be related to the size of individuals and to the size of their colonies when they belong to one. Among such traits, propensity to inquilinism in termites is known to relate positively to colony size. Larger termitaria hold larger diversity of facultative inquilines than smaller nests, whereas obligate inquilines seem unable to settle in nests smaller than a threshold volume. Respective underlying mechanisms, however, remain hypothetical. Here we test one of such hypotheses, namely, that nest defence correlates negatively to nest volume in Constrictotermes cyphergaster termites (Termitidae: Nasutitermitinae). As a surrogate to defence, we used ‘patrolling rate’, i.e., the number of termite individuals attending per unit time an experimentally damaged spot on the outer wall of their termitaria. We found that patrolling rate decayed allometrically with increasing nest size. Conspicuously higher patrolling rates occurred in smaller nests, while conspicuously lower rates occurred in larger nests presenting volumes in the vicinity of the threshold value for the establishment of inquilinism. This could be proven adaptive for the host and guest. At younger nest age, host colonies are smaller and presumably more vulnerable and unstable. Enhanced defence rates may, hence, prevent eventual risks to hosts from inquilinism at the same time that it prevents inquilines to settle in a still unstable nest. Conversely, when colonies grow and maturate enough to stand threats, they would invest in priorities other than active defence, opening an opportunity for inquilines to settle in nests which are more suitable or less risky. Under this two-fold process, cohabitation between host and inquiline could readily stabilize. PMID:26808197

Allometry and Interspecific Differences in the Facial Cranium of Two Closely Related Macaque Species

PubMed Central

Ito, Tsuyoshi; Nishimura, Takeshi; Takai, Masanaru

2011-01-01

Interpreting evolutionary history of macaque monkeys from fossil evidence is difficult, because their evolutionary fluctuations in body size might have removed or formed important morphological features differently in each lineage. We employed geometric morphometrics to explore allometric trajectories of craniofacial shape in two closely related species, Macaca fascicularis and M. fuscata. These two species exhibit a single shared allometric trajectory in superoinferior deflection of the anterior face, indicating that the differences in this feature can be explained by size variation. In contrast, two parallel trajectories are demonstrated in craniofacial protrusion, indicating that even if they are comparable in size, M. fuscata has a higher and shorter face than M. fascicularis. The degree of facial protrusion is most likely a critical feature for phyletic evaluation in the fascicularis group. Such analyses in various macaques would help to resolve controversies regarding phyletic interpretations of fossil macaques. PMID:22567301

Live tree carbon stock equivalence of fire and fuels extension to the Forest Vegetation Simulator and Forest Inventory and Analysis approaches

Treesearch

James E. Smith; Coeli M. Hoover

2017-01-01

The carbon reports in the Fire and Fuels Extension (FFE) to the Forest Vegetation Simulator (FVS) provide two alternate approaches to carbon estimates for live trees (Rebain 2010). These are (1) the FFE biomass algorithms, which are volumebased biomass equations, and (2) the Jenkins allometric equations (Jenkins and others 2003), which are diameter based. Here, we...

Effect of selection for growth rate on relative growth in rabbits.

PubMed

Pascual, M; Pla, M; Blasco, A

2008-12-01

The effect of selection for growth rate on relative growth of the rabbit body components was studied. Animals from the 18th generation of a line selected for growth rate were compared with a contemporary control group formed with offspring of embryos that were frozen at the seventh generation of selection of the same line. A total of 313 animals were slaughtered at 4, 9, 13, 20, and 40 wk old. The offal, organs, tissues, and retail cuts were weighed, and several carcass linear measurements were recorded. Huxley's allometric equations relating the weights of the components with respect to BW were fitted. Butterfield's quadratic equations relating the degree of maturity of the components and the degree of maturity of BW were also fitted. In most of the components studied, both models lead to similar patterns of growth. Blood was isometric or early maturing and skin was late maturing or isometric depending on the use of Huxley's or Butterfield's model. Full gastrointestinal tract, liver, kidneys, thoracic viscera, and head were early maturing, and the chilled carcass and reference carcass were late maturing. The retail cuts of the reference carcass showed isometry (forelegs) or late maturing growth (breast and ribs, loin, hind legs, and abdominal walls). Dissectible fat of the carcass and meat of the hind leg had a late development, whereas bone of the hind leg was early maturing. Lumbar circumference length was later maturing than the carcass length and thigh length. Sex did not affect the relative growth of most of the components. Butterfield's model showed that males had an earlier development of full gastrointestinal tract and later growth of kidneys than females. No effect of selection on the relative growth of any of the components studied was found, leading to similar patterns of growth and similar carcass composition at a given degree of maturity after 11 generations of selection for growth rate.

Estimating aspen volume and weight for individual trees, diameter classes, or entire stands.

Treesearch

Bryce E. Schlaegel

1975-01-01

Presents allometric volume and weight equations for Minnesota quaking aspen. Volume, green weight, and dry weight estimates can be made for wood, bark, and limbs on the basis of individual trees, diameter classes, or entire stands.

Allometric relationship of postmolt net ion uptake, ventilation, and circulation in the freshwater crayfish Procambarus clarkii: intraspecific scaling.

PubMed

Zanotto, F P; Wheatly, M G; Reiber, C L; Gannon, A T; Jalles-Filho, E

2004-01-01

There are few intraspecific studies relating physiological parameters to body mass. This study relates scaling of ionic regulation and respiratory parameters with body mass in crayfish (Procambarus clarkii). These animals were chosen because of their direct development, spanning four orders of magnitude in body mass. Usually, these animals are hyperregulators and must maintain hemolymph electrolyte levels above those in the ambient freshwater. This is especially important in the postmolt, when ion imbalance can occur. Maintaining hemolymph ion levels above ambient involves active processes that are independently related to metabolic rate, ventilation, and circulation. Therefore, this study investigates relationships among size and ionic regulation, heart rate, and ventilation in crayfish, spanning a size range of 0.003-24 g. Postmolt net ion uptake of Ca, titratable base, Na, Cl, and NH4 increase with body mass (positive allometry) with slopes of 0.92, 0.79, 0.90, 0.84, and 0.87, respectively. Between 72% and 97% of variation in ionic regulation was related to body mass. The slopes differed from each other for Ca and titratable base but not for Na, Cl, and NH4. For heart rate and ventilation rate, different relationships were derived for animals smaller and larger than 0.01 g (between first and third instar). Animals larger than 0.01 g show a negative allometric relationship between heart rate and body size ([body mass](0.15)), while smaller animals show positive allometry with body size, but only 29% of variation in heart rate is explained by body size alone. For ventilation rates, the negative allometry with body size for animals larger than 0.01 g is present, but less than 15% of variation in ventilation rate is explained by size, while for smaller animals the size dependency disappears. Based on these results, predictions of physiological parameters such as ionic regulation based on body size are useful in crayfish, but estimates of respiratory parameters and

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

ERIC Educational Resources Information Center

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

An estimator for the relative entropy rate of path measures for stochastic differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

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.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

Adaptive diversification of growth allometry in the plant Arabidopsis thaliana.

PubMed

Vasseur, François; Exposito-Alonso, Moises; Ayala-Garay, Oscar J; Wang, George; Enquist, Brian J; Vile, Denis; Violle, Cyrille; Weigel, Detlef

2018-03-27

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near-constant allometric scaling exponents across species. However, the observed variation in scaling exponents calls into question the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST was correlated with relative growth rate, seed production, and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4 , has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology and begin to link adaptive variation in allometric scaling to specific genes. Copyright © 2018 the Author(s). Published by PNAS.

Structural equation model of interactions between risk factors and work-related musculoskeletal complaints among Iranian hospital nurses.

PubMed

Mehralizadeh, Semira; Dehdashti, Alireza; Motalebi Kashani, Masoud

2017-01-01

Statistics indicate a high risk of developing work-related musculoskeletal disorders among hospital nurses. The challenge is to understand the associations between musculoskeletal symptoms and various individual and occupational risk factors. This study examined the direct and indirect interactions of various risk factors with musculoskeletal complaints in hospital nurses. In a cross-sectional design, Iranian hospital nurses from Semnan University of Medical Sciences participated in a questionnaire survey reporting their perceived perceptions of various work-related risk factors and musculoskeletal symptoms. We tested our proposed structural equation model to evaluate the relations between latent and observed concepts and the relative importance and strength of exogenous variables in explaining endogenous musculoskeletal complaints. Measurement model fits the data relatively acceptable. Our findings showed direct effects of psychological, role-related and work posture stressors on musculoskeletal complaints. Fatigue mediated the adverse indirect relations of psychological, role-related, work posture and individual factors with musculoskeletal complaints. Structural equation modeling may provide methodological opportunities in occupational health research with a potential to explain the complexity of interactions among risk factors. Prevention of work-related musculoskeletal disorders among nurses must account for physical and psychosocial conditions.

Final Harvest of Above-Ground Biomass and Allometric Analysis of the Aspen FACE Experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mark E. Kubiske

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 themore » 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.« less

Local Linear Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.

2011-01-01

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

A Relation Between the Eikonal Equation Associated to a Potential Energy Surface and a Hyperbolic Wave Equation.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang; Caballero, Marc

2012-12-11

The potential energy surface (PES) of a molecule can be decomposed into equipotential hypersurfaces. We show in this article that the hypersurfaces are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, or the steepest descent, or the steepest ascent lines of the PES. The energy seen as a reaction coordinate plays the central role in this treatment.

A Structural Equation Model of HIV-related Symptoms, Depressive Symptoms, and Medication Adherence.

PubMed

Yoo-Jeong, Moka; Waldrop-Valverde, Drenna; McCoy, Katryna; Ownby, Raymond L

2016-05-01

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.

A Structural Equation Model of HIV-related Symptoms, Depressive Symptoms, and Medication Adherence

PubMed Central

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

Phytoplankton productivity in relation to light intensity: A simple equation

USGS Publications Warehouse

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.

Entropy and entropy production in Fokker–Plank equation under the generalized fluctuation–dissipation relation

NASA Astrophysics Data System (ADS)

Guo, Ran

2018-04-01

In this paper, we investigate the definition of the entropy in the Fokker–Planck equation under the generalized fluctuation–dissipation relation (FDR), which describes a Brownian particle moving in a complex medium with friction and multiplicative noise. The friction and the noise are related by the generalized FDR. The entropy for such a system is defined first. According to the definition of the entropy, we calculate the entropy production and the entropy flux. Lastly, we make a numerical calculation to display the results in figures.

Group invariant solutions of the Ernst equation of general relativity theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pryse, P.V.

The local symmetry group of the Ernst Equation for stationary, axisymmetric, vacuum space-time manifolds is computed by application of the method of Olver. Several implicit solutions of the equation are found by use of this group. Each of these solutions is given in terms of a function defined as a solution of an ordinary differential equation. One of these equations is integrated by quadratures by use of its own local symmetry group, the result being three explicit solutions of the Ernst Equation. For one of these solutions the metric of the space-time manifold is constructed and studied. The solutions hasmore » a ring curvature singularity and it is asymptotically flat in the sense that the curvature invariants approach zero at spatial infinity. The timelike and null geodesics on the symmetry axis and in the plane of the ring singularity are described. The test particles following these geodesics are seen to be repelled by the ring, which suggests the interpretation of this solution as representing the exterior gravitational field of a rotating ring of matter with negative gravitational mass.« less

Optimization of one-way wave equations.

USGS Publications Warehouse

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

The Debye light scattering equation's scaling relation reveals the purity of synthetic dendrimers

NASA Astrophysics Data System (ADS)

Tseng, Hui-Yu; Chen, Hsiao-Ping; Tang, Yi-Hsuan; Chen, Hui-Ting; Kao, Chai-Lin; Wang, Shau-Chun

2016-03-01

Spherical dendrimer structures cannot be structurally modeled using conventional polymer models of random coil or rod-like configurations during the calibration of the static light scattering (LS) detectors used to determine the molecular weight (M.W.) of a dendrimer or directly assess the purity of a synthetic compound. In this paper, we used the Debye equation-based scaling relation, which predicts that the static LS intensity per unit concentration is linearly proportional to the M.W. of a synthetic dendrimer in a dilute solution, as a tool to examine the purity of high-generational compounds and to monitor the progress of dendrimer preparations. Without using expensive equipment, such as nuclear magnetic resonance or mass spectrometry, this method only required an affordable flow injection set-up with an LS detector. Solutions of the purified dendrimers, including the poly(amidoamine) (PAMAM) dendrimer and its fourth to seventh generation pyridine derivatives with size range of 5-9 nm, were used to establish the scaling relation with high linearity. The use of artificially impure mixtures of six or seven generations revealed significant deviations from linearity. The raw synthesized products of the pyridine-modified PAMAM dendrimer, which included incompletely reacted dendrimers, were also examined to gauge the reaction progress. As a reaction toward a particular generational derivative of the PAMAM dendrimers proceeded over time, deviations from the linear scaling relation decreased. The difference between the polydispersity index of the incompletely converted products and that of the pure compounds was only about 0.01. The use of the Debye equation-based scaling relation, therefore, is much more useful than the polydispersity index for monitoring conversion processes toward an indicated functionality number in a given preparation.

Estimating plant biomass for undergrowth species of northeastern Minnesota forest communities.

Treesearch

Lewis F. Ohmann; David F. Grigal; Lynn L. Rogers

1981-01-01

Biomass prediction equations were developed for some common ground cover plants from forest communities of northeastern Minnesota. The allometric function was used to predict biomass (dry weight) with ocular estimates of percent ground cover of the plant as the independent variable.

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.

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value

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…

Generalization of Einstein's gravitational field equations

NASA Astrophysics Data System (ADS)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

NASA Astrophysics Data System (ADS)

Li, Jinquan; Feng, Shuang; Mi, Honghai

In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

Conservative whole-organ scaling contrasts with highly labile suborgan scaling differences among compound eyes of closely related Formica ants.

PubMed

Perl, Craig D; Rossoni, Sergio; Niven, Jeremy E

2017-03-01

Static allometries determine how organ size scales in relation to body mass. The extent to which these allometric relationships are free to evolve, and how they differ among closely related species, has been debated extensively and remains unclear; changes in intercept appear common, but changes in slope are far rarer. Here, we compare the scaling relationships that govern the structure of compound eyes of four closely related ant species from the genus Formica . Comparison among these species revealed changes in intercept but not slope in the allometric scaling relationships governing eye area, facet number, and mean facet diameter. Moreover, the scaling between facet diameter and number was conserved across all four species. In contrast, facet diameters from distinct regions of the compound eye differed in both intercept and slope within a single species and when comparing homologous regions among species. Thus, even when species are conservative in the scaling of whole organs, they can differ substantially in regional scaling within organs. This, at least partly, explains how species can produce organs that adhere to genus wide scaling relationships while still being able to invest differentially in particular regions of organs to produce specific features that match their ecology.

Formal Derivation of Lotka-Volterra-Haken Amplitude Equations of Task-Related Brain Activity in Multiple, Consecutively Performed Tasks

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.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

Fire and the distribution and uncertainty of carbon sequestered as above-ground tree biomass in Yosemite and Sequoia & Kings Canyon National Parks

USGS Publications Warehouse

Lutz, James A.; Matchett, John R.; Tarnay, Leland W.; Smith, Douglas F.; Becker, Kendall M.L.; Furniss, Tucker J.; Brooks, Matthew L.

2017-01-01

Fire is one of the principal agents changing forest carbon stocks and landscape level distributions of carbon, but few studies have addressed how accurate carbon accounting of fire-killed trees is or can be. We used a large number of forested plots (1646), detailed selection of species-specific and location-specific allometric equations, vegetation type maps with high levels of accuracy, and Monte Carlo simulation to model the amount and uncertainty of aboveground tree carbon present in tree species (hereafter, carbon) within Yosemite and Sequoia & Kings Canyon National Parks. We estimated aboveground carbon in trees within Yosemite National Park to be 25 Tg of carbon (C) (confidence interval (CI): 23–27 Tg C), and in Sequoia & Kings Canyon National Park to be 20 Tg C (CI: 18–21 Tg C). Low-severity and moderate-severity fire had little or no effect on the amount of carbon sequestered in trees at the landscape scale, and high-severity fire did not immediately consume much carbon. Although many of our data inputs were more accurate than those used in similar studies in other locations, the total uncertainty of carbon estimates was still greater than ±10%, mostly due to potential uncertainties in landscape-scale vegetation type mismatches and trees larger than the ranges of existing allometric equations. If carbon inventories are to be meaningfully used in policy, there is an urgent need for more accurate landscape classification methods, improvement in allometric equations for tree species, and better understanding of the uncertainties inherent in existing carbon accounting methods.

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Stochastic differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 offshoremore » structures.« less

Differences in the 2nd to 4th digit length ratio in humans reflect shifts along the common allometric line

PubMed Central

Kratochvíl, Lukáš; Flegr, Jaroslav

2009-01-01

Ratios often lead to biased conclusions concerning the actual relationships between examined traits and comparisons of the relative size of traits among groups. Therefore, the use of ratios has been abandoned in most comparative studies. However, ratios such as body mass index and waist-to-hip ratio are widely used in evolutionary biology and medicine. One such, the ratio of the 2nd to the 4th finger (2D : 4D), has been the subject of much recent interest in both humans and animals. Most studies agree that 2D : 4D is sexually dimorphic. In men, the 2nd digit tends to be shorter than the 4th, while in women the 2nd digit tends to be of the same size or slightly longer than the 4th. Nevertheless, here we demonstrate that the sexes do not greatly differ in the scaling between the 2nd and 4th digit. Sexual differences in 2D : 4D are mainly caused by the shift along the common allometric line with non-zero intercept, which means 2D : 4D necessarily decreases with increasing finger length, and the fact that men have longer fingers than women. We conclude that previously published results on the 2D : 4D ratio are biased by its covariation with finger length. We strongly recommend regression-based approaches for comparisons of hand shape among different groups. PMID:19553247

Standing crop and aboveground biomass partitioning of a dwarf mangrove forest in Taylor River Slough, Florida

USGS Publications Warehouse

Coronado-Molina, C.; Day, J.W.; Reyes, E.; Perez, B.C.

2004-01-01

The structure and standing crop biomass of a dwarf mangrove forest, located in the salinity transition zone ofTaylor River Slough in the Everglades National Park, were studied. Although the four mangrove species reported for Florida occurred at the study site, dwarf Rhizophora mangle trees dominated the forest. The structural characteristics of the mangrove forest were relatively simple: tree height varied from 0.9 to 1.2 meters, and tree density ranged from 7062 to 23 778 stems haa??1. An allometric relationship was developed to estimate leaf, branch, prop root, and total aboveground biomass of dwarf Rhizophora mangle trees. Total aboveground biomass and their components were best estimated as a power function of the crown area times number of prop roots as an independent variable (Y = B ?? Xa??0.5083). The allometric equation for each tree component was highly significant (p<0.0001), with all r2 values greater than 0.90. The allometric relationship was used to estimate total aboveground biomass that ranged from 7.9 to 23.2 ton haa??1. Rhizophora mangle contributed 85% of total standing crop biomass. Conocarpus erectus, Laguncularia racemosa, and Avicennia germinans contributed the remaining biomass. Average aboveground biomass allocation was 69% for prop roots, 25% for stem and branches, and 6% for leaves. This aboveground biomass partitioning pattern, which gives a major role to prop roots that have the potential to produce an extensive root system, may be an important biological strategy in response to low phosphorus availability and relatively reduced soils that characterize mangrove forests in South Florida.

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.

The GUP and quantum Raychaudhuri equation

NASA Astrophysics Data System (ADS)

Vagenas, Elias C.; Alasfar, Lina; Alsaleh, Salwa M.; Ali, Ahmed Farag

2018-06-01

In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation parameter β0. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.

On the transition from the Ginzburg-Landau equation to the extended Fisher-Kolmogorov equation

NASA Astrophysics Data System (ADS)

Rottschäfer, Vivi; Doelman, Arjen

1998-07-01

The Ginzburg-Landau (GL) equation ‘generically’ describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains. In this paper we consider the transition from this generic situation to a degenerate (co-dimension 2) case in which the GL approach is no longer valid. Instead of studying a general underlying model problem, we consider a two-dimensional system of coupled reaction-diffusion equations in one spatial dimension. We show that near the degeneration the behaviour of small perturbations is governed by the extended Fisher-Kolmogorov (eFK) equation (at leading order). The relation between the GL-equation and the eFK-equation is quite subtle, but can be analysed in detail. The main goal of this paper is to study this relation, which we do asymptotically. The asymptotic analysis is compared to numerical simulations of the full reaction-diffusion system. As one approaches the co-dimension 2 point, we observe that the stable stationary periodic patterns predicted by the GL-equation evolve towards various different families of stable, stationary (but not necessarily periodic) so-called ‘multi-bump’ solutions. In the literature, these multi-bump patterns are shown to exist as solutions of the eFK-equation, but there is no proof of the asymptotic stability of these solutions. Our results suggest that these multi-bump patterns can also be asymptotically stable in large classes of model problems.

Estimating tree biomass, carbon, and nitrogen in two vegetation control treatments in an 11-year-old Douglas-fir plantation on a highly productive site

Treesearch

Warren D. Devine; Paul W. Footen; Robert B. Harrison; Thomas A. Terry; Constance A. Harrington; Scott M. Holub; Peter J. Gould

2013-01-01

We sampled trees grown with and without competing vegetation control in an 11-year-old Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirb.) Franco) plantation on a highly productive site in southwestern Washington to create diameter based allometric equations for estimating individual-tree bole, branch, foliar, and total...

"Negative of My Money, Positive of Her Money": Secondary Students' Ways of Relating Equations to a Debt Context

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.…

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Basal metabolic rate of endotherms can be modeled using heat-transfer principles and physiological concepts: reply to "can the basal metabolic rate of endotherms be explained by biophysical modeling?".

PubMed

Roberts, Michael F; Lightfoot, Edwin N; Porter, Warren P

2011-01-01

Our recent article (Roberts et al. 2010 ) proposes a mechanistic model for the relation between basal metabolic rate (BMR) and body mass (M) in mammals. The model is based on heat-transfer principles in the form of an equation for distributed heat generation within the body. The model can also be written in the form of the allometric equation BMR = aM(b), in which a is the coefficient of the mass term and b is the allometric exponent. The model generates two interesting results: it predicts that b takes the value 2/3, indicating that BMR is proportional to surface area in endotherms. It also provides an explanation of the physiological components that make up a, that is, respiratory heat loss, core-skin thermal conductance, and core-skin thermal gradient. Some of the ideas in our article have been questioned (Seymour and White 2011 ), and this is our response to those questions. We specifically address the following points: whether a heat-transfer model can explain the level of BMR in mammals, whether our test of the model is inadequate because it uses the same literature data that generated the values of the physiological variables, and whether geometry and empirical values combine to make a "coincidence" that makes the model only appear to conform to real processes.

DBH Prediction Using Allometry Described by Bivariate Copula Distribution

NASA Astrophysics Data System (ADS)

Xu, Q.; Hou, Z.; Li, B.; Greenberg, J. A.

2017-12-01

Forest biomass mapping based on single tree detection from the airborne laser scanning (ALS) usually depends on an allometric equation that relates diameter at breast height (DBH) with per-tree aboveground biomass. The incapability of the ALS technology in directly measuring DBH leads to the need to predict DBH with other ALS-measured tree-level structural parameters. A copula-based method is proposed in the study to predict DBH with the ALS-measured tree height and crown diameter using a dataset measured in the Lassen National Forest in California. Instead of exploring an explicit mathematical equation that explains the underlying relationship between DBH and other structural parameters, the copula-based prediction method utilizes the dependency between cumulative distributions of these variables, and solves the DBH based on an assumption that for a single tree, the cumulative probability of each structural parameter is identical. Results show that compared with the bench-marking least-square linear regression and the k-MSN imputation, the copula-based method obtains better accuracy in the DBH for the Lassen National Forest. To assess the generalization of the proposed method, prediction uncertainty is quantified using bootstrapping techniques that examine the variability of the RMSE of the predicted DBH. We find that the copula distribution is reliable in describing the allometric relationship between tree-level structural parameters, and it contributes to the reduction of prediction uncertainty.

Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

PubMed

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.

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ishii, M.

1977-10-01

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equation that specifies the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, shear stresses, and the interfacial momentum transfer, since these macroscopic effects govern the relative velocity between phases. A comparison of the model with various experimental data over various flow regimesmore » and a wide range of flow parameters shows a satisfactory agreement.« less

Static allometry of unicellular green algae: scaling of cellular surface area and volume in the genus Micrasterias (Desmidiales).

PubMed

Neustupa, J

2016-02-01

The surface area-to-volume ratio of cells is one of the key factors affecting fundamental biological processes and, thus, fitness of unicellular organisms. One of the general models for allometric increase in surface-to-volume scaling involves fractal-like elaboration of cellular surfaces. However, specific data illustrating this pattern in natural populations of the unicellular organisms have not previously been available. This study shows that unicellular green algae of the genus Micrasterias (Desmidiales) have positive allometric surface-to-volume scaling caused by changes in morphology of individual species, especially in the degree of cell lobulation. This allometric pattern was also detected within most of the cultured and natural populations analysed. Values of the allometric S:V scaling within individual populations were closely correlated to the phylogenetic structure of the clade. In addition, they were related to species-specific cellular morphology. Individual populations differed in their allometric patterns, and their position in the allometric space was strongly correlated with the degree of allometric S:V scaling. This result illustrates that allometric shape patterns are an important correlate of the capacity of individual populations to compensate for increases in their cell volumes by increasing the surface area. However, variation in allometric patterns was not associated with phylogenetic structure. This indicates that the position of the populations in the allometric space was not evolutionarily conserved and might be influenced by environmental factors. © 2015 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2015 European Society For Evolutionary Biology.

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.

Using structural equation modeling to construct calibration equations relating PM2.5 mass concentration samplers to the federal reference method sampler

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

Marcus equation

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.

The shallow water equation and the vorticity equation for a change in height of the topography.

PubMed

Da, ChaoJiu; Shen, BingLu; Yan, PengCheng; Ma, DeShan; Song, Jian

2017-01-01

We consider the shallow water equation and the vorticity equations for a variable height of topography. On the assumptions that the atmosphere is incompressible and a constant density, we simplify the coupled dynamic equations. The change in topographic height is handled as the sum of the inherent and changing topography using the perturbation method, together with appropriate boundary conditions of the atmosphere, to obtain the relationship between the relative height of the flow, the inherent topography and the changing topography. We generalize the conservation of the function of relative position, and quantify the relationship between the height of the topography and the relative position of a fluid element. If the height of the topography increases (decreases), the relative position of a fluid element descends (ascends). On this basis, we also study the relationship between the vorticity and the topography to find the vorticity decreasing (increasing) for an increasing (decreasing) height of the topography.

The shallow water equation and the vorticity equation for a change in height of the topography

PubMed Central

Shen, BingLu; Yan, PengCheng; Ma, DeShan; Song, Jian

2017-01-01

We consider the shallow water equation and the vorticity equations for a variable height of topography. On the assumptions that the atmosphere is incompressible and a constant density, we simplify the coupled dynamic equations. The change in topographic height is handled as the sum of the inherent and changing topography using the perturbation method, together with appropriate boundary conditions of the atmosphere, to obtain the relationship between the relative height of the flow, the inherent topography and the changing topography. We generalize the conservation of the function of relative position, and quantify the relationship between the height of the topography and the relative position of a fluid element. If the height of the topography increases (decreases), the relative position of a fluid element descends (ascends). On this basis, we also study the relationship between the vorticity and the topography to find the vorticity decreasing (increasing) for an increasing (decreasing) height of the topography. PMID:28591129

On the exterior Dirichlet problem for Hessian quotient equations

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Li, Zhisu

2018-06-01

In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior at infinity. This extends the previous related results on the Monge-Ampère equations and on the Hessian equations, and rearranges them in a systematic way. Based on the Perron's method, the main ingredient of this paper is to construct some appropriate subsolutions of the Hessian quotient equation, which is realized by introducing some new quantities about the elementary symmetric polynomials and using them to analyze the corresponding ordinary differential equation related to the generalized radially symmetric subsolutions of the original equation.

Ecosystem carbon stocks in Pinus palustris forests

Treesearch

Lisa Samuelson; Tom Stokes; John R. Butnor; Kurt H. Johnsen; Carlos A. Gonzalez-Benecke; Pete Anderson; Jason Jackson; Lorenzo Ferrari; Tim A. Martin; Wendell P. Cropper

2014-01-01

Longleaf pine (Pinus palustris Mill.) restoration in the southeastern United States offers opportunities for carbon (C) sequestration. Ecosystem C stocks are not well understood in longleaf pine forests, which are typically of low density and maintained by prescribed fire. The objectives of this research were to develop allometric equations for...

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

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.

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.

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

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…

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.

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.

Allometric considerations when assessing aortic aneurysms in Turner syndrome: Implications for activity recommendations and medical decision-making.

PubMed

Corbitt, Holly; Maslen, Cheryl; Prakash, Siddharth; Morris, Shaine A; Silberbach, Michael

2018-02-01

In Turner syndrome, the potential to form thoracic aortic aneurysms requires routine patient monitoring. However, the short stature that typically occurs complicates the assessment of severity and risk because the relationship of body size to aortic dimensions is different in Turner syndrome compared to the general population. Three allometric formula have been proposed to adjust aortic dimensions, all employing body surface area: aortic size index, Turner syndrome-specific Z-scores, and Z-scores based on a general pediatric and young adult population. In order to understand the differences between these formula we evaluated the relationship between age and aortic size index and compared Turner syndrome-specific Z-scores and pediatric/young adult based Z-scores in a group of girls and women with Turner syndrome. Our results suggest that the aortic size index is highly age-dependent for those under 15 years; and that Turner-specific Z-scores are significantly lower than Z-scores referenced to the general population. Higher Z-scores derived from the general reference population could result in stigmatization, inappropriate restriction from sports, and increasing the risk of unneeded medical or operative treatments. We propose that when estimating aortic dissection risk clinicians use Turner syndrome-specific Z-score for those under fifteen years of age. © 2017 Wiley Periodicals, Inc.

Relation between Water Balance and Climatic Variables Associated with the Geographical Distribution of Anurans

PubMed Central

Titon, Braz; Gomes, Fernando Ribeiro

2015-01-01

Amphibian species richness increases toward the equator, particularly in humid tropical forests. This relation between amphibian species richness and environmental water availability has been proposed to be a consequence of their high rates of evaporative water loss. In this way, traits that estimate water balance are expected to covary with climate and constrain a species’ geographic distribution. Furthermore, we predicted that coexisting species of anurans would have traits that are adapted to local hydric conditions. We compared the traits that describe water balance in 17 species of anurans that occur in the mesic Atlantic Forest and xeric Cerrado (savannah) habitats of Brazil. We predicted that species found in the warmer and dryer areas would show a lower sensitivity of locomotor performance to dehydration (SLPD), increased resistance to evaporative water loss (REWL) and higher rates of water uptake (RWU) than species restricted to the more mesic areas. We estimated the allometric relations between the hydric traits and body mass using phylogenetic generalized least squares. These regressions showed that REWL scaled negatively with body mass, whereas RWU scaled positively with body mass. Additionally, species inhabiting areas characterized by higher and more seasonally uniform temperatures, and lower and more seasonally concentrated precipitation, such as the Cerrado, had higher RWU and SLPD than species with geographical distributions more restricted to mesic environments, such as the Atlantic Forest. These results support the hypothesis that the interspecific variation of physiological traits shows an adaptation pattern to abiotic environmental traits. PMID:26469787

Articular scaling and body mass estimation in platyrrhines and catarrhines: Modern variation and application to fossil anthropoids.

PubMed

Perry, Jonathan M G; Cooke, Siobhán B; Runestad Connour, Jacqueline A; Burgess, M Loring; Ruff, Christopher B

2018-02-01

Body mass is an important component of any paleobiological reconstruction. Reliable skeletal dimensions for making estimates are desirable but extant primate reference samples with known body masses are rare. We estimated body mass in a sample of extinct platyrrhines and Fayum anthropoids based on four measurements of the articular surfaces of the humerus and femur. Estimates were based on a large extant reference sample of wild-collected individuals with associated body masses, including previously published and new data from extant platyrrhines, cercopithecoids, and hominoids. In general, scaling of joint dimensions is positively allometric relative to expectations of geometric isometry, but negatively allometric relative to expectations of maintaining equivalent joint surface areas. Body mass prediction equations based on articular breadths are reasonably precise, with %SEEs of 17-25%. The breadth of the distal femoral articulation yields the most reliable estimates of body mass because it scales similarly in all major anthropoid taxa. Other joints scale differently in different taxa; therefore, locomotor style and phylogenetic affinity must be considered when calculating body mass estimates from the proximal femur, proximal humerus, and distal humerus. The body mass prediction equations were applied to 36 Old World and New World fossil anthropoid specimens representing 11 taxa, plus two Haitian specimens of uncertain taxonomic affinity. Among the extinct platyrrhines studied, only Cebupithecia is similar to large, extant platyrrhines in having large humeral (especially distal) joints. Our body mass estimates differ from each other and from published estimates based on teeth in ways that reflect known differences in relative sizes of the joints and teeth. We prefer body mass estimators that are biomechanically linked to weight-bearing, and especially those that are relatively insensitive to differences in locomotor style and phylogenetic history. Whenever

Kinetic energy equations for the average-passage equation system

NASA Technical Reports Server (NTRS)

Johnson, Richard W.; Adamczyk, John J.

1989-01-01

Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.

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)

Lie symmetries for systems of evolution equations

NASA Astrophysics Data System (ADS)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

Extension of the Schrodinger equation

NASA Astrophysics Data System (ADS)

Somsikov, Vyacheslav

2017-03-01

Extension of the Schrodinger equation is submitted by removing its limitations appearing due to the limitations of the formalism of Hamilton, based on which this equation was obtained. For this purpose the problems of quantum mechanics arising from the limitations of classical mechanics are discussed. These limitations, in particular, preclude the use of the Schrodinger equation to describe the time symmetry violation. The extension of the Schrodinger equation is realized based on the principle of duality symmetry. According to this principle the dynamics of the systems is determined by the symmetry of the system and by the symmetry of the space. The extension of the Schrodinger equation was obtained from the dual expression of energy, represented in operator form. For this purpose the independent micro - and macro-variables that determine respectively the dynamics of quantum particle system relative to its center of mass and the movement of the center of mass in space are used. The solution of the extended Schrodinger equation for the system near equilibrium is submitted. The main advantage of the extended Schrodinger equation is that it is applicable to describe the interaction and evolution of quantum systems in inhomogeneous field of external forces.

On the non-stationary generalized Langevin equation

NASA Astrophysics Data System (ADS)

Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja

2017-12-01

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

Higuchi equation: derivation, applications, use and misuse.

PubMed

Siepmann, Juergen; Peppas, Nicholas A

2011-10-10

Fifty years ago, the legendary Professor Takeru Higuchi published the derivation of an equation that allowed for the quantification of drug release from thin ointment films, containing finely dispersed drug into a perfect sink. This became the famous Higuchi equation whose fiftieth anniversary we celebrate this year. Despite the complexity of the involved mass transport processes, Higuchi derived a very simple equation, which is easy to use. Based on a pseudo-steady-state approach, a direct proportionality between the cumulative amount of drug released and the square root of time can be demonstrated. In contrast to various other "square root of time" release kinetics, the constant of proportionality in the classical Higuchi equation has a specific, physically realistic meaning. The major benefits of this equation include the possibility to: (i) facilitate device optimization, and (ii) to better understand the underlying drug release mechanisms. The equation can also be applied to other types of drug delivery systems than thin ointment films, e.g., controlled release transdermal patches or films for oral controlled drug delivery. Later, the equation was extended to other geometries and related theories have been proposed. The aim of this review is to highlight the assumptions the derivation of the classical Higuchi equation is based on and to give an overview on the use and potential misuse of this equation as well as of related theories. Copyright © 2011 Elsevier B.V. All rights reserved.

Probabilistic delay differential equation modeling of event-related potentials.

PubMed

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. Copyright © 2016 Elsevier Inc. All rights reserved.

[Study on HIV prevention related knowledge-motivation-psychological model in men who have sex with men, based on a structural equation model].

PubMed

Jiang, Y; Dou, Y L; Cai, A J; Zhang, Z; Tian, T; Dai, J H; Huang, A L

2016-02-01

Knowledge-motivation-psychological model was set up and tested through structural equation model to provide evidence on HIV prevention related strategy in Men who have Sex with Men (MSM). Snowball sampling method was used to recruit a total of 550 MSM volunteers from two MSM Non-Governmental Organizations in Urumqi, Xinjiang province. HIV prevention related information on MSM was collected through a questionnaire survey. A total of 477 volunteers showed with complete information. HIV prevention related Knowledge-motivation-psychological model was built under related experience and literature. Relations between knowledge, motivation and psychological was studied, using a ' structural equation model' with data from the fitting questionnaires and modification of the model. Structural equation model presented good fitting results. After revising the fitting index: RMSEA was 0.035, NFI was 0.965 and RFI was 0.920. Thereafter the exogenous latent variables would include knowledge, motivation and psychological effects. The endogenous latent variable appeared as prevention related behaviors. The standardized total effects of motivation, knowledge, psychological on prevention behavior were 0.44, 0.41 and 0.17 respectively. Correlation coefficient of motivation and psychological effects was 0.16. Correlation coefficient on knowledge and psychological effects was -0.17 (P<0.05). Correlation coefficient of knowledge and motivation did not show statistical significance. Knowledge of HIV and motivation of HIV prevention did not show any accordance in MSM population. It was necessary to increase the awareness and to improve the motivation of HIV prevention in MSM population.

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.

Isolating Tracers of Phytoplankton with Allometric Zooplankton (TOPAZ) from Modular Ocean Model (MOM5) to Couple it with a Global Ocean Model

NASA Astrophysics Data System (ADS)

Jung, H. C.; Moon, B. K.; Wie, J.; Park, H. S.; Kim, K. Y.; Lee, J.; Byun, Y. H.

2017-12-01

This research is motivated by a need to develop a new coupled ocean-biogeochemistry model, a key tool for climate projections. The Modular Ocean Model (MOM5) is a global ocean/ice model developed by the Geophysical Fluid Dynamics Laboratory (GFDL) in the US, and it incorporates Tracers of Phytoplankton with Allometric Zooplankton (TOPAZ), which simulates the marine biota associated with carbon cycles. We isolated TOPAZ from MOM5 into a stand-alone version (TOPAZ-SA), and had it receive initial data and ocean physical fields required. Then, its reliability was verified by comparing the simulation results from the TOPAZ-SA with the MOM5/TOPAZ. This stand-alone version of TOPAZ is to be coupled to the Nucleus for European Modelling of the Ocean (NEMO). Here we present the preliminary results. Acknowledgements This research was supported by the project "Research and Development for KMA Weather, Climate, and Earth system Services" (NIMS-2016-3100) of the National Institute of Meteorological Sciences/Korea Meteorological Administration.

Hamiltonian structure of the Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-03-01

The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.

Uncertainty in accounting for carbon accumulation following forest harvesting

NASA Astrophysics Data System (ADS)

Lilly, P.; Yanai, R. D.; Arthur, M. A.; Bae, K.; Hamburg, S.; Levine, C. R.; Vadeboncoeur, M. A.

2014-12-01

Tree biomass and forest soils are both difficult to quantify with confidence, for different reasons. Forest biomass is estimated non-destructively using allometric equations, often from other sites; these equations are difficult to validate. Forest soils are destructively sampled, resulting in little measurement error at a point, but with large sampling error in heterogeneous soil environments, such as in soils developed on glacial till. In this study, we report C contents of biomass and soil pools in northern hardwood stands in replicate plots within replicate stands in 3 age classes following clearcut harvesting (14-19 yr, 26-29 yr, and > 100 yr) at the Bartlett Experimental Forest, USA. The rate of C accumulation in aboveground biomass was ~3 Mg/ha/yr between the young and mid-aged stands and <1 Mg/ha/yr between the mid-aged and mature stands. We propagated model uncertainty through allometric equations, and found errors ranging from 3-7%, depending on the stand. The variation in biomass among plots within stands (6-19%) was always larger than the allometric uncertainties. Soils were described by quantitative soil pits in three plots per stand, excavated by depth increment to the C horizon. Variation in soil mass among pits within stands averaged 28% (coefficient of variation); variation among stands within an age class ranged from 9-25%. Variation in carbon concentrations averaged 27%, mainly because the depth increments contained varying proportions of genetic horizons, in the upper part of the soil profile. Differences across age classes in soil C were not significant, because of the high variability. Uncertainty analysis can help direct the design of monitoring schemes to achieve the greatest confidence in C stores per unit of sampling effort. In the system we studied, more extensive sampling would be the best approach to reducing uncertainty, as natural spatial variation was higher than model or measurement uncertainties.

p-Euler equations and p-Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

A new model for simulating microbial cyanide production and optimizing the medium parameters for recovering precious metals from waste printed circuit boards.

PubMed

Yuan, Zhihui; Ruan, Jujun; Li, Yaying; Qiu, Rongliang

2018-04-10

Bioleaching is a green recycling technology for recovering precious metals from waste printed circuit boards (WPCBs). However, this technology requires increasing cyanide production to obtain desirable recovery efficiency. Luria-Bertani medium (LB medium, containing tryptone 10 g/L, yeast extract 5 g/L, NaCl 10 g/L) was commonly used in bioleaching of precious metal. In this study, results showed that LB medium did not produce highest yield of cyanide. Under optimal culture conditions (25 °C, pH 7.5), the maximum cyanide yield of the optimized medium (containing tryptone 6 g/L and yeast extract 5 g/L) was 1.5 times as high as that of LB medium. In addition, kinetics and relationship of cell growth and cyanide production was studied. Data of cell growth fitted logistics model well. Allometric model was demonstrated effective in describing relationship between cell growth and cyanide production. By inserting logistics equation into allometric equation, we got a novel hybrid equation containing five parameters. Kinetic data for cyanide production were well fitted to the new model. Model parameters reflected both cell growth and cyanide production process. Copyright © 2018 Elsevier B.V. All rights reserved.

Stand-level Allometry in Pinus taeda as Affected by Irrigation and Fertilization

Treesearch

J.S. King; T.J. Albaugh; H.L. Allen; L.W. Kress

1999-01-01

Changing environmental conditions have the potential to alter allometric relationships between plant parts, possibly leading to ecosystem-level feedbacks. We quantified allometric shifts in field-grown loblolly pine (Pinus taeda L.) in response to altered resource availability based on data from multiple harvests to correct for size-related changes...

Natural selection. IV. The Price equation.

PubMed

Frank, S A

2012-06-01

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen. © 2012 The Authors. Journal of Evolutionary Biology © 2012 European Society For Evolutionary Biology.

A Least-Squares Transport Equation Compatible with Voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Jon; Peterson, Jacob; Morel, Jim

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 transportmore » 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« less

Three-dimensional canopy fuel loading predicted using upward and downward sensing LiDAR systems

Treesearch

Nicholas S. Skowronski; Kenneth L. Clark; Matthew Duveneck; John. Hom

2011-01-01

We calibrated upward sensing profiling and downward sensing scanning LiDAR systems to estimates of canopy fuel loading developed from field plots and allometric equations, and then used the LiDAR datasets to predict canopy bulk density (CBD) and crown fuel weight (CFW) in wildfire prone stands in the New Jersey Pinelands. LiDAR-derived height profiles were also...

Hammett equation and generalized Pauling's electronegativity equation.

PubMed

Liu, Lei; Fu, Yao; Liu, Rui; Li, Rui-Qiong; Guo, Qing-Xiang

2004-01-01

Substituent interaction energy (SIE) was defined as the energy change of the isodesmic reaction X-spacer-Y + H-spacer-H --> X-spacer-H + H-spacer-Y. It was found that this SIE followed a simple equation, SIE(X,Y) = -ksigma(X)sigma(Y), where k was a constant dependent on the system and sigma was a certain scale of electronic substituent constant. It was demonstrated that the equation was applicable to disubstituted bicyclo[2.2.2]octanes, benzenes, ethylenes, butadienes, and hexatrienes. It was also demonstrated that Hammett's equation was a derivative form of the above equation. Furthermore, it was found that when spacer = nil the above equation was mathematically the same as Pauling's electronegativity equation. Thus it was shown that Hammett's equation was a derivative form of the generalized Pauling's electronegativity equation and that a generalized Pauling's electronegativity equation could be utilized for diverse X-spacer-Y systems. In addition, the total electronic substituent effects were successfully separated into field/inductive and resonance effects in the equation SIE(X,Y) = -k(1)F(X)F(Y) - k(2)R(X)R(Y) - k(3)(F(X)R(Y) + R(X)F(Y)). The existence of the cross term (i.e., F(X)R(Y) and R(X)F(Y)) suggested that the field/inductive effect was not orthogonal to the resonance effect because the field/inductive effect from one substituent interacted with the resonance effect from the other. Further studies on multi-substituted systems suggested that the electronic substituent effects should be pairwise and additive. Hence, the SIE in a multi-substituted system could be described using the equation SIE(X1, X2, ..., Xn) = Sigma(n-1)(i=1)Sigma(n)(j=i+1)k(ij)sigma(X)isigma(X)j.

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.

Alternative forms of the Spencer-Fano equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inokuti, M.; Kowari, K.

We point out a relation between the electron degradation spectra determined by two differing cross-section sets but subject to the same source. The relation takes a form of the Fredholm integral equation of the second kind and may be viewed as an alternative form of the Spencer-Fano equation. The relation leads to a precise definition of the partial degradation spectra of electrons of successive generations. It also provides a basis for the perturbation theory by which one calculates effects of small changes of cross-section data upon the electron degradation spectrum.

Comparison of amikacin pharmacokinetics in a killer whale (Orcinus orca) and a beluga whale (Delphinapterus leucas).

PubMed

KuKanich, Butch; Papich, Mark; Huff, David; Stoskopf, Michael

2004-06-01

Amikacin, an aminoglycoside antimicrobial, was administered to a killer whale (Orcinus orca) and a beluga whale (Delphinapterus leucas) for the treatment of clinical signs consistent with gram-negative aerobic bacterial infections. Dosage regimens were designed to target a maximal plasma concentration 8-10 times the minimum inhibitory concentrations of the pathogen and to reduce the risk of aminoglycoside toxicity. Allometric analysis of published pharmacokinetic parameters in mature animals yielded a relationship for amikacin's volume of distribution, in milliliters, given by the equation Vd = 151.058(BW)1.043. An initial dose for amikacin was estimated by calculating the volume of distribution and targeted maximal concentration. With this information, dosage regimens for i.m. administration were designed for a killer whale and a beluga whale. Therapeutic drug monitoring was performed on each whale to assess the individual pharmacokinetic parameters. The elimination half-life (5.99 hr), volume of distribution per bioavailability (319 ml/kg). and clearance per bioavailability (0.61 ml/min/kg) were calculated for the killer whale. The elimination half-life (5.03 hr), volume of distribution per bioavailability (229 ml/kg). and clearance per bioavailability (0.53 ml/min/kg) were calculated for the beluga whale. The volume of distribution predicted from the allometric equation for both whales was similar to the calculated pharmacokinetic parameter. Both whales exhibited a prolonged elimination half-life and decreased clearance when compared with other animal species despite normal renal parameters on biochemistry panels. Allometric principles and therapeutic drug monitoring were used to accurately determine the doses in these cases and to avoid toxicity.

The Effect of Tutoring With Nonstandard Equations for Students With Mathematics Difficulty.

PubMed

Powell, Sarah R; Driver, Melissa K; Julian, Tyler E

2015-01-01

Students often misinterpret the equal sign (=) as operational instead of relational. Research indicates misinterpretation of the equal sign occurs because students receive relatively little exposure to equations that promote relational understanding of the equal sign. No study, however, has examined effects of nonstandard equations on the equation solving and equal-sign understanding of students with mathematics difficulty (MD). In the present study, second-grade students with MD (n = 51) were randomly assigned to standard equations tutoring, combined tutoring (standard and nonstandard equations), and no-tutoring control. Combined tutoring students demonstrated greater gains on equation-solving assessments and equal-sign tasks compared to the other two conditions. Standard tutoring students demonstrated improved skill on equation solving over control students, but combined tutoring students' performance gains were significantly larger. Results indicate that exposure to and practice with nonstandard equations positively influence student understanding of the equal sign. © Hammill Institute on Disabilities 2013.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

Performance of bed-load transport equations relative to geomorphic significance: Predicting effective discharge and its transport rate

Treesearch

Jeffrey J. Barry; John M. Buffington; Peter Goodwin; John .G. King; William W. Emmett

2008-01-01

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation...

THE COSMIC RAY EQUATOR AND THE GEOMAGNETISM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakurai, K.

1960-01-01

It was formerly thought that the disagreement of the position of geomagnetic dipole equator with that of the cosmic ray equator was caused by 45 deg westward shifting of the latter. Referring to the theory of geomagnetic effect on cosmic rays, it was determined whether such westward shifting could be existent or not. It was found that the deviation of the cosmic ray equator from the geomagnetic dipole equator is negligible even if the magnetic cavity is present around the earth's outer atmosphere. Taking into account such results, the origin of the cosmic ray equator was investigated. It was foundmore » that this equater could be produced by the higher harmonic components combined with the dipole component of geomagnetism. The relation of the origin of the cosmic ray equater to the eccentric dipoles, near the outer pant of the earth's core, contributing to the secular variation of geomagnetism was considered. (auth)« less

Nonlinear equations of dynamics for spinning paraboloidal antennas

NASA Technical Reports Server (NTRS)

Utku, S.; Shoemaker, W. L.; Salama, M.

1983-01-01

The nonlinear strain-displacement and velocity-displacement relations of spinning imperfect rotational paraboloidal thin shell antennas are derived for nonaxisymmetrical deformations. Using these relations with the admissible trial functions in the principle functional of dynamics, the nonlinear equations of stress inducing motion are expressed in the form of a set of quasi-linear ordinary differential equations of the undetermined functions by means of the Rayleigh-Ritz procedure. These equations include all nonlinear terms up to and including the third degree. Explicit expressions are given for the coefficient matrices appearing in these equations. Both translational and rotational off-sets of the axis of revolution (and also the apex point of the paraboloid) with respect to the spin axis are considered. Although the material of the antenna is assumed linearly elastic, it can be anisotropic.

Maxwell Equations and the Redundant Gauge Degree of Freedom

ERIC Educational Resources Information Center

Wong, Chun Wa

2009-01-01

On transformation to the Fourier space (k,[omega]), the partial differential Maxwell equations simplify to algebraic equations, and the Helmholtz theorem of vector calculus reduces to vector algebraic projections. Maxwell equations and their solutions can then be separated readily into longitudinal and transverse components relative to the…

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Preservice Mathematics Teachers' Experiences about Function and Equation Concepts

ERIC Educational Resources Information Center

Dede, Yuksel; Soybas, Danyal

2011-01-01

The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were…

EQUATIONS AND THE EQUAL SIGN IN ELEMENTARY MATHEMATICS TEXTBOOKS

PubMed Central

Powell, Sarah R.

2012-01-01

To promote a relational understanding of the equal sign (=), students may require exposure to a variety of equation types (i.e., 3 = 8 − 5; 2 + 3 = 1 + 4; 9 − 3 = 6). The purpose of this study was to evaluate 8 elementary curricula for degree of exposure to equation types. Across 6 elementary grade levels, curricula were coded for the number of standard and nonstandard equation types appearing within the student textbook. Except in 1 of the 8 curricula, students typically do not receive exposure to nonstandard equation types that promote a relational understanding of the equal sign. An analysis of the accompanying teacher manual for each textbook suggests that students receive minimal instruction on relational definitions of the equal sign, with the majority of instruction occurring in grades K–2 and minimal instruction provided in grades 3–5. PMID:22707760

EQUATIONS AND THE EQUAL SIGN IN ELEMENTARY MATHEMATICS TEXTBOOKS.

PubMed

Powell, Sarah R

2012-06-01

To promote a relational understanding of the equal sign (=), students may require exposure to a variety of equation types (i.e., 3 = 8 - 5; 2 + 3 = 1 + 4; 9 - 3 = 6). The purpose of this study was to evaluate 8 elementary curricula for degree of exposure to equation types. Across 6 elementary grade levels, curricula were coded for the number of standard and nonstandard equation types appearing within the student textbook. Except in 1 of the 8 curricula, students typically do not receive exposure to nonstandard equation types that promote a relational understanding of the equal sign. An analysis of the accompanying teacher manual for each textbook suggests that students receive minimal instruction on relational definitions of the equal sign, with the majority of instruction occurring in grades K-2 and minimal instruction provided in grades 3-5.

Solving differential equations with unknown constitutive relations as recurrent neural networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.

We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learningmore » literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.« less

Evolution of brain-body allometry in Lake Tanganyika cichlids.

PubMed

Tsuboi, Masahito; Kotrschal, Alexander; Hayward, Alexander; Buechel, Severine Denise; Zidar, Josefina; Løvlie, Hanne; Kolm, Niclas

2016-07-01

Brain size is strongly associated with body size in all vertebrates. This relationship has been hypothesized to be an important constraint on adaptive brain size evolution. The essential assumption behind this idea is that static (i.e., within species) brain-body allometry has low ability to evolve. However, recent studies have reported mixed support for this view. Here, we examine brain-body static allometry in Lake Tanganyika cichlids using a phylogenetic comparative framework. We found considerable variation in the static allometric intercept, which explained the majority of variation in absolute and relative brain size. In contrast, the slope of the brain-body static allometry had relatively low variation, which explained less variation in absolute and relative brain size compared to the intercept and body size. Further examination of the tempo and mode of evolution of static allometric parameters confirmed these observations. Moreover, the estimated evolutionary parameters indicate that the limited observed variation in the static allometric slope could be a result of strong stabilizing selection. Overall, our findings suggest that the brain-body static allometric slope may represent an evolutionary constraint in Lake Tanganyika cichlids. © 2016 The Author(s).

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Youkhana, Adel H.; Ogoshi, Richard M.; Kiniry, James R.

Biomass is a promising renewable energy option that provides a more environmentally sustainable alternative to fossil resources by reducing the net flux of greenhouse gasses to the atmosphere. Yet, allometric models that allow the prediction of aboveground biomass (AGB), biomass carbon (C) stock non-destructively have not yet been developed for tropical perennial C 4 grasses currently under consideration as potential bioenergy feedstock in Hawaii and other subtropical and tropical locations. The objectives of this study were to develop optimal allometric relationships and site-specific models to predict AGB, biomass C stock of napiergrass, energycane, and sugarcane under cultivation practices for renewablemore » energy and validate these site-specific models against independent data sets generated from sites with widely different environments. Several allometric models were developed for each species from data at a low elevation field on the island of Maui, Hawaii. A simple power model with stalk diameter (D) was best related to AGB and biomass C stock for napiergrass, energycane, and sugarcane, (R 2 = 0.98, 0.96, and 0.97, respectively). The models were then tested against data collected from independent fields across an environmental gradient. For all crops, the models over-predicted AGB in plants with lower stalk D, but AGB was under-predicted in plants with higher stalk D. The models using stalk D were better for biomass prediction compared to dewlap H (Height from the base cut to most recently exposed leaf dewlap) models, which showed weak validation performance. Although stalk D model performed better, however, the mean square error (MSE)-systematic was ranged from 23 to 43 % of MSE for all crops. A strong relationship between model coefficient and rainfall was existed, although these were irrigated systems; suggesting a simple site-specific coefficient modulator for rainfall to reduce systematic errors in water-limited areas. These allometric equations

A structural equation model relating impaired sensorimotor function, fear of falling and gait patterns in older people.

PubMed

Menz, Hylton B; Lord, Stephen R; Fitzpatrick, Richard C

2007-02-01

Many falls in older people occur while walking, however the mechanisms responsible for gait instability are poorly understood. Therefore, the aim of this study was to develop a plausible model describing the relationships between impaired sensorimotor function, fear of falling and gait patterns in older people. Temporo-spatial gait parameters and acceleration patterns of the head and pelvis were obtained from 100 community-dwelling older people aged between 75 and 93 years while walking on an irregular walkway. A theoretical model was developed to explain the relationships between these variables, assuming that head stability is a primary output of the postural control system when walking. This model was then tested using structural equation modeling, a statistical technique which enables the testing of a set of regression equations simultaneously. The structural equation model indicated that: (i) reduced step length has a significant direct and indirect association with reduced head stability; (ii) impaired sensorimotor function is significantly associated with reduced head stability, but this effect is largely indirect, mediated by reduced step length, and; (iii) fear of falling is significantly associated with reduced step length, but has little direct influence on head stability. These findings provide useful insights into the possible mechanisms underlying gait characteristics and risk of falling in older people. Particularly important is the indication that fear-related step length shortening may be maladaptive.

The importance of body mass normalisation for ultrasound measurement of the transversus abdominis muscle: The effect of age, gender and sport practice.

PubMed

Linek, Pawel

2017-04-01

Some studies have not considered body mass as a confounder in TrA analysis, which may have led to improper interpretation of results. To assess the differences in the effect of age, gender and physical activity between normalised for body mass and actual values of the TrA as well as to establish the effect of age, gender and physical activity on normalised for body mass TrA thickness in adolescents. The study was a cross-sectional study conducted at selected primary and secondary schools, and colleges in the Silesian region of Poland. A real-time ultrasound was used to obtain images of the TrA muscle. Body mass normalisation for TrA thickness was performed with allometric scaling and the following equation: Allometric-scaled TrA = TrA thickness/body mass 0.61 . Analysis has shown that boys have significantly thicker muscle by 0.27 mm (95% CI 0.04-0.50) than girls, and those who practise sports have thicker muscle by 0.30 mm (95% CI 0.06-0.52) than non-active individuals. For allometric-scaled TrA, there were no significant effects (p > 0.50). There was a significant correlation between participants age and the actual value of the TrA (r = 0.42, p < 0.05). The correlation between age and allometric-scaled TrA was insignificant and close to zero (r = -0.006, p = 0.93). An analysis of TrA thickness without body mass normalisation can deliver improper interpretation of study results. Thus, it is recommended in future researches to analyse TrA thickness measurement after normalisation rather than actual values. In the adolescent population, there is no effect of gender, age and physical activity on allometric-scaled TrA thickness. Copyright © 2017 Elsevier Ltd. All rights reserved.

Moment of inertia, quadrupole moment, Love number of neutron star and their relations with strange-matter equations of state

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Debades; Bhat, Sajad A.; Char, Prasanta; Chatterjee, Debarati

2018-02-01

We investigate the impact of strange-matter equations of state involving Λ hyperons, Bose-Einstein condensate of K- mesons and first-order hadron-quark phase transition on moment of inertia, quadrupole moment and tidal deformability parameter of slowly rotating neutron stars. All these equations of state are compatible with the 2 M_{solar} constraint. The main findings of this investigation are the universality of the I- Q and I -Love number relations, which are preserved by the EoSs including Λ hyperons and antikaon condensates, but broken in the presence of a first-order hadron-quark phase transition. Furthermore, it is also noted that the quadrupole moment approaches the Kerr value of a black hole for maximum-mass neutron stars.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

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.

Explicit integration of Friedmann's equation with nonlinear equations of state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong, E-mail: chensx@henu.edu.cn, E-mail: gwg1@damtp.cam.ac.uk, E-mail: yisongyang@nyu.edu

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 generalmore » 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.« less

Allometric comparison of Georgia dairy heifers on farms and at youth shows.

PubMed

White, D S; Duberstein, K J; Fain Bohlen, J L; Bertrand, J K; Nelson, A H; Froetschel, M A; Davidson, B E; Graves, W M

2015-02-01

Studies were conducted to determine the relationship between allometric measures of growth of Holstein dairy heifers and placing in the show ring, and to compare differences in growth between Holstein heifers that are shown and not shown. In the first study, 494 Holstein show heifers were evaluated at the 2012 and 2013 Georgia Junior National Livestock Shows. Measurements were obtained for weight, head length, withers height, hip height, thurl width, and tail length. Heifer mass index (HMI), average daily gain (ADG), and age were calculated. In total, 72.5% of Holstein show heifers were underweight. Average ADG was 0.63 kg/d, which is below the industry recommendation of 0.7 to 0.8 kg/d. Variables were ranked and converted to percentages to account for differences in class size. Withers height, head length, and HMI were most indicative of show placing. In the second study, we compared differences between growth patterns of show heifers and non-show heifers. An additional 293 non-show Holstein heifers were evaluated on 3 Georgia dairy farms during the same period as the show. In total, 43.3% of non-show heifers were underweight. Average ADG for non-show heifers was 0.71 kg/d, which is within the industry recommendation of 0.7 to 0.8 kg/d. Show heifers weighed less for their age than non-show heifers and tended to be taller at the withers than non-show heifers. The HMI scores were similar for younger show and non-show heifers, but older show heifers had lower HMI scores than non-show heifers of the same age. Show heifers had HMI scores that were lower than values calculated from standard growth data. As show heifers matured, ADG decreased, whereas as non-show heifers matured, ADG increased. Youth, leaders, and parents need to be aware of the importance of growing replacement heifers correctly so that heifers calve at 22 to 24 mo of age at an acceptable size and scale and become profitable members of the milking herd. Copyright © 2015 American Dairy Science

Stand Density Effects on Biomass Allocation Patterns and Subsequent Soil Nitrogen Demand

Treesearch

Christopher A. Dicus; Thomas J. Dean

1998-01-01

Growth and yield data from a loblolly pine plantation in southeastern Louisiana were obtained yearly from 1993 to 1996 on numbered trees within two stands initially planted on a 1.22- by 1.22-meter spacing, and two stands planted on a 2.44- by 2.44-meter spacing. Using allometric equations derived from a 1994 on-site destructive harvest, cited nitrogen...

Interspecies differences in the empty body chemical composition of domestic animals.

PubMed

Maeno, H; Oishi, K; Hirooka, H

2013-07-01

Domestication of animals has resulted in phenotypic changes by means of natural and human-directed selection. Body composition is important for farm animals because it reflects the status of energy reserves. Thus, there is the possibility that farm animals as providers of food have been more affected by human-directed selection for body composition than laboratory animals. In this study, an analysis was conducted to determine what similarities and differences in body composition occur between farm and laboratory animals using literature data obtained from seven comparative slaughter studies (n = 136 observations). Farm animals from four species (cattle, goats, pigs and sheep) were all castrated males, whereas laboratory animals from three species (dogs, mice and rats) comprised males and/or females. All animals were fed ad libitum. The allometric equation, Y = aX b , was used to determine the influence of species on the accretion rates of chemical components (Y, kg) relative to the growth of the empty body, fat-free empty body or protein weights (X, kg). There were differences between farm and laboratory animals in terms of the allometric growth coefficients for chemical components relative to the empty BW and fat-free empty BW (P < 0.01); farm animals had more rapid accretion rates of fat (P < 0.01) but laboratory animals had more rapid accretion rates of protein, water and ash (P < 0.01). In contrast, there was no difference in terms of the allometric growth coefficients for protein and water within farm animals (P > 0.2). The allometric growth coefficients for ash weight relative to protein weight for six species except sheep were not different from a value of 1 (P > 0.1), whereas that of sheep was smaller than 1 (P < 0.01). When compared at the same fat content of the empty body, the rate of change in water content (%) per unit change in fat content (%) was not different (P > 0.05) across farm animal species and similar ash-to-protein ratios were obtained

Generalized recursive solutions to Ornstein-Zernike integral equations

NASA Astrophysics Data System (ADS)

Rossky, Peter J.; Dale, William D. T.

1980-09-01

Recursive procedures for the solution of a class of integral equations based on the Ornstein-Zernike equation are developed; the hypernetted chain and Percus-Yevick equations are two special cases of the class considered. It is shown that certain variants of the new procedures developed here are formally equivalent to those recently developed by Dale and Friedman, if the new recursive expressions are initialized in the same way as theirs. However, the computational solution of the new equations is significantly more efficient. Further, the present analysis leads to the identification of various graphical quantities arising in the earlier study with more familiar quantities related to pair correlation functions. The analysis is greatly facilitated by the use of several identities relating simple chain sums whose graphical elements can be written as a sum of two or more parts. In particular, the use of these identities permits renormalization of the equivalent series solution to the integral equation to be directly incorporated into the recursive solution in a straightforward manner. Formulas appropriate to renormalization with respect to long and short range parts of the pair potential, as well as more general components of the direct correlation function, are obtained. To further illustrate the utility of this approach, we show that a simple generalization of the hypernetted chain closure relation for the direct correlation function leads directly to the reference hypernetted chain (RHNC) equation due to Lado. The form of the correlation function used in the exponential approximation of Andersen and Chandler is then seen to be equivalent to the first estimate obtained from a renormalized RHNC equation.

Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated with Respect to Multiple Equating Criteria. Research Report. ETS RR-11-20

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…

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.

Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.

2016-01-01

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

Exact RG flow equations and quantum gravity

NASA Astrophysics Data System (ADS)

de Alwis, S. P.

2018-03-01

We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

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

Constitutive Equation with Varying Parameters for Superplastic Flow Behavior

NASA Astrophysics Data System (ADS)

Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui

2014-03-01

In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.

Boundary-layer equations in generalized curvilinear coordinates

NASA Technical Reports Server (NTRS)

Panaras, Argyris G.

1987-01-01

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

An exceptionally preserved armored dinosaur reveals the morphology and allometry of osteoderms and their horny epidermal coverings.

PubMed

Brown, Caleb M

2017-01-01

Although the evolution and function of "exaggerated" bony projections in ornithischian dinosaurs has been subject to significant debate recently, our understanding of the structure and morphology of their epidermal keratinized coverings is greatly limited. The holotype of Borealopelta , a new nodosaurid ankylosaur, preserves osteoderms and extensive epidermal structures (dark organic residues), in anatomic position across the entire precaudal length. Contrasting previous specimens, organic epiosteodermal scales, often in the form of horn-like (keratinous) sheaths, cap and exaggerate nearly all osteoderms, allowing for morphometric and allometric analyses of both the bony osteoderms and their horny sheaths. A total of 172 osteoderms were quantified, with osteoderm spine length and height being positively allometric with respect to basal length and width. Despite tight correlations between the different measures amongst all other osteoderms, the large parascapular spines represent consistent outliers. Thickness and relative contribution of the keratinized epiosteodermal scales/sheaths varies greatly by region, ranging from 2% to 6% for posterior thoracics, to ∼25% (1.3×) for the parascapular spines-similar to horn sheaths in some bovid analogues. Relative to the bony cores, the horny portions of the spines are strongly positively allometric (slope = 2.3, CI = 1.8-2.8). Strong allometric scaling, species-specific morphology, and significant keratinous extension of the cervicoscapular spines is consistent with elaboration under socio-sexual selection. This marks the first allometric analysis of ornithischian soft tissues.

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances

An alternative to the breeder's and Lande's equations.

PubMed

Houchmandzadeh, Bahram

2014-01-10

The breeder's equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) - E(Z0) to the selection differential S = E(ZW) - E(Z0) through a simple proportionality relation R = h(2)S, where the heritability coefficient h(2) is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R' = j(2)S' can be derived, regardless of the parental genotype distribution. Here R' = E(Z1) - μ and S' = E(ZW) - μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j(2) is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande's equation Δ(z) = GP(-1)S. The linearity coefficient of the alternative equation are not changed by Gaussian selection.

Natural selection. IV. The Price equation*

PubMed Central

Frank, Steven A.

2012-01-01

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation’s greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection, and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen. PMID:22487312

Basic lubrication equations

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.

Sizing ocean giants: patterns of intraspecific size variation in marine megafauna

PubMed Central

Balk, Meghan A.; Benfield, Mark C.; Branch, Trevor A.; Chen, Catherine; Cosgrove, James; Dove, Alistair D.M.; Gaskins, Lindsay C.; Helm, Rebecca R.; Hochberg, Frederick G.; Lee, Frank B.; Marshall, Andrea; McMurray, Steven E.; Schanche, Caroline; Stone, Shane N.; Thaler, Andrew D.

2015-01-01

What are the greatest sizes that the largest marine megafauna obtain? This is a simple question with a difficult and complex answer. Many of the largest-sized species occur in the world’s oceans. For many of these, rarity, remoteness, and quite simply the logistics of measuring these giants has made obtaining accurate size measurements difficult. Inaccurate reports of maximum sizes run rampant through the scientific literature and popular media. Moreover, how intraspecific variation in the body sizes of these animals relates to sex, population structure, the environment, and interactions with humans remains underappreciated. Here, we review and analyze body size for 25 ocean giants ranging across the animal kingdom. For each taxon we document body size for the largest known marine species of several clades. We also analyze intraspecific variation and identify the largest known individuals for each species. Where data allows, we analyze spatial and temporal intraspecific size variation. We also provide allometric scaling equations between different size measurements as resources to other researchers. In some cases, the lack of data prevents us from fully examining these topics and instead we specifically highlight these deficiencies and the barriers that exist for data collection. Overall, we found considerable variability in intraspecific size distributions from strongly left- to strongly right-skewed. We provide several allometric equations that allow for estimation of total lengths and weights from more easily obtained measurements. In several cases, we also quantify considerable geographic variation and decreases in size likely attributed to humans. PMID:25649000

A Constitutive Equation Relating Composition and Microstructure to Properties in Ti-6Al-4V: As Derived Using a Novel Integrated Computational Approach

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.

Relativistic Tsiolkovsky equation -- a case study in special relativity

NASA Astrophysics Data System (ADS)

Redd, Jeremy; Panin, Alexander

2011-10-01

A possibility of using antimatter in future space propulsion systems is seriously discussed in scientific literature. Annihilation of matter and antimatter is not only the energy source of ultimate density 9x10^16 J/kg (provided that antimatter fuel is available on board or can be collected along the journey) but also potentially allows to reach ultimate exhaust speed -- speed of light c. Using relativistic rocket equation we discuss the feasibility of achieving relativistic velocities with annihilation powered photon engine, as well as the advantages and disadvantages of interstellar travel with relativistic and ultrarelativistic velocities.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

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…

Planck constant as spectral parameter in integrable systems and KZB equations

NASA Astrophysics Data System (ADS)

Levin, A.; Olshanetsky, M.; Zotov, A.

2014-10-01

We construct special rational gl N Knizhnik-Zamolodchikov-Bernard (KZB) equations with Ñ punctures by deformation of the corresponding quantum gl N rational R-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is τ. At the level of classical mechanics the deformation parameter τ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized R-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in R matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical r-matrices which can be treated as halves of the classical Yang-Baxter equation. At last we discuss the R-matrix valued linear problems which provide gl Ñ CM models and Painlevé equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum R-matrix. When the quantum gl N R-matrix is scalar ( N = 1) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the gl Ñ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

Non-invertible transformations of differential-difference equations

NASA Astrophysics Data System (ADS)

Garifullin, R. N.; Yamilov, R. I.; Levi, D.

2016-09-01

We discuss aspects of the theory of non-invertible transformations of differential-difference equations and, in particular, the notion of Miura type transformation. We introduce the concept of non-Miura type linearizable transformation and we present techniques that allow one to construct simple linearizable transformations and might help one to solve classification problems. This theory is illustrated by the example of a new integrable differential-difference equation depending on five lattice points, interesting from the viewpoint of the non-invertible transformation, which relate it to an Itoh-Narita-Bogoyavlensky equation.

Boundary transfer matrices and boundary quantum KZ equations

NASA Astrophysics Data System (ADS)

Vlaar, Bart

2015-07-01

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.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Competitive regulation of plant allometry and a generalized model for the plant self-thinning process.

PubMed

Wang, Gang; Yuan, Jianli; Wang, Xizhi; Xiao, Sa; Huang, Wenbing

2004-11-01

Taking into account the individual growth form (allometry) in a plant population and the effects of intraspecific competition on allometry under the population self-thinning condition, and adopting Ogawa's allometric equation 1/y = 1/axb + 1/c as the expression of complex allometry, the generalized model describing the change mode of r (the self-thinning exponential in the self-thinning equation, log M = K + log N, where M is mean plant mass, K is constant, and N is population density) was constructed. Meanwhile, with reference to the changing process of population density to survival curve type B, the exponential, r, was calculated using the software MATHEMATICA 4.0. The results of the numerical simulation show that (1) the value of the self-thinning exponential, r, is mainly determined by allometric parameters; it is most sensitive to change of b of the three allometric parameters, and a and c take second place; (2) the exponential, r, changes continuously from about -3 to the asymptote -1; the slope of -3/2 is a transient value in the population self-thinning process; (3) it is not a 'law' that the slope of the self-thinning trajectory equals or approaches -3/2, and the long-running dispute in ecological research over whether or not the exponential, r, equals -3/2 is meaningless. So future studies on the plant self-thinning process should focus on investigating how plant neighbor competition affects the phenotypic plasticity of plant individuals, what the relationship between the allometry mode and the self-thinning trajectory of plant population is and, in the light of evolution, how plants have adapted to competition pressure by plastic individual growth.

Illness-death model: statistical perspective and differential equations.

PubMed

Brinks, Ralph; Hoyer, Annika

2018-01-27

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

[Specific growth rate and the rate of energy metabolism in the ontogenesis of axolotl, Ambystoma mexicanum (Amphibia: Ambystomatidae)].

PubMed

Vladimirova, I G; Kleĭmenov, S Iu; Alekseeva, T A; Radzinskaia, L I

2003-01-01

Concordant changes in the rate of energy metabolism and specific growth rate of axolotls have been revealed. Several periods of ontogeny are distinguished, which differ in the ratio of energy metabolism to body weight and, therefore, are described by different allometric equations. It is suggested that the specific growth rate of an animal determines the type of dependence of energy metabolism on body weight.

Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle

NASA Astrophysics Data System (ADS)

Triantafyllopoulos, A.; Stavrinos, P. C.

2018-04-01

We study field equations for a weak anisotropic model on the tangent Lorentz bundle TM of a spacetime manifold. A geometrical extension of general relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer 4‑velocity. In this approach, we consider a metric on TM as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein–Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.

Evaluating scaling models in biology using hierarchical Bayesian approaches

PubMed Central

Price, Charles A; Ogle, Kiona; White, Ethan P; Weitz, Joshua S

2009-01-01

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity. PMID:19453621

Size-Related Changes in Foot Impact Mechanics in Hoofed Mammals

PubMed Central

Warner, Sharon Elaine; Pickering, Phillip; Panagiotopoulou, Olga; Pfau, Thilo; Ren, Lei; Hutchinson, John Richard

2013-01-01

Foot-ground impact is mechanically challenging for all animals, but how do large animals mitigate increased mass during foot impact? We hypothesized that impact force amplitude scales according to isometry in animals of increasing size through allometric scaling of related impact parameters. To test this, we measured limb kinetics and kinematics in 11 species of hoofed mammals ranging from 18–3157 kg body mass. We found impact force amplitude to be maintained proportional to size in hoofed mammals, but that other features of foot impact exhibit differential scaling patterns depending on the limb; forelimb parameters typically exhibit higher intercepts with lower scaling exponents than hind limb parameters. Our explorations of the size-related consequences of foot impact advance understanding of how body size influences limb morphology and function, foot design and locomotor behaviour. PMID:23382967

Health-related physical fitness measures: reference values and reference equations for use in clinical practice.

PubMed

Tveter, Anne Therese; Dagfinrud, Hanne; Moseng, Tuva; Holm, Inger

2014-07-01

To provide reference values and reference equations for frequently used clinical field tests of health-related physical fitness for use in clinical practice. Cross-sectional design. General community. Convenience sample of volunteers (N=370) between 18 and 90 years of age were recruited from a wide range of settings (ie, work sites, schools, community centers for older adults) and different geographic locations (ie, urban, suburban, rural) in southeastern Norway. Not applicable. The participants conducted 5 clinical field tests (6-minute walk test, stair test, 30-second sit-to-stand test, handgrip test, fingertip-to-floor test). The results of the field tests showed that performance remained unchanged until approximately 50 years of age; after that, performance deteriorated with increasing age. Grip strength (79%), meters walked in 6 minutes (60%), and seconds used on the stair test (59%) could be well predicted by age, sex, height, and weight in participants ≥50 years of age, whereas the performance on all tests was less well predicted in participants <50 years of age. The reference values and reference equations provided in this study may increase the applicability and interpretability of the 6-minute walk test, stair test, 30-second sit-to-stand test, handgrip test, and fingertip-to-floor test in clinical practice. Copyright © 2014 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Analysis of the Poisson-Nernst-Planck equation in a ball for modeling the Voltage-Current relation in neurobiological microdomains

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

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…

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.

Proposed standard-weight equations for brook trout

USGS Publications Warehouse

Hyatt, M.W.; Hubert, W.A.

2001-01-01

Weight and length data were obtained for 113 populations of brook trout Salvelinus fontinalis across the species' geographic range in North America to estimate a standard-weight (Ws) equation for this species. Estimation was done by applying the regression-line-percentile technique to fish of 120-620 mm total length (TL). The proposed metric-unit (g and mm) equation is log10Ws = -5.186 + 3.103 log10TL; the English-unit (lb and in) equivalent is log10Ws = -3.483 + 3.103 log10TL. No systematic length bias was evident in the relative-weight values calculated from these equations.

Allometric multilevel modelling of agility and dribbling speed by skeletal age and playing position in youth soccer players.

PubMed

Valente-dos-Santos, J; Coelho-e-Silva, M J; Duarte, J; Pereira, J; Rebelo-Gonçalves, R; Figueiredo, A; Mazzuco, M A; Sherar, L B; Elferink-Gemser, M T; Malina, R M

2014-08-01

This study evaluates the contributions of age, skeletal maturation, body size and composition, training and playing position to the development of agility and dribbling speed in young male soccer players (10-18 years) followed longitudinally. 83 players [defenders (n=35), midfielders (n=27), forwards (n=21)] were followed annually over 5 years (average: 4.4 observations per player). Skeletal age (SA), stature, body mass, triceps and subscapular skinfolds, agility and dribbling speed were measured annually. Body composition was estimated from the 2 skinfolds. Annual training volume was estimated from weekly participation forms completed by coaches. The multiplicative allometric models with the best statistical fit showed that statural growth of 1 cm predicts 1.334 s and 1.927 s of improvement in agility and dribbling speed, respectively. Significant independent effects of fat-free mass and annual volume training were found for agility and dribbling speed, respectively (P<0.05). Predicted agility (from 12 to 18 years of SA) and dribbling speed (from 13 to 18 years of SA) differed significantly among players by playing positions (midfielders>forwards>defenders). The present results provide developmental models for the interpretation of intra- and inter-individual variability in agility and dribbling speed among youth soccer players across adolescence, and may provide a framework for trainers and coaches to develop and evaluate individualized training protocols. © Georg Thieme Verlag KG Stuttgart · New York.

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…

Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

NASA Astrophysics Data System (ADS)

Rahmani, Faramarz; Golshani, Mehdi

2018-01-01

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.

A stockability equation for forest land in Siskiyou County, California.

Treesearch

Neil. McKay

1985-01-01

An equation is presented that estimates the relative stocking capacity of forest land in Siskiyou County, California, from the amount of precipitation and the presence of significant indicator plants. The equation is a toot for identifying sites incapable of supporting normal stocking. Estimated relative stocking capacity may be used to discount normal yields to levels...

State Equation Determination of Cow Dung Biogas

NASA Astrophysics Data System (ADS)

Marzuki, A.; Wicaksono, L. B.

2017-08-01

A state function is a thermodynamic function which relates various macroscopically measurable properties of a system (state variable) describing the state of matter under a given set of physical conditions. A good understanding of a biogas state function plays a very important role in an effort to maximize biogas processes and to help predicting combation performance. This paper presents a step by step process of an experimental study aimed at determining the equation of state of cow dung biogas. The equation was derived from the data obtained from the experimental results of compressibility (κ) and expansivity (β) following the general form of gas state equation dV = βdT + κdP. In this equation, dV is gas volume variation, dT is temperature variation, and dP is pressure variation. From these results, we formulated a unique state equation from which the biogas critical temperature (Tc) and critical pressure were then determined (Tc = 266.7 K, Pc = 5096647.5 Pa).

The Effect of Tutoring with Nonstandard Equations for Students with Mathematics Difficulty

ERIC Educational Resources Information Center

Powell, Sarah R.; Driver, Melissa K.; Julian, Tyler E.

2015-01-01

Students often misinterpret the equal sign (=) as operational instead of relational. Research indicates misinterpretation of the equal sign occurs because students receive relatively little exposure to equations that promote relational understanding of the equal sign. No study, however, has examined effects of nonstandard equations on the equation…

Mixed-power scaling of whole-plant respiration from seedlings to giant trees

PubMed Central

Mori, Shigeta; Yamaji, Keiko; Ishida, Atsushi; Prokushkin, Stanislav G.; Masyagina, Oxana V.; Hagihara, Akio; Hoque, A.T.M. Rafiqul; Suwa, Rempei; Osawa, Akira; Nishizono, Tomohiro; Ueda, Tatsushiro; Kinjo, Masaru; Miyagi, Tsuyoshi; Kajimoto, Takuya; Koike, Takayoshi; Matsuura, Yojiro; Toma, Takeshi; Zyryanova, Olga A.; Abaimov, Anatoly P.; Awaya, Yoshio; Araki, Masatake G.; Kawasaki, Tatsuro; Chiba, Yukihiro; Umari, Marjnah

2010-01-01

The scaling of respiratory metabolism with body mass is one of the most pervasive phenomena in biology. Using a single allometric equation to characterize empirical scaling relationships and to evaluate alternative hypotheses about mechanisms has been controversial. We developed a method to directly measure respiration of 271 whole plants, spanning nine orders of magnitude in body mass, from small seedlings to large trees, and from tropical to boreal ecosystems. Our measurements include the roots, which have often been ignored. Rather than a single power-law relationship, our data are fit by a biphasic, mixed-power function. The allometric exponent varies continuously from 1 in the smallest plants to 3/4 in larger saplings and trees. Therefore, our findings support the recent findings of Reich et al. [Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size, and nitrogen in plants. Nature 439:457–461] and West, Brown, and Enquist [West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122 -126.]. The transition from linear to 3/4-power scaling may indicate fundamental physical and physiological constraints on the allocation of plant biomass between photosynthetic and nonphotosynthetic organs over the course of ontogenetic plant growth. PMID:20080600

Mixed-power scaling of whole-plant respiration from seedlings to giant trees.

PubMed

Mori, Shigeta; Yamaji, Keiko; Ishida, Atsushi; Prokushkin, Stanislav G; Masyagina, Oxana V; Hagihara, Akio; Hoque, A T M Rafiqul; Suwa, Rempei; Osawa, Akira; Nishizono, Tomohiro; Ueda, Tatsushiro; Kinjo, Masaru; Miyagi, Tsuyoshi; Kajimoto, Takuya; Koike, Takayoshi; Matsuura, Yojiro; Toma, Takeshi; Zyryanova, Olga A; Abaimov, Anatoly P; Awaya, Yoshio; Araki, Masatake G; Kawasaki, Tatsuro; Chiba, Yukihiro; Umari, Marjnah

2010-01-26

The scaling of respiratory metabolism with body mass is one of the most pervasive phenomena in biology. Using a single allometric equation to characterize empirical scaling relationships and to evaluate alternative hypotheses about mechanisms has been controversial. We developed a method to directly measure respiration of 271 whole plants, spanning nine orders of magnitude in body mass, from small seedlings to large trees, and from tropical to boreal ecosystems. Our measurements include the roots, which have often been ignored. Rather than a single power-law relationship, our data are fit by a biphasic, mixed-power function. The allometric exponent varies continuously from 1 in the smallest plants to 3/4 in larger saplings and trees. Therefore, our findings support the recent findings of Reich et al. [Reich PB, Tjoelker MG, Machado JL, Oleksyn J (2006) Universal scaling of respiratory metabolism, size, and nitrogen in plants. Nature 439:457-461] and West, Brown, and Enquist [West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric scaling laws in biology. Science 276:122 -126.]. The transition from linear to 3/4-power scaling may indicate fundamental physical and physiological constraints on the allocation of plant biomass between photosynthetic and nonphotosynthetic organs over the course of ontogenetic plant growth.

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…

Structural Equation Model Trees

ERIC Educational Resources Information Center

Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

2013-01-01

In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

Modelling by Differential Equations

ERIC Educational Resources Information Center

Chaachoua, Hamid; Saglam, Ayse

2006-01-01

This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

On inter-tidal transport equation

USGS Publications Warehouse

Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi

1989-01-01

The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the Eulerian residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the Lagrangian residual current suggest that the long-term transport problem is more closely related to the Lagrangian residual current than to the Eulerian residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order Lagrangian residual current (the sum of the Eulerian residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.

Comparison of the One- and Bi-Direction Chained Equipercentile Equating

ERIC Educational Resources Information Center

Oh, Hyeonjoo; Moses, Tim

2012-01-01

This study investigated differences between two approaches to chained equipercentile (CE) equating (one- and bi-direction CE equating) in nearly equal groups and relatively unequal groups. In one-direction CE equating, the new form is linked to the anchor in one sample of examinees and the anchor is linked to the reference form in the other…

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

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.

Magnetic monopoles, Galilean invariance, and Maxwell's equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crawford, F.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 electrodynamicsmore » are Galilean invariant---i.e., they have the same form in every inertial frame, to a first approximation; (c) magnetic poles (as well as the usual electric charges) exist; (d) the complete Lorentz force on an electric charge is known; (e) the force on a monopole at rest is known; (f) the Coulomb-like field produced by a resting electric charge and by a resting monopole are known. Everything else is deduced. History is followed in the assumption that Newtonian mechanics have been discovered, but not special relativity. (Only particle velocities {ital v}{much lt}{ital c} are considered.) This ends up with Maxwell's equations (Maxwell did not need special relativity, so why should we,) but facing Einstein's paradox, the solution of which is encapsulated in the Einstein velocity-addition formula.« less

A systematic approach to sketch Bethe-Salpeter equation

NASA Astrophysics Data System (ADS)

Qin, Si-xue

2016-03-01

To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark-anti-quark scattering kernel are key pieces to solve those equations. Predicted by lattice-QCD and Dyson-Schwinger analyses of QCD's gauge sector, gluons are non-perturbatively massive. In the matter sector, the modeled gluon propagator which can produce a veracious description of meson properties needs to possess a mass scale, accordingly. Solving the well-known longitudinal Ward-Green-Takahashi identities (WGTIs) and the less-known transverse counterparts together, one obtains a nontrivial solution which can shed light on the structure of the quark-gluon vertex. It is highlighted that the phenomenologically proposed anomalous chromomagnetic moment (ACM) vertex originates from the QCD Lagrangian symmetries and its strength is proportional to the magnitude of dynamical chiral symmetry breaking (DCSB). The color-singlet vector and axial-vector WGTIs can relate the BS kernel and the dressed quark-gluon vertex to each other. Using the relation, one can truncate the gap equation and the BS equation, systematically, without violating crucial symmetries, e.g., gauge symmetry and chiral symmetry.

Empirical Allometric Models to Estimate Total Needle Biomass For Loblolly Pine

Treesearch

Hector M. de los Santos-Posadas; Bruce E. Borders

2002-01-01

Empirical geometric models based on the cone surface formula were adapted and used to estimate total dry needle biomass (TNB) and live branch basal area (LBBA). The results suggest that the empirical geometric equations produced good fit and stable parameters while estimating TNB and LBBA. The data used include trees form a spacing study of 12 years old and a set of...

Calculating work in weakly driven quantum master equations: Backward and forward equations

NASA Astrophysics Data System (ADS)

Liu, Fei

2016-01-01

I present a technical report indicating that the two methods used for calculating characteristic functions for the work distribution in weakly driven quantum master equations are equivalent. One involves applying the notion of quantum jump trajectory [Phys. Rev. E 89, 042122 (2014), 10.1103/PhysRevE.89.042122], while the other is based on two energy measurements on the combined system and reservoir [Silaev et al., Phys. Rev. E 90, 022103 (2014), 10.1103/PhysRevE.90.022103]. These represent backward and forward methods, respectively, which adopt a very similar approach to that of the Kolmogorov backward and forward equations used in classical stochastic theory. The microscopic basis for the former method is also clarified. In addition, a previously unnoticed equality related to the heat is also revealed.

The differential equation of an arbitrary reflecting surface

NASA Astrophysics Data System (ADS)

Melka, Richard F.; Berrettini, Vincent D.; Yousif, Hashim A.

2018-05-01

A differential equation describing the reflection of a light ray incident upon an arbitrary reflecting surface is obtained using the law of reflection. The derived equation is written in terms of a parameter and the value of this parameter determines the nature of the reflecting surface. Under various parametric constraints, the solution of the differential equation leads to the various conic surfaces but is not generally solvable. In addition, the dynamics of the light reflections from the conic surfaces are executed in the Mathematica software. Our derivation is the converse of the traditional approach and our analysis assumes a relation between the object distance and the image distance. This leads to the differential equation of the reflecting surface.

Gravitational closure of matter field equations

NASA Astrophysics Data System (ADS)

Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

2018-04-01

The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

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.

Chemical Equation Balancing.

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)

Reply to ``Comment on `Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation' ''

NASA Astrophysics Data System (ADS)

Reis, T.; Phillips, T. N.

2008-12-01

In this reply to the comment by Lallemand and Luo, we defend our assertion that the alternative approach for the solution of the dispersion relation for a generalized lattice Boltzmann dispersion equation [T. Reis and T. N. Phillips, Phys. Rev. E 77, 026702 (2008)] is mathematically transparent, elegant, and easily justified. Furthermore, the rigorous perturbation analysis used by Reis and Phillips does not require the reciprocals of the relaxation parameters to be small.

Equations on knot polynomials and 3d/5d duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mironov, A.; Morozov, A.; ITEP, Moscow

2012-09-24

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. Themore » shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.« less

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Republication of: Geometrodynamics in the null case. Exact solutions of the field equations of the general theory of relativity III

NASA Astrophysics Data System (ADS)

Jordan, Pascual; Kundt, Wolfgang

2014-03-01

This is an English translation of a paper by Pascual Jordan and Wolfgang Kundt, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 3 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1, 2 and 4 of the series have already been reprinted, part 5 will be printed as a Golden Oldie in near future.) This third paper shows how solutions of the Einstein-Maxwell equations with null Maxwell field can be incorporated into the scheme of geometrodynamics. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Charles Misner.

Size matters: insights from an allometric approach to evaluate control methods for invasive Australian Rhinella marina.

PubMed

Beaty, Lynne E; Salice, Christopher J

2013-10-01

Invasive species are costly and difficult to control. In order to gain a mechanistic understanding of potential control measures, individual-based models uniquely parameterized to reflect the salient life-history characteristics of invasive species are useful. Using invasive Australian Rhinella marina as a case study, we constructed a cohort- and individual-based population simulation that incorporates growth and body size of terrestrial stages. We used this allometric approach to examine the efficacy of nontraditional control methods (i.e., tadpole alarm chemicals and native meat ants) that may have indirect effects on population dynamics mediated by effects on body size. We compared population estimates resulting from these control methods with traditional hand removal. We also conducted a sensitivity analysis to investigate the effect that model parameters, specifically those associated with growth and body size, had on adult population estimates. Incremental increases in hand removal of adults and juveniles caused nonlinear decreases in adult population estimates, suggesting less return with increased investment in hand-removal efforts. Applying tadpole alarm chemicals or meat ants decreased adult population estimates on the same level as removing 15-25% of adults and juveniles by hand. The combined application of tadpole alarm chemicals and meat ants resulted in approximately 80% decrease in adult abundance, the largest of any applied control method. In further support of the nontraditional control methods, which greatly affected the metamorph stage, our model was most sensitive to changes in metamorph survival, juvenile survival, metamorph growth rate, and adult survival. Our results highlight the use and insights that can be gained from individual-based models that incorporate growth and body size and the potential success that nontraditional control methods could have in controlling established, invasive Rhinella marina populations.

Combinatorics of Generalized Bethe Equations

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.; Sklyanin, Evgeny K.

2013-10-01

A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over {{Z}^M}, and on the other hand, they count integer points in certain M-dimensional polytopes.

Length-weight relationship and a relative condition factor equation for lake sturgeon (Acipenser fulvescens) from the St Clair River system (Michigan, USA)

USGS Publications Warehouse

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.

Length-weight relationship and a relative condition factor equation for lake sturgeon (Acipenser fulvescens) from the St. Clair River system (Michigan, USA)

USGS Publications Warehouse

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.

Allometric Scaling in Biology

NASA Astrophysics Data System (ADS)

Banavar, Jayanth

2009-03-01

The unity of life is expressed not only in the universal basis of inheritance and energetics at the molecular level, but also in the pervasive scaling of traits with body size at the whole-organism level. More than 75 years ago, Kleiber and Brody and Proctor independently showed that the metabolic rates, B, of mammals and birds scale as the three-quarter power of their mass, M. Subsequent studies showed that most biological rates and times scale as M-1/4 and M^1/4 respectively, and that these so called quarter-power scaling relations hold for a variety of organisms, from unicellular prokaryotes and eukaryotes to trees and mammals. The wide applicability of Kleiber's law, across the 22 orders of magnitude of body mass from minute bacteria to giant whales and sequoias, raises the hope that there is some simple general explanation that underlies the incredible diversity of form and function. We will present a general theoretical framework for understanding the relationship between metabolic rate, B, and body mass, M. We show how the pervasive quarter-power biological scaling relations arise naturally from optimal directed resource supply systems. This framework robustly predicts that: 1) whole organism power and resource supply rate, B, scale as M^3/4; 2) most other rates, such as heart rate and maximal population growth rate scale as M-1/4; 3) most biological times, such as blood circulation time and lifespan, scale as M^1/4; and 4) the average velocity of flow through the network, v, such as the speed of blood and oxygen delivery, scales as M^1/12. Our framework is valid even when there is no underlying network. Our theory is applicable to unicellular organisms as well as to large animals and plants. This work was carried out in collaboration with Amos Maritan along with Jim Brown, John Damuth, Melanie Moses, Andrea Rinaldo, and Geoff West.

Allometric Analysis Detects Brain Size-Independent Effects of Sex and Sex Chromosome Complement on Human Cerebellar Organization

PubMed Central

Mankiw, Catherine; Park, Min Tae M.; Reardon, P.K.; Fish, Ari M.; Clasen, Liv S.; Greenstein, Deanna; Blumenthal, Jonathan D.; Lerch, Jason P.; Chakravarty, M. Mallar

2017-01-01

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 (1) localize normative male–female differences in raw cerebellar volume, (2) compare these to sex chromosome effects estimated across five rare sex (X/Y) chromosome aneuploidy (SCA) syndromes, and (3) clarify brain size-independent effects of sex and SCA on cerebellar anatomy using a generalizable allometric approach that considers scaling relationships between regional cerebellar volume and brain volume in health. The integration of these approaches shows that (1) sex and SCA effects on raw cerebellar volume are large and distributed, but regionally heterogeneous, (2) human cerebellar volume scales with brain volume in a highly nonlinear and regionally heterogeneous fashion that departs from documented patterns of cerebellar scaling in phylogeny, and (3) 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 STATEMENT Cerebellar systems are implicated in diverse domains of sex-biased behavior and pathology, but we lack a basic understanding of how sex differences in the

Allometric Analysis Detects Brain Size-Independent Effects of Sex and Sex Chromosome Complement on Human Cerebellar Organization.

PubMed

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

2017-05-24

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 (1) localize normative male-female differences in raw cerebellar volume, (2) compare these to sex chromosome effects estimated across five rare sex (X/Y) chromosome aneuploidy (SCA) syndromes, and (3) clarify brain size-independent effects of sex and SCA on cerebellar anatomy using a generalizable allometric approach that considers scaling relationships between regional cerebellar volume and brain volume in health. The integration of these approaches shows that (1) sex and SCA effects on raw cerebellar volume are large and distributed, but regionally heterogeneous, (2) human cerebellar volume scales with brain volume in a highly nonlinear and regionally heterogeneous fashion that departs from documented patterns of cerebellar scaling in phylogeny, and (3) 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 STATEMENT Cerebellar 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

Assessing Equating Results on Different Equating Criteria

ERIC Educational Resources Information Center

Tong, Ye; Kolen, Michael

2005-01-01

The performance of three equating methods--the presmoothed equipercentile method, the item response theory (IRT) true score method, and the IRT observed score method--were examined based on three equating criteria: the same distributions property, the first-order equity property, and the second-order equity property. The magnitude of the…

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2004-07-01

We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.

On the Monge-Ampere equivalent of the sine-Gordon equation

NASA Astrophysics Data System (ADS)

Ferapontov, E. V.; Nutku, Y.

1994-12-01

Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1993-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1992-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

The stability of locus equation slopes across stop consonant voicing/aspiration

NASA Astrophysics Data System (ADS)

Sussman, Harvey M.; Modarresi, Golnaz

2004-05-01

The consistency of locus equation slopes as phonetic descriptors of stop place in CV sequences across voiced and voiceless aspirated stops was explored in the speech of five male speakers of American English and two male speakers of Persian. Using traditional locus equation measurement sites for F2 onsets, voiceless labial and coronal stops had significantly lower locus equation slopes relative to their voiced counterparts, whereas velars failed to show voicing differences. When locus equations were derived using F2 onsets for voiced stops that were measured closer to the stop release burst, comparable to the protocol for measuring voiceless aspirated stops, no significant effects of voicing/aspiration on locus equation slopes were observed. This methodological factor, rather than an underlying phonetic-based explanation, provides a reasonable account for the observed flatter locus equation slopes of voiceless labial and coronal stops relative to voiced cognates reported in previous studies [Molis et al., J. Acoust. Soc. Am. 95, 2925 (1994); O. Engstrand and B. Lindblom, PHONUM 4, 101-104]. [Work supported by NIH.

Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

NASA Astrophysics Data System (ADS)

Ormerod, Christopher M.

2014-01-01

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E_6^{(1)} symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

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.

The Effectiveness of Circular Equating as a Criterion for Evaluating Equating.

ERIC Educational Resources Information Center

Wang, Tianyou; Hanson, Bradley A.; Harris, Deborah J.

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

New conditions for obtaining the exact solutions of the general Riccati equation.

PubMed

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.

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

ERIC Educational Resources Information Center

Chen, Haiwen; Holland, Paul

2010-01-01

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

NASA Astrophysics Data System (ADS)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

Fractal ladder models and power law wave equations

PubMed Central

Kelly, James F.; McGough, Robert J.

2009-01-01

The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers–Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters. PMID:19813816

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

Schedule-induced drinking: rate of food delivery and Herrnstein's equation.

PubMed Central

Wetherington, C L

1979-01-01

Schedule-induced drinking was measured in four rats exposed to fixed-time schedules of food ranging from 30 to 480 seconds. Herrnstein's (1970, 1974) equation relating rate of a single response as a hyperbolic function of reinforcement rate provided a good fit to three measures of drinking: lick rate, ingestion rate, and relative time spent drinking. The functions relating the three measures of drinking to reinforcement rate were of similar form. Herrnstein's equation also provided a good description of some already published data on schedule-induced drinking. The fit both to the present data and to the already published data was improved somewhat by computing the measures by subtracting from the time base a latency constant representing the minimal time required to consume the food pellet and travel to the water source. The data from this study provide two correspondences between operant behavior and schedule-induced behavior: (a) conformity to Herrnstein's equation and (b) equivalence of rate and relative time measures. PMID:512568

An Alternative to the Breeder’s and Lande’s Equations

PubMed Central

Houchmandzadeh, Bahram

2013-01-01

The breeder’s equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) − E(Z0) to the selection differential S = E(ZW) − E(Z0) through a simple proportionality relation R = h2S, where the heritability coefficient h2 is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R′ = j2S′ can be derived, regardless of the parental genotype distribution. Here R′ = E(Z1) − μ and S′ = E(ZW) − μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j2 is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande’s equation Δz¯=GP−1S. The linearity coefficient of the alternative equation are not changed by Gaussian selection. PMID:24212080

Entropic nonadditivity, H theorem, and nonlinear Klein-Kramers equations.

PubMed

Dos Santos, M A F; Lenzi, E K

2017-11-01

We use the H theorem to establish the entropy and the entropic additivity law for a system composed of subsystems, with the dynamics governed by the Klein-Kramers equations, by considering relations among the dynamics of these subsystems and their entropies. We start considering the subsystems governed by linear Klein-Kramers equations and verify that the Boltzmann-Gibbs entropy is appropriated to this dynamics, leading us to the standard entropic additivity, S_{BG}^{(1∪2)}=S_{BG}^{1}+S_{BG}^{2}, consistent with the fact that the distributions of the subsystem are independent. We then extend the dynamics of these subsystems to independent nonlinear Klein-Kramers equations. For this case, the results show that the H theorem is verified for a generalized entropy, which does not preserve the standard entropic additivity for independent distributions. In this scenario, consistent results are obtained when a suitable coupling among the nonlinear Klein-Kramers equations is considered, in which each subsystem modifies the other until an equilibrium state is reached. This dynamics, for the subsystems, results in the Tsallis entropy for the system and, consequently, verifies the relation S_{q}^{(1∪2)}=S_{q}^{1}+S_{q}^{2}+(1-q)S_{q}^{1}S_{q}^{2}/k, which is a nonadditive entropic relation.

A composite velocity procedure for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1982-01-01

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Standard weight (Ws) equations for four rare desert fishes

USGS Publications Warehouse

Didenko, A.V.; Bonar, Scott A.; Matter, W.J.

2004-01-01

Standard weight (Ws) equations have been used extensively to examine body condition in sport fishes. However, development of these equations for nongame fishes has only recently been emphasized. We used the regression-line-percentile technique to develop standard weight equations for four rare desert fishes: flannelmouth sucker Catostomus latipinnis, razorback sucker Xyrauchen texanus, roundtail chub Gila robusta, and humpback chub G. cypha. The Ws equation for flannelmouth suckers of 100-690 mm total length (TL) was developed from 17 populations: log10Ws = -5.180 + 3.068 log10TL. The Ws equation for razorback suckers of 110-885 mm TL was developed from 12 populations: log 10Ws = -4.886 + 2.985 log10TL. The W s equation for roundtail chub of 100-525 mm TL was developed from 20 populations: log10Ws = -5.065 + 3.015 log10TL. The Ws equation for humpback chub of 120-495 mm TL was developed from 9 populations: log10Ws = -5.278 + 3.096 log 10TL. These equations meet criteria for acceptable standard weight indexes and can be used to calculate relative weight, an index of body condition.

Turning Equations Into Stories: Using "Equation Dictionaries" in an Introductory Geophysics Class

NASA Astrophysics Data System (ADS)

Caplan-Auerbach, J.

2008-12-01

To students with math fear, equations can be intimidating and overwhelming. This discomfort is reflected in some of the frequent questions heard in introductory geophysics: "which equation should I use?" and "does T stand for travel time or period?" Questions such as these indicate that many students view equations as a series of variables and operators rather than as a representation of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume that it meets their needs, rather than selecting an equation that represents the appropriate physical process. These issues can be addressed by encouraging students to think of equations as stories, and to describe them in prose. This is the goal of the Equation Dictionary project, used in Western Washington University's introductory geophysics course. Throughout the course, students create personal equation dictionaries, adding an entry each time an equation is introduced. Entries consist of (a) the equation itself, (b) a brief description of equation variables, (c) a prose description of the physical process described by the equation, and (d) any additional notes that help them understand the equation. Thus, rather than simply writing down the equations for the velocity of body waves, a student might write "The speed of a seismic body wave is controlled by the material properties of the medium through which it passes." In a study of gravity a student might note that the International Gravity Formula describes "the expected value of g at a given latitude, correcting for Earth's shape and rotation." In writing these definitions students learn that equations are simplified descriptions of physical processes, and that understanding the process is more useful than memorizing a sequence of variables. Dictionaries also serve as formula sheets for exams, which encourages students to write definitions that are meaningful to them, and to organize their thoughts clearly. Finally

BHR equations re-derived with immiscible particle effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schwarzkopf, John Dennis; Horwitz, Jeremy A.

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied tomore » the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.« less

Entropy production and nonlinear Fokker-Planck equations.

PubMed

Casas, G A; Nobre, F D; Curado, E M F

2012-12-01

The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

Approach to first-order exact solutions of the Ablowitz-Ladik equation.

PubMed

Ankiewicz, Adrian; Akhmediev, Nail; Lederer, Falk

2011-05-01

We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE). © 2011 American Physical Society

Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations

NASA Astrophysics Data System (ADS)

Rosu, Haret C.; Mancas, Stefan C.

2017-04-01

A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

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.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

Extension of Gibbs-Duhem equation including influences of external fields

NASA Astrophysics Data System (ADS)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

Nonlinear flap-lag axial equations of a rotating beam

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kvaternik, R. G.

1977-01-01

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Common allometric response of open-grown leader shoots to tree height in co-occurring deciduous broadleaved trees

PubMed Central

Miyata, Rie; Kubo, Takuya; Nabeshima, Eri; Kohyama, Takashi S.

2011-01-01

Background and Aims Morphology of crown shoots changes with tree height. The height of forest trees is usually correlated with the light environment and this makes it difficult to separate the effects of tree size and of light conditions on the morphological plasticity of crown shoots. This paper addresses the tree-height dependence of shoot traits under full-light conditions where a tree crown is not shaded by other crowns. Methods Focus is given to relationships between tree height and top-shoot traits, which include the shoot's leaf-blades and non-leafy mass, its total leaf-blade area and the length and basal diameter of the shoot's stem. We examine the allometric characteristics of open-grown current-year leader shoots at the tops of forest tree crowns up to 24 m high and quantify their responses to tree height in 13 co-occurring deciduous hardwood species in a cool-temperate forest in northern Japan. Key Results Dry mass allocated to leaf blades in a leader shoot increased with tree height in all 13 species. Specific leaf area decreased with tree height. Stem basal area was almost proportional to total leaf area in a leader shoot, where the proportionality constant did not depend on tree height, irrespective of species. Stem length for a given stem diameter decreased with tree height. Conclusions In the 13 species observed, height-dependent changes in allometry of leader shoots were convergent. This finding suggests that there is a common functional constraint in tree-height development. Under full-light conditions, leader shoots of tall trees naturally experience more severe water stress than those of short trees. We hypothesize that the height dependence of shoot allometry detected reflects an integrated response to height-associated water stress, which contributes to successful crown expansion and height gain. PMID:21914698

Length-weight relationship and a relative condition factor equation for lake sturgeon (Acipenser fulvescens) from the St. Clair River system (Michigan, USA)

USGS Publications Warehouse

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.

Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order

DOE PAGES

Favalli, Andrea; Croft, Stephen; Santi, Peter

2015-06-15

Various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclearmore » data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. This study represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.« less

Covariant Derivatives and the Renormalization Group Equation

NASA Astrophysics Data System (ADS)

Dolan, Brian P.

The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.

Equations and the Equal Sign in Elementary Mathematics Textbooks

ERIC Educational Resources Information Center

Powell, Sarah R.

2012-01-01

To promote a relational understanding of the equal sign (=), students may require exposure to a variety of equation types (i.e., 3 = 8 - 5; 2 + 3 = 1 + 4; 9 - 3 = 6). The purpose of this study was to evaluate 8 elementary curricula for degree of exposure to equation types. Across 6 elementary grade levels, curricula were coded for the number of…

How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

ERIC Educational Resources Information Center

Heras, Jose A.

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Experimental realization of the Yang-Baxter Equation via NMR interferometry.

PubMed

Vind, F Anvari; Foerster, A; Oliveira, I S; Sarthour, R S; Soares-Pinto, D O; Souza, A M; Roditi, I

2016-02-10

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Psychosocial factors, musculoskeletal disorders and work-related fatigue amongst nurses in Brunei: structural equation model approach.

PubMed

Abdul Rahman, Hanif; Abdul-Mumin, Khadizah; Naing, Lin

2017-09-01

Psychosocial factors, musculoskeletal disorders and work-related fatigue have adverse effects on individual nurses and place a substantial financial burden on health care. Evidence of an association has been reported in the literature, but no theoretical explanation has been published to date. To explore and develop a structural model to provide a theoretical explanation for this relationship. A cross-sectional study using data from 201 valid samples of emergency and critical care nurses across public hospitals in Brunei was performed via self-administered questionnaire. The structural equation model was assessed using partial least squares analysis. A valid and robust structural model was constructed. This revealed that 61.5% of the variance in chronic fatigue could be explained by psychosocial factors and musculoskeletal disorders pathways. Among the psychosocial factors, work-family conflict was identified as a key mediator for progression of musculoskeletal problems and subsequent fatigue through stress and burnout. This report provides a novel theoretical contribution to understanding the relationship between psychosocial factors, musculoskeletal disorders and work-related fatigue. These preliminary results may be useful for future studies on the development of work-related fatigue and musculoskeletal disorders, particularly the central role of work-family conflict. Copyright © 2017 Elsevier Ltd. All rights reserved.

The Cluster Orbits With Perturbations of Keplerian Elements (COWPOKE) Equations

DTIC Science & Technology

2004-03-20

Hill’s equations2 (also known as the Clohessy - Wiltshire equations3). Hill’s equations describe the relative motion of spacecraft using a spacecraft- 2...January 2002, AAS 02-115. 2. Hill, G. W., “Researches in the Lunar Theory,” American Journal of Mathematics, Vol. 1, No. 1, 1878, pp. 5-26. 3. Clohessy ...W. H., R. S. Wiltshire , “Terminal Guidance System for Satellite Rendezvous,” Journal of the Aerospace Sciences, September 1960, pp. 653-658 4. Gim

Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

PubMed

Ercan, Ali; Kavvas, M Levent

2017-07-25

Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

Fluid equations with nonlinear wave-particle resonances^

NASA Astrophysics Data System (ADS)

Mattor, Nathan

1997-11-01

We have derived fluid equations that include linear and nonlinear wave-particle resonance effects. This greatly extends previous ``Landau-fluid'' closures, which include linear Landau damping. (G.W. Hammett and F.W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990).^, (Z. Chang and J. D. Callen, Phys. Fluids B 4,) 1167 (1992). The new fluid equations are derived with no approximation regarding nonlinear kinetic interaction, and so additionally include numerous nonlinear kinetic effects. The derivation starts with the electrostatic drift kinetic equation for simplicity, with a Maxwellian distribution function. Fluid closure is accomplished through a simple integration trick applied to the drift kinetic equation, using the property that the nth moment of Maxwellian distribution is related to the nth derivative. The result is a compact closure term appearing in the highest moment equation, a term which involves a plasma dispersion function of the electrostatic field and its derivatives. The new term reduces to the linear closures in appropriate limits, so both approaches retain linear Landau damping. But the nonlinearly closed equations have additional desirable properties. Unlike linear closures, the nonlinear closure retains the time-reversibility of the original kinetic equation. We have shown directly that the nonlinear closure retains at least two nonlinear resonance effects: wave-particle trapping and Compton scattering. Other nonlinear kinetic effects are currently under investigation. The new equations correct two previous discrepancies between kinetic and Landau-fluid predictions, including a propagator discrepancy (N. Mattor, Phys. Fluids B 4,) 3952 (1992). and a numerical discrepancy for the 3-mode shearless bounded slab ITG problem. (S. E. Parker et al.), Phys. Plasmas 1, 1461 (1994). ^* In collaboration with S. E. Parker, Department of Physics, University of Colorado, Boulder. ^ Work performed at LLNL under DoE contract No. W7405-ENG-48.

Expressions of the fundamental equation of gradient elution and a numerical solution of these equations under any gradient profile.

PubMed

Nikitas, P; Pappa-Louisi, A

2005-09-01

The original work carried out by Freiling and Drake in gradient liquid chromatography is rewritten in the current language of reversed-phase liquid chromatography. This allows for the rigorous derivation of the fundamental equation for gradient elution and the development of two alternative expressions of this equation, one of which is free from the constraint that the holdup time must be constant. In addition, the above derivation results in a very simple numerical solution of the various equations of gradient elution under any gradient profile. The theory was tested using eight catechol-related solutes in mobile phases modified with methanol, acetonitrile, or 2-propanol. It was found to be a satisfactory prediction of solute gradient retention behavior even if we used a simple linear description for the isocratic elution of these solutes.

Effects of phenology, water availability and seed source on loblolly pine biomass partitioning and transpiration.

PubMed

Barnes, Andrew D

2002-07-01

One-year-old loblolly pine (Pinus taeda L.) seedlings from four seed sources (Arkansas, Georgia, Texas and Virginia) grown in 1-m-deep sand-filled pits in two water regimes (well-watered and drought) were studied, to gain insight into the process of seedling establishment. Whole-plant transpiration was measured biweekly from July to December. Whole-plant harvests were conducted at 6-week intervals from April to December. Whole-plant transpiration and transpiration per unit leaf and root area were affected by treatment, seedlot and phenology. Seedlings of the Arkansas seedlot maintained significantly higher transpiration rates per unit leaf and root area during drought than seedlings of the Virginia, Georgia or Texas seedlots, but did not accumulate greater biomass. The high transpiration rates of the Arkansas seedlings were attributed to their deep root systems. Allometric relationships indicated that, relative to the whole plant, biomass allocation to needles of drought-treated seedlings was enhanced during the summer (allometric ratio 1.09), whereas allocation to roots was enhanced in the spring and fall (allometric ratios of 1.13 and 1.09, respectively). Relative to the whole plant, biomass allocation to needles of well-watered seedlings was enhanced throughout the experiment (allometric ratio of 1.16 declining to 1.05), whereas the allometric ratio of root to total biomass was 0.89 or less throughout. Allometric relationships also indicated variation in biomass partitioning to roots in three soil layers (0-30, 30-60 and 60-100 cm), which differed among harvests in each soil layer. Root growth in both well-watered and drought-treated seedlings was concentrated in the top soil layer in the spring, shifted to the middle and bottom soil layers in the summer, and then increased in the top soil layer in the fall. Compared with well-watered seedlings, drought-treated seedlings had higher rates of root growth in the bottom soil layer in the fall, a characteristic that

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=( D( u, ux) ux) x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=( vx/∣ v∣) x and ut= uxx/∣ ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed.

The general relativistic thin disc evolution equation

NASA Astrophysics Data System (ADS)

Balbus, Steven A.

2017-11-01

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

The Pendulum Equation

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…

On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev-Petviashvili I Equation

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Ablowitz, Mark J.

The discrete spectrum of the nonstationary Schrödinger equation and localized solutions of the Kadomtsev-Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics.

Caudal fin allometry in the white shark Carcharodon carcharias: implications for locomotory performance and ecology

NASA Astrophysics Data System (ADS)

Lingham-Soliar, Theagarten

2005-05-01

Allometric scaling analysis was employed to investigate the consequences of size evolution on hydrodynamic performance and ecology in the white shark Carcharodon carcharias. Discriminant analysis using the power equation y=axb was negative for caudal fin span (S) versus fork length (FL) in C. carcharias. In contrast in two delphinid species, Delphinus capensis and Tursiops aduncus, the span of the flukes versus fork length rises in positive allometric fashion, and strong positive allometry of S versus √A (area) was also recorded. The latter reflects a high lift/drag ratio. S versus √A in C. carcharias displays negative allometry and consequently a lower lift/drag ratio. A lower aspect ratio (AR) caudal fin in C. carcharias compared to that of the delphinids (mean 3.33 and 4.1, respectively) and other thunniform swimmers provides the potential for better maneuverability and acceleration. The liver in sharks is frequently associated with a buoyancy function and was found to be positively allometric in C. carcharias. The overall findings suggest that the negatively allometric caudal fin morphometrics in C. carcharias are unlikely to have deleterious evolutionary fitness consequences for predation. On the contrary, when considered in the context of positive liver allometry in C. carcharias it is hereby suggested that buoyancy may play a dominant role in larger white sharks in permitting slow swimming while minimizing energy demands needed to prevent sinking. In contrast hydrodynamic lift is considered more important in smaller white sharks. Larger caudal fin spans and higher lift/drag ratio in smaller C. carcharias indicate greater potential for prolonged, intermediate swimming speeds and for feeding predominantly on fast-moving fish, in contrast to slow-swimming search patterns of larger individuals for predominantly large mammalian prey. Such data may provide some answers to the lifestyle and widespread habitat capabilities of this still largely mysterious animal.

Repeat, Low Altitude Measurements of Vegetation Status and Biomass Using Manned Aerial and UAS Imagery in a Piñon-Juniper Woodland

NASA Astrophysics Data System (ADS)

Krofcheck, D. J.; Lippitt, C.; Loerch, A.; Litvak, M. E.

2015-12-01

Measuring the above ground biomass of vegetation is a critical component of any ecological monitoring campaign. Traditionally, biomass of vegetation was measured with allometric-based approach. However, it is also time-consuming, labor-intensive, and extremely expensive to conduct over large scales and consequently is cost-prohibitive at the landscape scale. Furthermore, in semi-arid ecosystems characterized by vegetation with inconsistent growth morphologies (e.g., piñon-juniper woodlands), even ground-based conventional allometric approaches are often challenging to execute consistently across individuals and through time, increasing the difficulty of the required measurements and consequently the accuracy of the resulting products. To constrain the uncertainty associated with these campaigns, and to expand the extent of our measurement capability, we made repeat measurements of vegetation biomass in a semi-arid piñon-juniper woodland using structure-from-motion (SfM) techniques. We used high-spatial resolution overlapping aerial images and high-accuracy ground control points collected from both manned aircraft and multi-rotor UAS platforms, to generate digital surface model (DSM) for our experimental region. We extracted high-precision canopy volumes from the DSM and compared these to the vegetation allometric data, s to generate high precision canopy volume models. We used these models to predict the drivers of allometric equations for Pinus edulis and Juniperous monosperma (canopy height, diameter at breast height, and root collar diameter). Using this approach, we successfully accounted for the carbon stocks in standing live and standing dead vegetation across a 9 ha region, which contained 12.6 Mg / ha of standing dead biomass, with good agreement to our field plots. Here we present the initial results from an object oriented workflow which aims to automate the biomass estimation process of tree crown delineation and volume calculation, and partition

Density-dependence as a size-independent regulatory mechanism.

PubMed

de Vladar, Harold P

2006-01-21

The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.

Forest biomass density across large climate gradients in northern South America is related to water availability but not with temperature

PubMed Central

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

Forest biomass density across large climate gradients in northern South America is related to water availability but not with temperature.

PubMed

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.

How Darcy's equation is linked to the linear reservoir at catchment scale

NASA Astrophysics Data System (ADS)

Savenije, Hubert H. G.

2017-04-01

In groundwater hydrology two simple linear equations exist that describe the relation between groundwater flow and the gradient that drives it: Darcy's equation and the linear reservoir. Both equations are empirical at heart: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they show similarity, without having detailed knowledge of the structure of the underlying aquifers it is not trivial to upscale Darcy's equation to the watershed scale. In this paper, a relatively simple connection is provided between the two, based on the assumption that the groundwater system is organized by an efficient drainage network, a mostly invisible pattern that has evolved over geological time scales. This drainage network provides equally distributed resistance to flow along the streamlines that connect the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance.

Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

NASA Astrophysics Data System (ADS)

Verweij, Martin D.; Huijssen, Jacob

2006-05-01

In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Constraining the equation of state of neutron stars from binary mergers.

PubMed

Takami, Kentaro; Rezzolla, Luciano; Baiotti, Luca

2014-08-29

Determining the equation of state of matter at nuclear density and hence the structure of neutron stars has been a riddle for decades. We show how the imminent detection of gravitational waves from merging neutron star binaries can be used to solve this riddle. Using a large number of accurate numerical-relativity simulations of binaries with nuclear equations of state, we find that the postmerger emission is characterized by two distinct and robust spectral features. While the high-frequency peak has already been associated with the oscillations of the hypermassive neutron star produced by the merger and depends on the equation of state, a new correlation emerges between the low-frequency peak, related to the merger process, and the total compactness of the stars in the binary. More importantly, such a correlation is essentially universal, thus providing a powerful tool to set tight constraints on the equation of state. If the mass of the binary is known from the inspiral signal, the combined use of the two frequency peaks sets four simultaneous constraints to be satisfied. Ideally, even a single detection would be sufficient to select one equation of state over the others. We test our approach with simulated data and verify it works well for all the equations of state considered.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2017-11-01

We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo-Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper. A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues-Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given. Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo-Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass. The equations obtained in

An improvement of convergence of a dispersion-relation preserving method for the classical Boussinesq equation

NASA Astrophysics Data System (ADS)

Jang, T. S.

2018-03-01

A dispersion-relation preserving (DRP) method, as a semi-analytic iterative procedure, has been proposed by Jang (2017) for integrating the classical Boussinesq equation. It has been shown to be a powerful numerical procedure for simulating a nonlinear dispersive wave system because it preserves the dispersion-relation, however, there still exists a potential flaw, e.g., a restriction on nonlinear wave amplitude and a small region of convergence (ROC) and so on. To remedy the flaw, a new DRP method is proposed in this paper, aimed at improving convergence performance. The improved method is proved to have convergence properties and dispersion-relation preserving nature for small waves; of course, unique existence of the solutions is also proved. In addition, by a numerical experiment, the method is confirmed to be good at observing nonlinear wave phenomena such as moving solitary waves and their binary collision with different wave amplitudes. Especially, it presents a ROC (much) wider than that of the previous method by Jang (2017). Moreover, it gives the numerical simulation of a high (or large-amplitude) nonlinear dispersive wave. In fact, it is demonstrated to simulate a large-amplitude solitary wave and the collision of two solitary waves with large-amplitudes that we have failed to simulate with the previous method. Conclusively, it is worth noting that better convergence results are achieved compared to Jang (2017); i.e., they represent a major improvement in practice over the previous method.

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

Comment on ``Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation''

NASA Astrophysics Data System (ADS)

Lallemand, Pierre; Luo, Li-Shi

2008-12-01

Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

A cross-lagged structural equation model of relational aggression, physical aggression, and peer status in a Chinese culture.

PubMed

Tseng, Wan-Ling; Banny, Adrienne M; Kawabata, Yoshito; Crick, Nicki R; Gau, Susan Shur-Fen

2013-01-01

This short-term longitudinal study examined the associations among relational aggression, physical aggression, and peer status (i.e., acceptance, rejection, and perceived popularity) across three time points, six months apart, in a Taiwanese sample. Participants were 198 fifth grade students (94 girls and 104 boys; Mean age = 10.35 years) from Taipei, Taiwan. Study variables were assessed using peer nomination procedure. Results from the cross-lagged structural equation models demonstrated that there were longitudinal associations between relational aggression and each of the peer status constructs while only one longitudinal association was found for physical aggression such that physical aggression positively predicted subsequent peer rejection. The longitudinal associations did not vary with gender. Results also showed high stabilities of relational aggression, physical aggression, and the three peer status constructs over 1 year as well as high concurrent association between relational and physical aggression. In addition, relational aggression and physical aggression were concurrently related to less acceptance, more rejection, and less perceived popularity, especially at the outset of the study. Findings of this study demonstrated both similarities and differences in relation to previous literature in primarily Western cultures. This study also highlights the bidirectional and complex nature of the association between aggression and peer status, which appears to depend on the form of aggression and on the particular indicator of peer status under study. Copyright © 2013 Wiley Periodicals, Inc.

How does biomass distribution change with size and differ among species? An analysis for 1200 plant species from five continents.

PubMed

Poorter, Hendrik; Jagodzinski, Andrzej M; Ruiz-Peinado, Ricardo; Kuyah, Shem; Luo, Yunjian; Oleksyn, Jacek; Usoltsev, Vladimir A; Buckley, Thomas N; Reich, Peter B; Sack, Lawren

2015-11-01

We compiled a global database for leaf, stem and root biomass representing c. 11 000 records for c. 1200 herbaceous and woody species grown under either controlled or field conditions. We used this data set to analyse allometric relationships and fractional biomass distribution to leaves, stems and roots. We tested whether allometric scaling exponents are generally constant across plant sizes as predicted by metabolic scaling theory, or whether instead they change dynamically with plant size. We also quantified interspecific variation in biomass distribution among plant families and functional groups. Across all species combined, leaf vs stem and leaf vs root scaling exponents decreased from c. 1.00 for small plants to c. 0.60 for the largest trees considered. Evergreens had substantially higher leaf mass fractions (LMFs) than deciduous species, whereas graminoids maintained higher root mass fractions (RMFs) than eudicotyledonous herbs. These patterns do not support the hypothesis of fixed allometric exponents. Rather, continuous shifts in allometric exponents with plant size during ontogeny and evolution are the norm. Across seed plants, variation in biomass distribution among species is related more to function than phylogeny. We propose that the higher LMF of evergreens at least partly compensates for their relatively low leaf area : leaf mass ratio. © 2015 The Authors. New Phytologist © 2015 New Phytologist Trust.

A rain splash transport equation assimilating field and laboratory measurements

USGS Publications Warehouse

Dunne, T.; Malmon, D.V.; Mudd, S.M.

2010-01-01

Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

ERIC Educational Resources Information Center

Caplan-Auerbach, Jacqueline

2009-01-01

Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

2018-04-01

In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

Generalized Spencer-Lewis equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

Propagation estimates for dispersive wave equations: Application to the stratified wave equation

NASA Astrophysics Data System (ADS)

Pravica, David W.

1999-01-01

The plane-stratified wave equation (∂t2+H)ψ=0 with H=-c(y)2∇z2 is studied, where z=x⊕y, x∈Rk, y∈R1 and |c(y)-c∞|→0 as |y|→∞. Solutions to such an equation are solved for the propagation of waves through a layered medium and can include waves which propagate in the x-directions only (i.e., trapped modes). This leads to a consideration of the pseudo-differential wave equation (∂t2+ω(-Δx))ψ=0 such that the dispersion relation ω(ξ2) is analytic and satisfies c1⩽ω'(ξ2)⩽c2 for c*>0. Uniform propagation estimates like ∫|x|⩽|t|αE(UtP±φ0)dkx⩽Cα,β(1+|t|)-β∫E(φ0)dkx are obtained where Ut is the evolution group, P± are projection operators onto the Hilbert space of initial conditions φ∈H and E(ṡ) is the local energy density. In special cases scattering of trapped modes off a local perturbation satisfies the causality estimate ||P+ρΛjSP-ρΛk||⩽Cνρ-ν for each ν<1/2. Here P+ρΛj (P-ρΛk) are remote outgoing/detector (incoming/transmitter) projections for the jth (kth) trapped mode. Also Λ⋐R+ is compact, so the projections localize onto formally-incoming (eventually-outgoing) states.

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

A neuro approach to solve fuzzy Riccati differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Shallow water equations: viscous solutions and inviscid limit

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Perepelitsa, Mikhail

2012-12-01

We establish the inviscid limit of the viscous shallow water equations to the Saint-Venant system. For the viscous equations, the viscosity terms are more degenerate when the shallow water is close to the bottom, in comparison with the classical Navier-Stokes equations for barotropic gases; thus, the analysis in our earlier work for the classical Navier-Stokes equations does not apply directly, which require new estimates to deal with the additional degeneracy. We first introduce a notion of entropy solutions to the viscous shallow water equations and develop an approach to establish the global existence of such solutions and their uniform energy-type estimates with respect to the viscosity coefficient. These uniform estimates yield the existence of measure-valued solutions to the Saint-Venant system generated by the viscous solutions. Based on the uniform energy-type estimates and the features of the Saint-Venant system, we further establish that the entropy dissipation measures of the viscous solutions for weak entropy-entropy flux pairs, generated by compactly supported C 2 test-functions, are confined in a compact set in H -1, which yields that the measure-valued solutions are confined by the Tartar-Murat commutator relation. Then, the reduction theorem established in Chen and Perepelitsa [5] for the measure-valued solutions with unbounded support leads to the convergence of the viscous solutions to a finite-energy entropy solution of the Saint-Venant system with finite-energy initial data, which is relative with respect to the different end-states of the bottom topography of the shallow water at infinity. The analysis also applies to the inviscid limit problem for the Saint-Venant system in the presence of friction.

The eight tetrahedron equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hietarinta, J.; Nijhoff, F.

1997-07-01

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalizing the Yang{endash}Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron equations. {copyright} {ital 1997 American Institute of Physics.}

Energy requirements of adult dogs: a meta-analysis.

PubMed

Bermingham, Emma N; Thomas, David G; Cave, Nicholas J; Morris, Penelope J; Butterwick, Richard F; German, Alexander J

2014-01-01

A meta-analysis was conducted to determine the maintenance energy requirements of adult dogs. Suitable publications were first identified, and then used to generate relationships amongst energy requirements, husbandry, activity level, methodology, sex, neuter status, dog size, and age in healthy adult dogs. Allometric equations for maintenance energy requirements were determined using log-log linear regression. So that the resulting equations could readily be compared with equations reported by the National Research Council, maintenance energy requirements in the current study were determined in kcal/kg(0.75) body weight (BW). Ultimately, the data of 70 treatment groups from 29 publications were used, and mean (± standard deviation) maintenance energy requirements were 142.8±55.3 kcal·kgBW(-0.75)·day(-1). The corresponding allometric equation was 81.5 kcal·kgBW(-0.9)·day(-1) (adjusted R2 = 0.64; 70 treatment groups). Type of husbandry had a significant effect on maintenance energy requirements (P<0.001): requirements were greatest in racing dogs, followed by working dogs and hunting dogs, whilst the energy requirements of pet dogs and kennel dogs were least. Maintenance energy requirements were less in neutered compared with sexually intact dogs (P<0.001), but there was no effect of sex. Further, reported activity level tended to effect the maintenance energy requirement of the dog (P = 0.09). This review suggests that estimating maintenance energy requirements based on BW alone may not be accurate, but that predictions that factor in husbandry, neuter status and, possibly, activity level might be superior. Additionally, more information on the nutrient requirements of older dogs, and those at the extremes of body size (i.e. giant and toy breeds) is needed.

Energy Requirements of Adult Dogs: A Meta-Analysis

PubMed Central

Bermingham, Emma N.; Thomas, David G.; Cave, Nicholas J.; Morris, Penelope J.; Butterwick, Richard F.; German, Alexander J.

2014-01-01

A meta-analysis was conducted to determine the maintenance energy requirements of adult dogs. Suitable publications were first identified, and then used to generate relationships amongst energy requirements, husbandry, activity level, methodology, sex, neuter status, dog size, and age in healthy adult dogs. Allometric equations for maintenance energy requirements were determined using log-log linear regression. So that the resulting equations could readily be compared with equations reported by the National Research Council, maintenance energy requirements in the current study were determined in kcal/kg0.75 body weight (BW). Ultimately, the data of 70 treatment groups from 29 publications were used, and mean (± standard deviation) maintenance energy requirements were 142.8±55.3 kcal.kgBW−0.75.day−1. The corresponding allometric equation was 81.5 kcal.kgBW−0.93.day−1 (adjusted R2 = 0.64; 70 treatment groups). Type of husbandry had a significant effect on maintenance energy requirements (P<0.001): requirements were greatest in racing dogs, followed by working dogs and hunting dogs, whilst the energy requirements of pet dogs and kennel dogs were least. Maintenance energy requirements were less in neutered compared with sexually intact dogs (P<0.001), but there was no effect of sex. Further, reported activity level tended to effect the maintenance energy requirement of the dog (P = 0.09). This review suggests that estimating maintenance energy requirements based on BW alone may not be accurate, but that predictions that factor in husbandry, neuter status and, possibly, activity level might be superior. Additionally, more information on the nutrient requirements of older dogs, and those at the extremes of body size (i.e. giant and toy breeds) is needed. PMID:25313818

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material.

PubMed

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-04-13

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10 -4 -10 -2 s -1 ) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations.

Equation of State for Detonation Product Gases

NASA Astrophysics Data System (ADS)

Nagayama, Kunihito; Kubota, Shiro

2013-06-01

Based on the empirical linear relationship between detonation velocity and loading density, an approximate description for the Chapman-Jouguet state for detonation product gases of solid phase high explosives has been developed. Provided that the Grüneisen parameter is a function only of volume, systematic and closed system of equations for the Grüneisen parameter and CJ volume have been formulated. These equations were obtained by combining this approximation with the Jones-Stanyukovich-Manson relation together with JWL isentrope for detonation of crystal density PETN. A thermodynamic identity between the Grüneisen parameter and another non-dimensional material parameter introduced by Wu and Jing can be used to derive the enthalpy-pressure-volume equation of state for detonation gases. This Wu-Jing parameter is found to be the ratio of the Grüneisen parameter and the adiabatic index. Behavior of this parameter as a function of pressure was calculated and revealed that their change with pressure is very gradual. By using this equation of state, several isentropes down from the Chapman-Jouguet states reached by four different lower initial density PETN have been calculated and compared with available cylinder expansion tests.

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

NASA Astrophysics Data System (ADS)

Brenier, Yann

2009-10-01

We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61-97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge-Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375-417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141-1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131-151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20-31, 1991, Arch. Ration. Mech. Anal. 185:341-363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450-1461, 1998; Loeper in SIAM J. Math. Anal. 38:795-823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29-59, 2001) and of the Keller-Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225-234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819-824, 1992; Chalub et al. in Mon. Math. 142:123-141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier-Stokes-Boussinesq equations

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Density-velocity equations with bulk modulus for computational hydro-acoustics

NASA Astrophysics Data System (ADS)

Lin, Po-Hsien; Chen, Yung-Yu; John Yu, S.-T.

2014-02-01

This paper reports a new set of model equations for Computational Hydro Acoustics (CHA). The governing equations include the continuity and the momentum equations. The definition of bulk modulus is used to relate density with pressure. For 3D flow fields, there are four equations with density and velocity components as the unknowns. The inviscid equations are proved to be hyperbolic because an arbitrary linear combination of the three Jacobian matrices is diagonalizable and has a real spectrum. The left and right eigenvector matrices are explicitly derived. Moreover, an analytical form of the Riemann invariants are derived. The model equations are indeed suitable for modeling wave propagation in low-speed, nearly incompressible air and water flows. To demonstrate the capability of the new formulation, we use the CESE method to solve the 2D equations for aeolian tones generated by air flows passing a circular cylinder at Re = 89,000, 46,000, and 22,000. Numerical results compare well with previously published data. By simply changing the value of the bulk modulus, the same code is then used to calculate three cases of water flows passing a cylinder at Re = 89,000, 67,000, and 44,000.

Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation

NASA Astrophysics Data System (ADS)

Gegenhasi; Li, Ya-Qian; Zhang, Duo-Duo

2018-04-01

In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources. Supported by the National Natural Science Foundation of China under Grant Nos. 11601247 and 11605096, the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant Nos. 2016MS0115 and 2015MS0116 and the Innovation Fund Programme of Inner Mongolia University No. 20161115

Nonlocal conservation laws of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam; Marvan, Michal

2017-03-01

For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. The corresponding potentials are functionally independent modulo a Wronskian type relation.

On the relationship between ontogenetic and static allometry.

PubMed

Pélabon, Christophe; Bolstad, Geir H; Egset, Camilla K; Cheverud, James M; Pavlicev, Mihaela; Rosenqvist, Gunilla

2013-02-01

Ontogenetic and static allometries describe how a character changes in size when the size of the organism changes during ontogeny and among individuals measured at the same developmental stage, respectively. Understanding the relationship between these two types of allometry is crucial to understanding the evolution of allometry and, more generally, the evolution of shape. However, the effects of ontogenetic allometry on static allometry remain largely unexplored. Here, we first show analytically how individual variation in ontogenetic allometry and body size affect static allometry. Using two longitudinal data sets on ontogenetic and static allometry, we then estimate variances and covariances for the different parameters of the ontogenetic allometry defined in our model and assess their relative contribution to the static allometric slope. The mean ontogenetic allometry is the main parameter that determines the static allometric slope, while the covariance between the ontogenetic allometric slope and body size generates most of the discrepancies between ontogenetic and static allometry. These results suggest that the apparent evolutionary stasis of the static allometric slope is not generated by internal (developmental) constraints but more likely results from external constraints imposed by selection.

Correlations and the Ring-Kinetic Equation in Dense Sheared Granular Flows

NASA Astrophysics Data System (ADS)

Kumaran, V.

A formal way of deriving fluctuation-correlation relations in densesheared granular media, starting with the Enskog approximation for the collision integral in the Chapman-Enskog theory, is discussed. The correlation correction to the viscosity is obtained using the ring-kinetic equation, in terms of the correlations in the hydrodynamic modes of the linearised Enskog equation. It is shown that the Green-Kubo formula for the shear viscosity emerges from the two-body correlation function obtained from the ring-kinetic equation.

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

Breastfeeding attitude, health-related quality of life and maternal obesity among multi-ethnic pregnant women: A multi-group structural equation approach.

PubMed

Lau, Ying; Htun, Tha Pyai; Lim, Peng Im; Ho-Lim, Sarah Su Tin; Chi, Claudia; Tsai, Cammy; Ong, Kai Wen; Klainin-Yobas, Piyanee

2017-02-01

Identifying the factors influencing breastfeeding attitude is significant for the implementation of effective promotion policies and counselling activities. To our best knowledge, no previous studies have modelled the relationships among breastfeeding attitude, health-related quality of life and maternal obesity among multi-ethnic pregnant women; the current study attempts to fill this research gap. This study investigated the relationships among maternal characteristics, health-related quality of life and breastfeeding attitude amidst normal weight and overweight/obese pregnant women using a multi-group structural equation modelling approach. Exploratory cross-sectional design was used. Antenatal clinics of a university-affiliated hospital PARTICIPANTS: Pregnant women were invited to participate; 708 (78.8%) agreed to participate in the study. We examined a hypothetical model on the basis of integrating the concepts of a breastfeeding decision-making model, theory of planned behaviour-based model for breastfeeding and health-related quality of life model among 708 multi-ethnic pregnant women in Singapore. The Iowa Infant Feeding Attitude Scale and Medical Outcomes Study Short Form Health Survey were used to measure breastfeeding attitude and health-related quality of life, respectively. Two structural equation models demonstrated that better health-related quality of life, higher monthly household income, planned pregnancy and previous exclusive breastfeeding experience were significantly associated with positive breastfeeding attitude among normal and overweight/obese pregnant women. Among normal weight pregnant women, those who were older with higher educational level were more likely to have positive breastfeeding attitude. Among overweight/obese pregnant women, Chinese women with confinement nanny plan were less likely to have positive breastfeeding attitude. No significant difference existed between normal weight and overweight/obese pregnant women concerning

True amplitude wave equation migration arising from true amplitude one-way wave equations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

2017-11-01

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

Taming the nonlinearity of the Einstein equation.

PubMed

Harte, Abraham I

2014-12-31

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.

The Thin Oil Film Equation

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.

Tree height–diameter allometry across the United States

PubMed Central

Hulshof, Catherine M; Swenson, Nathan G; Weiser, Michael D

2015-01-01

The relationship between tree height and diameter is fundamental in determining community and ecosystem structure as well as estimates of biomass and carbon storage. Yet our understanding of how tree allometry relates to climate and whole organismal function is limited. We used the Forest Inventory and Analysis National Program database to determine height–diameter allometries of 2,976,937 individuals of 293 tree species across the United States. The shape of the allometric relationship was determined by comparing linear and nonlinear functional forms. Mixed-effects models were used to test for allometric differences due to climate and floristic (between angiosperms and gymnosperms) and functional groups (leaf habit and shade tolerance). Tree allometry significantly differed across the United States largely because of climate. Temperature, and to some extent precipitation, in part explained tree allometric variation. The magnitude of allometric variation due to climate, however, had a phylogenetic signal. Specifically, angiosperm allometry was more sensitive to differences in temperature compared to gymnosperms. Most notably, angiosperm height was more negatively influenced by increasing temperature variability, whereas gymnosperm height was negatively influenced by decreasing precipitation and increasing altitude. There was little evidence to suggest that shade tolerance influenced tree allometry except for very shade-intolerant trees which were taller for any given diameter. Tree allometry is plastic rather than fixed and scaling parameters vary around predicted central tendencies. This allometric variation provides insight into life-history strategies, phylogenetic history, and environmental limitations at biogeographical scales. PMID:25859325

Tree height-diameter allometry across the United States.

PubMed

Hulshof, Catherine M; Swenson, Nathan G; Weiser, Michael D

2015-03-01

The relationship between tree height and diameter is fundamental in determining community and ecosystem structure as well as estimates of biomass and carbon storage. Yet our understanding of how tree allometry relates to climate and whole organismal function is limited. We used the Forest Inventory and Analysis National Program database to determine height-diameter allometries of 2,976,937 individuals of 293 tree species across the United States. The shape of the allometric relationship was determined by comparing linear and nonlinear functional forms. Mixed-effects models were used to test for allometric differences due to climate and floristic (between angiosperms and gymnosperms) and functional groups (leaf habit and shade tolerance). Tree allometry significantly differed across the United States largely because of climate. Temperature, and to some extent precipitation, in part explained tree allometric variation. The magnitude of allometric variation due to climate, however, had a phylogenetic signal. Specifically, angiosperm allometry was more sensitive to differences in temperature compared to gymnosperms. Most notably, angiosperm height was more negatively influenced by increasing temperature variability, whereas gymnosperm height was negatively influenced by decreasing precipitation and increasing altitude. There was little evidence to suggest that shade tolerance influenced tree allometry except for very shade-intolerant trees which were taller for any given diameter. Tree allometry is plastic rather than fixed and scaling parameters vary around predicted central tendencies. This allometric variation provides insight into life-history strategies, phylogenetic history, and environmental limitations at biogeographical scales.

Maximum entropy and equations of state for random cellular structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivier, N.

Random, space-filling cellular structures (biological tissues, metallurgical grain aggregates, foams, etc.) are investigated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These relations are known empirically as Lewis's law in Botany, or Desch's relation in Metallurgy. Here, the functional form of the constraints is now known as a priori, and one takes advantage of this arbitrariness to increase the entropy further. The resulting structural equations of state are independent of priors, they are measurable experimentally and constitute therefore a direct test for the applicability of MaxEnt inferencemore » (given that the structure is in statistical equilibrium, a fact which can be tested by another simple relation (Aboav's law)). 23 refs., 2 figs., 1 tab.« less