Foerster, Steffen; Zhong, Ying; Pintea, Lilian; Murray, Carson M; Wilson, Michael L; Mjungu, Deus C; Pusey, Anne E
2016-01-01
The distribution and abundance of food resources are among the most important factors that influence animal behavioral strategies. Yet, spatial variation in feeding habitat quality is often difficult to assess with traditional methods that rely on extrapolation from plot survey data or remote sensing. Here, we show that maximum entropy species distribution modeling can be used to successfully predict small-scale variation in the distribution of 24 important plant food species for chimpanzees at Gombe National Park, Tanzania. We combined model predictions with behavioral observations to quantify feeding habitat quality as the cumulative dietary proportion of the species predicted to occur in a given location. This measure exhibited considerable spatial heterogeneity with elevation and latitude, both within and across main habitat types. We used model results to assess individual variation in habitat selection among adult chimpanzees during a 10-year period, testing predictions about trade-offs between foraging and reproductive effort. We found that nonswollen females selected the highest-quality habitats compared with swollen females or males, in line with predictions based on their energetic needs. Swollen females appeared to compromise feeding in favor of mating opportunities, suggesting that females rather than males change their ranging patterns in search of mates. Males generally occupied feeding habitats of lower quality, which may exacerbate energetic challenges of aggression and territory defense. Finally, we documented an increase in feeding habitat quality with community residence time in both sexes during the dry season, suggesting an influence of familiarity on foraging decisions in a highly heterogeneous landscape.
Gao, Yu; Ma, Lei; Liu, Jiaxun; Zhuang, Zhuzhou; Huang, Qiuhao; Li, Manchun
2017-01-01
Fragmentation and reduced continuity of habitat patches threaten the environment and biodiversity. Recently, ecological networks are increasingly attracting the attention of researchers as they provide fundamental frameworks for environmental protection. This study suggests a set of procedures to construct an ecological network. First, we proposed a method to construct a landscape resistance surface based on the assessment of habitat quality. Second, to analyze the effect of the resistance surface on corridor simulations, we used three methods to construct resistance surfaces: (1) the method proposed in this paper, (2) the entropy coefficient method, and (3) the expert scoring method. Then, we integrated habitat patches and resistance surfaces to identify potential corridors using graph theory. These procedures were tested in Changzhou, China. Comparing the outputs of using different resistance surfaces demonstrated that: (1) different landscape resistance surfaces contribute to how corridors are identified, but only slightly affect the assessment of the importance of habitat patches and potential corridors; (2) the resistance surface, which is constructed based on habitat quality, is more applicable to corridor simulations; and (3) the assessment of the importance of habitat patches is fundamental for ecological network optimization in the conservation of critical habitat patches and corridors. PMID:28393879
Gao, Yu; Ma, Lei; Liu, Jiaxun; Zhuang, Zhuzhou; Huang, Qiuhao; Li, Manchun
2017-04-01
Fragmentation and reduced continuity of habitat patches threaten the environment and biodiversity. Recently, ecological networks are increasingly attracting the attention of researchers as they provide fundamental frameworks for environmental protection. This study suggests a set of procedures to construct an ecological network. First, we proposed a method to construct a landscape resistance surface based on the assessment of habitat quality. Second, to analyze the effect of the resistance surface on corridor simulations, we used three methods to construct resistance surfaces: (1) the method proposed in this paper, (2) the entropy coefficient method, and (3) the expert scoring method. Then, we integrated habitat patches and resistance surfaces to identify potential corridors using graph theory. These procedures were tested in Changzhou, China. Comparing the outputs of using different resistance surfaces demonstrated that: (1) different landscape resistance surfaces contribute to how corridors are identified, but only slightly affect the assessment of the importance of habitat patches and potential corridors; (2) the resistance surface, which is constructed based on habitat quality, is more applicable to corridor simulations; and (3) the assessment of the importance of habitat patches is fundamental for ecological network optimization in the conservation of critical habitat patches and corridors.
Cozzoli, Francesco; Smolders, Sven; Eelkema, Menno; Ysebaert, Tom; Escaravage, Vincent; Temmerman, Stijn; Meire, Patrick; Herman, Peter M. J.; Bouma, Tjeerd J.
2017-01-01
The natural coastal hydrodynamics and morphology worldwide is altered by human interventions such as embankments, shipping and dredging, which may have consequences for ecosystem functionality. To ensure long-term ecological sustainability, requires capability to predict long-term large-scale ecological effects of altered hydromorphology. As empirical data sets at relevant scales are missing, there is need for integrating ecological modeling with physical modeling. This paper presents a case study showing the long-term, large-scale macrozoobenthic community response to two contrasting human alterations of the hydromorphological habitat: deepening of estuarine channels to enhance navigability (Westerschelde) vs. realization of a storm surge barrier to enhance coastal safety (Oosterschelde). A multidisciplinary integration of empirical data and modeling of estuarine morphology, hydrodynamics and benthic ecology was used to reconstruct the hydrological evolution and resulting long-term (50 years) large-scale ecological trends for both estuaries over the last. Our model indicated that hydrodynamic alterations following the deepening of the Westerschelde had negative implications for benthic life, while the realization of the Oosterschelde storm surge barriers had mixed and habitat-dependent responses, that also include unexpected improvement of environmental quality. Our analysis illustrates long-term trends in the natural community caused by opposing management strategies. The divergent human pressures on the Oosterschelde and Westerschelde are examples of what could happen in a near future for many global coastal ecosystems. The comparative analysis of the two basins is a valuable source of information to understand (and communicate) the future ecological consequences of human coastal development.
Hiebeler, David E; Michaud, Isaac J; Wasserman, Ben A; Buchak, Timothy D
2013-01-21
We explore a spatially implicit patch-occupancy model of a population on a landscape with continuous-valued heterogeneous habitat quality, primarily considering the case where the habitat quality of a site affects the mortality rate but not the fecundity of individuals at that site. Two analytical approaches to the model are constructed, by summing over the sites in the landscape and by integrating over the range of habitat quality. We obtain results relating the equilibrium population density and all moments of the probability distribution of the habitat quality of occupied sites, and relating the probability distributions of total habitat quality and occupied habitat quality. Special cases are considered for landscapes where habitat quality has either a uniform or a linear probability density function. For these cases, we demonstrate habitat association, where the quality of occupied sites is higher than the overall mean quality of all sites; the discrepancy between the two is reduced at larger population densities. The variance of the quality of occupied sites may be greater or less than the overall variance of habitat quality, depending on the distribution of habitat quality across the landscape. Increasing the variance of habitat quality is also shown to increase the ability of a population to persist on a landscape.
Combining catchment and instream modelling to assess physical habitat quality
DEFF Research Database (Denmark)
Olsen, Martin
observations showed that juvenile trout in stream Ledreborg prefered lower water depths and water velocities than juvenile trout in larger Danish streams, e.g. River Gudenå. Repeated electrofishing in the stream revealed big differences in temporal and spatial distribution of the trouts on the four reaches...... and abundance of trout on the reaches. • Comparison of reference condition minimum run-off and WUA curves suggested that summer low flow were not a limiting factor on the physical habitat quality for juvenile trout under reference conditions. • Habitat hydraulic modelling suggested that stream Ledreborg had...... the best potential physical habitat quality for trout fry and juvenile trout and the lowest potential physical habitat quality for adult trout. This finding supports previous evaluations of the stream as a trout habitat, concluding that stream Ledreborg has very few suitable habitats for adult trout...
New integrability case for the Riccati equation
Mak, M K
2012-01-01
A new integrability condition of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation depending on a generating function $f(x)$, the general solution of the Riccati equation can be obtained if the coefficients $a(x)$, $b(x)$, $c(x)$, and the function $f(x)$ satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed.
Determining habitat quality for species that demonstrate dynamic habitat selection
Beerens, James; Frederick, Peter C; Noonburg, Erik G; Gawlik, Dale E.
2015-01-01
Determining habitat quality for wildlife populations requires relating a species' habitat to its survival and reproduction. Within a season, species occurrence and density can be disconnected from measures of habitat quality when resources are highly seasonal, unpredictable over time, and patchy. Here we establish an explicit link among dynamic selection of changing resources, spatio-temporal species distributions, and fitness for predictive abundance and occurrence models that are used for short-term water management and long-term restoration planning. We used the wading bird distribution and evaluation models (WADEM) that estimate (1) daily changes in selection across resource gradients, (2) landscape abundance of flocks and individuals, (3) conspecific foraging aggregation, and (4) resource unit occurrence (at fixed 400 m cells) to quantify habitat quality and its consequences on reproduction for wetland indicator species. We linked maximum annual numbers of nests detected across the study area and nesting success of Great Egrets (Ardea alba), White Ibises (Eudocimus albus), and Wood Storks (Mycteria americana) over a 20-year period to estimated daily dynamics of food resources produced by WADEM over a 7490 km2 area. For all species, increases in predicted species abundance in March and high abundance in April were strongly linked to breeding responses. Great Egret nesting effort and success were higher when birds also showed greater conspecific foraging aggregation. Synthesis and applications: This study provides the first empirical evidence that dynamic habitat selection processes and distributions of wading birds over environmental gradients are linked with reproductive measures over periods of decades. Further, predictor variables at a variety of temporal (daily-multiannual) resolutions and spatial (400 m to regional) scales effectively explained variation in ecological processes that change habitat quality. The process used here allows managers to develop
Directory of Open Access Journals (Sweden)
Ainhoa Magrach
Full Text Available Habitat fragmentation has become one of the major threats to biodiversity worldwide, particularly in the case of forests, which have suffered enormous losses during the past decades. We analyzed how changes in patch configuration and habitat quality derived from the fragmentation of austral temperate rainforests affect the distribution of six species of forest-dwelling climbing and epiphytic angiosperms. Epiphyte and vine abundance is primarily affected by the internal characteristics of patches (such as tree size, the presence of logging gaps or the proximity to patch edges rather than patch and landscape features (such as patch size, shape or connectivity. These responses were intimately related to species-specific characteristics such as drought- or shade-tolerance. Our study therefore suggests that plant responses to fragmentation are contingent on both the species' ecology and the specific pathways through which the study area is being fragmented, (i.e. extensive logging that shaped the boundaries of current forest patches plus recent, unregulated logging that creates gaps within patches. Management practices in fragmented landscapes should therefore consider habitat quality within patches together with other spatial attributes at landscape or patch scales.
Magrach, Ainhoa; Larrinaga, Asier R; Santamaría, Luis
2012-01-01
Habitat fragmentation has become one of the major threats to biodiversity worldwide, particularly in the case of forests, which have suffered enormous losses during the past decades. We analyzed how changes in patch configuration and habitat quality derived from the fragmentation of austral temperate rainforests affect the distribution of six species of forest-dwelling climbing and epiphytic angiosperms. Epiphyte and vine abundance is primarily affected by the internal characteristics of patches (such as tree size, the presence of logging gaps or the proximity to patch edges) rather than patch and landscape features (such as patch size, shape or connectivity). These responses were intimately related to species-specific characteristics such as drought- or shade-tolerance. Our study therefore suggests that plant responses to fragmentation are contingent on both the species' ecology and the specific pathways through which the study area is being fragmented, (i.e. extensive logging that shaped the boundaries of current forest patches plus recent, unregulated logging that creates gaps within patches). Management practices in fragmented landscapes should therefore consider habitat quality within patches together with other spatial attributes at landscape or patch scales.
A New Integral Equation for the Spheroidal equations in case of m equal 1
Tian, Guihua
2012-01-01
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given explicitly. Though there are already some integral equations for the spheroidal equations, the relation between their two kinds of eigenvalues is not known till now. This is the great advantage of our integral equation, which will provide useful information through the study of the integral equation. Also an example is given for the special case, which shows another way to study the eigenvalue problem.
Ye, X.; Skidmore, A.K.; Wang, T.
2013-01-01
Patch geometry and habitat quality among patches are widely recognized as important factors affecting population dynamics in fragmented landscapes. Little is known, however, about the influence of within-patch habitat quality on population dynamics. In this paper, we investigate the relative importa
Kleijn, D.; Langevelde, van F.
2006-01-01
Landscape context and habitat quality may have pronounced effects on the diversity of flower visiting insects. We investigated whether the effects of landscape context and habitat quality on flower visiting insects interact in agricultural landscapes in the Netherlands. Landscape context was express
Vere, de N.; Jongejans, E.; Plowman, A.; Williams, E.
2009-01-01
Remaining populations of plant species in fragmented landscapes are threatened by declining habitat quality and reduced genetic diversity, but the interactions of these major factors are rarely studied together for species conservation. In this study, the interactions between population size,
Serengeti real estate: density vs. fitness-based indicators of lion habitat quality.
Mosser, Anna; Fryxell, John M; Eberly, Lynn; Packer, Craig
2009-10-01
Habitat quality is typically inferred by assuming a direct relationship between consumer density and resource abundance, although it has been suggested that consumer fitness may be a more accurate measure of habitat quality. We examined density vs. fitness-based measures of habitat quality for lions in the Serengeti National Park, Tanzania. A 40-year average of female reproductive success (yearling cubs per female) was best explained by proximity to river confluences, whereas patterns of productivity (yearling cubs per km(2)) and adult female density (individuals per km(2)) were associated with more general measures of habitat quality and areas of shelter in poor habitat. This suggests that density may not accurately distinguish between high-quality 'source' areas and low-quality sites that merely provide refuges for effectively non-reproductive individuals. Our results indicate that density may be a misleading indicator of real estate value, particularly for populations that do not conform to an ideal free distribution.
Wolves adapt territory size, not pack size to local habitat quality
National Research Council Canada - National Science Library
Kittle, Andrew M; Anderson, Morgan; Avgar, Tal; Baker, James A; Brown, Glen S; Hagens, Jevon; Iwachewski, Ed; Moffatt, Scott; Mosser, Anna; Patterson, Brent R; Reid, Douglas E.B; Rodgers, Arthur R; Shuter, Jen; Street, Garrett M; Thompson, Ian D; Vander Vennen, Lucas M; Fryxell, John M; Lele, Subhash
2015-01-01
.... Next, we compared habitat quality metrics emerging from this analysis as well as an independent measure of prey abundance, with pack size and territory size to investigate which hypothesis was most...
Seasonal and interannual effects of hypoxia on fish habitat quality in central Lake Erie
Arend, Kristin K.; Beletsky, Dmitry; DePinto, Joseph; Ludsin, Stuart A.; Roberts, James J.; Rucinski, Daniel K.; Scavia, Donald; Schwab, David J.; Höök, Tomas O.
2011-01-01
1. Hypoxia occurs seasonally in many stratified coastal marine and freshwater ecosystems when bottom dissolved oxygen (DO) concentrations are depleted below 2–3 mg O2 L-1. 2. We evaluated the effects of hypoxia on fish habitat quality in the central basin of Lake Erie from 1987 to 2005, using bioenergetic growth rate potential (GRP) as a proxy for habitat quality. We compared the effect of hypoxia on habitat quality of (i) rainbow smelt, Osmerus mordax mordax Mitchill (young-of-year, YOY, and adult), a cold-water planktivore, (ii) emerald shiner, Notropis atherinoides Rafinesque (adult), a warm-water planktivore, (iii) yellow perch, Perca flavescens Mitchill (YOY and adult), a cool-water benthopelagic omnivore and (iv) round goby Neogobius melanostomus Pallas (adult) a eurythermal benthivore. Annual thermal and DO profiles were generated from 1D thermal and DO hydrodynamics models developed for Lake Erie’s central basin. 3. Hypoxia occurred annually, typically from mid-July to mid-October, which spatially and temporally overlaps with otherwise high benthic habitat quality. Hypoxia reduced the habitat quality across fish species and life stages, but the magnitude of the reduction varied both among and within species because of the differences in tolerance to low DO levels and warm-water temperatures. 4. Across years, trends in habitat quality mirrored trends in phosphorus concentration and water column oxygen demand in central Lake Erie. The per cent reduction in habitat quality owing to hypoxia was greatest for adult rainbow smelt and round goby (mean: -35%), followed by adult emerald shiner (mean: -12%), YOY rainbow smelt (mean: -10%) and YOY and adult yellow perch (mean: -8.5%). 5. Our results highlight the importance of differential spatiotemporally interactive effects of DO and temperature on relative fish habitat quality and quantity. These effects have the potential to influence the performance of individual fish species as well as population dynamics
Spatial, temporal, and density-dependent components of habitat quality for a desert owl.
Directory of Open Access Journals (Sweden)
Aaron D Flesch
Full Text Available Spatial variation in resources is a fundamental driver of habitat quality but the realized value of resources at any point in space may depend on the effects of conspecifics and stochastic factors, such as weather, which vary through time. We evaluated the relative and combined effects of habitat resources, weather, and conspecifics on habitat quality for ferruginous pygmy-owls (Glaucidium brasilianum in the Sonoran Desert of northwest Mexico by monitoring reproductive output and conspecific abundance over 10 years in and around 107 territory patches. Variation in reproductive output was much greater across space than time, and although habitat resources explained a much greater proportion of that variation (0.70 than weather (0.17 or conspecifics (0.13, evidence for interactions among each of these components of the environment was strong. Relative to habitat that was persistently low in quality, high-quality habitat buffered the negative effects of conspecifics and amplified the benefits of favorable weather, but did not buffer the disadvantages of harsh weather. Moreover, the positive effects of favorable weather at low conspecific densities were offset by intraspecific competition at high densities. Although realized habitat quality declined with increasing conspecific density suggesting interference mechanisms associated with an Ideal Free Distribution, broad spatial heterogeneity in habitat quality persisted. Factors linked to food resources had positive effects on reproductive output but only where nest cavities were sufficiently abundant to mitigate the negative effects of heterospecific enemies. Annual precipitation and brooding-season temperature had strong multiplicative effects on reproductive output, which declined at increasing rates as drought and temperature increased, reflecting conditions predicted to become more frequent with climate change. Because the collective environment influences habitat quality in complex ways
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small, which is a limiting case of the regularity criteria derived by Kim and Kozono. Our result gives a positive answer to the question proposed by Kim and Kozono. For the incompressible magnetohydrodynamic equations, we also show the regularity of weak solution only under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small.
Semiconservative quasispecies equations for polysomic genomes: The general case
Itan, Eran; Tannenbaum, Emmanuel
2010-06-01
This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analog of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for noncomplementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.
Spatial scale of local breeding habitat quality and adjustment of breeding decisions.
Doligez, Blandine; Berthouly, Anne; Doligez, Damien; Tanner, Marion; Saladin, Verena; Bonfils, Danielle; Richner, Heinz
2008-05-01
Experimental studies provide evidence that, in spatially and temporally heterogeneous environments, individuals track variation in breeding habitat quality to adjust breeding decisions to local conditions. However, most experiments consider environmental variation at one spatial scale only, while the ability to detect the influence of a factor depends on the scale of analysis. We show that different breeding decisions by adults are based on information about habitat quality at different spatial scales. We manipulated (increased or decreased) local breeding habitat quality through food availability and parasite prevalence at a small (territory) and a large (patch) scale simultaneously in a wild population of Great Tits (Parus major). Females laid earlier in high-quality large-scale patches, but laying date did not depend on small-scale territory quality. Conversely, offspring sex ratio was higher (i.e., biased toward males) in high-quality, small-scale territories but did not depend on large-scale patch quality. Clutch size and territory occupancy probability did not depend on our experimental manipulation of habitat quality, but territories located at the edge of patches were more likely to be occupied than central territories. These results suggest that integrating different decisions taken by breeders according to environmental variation at different spatial scales is required to understand patterns of breeding strategy adjustment.
Competition and habitat quality influence age and sex distribution in wintering Rusty Blackbirds
Claudia Mettke-Hofmann; Paul B. Hamel; Gerhard Hofmann; Theodore J. Zenzal Jr.; Anne Pellegrini; Jennifer Malpass; Megan Garfinkel; Nathan Schiff; Russell Greenberg
2015-01-01
Bird habitat quality is often inferred from species abundance measures during the breeding and non-breeding season and used for conservation management decisions. However, during the non-breeding season age and sex classes often occupy different habitats which suggest a need for more habitat-specific data. Rusty Blackbird (Euphagus carolinus) is a...
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
Lee, Sik-Yum; Lu, Bin
2003-01-01
In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…
Wolves adapt territory size, not pack size to local habitat quality.
Kittle, Andrew M; Anderson, Morgan; Avgar, Tal; Baker, James A; Brown, Glen S; Hagens, Jevon; Iwachewski, Ed; Moffatt, Scott; Mosser, Anna; Patterson, Brent R; Reid, Douglas E B; Rodgers, Arthur R; Shuter, Jen; Street, Garrett M; Thompson, Ian D; Vander Vennen, Lucas M; Fryxell, John M
2015-09-01
1. Although local variation in territorial predator density is often correlated with habitat quality, the causal mechanism underlying this frequently observed association is poorly understood and could stem from facultative adjustment in either group size or territory size. 2. To test between these alternative hypotheses, we used a novel statistical framework to construct a winter population-level utilization distribution for wolves (Canis lupus) in northern Ontario, which we then linked to a suite of environmental variables to determine factors influencing wolf space use. Next, we compared habitat quality metrics emerging from this analysis as well as an independent measure of prey abundance, with pack size and territory size to investigate which hypothesis was most supported by the data. 3. We show that wolf space use patterns were concentrated near deciduous, mixed deciduous/coniferous and disturbed forest stands favoured by moose (Alces alces), the predominant prey species in the diet of wolves in northern Ontario, and in proximity to linear corridors, including shorelines and road networks remaining from commercial forestry activities. 4. We then demonstrate that landscape metrics of wolf habitat quality - projected wolf use, probability of moose occupancy and proportion of preferred land cover classes - were inversely related to territory size but unrelated to pack size. 5. These results suggest that wolves in boreal ecosystems alter territory size, but not pack size, in response to local variation in habitat quality. This could be an adaptive strategy to balance trade-offs between territorial defence costs and energetic gains due to resource acquisition. That pack size was not responsive to habitat quality suggests that variation in group size is influenced by other factors such as intraspecific competition between wolf packs. © 2015 The Authors. Journal of Animal Ecology © 2015 British Ecological Society.
BIOMONITORING OF URBAN HABITAT QUALITY BY ANATOMICAL LEAF PARAMETERS IN TIMIŞOARA
Directory of Open Access Journals (Sweden)
NICOLETA IANOVICI
2009-01-01
Full Text Available The use of anatomical features from the leaf has been evaluated in solving different kind of problems.The interactions between different plant species and urban habitat quality were extensively investigated by different authors. Studies concerning the anatomy of the vegetative organs under conditions of pollution have been carried out. The necessity of studying the capacity of plant species for bioindication of anthropogenic pollution defines the aim of this study: to analyze some anatomical leaf characteristics in urban area. The photos were taken with an Cannon photo camera, using an Optika research microscope. In the mesophyll and epidermis of the plants from polluted sites isolate dark spots or massive deposits of polyphenolic compounds could be observed. We conclude that Plantago is a suitable bioindicator of urban habitat quality as it is a commonly distributed species, which is easy to sample and shows a clear anatomical response to differences in habitat quality. The thickness of the foliar lamina has decreased. The stomatal density was higher at the abaxial side in comparison with the adaxial side. The present study provides a good basis for further research on impact of the environment to anatomical structure of the plants.
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Wu, Jian-sheng; Cao, Qi-wen; Shi, Shu-qin; Huang, Xiu-lan; Lu, Zhi-qiang
2015-11-01
Land use change is the core content of global change. To achieve sustainable land use planning, it is necessary to evaluate the habitat quality pattern and its spatio-temporal variation resulted from land use change, which can provide basis for the formulation of land management policy. Based on the analysis of land use change from 2000 to 2010, this study investigated the spatio-temporal variation of habitat quality pattern of Beijing-Tianjin-Hebei Area. We used the watershed profile sampling points and spatial autocorrelation analysis based on watershed subdivision. The results showed that the main land use change types from 2000 to 2010 in this area included the transition from cultivated land to construction land, the transition between forest and grassland, and the transition from water bodies to cultivated land. This land use/cover change process led to the decrease of heterogeneity of landscape structure and increase of fragmentation. The overall spatial pattern of habitat quality was that southeast and south areas were relatively lower, while north and west areas were relatively higher. The analysis based on watershed profile showed that the habitat quality of each watershed presented significant difference in each part. Habitat quality of most sampling points degraded in a way, while some improved compared with 2000. In general, the habitat quality of the bottom part of Luanhe River basin, the medium part of Bai-Chaobai-Chaobaixin River basin, the medium and the bottom part of Yongding River basin and medium part of Laozhang-Fudongpai- Beipai River basin were poor and volatile, while other parts were relatively good. There was a decreasing agglomeration characteristic of distribution of habitat quality in Beijing-Tianjin-Hebei Area under the disturbance of human activities. Areas of high habitat quality in 2000 were mainly located in Luanhe River basin and top part of Baihe basin. Areas of low habitat quality were mainly located in medium and bottom part
Modeling population dynamics of solitary bees in relation to habitat quality
Directory of Open Access Journals (Sweden)
K. Ulbrich
2001-09-01
Full Text Available To understand associations between habitat, individual behaviour, and population development of solitary bees we developed an individual-based model. This model is based on field observations of Osmia rufa (L (Apoideae: Megachilidae and describes population dynamics of solitary bees. Model rules are focused on maternal investment, in particular on the female’s individual decisions about sex and size of progeny. In the present paper, we address the effect of habitat quality on population size and sex ratio. We examine how food availability and the risk of parasitism influence long-term population development. It can be shown how population properties result from individual maternal investment which is described as a functional response to fluctuations of environmental conditions. We found that habitat quality can be expressed in terms of cell construction time. This interface factor influences the rate of open cell parasitism as the risk for a brood cell to be parasitized is positively correlated with the time of its construction. Under conditions of scarce food and under resulting long provision times even low parasitism rates lead to a high extinction risk of the population, whereas in rich habitats probabilities of extinction are low even for high rates of parasitism. For a given level of food and parasitism there is an optimum time for cell construction which minimizes the extinction risk of the population. Model results demonstrate that under fluctuating environmental conditions, decreasing habitat quality leads to a decrease in population size but also to rapid shifts in sex ratio.
Assessing habitat quality of the mountain nyala Tragelaphus buxtoni in the Bale Mountains, Ethiopia
Institute of Scientific and Technical Information of China (English)
Paul H.EVANGELISTA; John NORMAN Ⅲ; Paul SWARTZINKI; Nicholas E.YOUNG
2012-01-01
Populations of the endangered mountain nyala Tragelaphus buxtoni are significantly threatened by the loss of critical habitat.Population estimates are tentative,and information on the species' distribution and available habitat is required for formulating immediate management and conservation strategies.To support management decisions and conservation priorities,we integrated information from a number of small-scale observational studies,interviews and reports from multiple sources to define habitat parameters and create a habitat quality model for mountain nyala in the Bale Mountains.For our analysis,we used the FunConn model,an expertise-based model that considers spatial relationships (i.e,patch size,distance) between the species and vegetation type,topography and disturbance to create a habitat quality surface.The habitat quality model showed that approximately 18,610 km2 (82.7％ of our study area) is unsuitable or poor habitat for the mountain nyala,while 2,857 km2 (12.7％) and 1,026 km2 (4.6％) was ranked as good or optimal habitat,respectively.Our results not only reflected human induced habitat degradation,but also revealed an extensive area of intact habitat on the remote slopes of the Bale Mountain's southern and southeastern escarpments.This study provides an example of the roles that expert knowledge can still play in modem geospatial modeling of wildlife habitat.New geospatial tools,such as the FunConn model,are readily available to wildlife managers and allow them to perform spatial analyses with minimal software,data and training requirements.This approach may be especially useful for species that are obscure to science or when field surveys are not practical.
Flitcroft, Rebecca L; Falke, Jeffrey A.; Reeves, Gordon H.; Hessburg, Paul F.; McNyset, Kris M.; Benda, Lee E.
2016-01-01
Pacific Northwest salmonids are adapted to natural disturbance regimes that create dynamic habitat patterns over space and through time. However, human land use, particularly long-term fire suppression, has altered the intensity and frequency of wildfire in forested upland and riparian areas. To examine the potential impacts of wildfire on aquatic systems, we developed stream-reach-scale models of freshwater habitat for three life stages (adult, egg/fry, and juvenile) of spring Chinook salmon (Oncorhynchus tshawytscha) in the Wenatchee River subbasin, Washington. We used variables representing pre- and post-fire habitat conditions and employed novel techniques to capture changes in in-stream fine sediment, wood, and water temperature. Watershed-scale comparisons of high-quality habitat for each life stage of spring Chinook salmon habitat suggested that there are smaller quantities of high-quality juvenile overwinter habitat as compared to habitat for other life stages. We found that wildfire has the potential to increase quality of adult and overwintering juvenile habitat through increased delivery of wood, while decreasing the quality of egg and fry habitat due to the introduction of fine sediments. Model results showed the largest effect of fire on habitat quality associated with the juvenile life stage, resulting in increases in high-quality habitat in all watersheds. Due to the limited availability of pre-fire high-quality juvenile habitat, and increased habitat quality for this life stage post-fire, occurrence of characteristic wildfires would likely create a positive effect on spring Chinook salmon habitat in the Wenatchee River subbasin. We also compared pre- and post-fire model results of freshwater habitat for each life stage, and for the geometric mean of habitat quality across all life stages, using current compared to the historic distribution of spring Chinook salmon. We found that spring Chinook salmon are currently distributed in stream channels in
Evaluation of habitat quality for selected wildlife species associated with back channels.
Anderson, James T.; Zadnik, Andrew K.; Wood, Petra Bohall; Bledsoe, Kerry
2013-01-01
The islands and associated back channels on the Ohio River, USA, are believed to provide critical habitat features for several wildlife species. However, few studies have quantitatively evaluated habitat quality in these areas. Our main objective was to evaluate the habitat quality of back and main channel areas for several species using habitat suitability index (HSI) models. To test the effectiveness of these models, we attempted to relate HSI scores and the variables measured for each model with measures of relative abundance for the model species. The mean belted kingfisher (Ceryle alcyon) HSI was greater on the main than back channel. However, the model failed to predict kingfisher abundance. The mean reproduction component of the great blue heron (Ardea herodias) HSI, total common muskrat (Ondatra zibethicus) HSI, winter cover component of the snapping turtle (Chelydra serpentina) HSI, and brood-rearing component of the wood duck (Aix sponsa) HSI were all greater on the back than main channel, and were positively related with the relative abundance of each species. We found that island back channels provide characteristics not found elsewhere on the Ohio River and warrant conservation as important riparian wildlife habitat. The effectiveness of using HSI models to predict species abundance on the river was mixed. Modifications to several of the models are needed to improve their use on the Ohio River and, likely, other large rivers.
Strongly asymmetric discrete Painlevé equations: The multiplicative case
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
2016-04-01
We examine a class of multiplicative discrete Painlevé equations which may possess a strongly asymmetric form. When the latter occurs, the equation is written as a system of two equations the right hand sides of which have different functional forms. The present investigation focuses upon two canonical families of the Quispel-Roberts-Thompson classification which contain equations associated with the affine Weyl groups D5 ( 1 ) and E6 ( 1 ) (or groups appearing lower in the degeneration cascade of these two). Many new discrete Painlevé equations with strongly asymmetric forms are obtained.
Liao, Jinbao; Li, Zhenqing; Hiebeler, David E; Iwasa, Yoh; Bogaert, Jan; Nijs, Ivan
2013-10-21
Habitat degradation has become a major threat to species persistence. Although several models have explicitly integrated habitat quality into metapopulation dynamics, we still lack knowledge of the spatial variability of species persistence which may result from the clustering of habitat patches of differing quality. Here we construct both pair approximation (PA) and cellular automaton (CA) models for species persistence in homogeneous versus heterogeneous landscapes. Heterogeneous landscapes are generated by varying the orthogonal-neighbour correlation between two different-quality habitats. In our simulations, the PA model exhibits similar population dynamics to the CA model, though it overestimates species persistence due to the doublet approximation neglecting correlation beyond nearest neighbours. Generally, landscape heterogeneity enhances species persistence relative to landscape homogeneity, especially with enlarging habitat-quality difference. This indicates that models based on homogeneous landscapes may overestimate species extinction rate. In heterogeneous landscapes, habitat clumping does not influence global dispersers because of random establishment, although it does promote the persistence of local dispersers, especially under severe habitat degradation. However, habitat configurational fragmentation improves the persistence of global dispersers that are highly sensitive to local crowding, probably by reducing density dependence, but this positive fragmentation effect on local dispersers is overshadowed by the stronger negative border effect on impeding local extension. Furthermore, increasing density dependence promotes the extinction risk of local dispersers, while global dispersers are not influenced. For conservation and habitat management, our results suggest that minimising random anthropogenic disturbance should take priority over increasing the connectivity of good-quality habitat, as random habitat degradation poses a more serious threat to
Piazza, Bryan P.; La Peyre, M.K.
2010-01-01
Numerous indices have been used to estimate fish growth and condition however, differences in sensitivity and reliability of the methods have hampered efforts to identify appropriate indicators for routine evaluation of habitat quality in the field. We compared common morphometric (length, weight, somatic growth, length-weight condition) and biochemical (RNA:DNA ratio, relative DNA content, energy density) growth indices on the same wild-caught mosquitofish Gambusia affinis to examine their usefulness as indicators of habitat quality. A laboratory experiment was used to quantify growth rates of wild-caught G. affinis under different feeding treatments. Field studies consisted of both a short-term enclosure experiment (10 d) and weekly (7 wk) fish collections to compare growth indices in managed inflow and reference marshes during a winter/spring freshwater pulse event in upper Breton Sound, Louisiana, USA. Marshes flooded by restored freshwater pulses were capable of producing optimum growth (0.001 g DW d-1 DW = dry weight) and energetically valuable habitat (>6000 cal g-1 DW) for trophic transport. Because of differences in timing of response, morphometric and biochemical indices were generally not directly correlated, but there was clear agreement in direction and magnitude of response. The most striking difference in timing was that biochemical indices (RNA:DNA) responded more slowly to treatments than did morphometric growth indices. While gross patterns are comparable between indicators, differences in sensitivity and response time between indicators suggest that choice of indicator needs to be accounted for in interpretation and analysis of effects. ?? Inter-Research 2010, www.int-res.com.
Differential equations and integrable models the $SU(3)$ case
Dorey, P; Dorey, Patrick; Tateo, Roberto
2000-01-01
We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schrödinger equation. This forms part of a more general correspondence involving $A_2$-related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the nonlinear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators $\\phi_{12}$, $\\phi_{21}$ and $\\phi_{15}$. This is checked against previous results obtained using the thermodynamic Bethe ansatz.
Teaching Linear Equations: Case Studies from Finland, Flanders and Hungary
Andrews, Paul; Sayers, Judy
2012-01-01
In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived…
Teaching Linear Equations: Case Studies from Finland, Flanders and Hungary
Andrews, Paul; Sayers, Judy
2012-01-01
In this paper we compare how three teachers, one from each of Finland, Flanders and Hungary, introduce linear equations to grade 8 students. Five successive lessons were videotaped and analysed qualitatively to determine how teachers, each of whom was defined against local criteria as effective, addressed various literature-derived…
Does foraging habitat quality affect reproductive performance in the Little Egret, Egretta garzetta?
Directory of Open Access Journals (Sweden)
Tourenq, C.
2001-06-01
Full Text Available In order to understand the role of foraging habitat quality on fecundity parameters we measured habitat use, breeding parameters, and body condition of chicks in six colonies of Little Egrets in southern France. The foraging habitat available differed between colonies; it was mainly natural marshes around the Carrelet colony, agricultural lands (rice fields and dry crops around the Agon colony, a mix of agricultural and natural lands around the Redon and Fiélouse colonies, a mix of natural and urbanised/industrial lands around the Palissade colony, and mainly cultivated and urbanised lands around the Chaumont colony. The habitat attractiveness to adult Little Egret breeding was higher for natural marshes than for other habitat types. Agricultural marshes (rice fields came next. Other human¿made habitats came last. Clutch size and body condition index of chicks did not differ between colonies. Brood size was influenced by both the association of the proportion of natural marshes in the foraging area and clutch size, and the association of clutch size and the total number of heron pairs in the colony. The effect of the proportion of natural marshes could not be distinguished from the effects of the colony size. The potential influence of other parameters not taken into account in this study is discussed.
Seasonal change in tropical habitat quality and body condition for a declining migratory songbird.
McKinnon, Emily A; Rotenberg, James A; Stutchbury, Bridget J M
2015-10-01
Many migratory songbirds spend their non-breeding season in tropical humid forests, where climate change is predicted to increase the severity and frequency of droughts and decrease rainfall. For conservation of these songbirds, it is critical to understand how resources during the non-breeding season are affected by seasonal patterns of drying, and thereby predict potential long-term effects of climate change. We studied habitat quality for a declining tropical forest-dwelling songbird, the wood thrush (Hylocichla mustelina), and tested the hypothesis that habitat moisture and arthropod abundance are drivers of body condition during the overwintering period. We examined habitat moisture, abundance of arthropods and fruit, and condition of individual birds (n = 418) in three habitat types--mature forest, mature forest with increased presence of human activity, and riparian scrub--from October to April. We found a strong pattern of habitat drying from October (wet season) to March (prior to spring migration) in all habitats, with concurrent declines in arthropod and fruit abundance. Body condition of birds also declined (estimated ~5 % decline over the wintering period), with no significant difference by habitat. Relatively poor condition (low body condition index, low fat and pectoral muscles scores) was equally apparent in all habitat types in March. Climate change is predicted to increase the severity of dry seasons in Central America, and our results suggest that this could negatively affect the condition of individual wood thrushes.
The Curious Case of Lemaitre's Equation No. 24
Bergh, Sidney van den
2011-01-01
The 1927 discovery of the expansion of the Universe by Lemaitre was published in French in a low-impact journal. In the 1931 high-impact English translation of this article a critical equation was changed by omitting reference to what is now known as the Hubble constant. That the section of the text of this paper dealing with the expansion of the Universe was also deleted from that English translation suggests a deliberate omission by the unknown translator.
Analytic Representation of Relativistic Wave Equations I The Dirac Case
Tepper, L; Zachary, W W
2003-01-01
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. It is well known that the Foldy-Wouthuysen transformation leads to a diagonalization that is nonlocal in space. We interpret the zitterbewegung, and the result that a velocity measurement (of a Dirac particle) at any instant in time is +(-)c, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. This suggests that although the Dirac Hamiltonian and the square-root Hamiltonian, are mathematically, they are not physically, equivalent. Furthermore, we see that alt! ho! ugh the form of the Dirac equation serve...
Jalcovikova, Monika; Skrovinova, Marcela; Stankoci, Ivan; Bajtek, Zbynek
2010-05-01
In 2008 was implemented topographical and ichtyological research on the chosen streams on the east of Slovakia. For hydraulic modeling was used RHABSIM model which is component of the IFIM (Instream Flow Incremental Methodology). IFIM is an interdisciplinary decision-making system, which has arisen as a result of the knowledge that most fish species prefer certain combinations of water depths, flow velocities, hiding places and materials of a riverbed. The research was aimed at the relationship between the quantitative parameters of ichthyofauna as a bioindicator and the ratio of habitat suitability. In the IFIM methodology the relationship between abiotic and biotic characteristics is represented by the habitat suitability curves of various fish species. Fish are the best bioindicators that most sensitively indicate the quality of a stream microhabitat. The habitat suitability curves of particular fish species are determined for the two most important abiotic characteristics - flow velocity and water depth. From our research, it follows that the technique of processing for the habitat suitability curve is a very important factor that significantly influences the whole process of habitat modeling. The assessment of the habitat quality proves the appropriate input for water-management planning and decision-making, e.g. determination of the minimal (ecological) flow, river restoration planning, or the assessment of the river regulation influence on the quality and quantity of its biological guilds. It can also be used as a substitute of the ichthyofauna biodiversity assessment. These models provide a basic overview of time and spatial interaction of physical and biological components of the river system. This methodology can even be used for modeling the unaffected character of stream according to the EU framework directive 2000/60/EC. Modeling of the aquatic habitat quality using the RHABSIM model requires the simulation of the velocity field verified for two water
Directory of Open Access Journals (Sweden)
Nicholas J. Bayly
2016-12-01
Full Text Available Long-distance migratory birds are declining globally and migration has been identified as the primary source of mortality in this group. Despite this, our lack of knowledge of habitat use and quality at stopovers, i.e., sites where the energy for migration is accumulated, remains a barrier to designing appropriate conservation measures, especially in tropical regions. There is therefore an urgent need to assess stopover habitat quality and concurrently identify efficient and cost-effective methods for doing so. Given that fuel deposition rates directly influence stopover duration, departure fuel load, and subsequent speed of migration, they are expected to provide a direct measure of habitat quality and have the advantage of being measurable through body-mass changes. Here, we examined seven potential indicators of quality, including body-mass change, for two ecologically distinct Neotropical migratory landbirds on stopover in shade-coffee plantations and tropical humid premontane forest during spring migration in Colombia: (1 rate of body-mass change; (2 foraging rate; (3 recapture rate; (4 density; (5 flock size; (6 age and sex ratios; and (7 body-mass distribution. We found higher rates of mass change in premontane forest than in shade-coffee in Tennessee Warbler Oreothlypis peregrina, a difference that was mirrored in higher densities and body masses in forest. In Gray-cheeked Thrush Catharus minimus, a lack of recaptures in shade-coffee and higher densities in forest, also suggested that forest provided superior fueling conditions. For a reliable assessment of habitat quality, we therefore recommend using a suite of indicators, taking into account each species' ecology and methodological considerations. Our results also imply that birds stopping over in lower quality habitats may spend a longer time migrating and require more stopovers, potentially leading to important carryover effects on reproductive fitness. Evaluating habitat quality is
TIME-DOMAIN VOLUME INTEGRAL EQUATION FOR TRANSIENT SCATTERING FROM INHOMOGENEOUS OBJECTS-2D TM CASE
Institute of Scientific and Technical Information of China (English)
Wang Jianguo; Fan Ruyu
2001-01-01
This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse magnetic case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.
TIME-DOMAIN VOLUME INTEGRAL EQUATION FOR TRANSIENT SCATTERING FROM INHOMOGENEOUS OBJECTS-2D TE CASE
Institute of Scientific and Technical Information of China (English)
Wang Jianguo; Fan Ruyu
2001-01-01
This letter proposes a time-domain volume integral equation based method for analyzing the transient scattering from a 2D inhomogeneous cylinder by involking the volume equivalence principle for the transverse electric case. This integral equation is solved by using an MOT scheme. Numerical results obtained using this method agree very well with those obtained using the FDTD method.
Dickson, Brett G; Roemer, Gary W; McRae, Brad H; Rundall, Jill M
2013-01-01
The impact of landscape changes on the quality and connectivity of habitats for multiple wildlife species is of global conservation concern. In the southwestern United States, pumas (Puma concolor) are a well distributed and wide-ranging large carnivore that are sensitive to loss of habitat and to the disruption of pathways that connect their populations. We used an expert-based approach to define and derive variables hypothesized to influence the quality, location, and permeability of habitat for pumas within an area encompassing the entire states of Arizona and New Mexico. Survey results indicated that the presence of woodland and forest cover types, rugged terrain, and canyon bottom and ridgeline topography were expected to be important predictors of both high quality habitat and heightened permeability. As road density, distance to water, or human population density increased, the quality and permeability of habitats were predicted to decline. Using these results, we identified 67 high quality patches across the study area, and applied concepts from electronic circuit theory to estimate regional patterns of connectivity among these patches. Maps of current flow among individual pairs of patches highlighted possible pinch points along two major interstate highways. Current flow summed across all pairs of patches highlighted areas important for keeping the entire network connected, regardless of patch size. Cumulative current flow was highest in Arizona north of the Colorado River and around Grand Canyon National Park, and in the Sky Islands region owing to the many small habitat patches present. Our outputs present a first approximation of habitat quality and connectivity for dispersing pumas in the southwestern United States. Map results can be used to help target finer-scaled analyses in support of planning efforts concerned with the maintenance of puma metapopulation structure, as well as the protection of landscape features that facilitate the dispersal
Remote-sensing based approach to forecast habitat quality under climate change scenarios
Requena-Mullor, Juan M.; López, Enrique; Castro, Antonio J.; Alcaraz-Segura, Domingo; Castro, Hermelindo; Reyes, Andrés; Cabello, Javier
2017-01-01
As climate change is expected to have a significant impact on species distributions, there is an urgent challenge to provide reliable information to guide conservation biodiversity policies. In addressing this challenge, we propose a remote sensing-based approach to forecast the future habitat quality for European badger, a species not abundant and at risk of local extinction in the arid environments of southeastern Spain, by incorporating environmental variables related with the ecosystem functioning and correlated with climate and land use. Using ensemble prediction methods, we designed global spatial distribution models for the distribution range of badger using presence-only data and climate variables. Then, we constructed regional models for an arid region in the southeast Spain using EVI (Enhanced Vegetation Index) derived variables and weighting the pseudo-absences with the global model projections applied to this region. Finally, we forecast the badger potential spatial distribution in the time period 2071–2099 based on IPCC scenarios incorporating the uncertainty derived from the predicted values of EVI-derived variables. By including remotely sensed descriptors of the temporal dynamics and spatial patterns of ecosystem functioning into spatial distribution models, results suggest that future forecast is less favorable for European badgers than not including them. In addition, change in spatial pattern of habitat suitability may become higher than when forecasts are based just on climate variables. Since the validity of future forecast only based on climate variables is currently questioned, conservation policies supported by such information could have a biased vision and overestimate or underestimate the potential changes in species distribution derived from climate change. The incorporation of ecosystem functional attributes derived from remote sensing in the modeling of future forecast may contribute to the improvement of the detection of ecological
Assessment of River Habitat Quality in the Hai River Basin, Northern China
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Yuekui Ding
2015-09-01
Full Text Available We applied a river habitat quality (RHQ assessment method to the Hai River Basin (HRB; an important economic centre in China; to obtain baseline information for water quality improvement; river rehabilitation; and watershed management. The results of the assessment showed that the river habitat in the HRB is seriously degraded. Specifically; 42.41% of the sites; accounting for a river length of 3.31 × 104 km; were designated poor and bad. Habitat in the plain areas is seriously deteriorated; and nearly 50% of the sites; accounting for a river length of 1.65 × 104 km; had either poor or bad habitats. River habitat degradation was attributable to the limited width of the riparian zone (≤5 m; lower coverage of riparian vegetation (≤40%; artificial land use patterns (public and industrial land; frequent occurrence of farming on the river banks and high volumes of solid waste (nearly 10 m3; single flow channels; and rare aquatic plants (≤1 category. At the regional scale; intensive artificial land use types caused by urbanization had a significant impact on the RHQ in the HRB. RHQ was significantly and negatively correlated with farmland (r = 1.000; p < 0.01 and urban land (r = 0.998; p < 0.05; and was significantly and positively correlated with grassland and woodland (r = 1.000; p < 0.01. Intensive artificial land use; created through urbanization processes; has led to a loss of the riparian zone and its native vegetation; and has disrupted the lateral connectivity of the rivers. The degradation of the already essentially black rivers is exacerbated by poor longitudinal connectivity (index of connectivity is 2.08–16.56; caused by reservoirs and sluices. For river habitat rehabilitation to be successful; land use patterns need to be changed and reservoirs and sluices will have to be regulated.
Directory of Open Access Journals (Sweden)
Brett G Dickson
Full Text Available The impact of landscape changes on the quality and connectivity of habitats for multiple wildlife species is of global conservation concern. In the southwestern United States, pumas (Puma concolor are a well distributed and wide-ranging large carnivore that are sensitive to loss of habitat and to the disruption of pathways that connect their populations. We used an expert-based approach to define and derive variables hypothesized to influence the quality, location, and permeability of habitat for pumas within an area encompassing the entire states of Arizona and New Mexico. Survey results indicated that the presence of woodland and forest cover types, rugged terrain, and canyon bottom and ridgeline topography were expected to be important predictors of both high quality habitat and heightened permeability. As road density, distance to water, or human population density increased, the quality and permeability of habitats were predicted to decline. Using these results, we identified 67 high quality patches across the study area, and applied concepts from electronic circuit theory to estimate regional patterns of connectivity among these patches. Maps of current flow among individual pairs of patches highlighted possible pinch points along two major interstate highways. Current flow summed across all pairs of patches highlighted areas important for keeping the entire network connected, regardless of patch size. Cumulative current flow was highest in Arizona north of the Colorado River and around Grand Canyon National Park, and in the Sky Islands region owing to the many small habitat patches present. Our outputs present a first approximation of habitat quality and connectivity for dispersing pumas in the southwestern United States. Map results can be used to help target finer-scaled analyses in support of planning efforts concerned with the maintenance of puma metapopulation structure, as well as the protection of landscape features that facilitate
Remote-sensing based approach to forecast habitat quality under climate change scenarios.
Requena-Mullor, Juan M; López, Enrique; Castro, Antonio J; Alcaraz-Segura, Domingo; Castro, Hermelindo; Reyes, Andrés; Cabello, Javier
2017-01-01
As climate change is expected to have a significant impact on species distributions, there is an urgent challenge to provide reliable information to guide conservation biodiversity policies. In addressing this challenge, we propose a remote sensing-based approach to forecast the future habitat quality for European badger, a species not abundant and at risk of local extinction in the arid environments of southeastern Spain, by incorporating environmental variables related with the ecosystem functioning and correlated with climate and land use. Using ensemble prediction methods, we designed global spatial distribution models for the distribution range of badger using presence-only data and climate variables. Then, we constructed regional models for an arid region in the southeast Spain using EVI (Enhanced Vegetation Index) derived variables and weighting the pseudo-absences with the global model projections applied to this region. Finally, we forecast the badger potential spatial distribution in the time period 2071-2099 based on IPCC scenarios incorporating the uncertainty derived from the predicted values of EVI-derived variables. By including remotely sensed descriptors of the temporal dynamics and spatial patterns of ecosystem functioning into spatial distribution models, results suggest that future forecast is less favorable for European badgers than not including them. In addition, change in spatial pattern of habitat suitability may become higher than when forecasts are based just on climate variables. Since the validity of future forecast only based on climate variables is currently questioned, conservation policies supported by such information could have a biased vision and overestimate or underestimate the potential changes in species distribution derived from climate change. The incorporation of ecosystem functional attributes derived from remote sensing in the modeling of future forecast may contribute to the improvement of the detection of ecological
Maxwell's equations as a special case of deformation of a solid lattice in Euler's coordinates
Gremaud, G
2016-01-01
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing topological defects as dislocations and disclinations, in the case of constant and homogenous expansion. The analogy between these two physical systems is complete, as it is not restricted to one of the two Maxwell's equation couples in the vacuum, but generalized to the two equation couples as well as to the diverse phenomena of dielectric polarization and magnetization of matter, just as to the electrical charges and the electrical currents. The eulerian approach of the solid lattice developed here includes Maxwell's equations as a special case, since it stems from a tensor theory, which is reduced to a vector one by contraction on the tensor indices. Considering the tensor aspect of the eulerian solid lattice deformation theory, the analogy can be extended to other ...
Optimization on class of operator equations in the probabilistic case setting
Institute of Scientific and Technical Information of China (English)
Gen-sun FANG; Li-xin QIAN
2007-01-01
In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Freldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting.
Optimization on class of operator equations in the probabilistic case setting
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Preldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting.
About regression-kriging: from equations to case studies
Hengl, T.; Heuvelink, G.B.M.; Rossiter, D.G.
2007-01-01
This paper discusses the characteristics of regression-kriging (RK), its strengths and limitations, and illustrates these with a simple example and three case studies. RK is a spatial interpolation technique that combines a regression of the dependent variable on auxiliary variables (such as land su
Dirac equation from the Hamiltonian and the case with a gravitational field
Arminjon, M
2006-01-01
Starting from an interpretation of the classical-quantum correspondence, we derive the Dirac equation by factorizing the algebraic relation satisfied by the classical Hamiltonian, before applying the correspondence. This derivation applies in the same form to a free particle, to one in an electromagnetic field, and to one subjected to geodesic motion in a static metric, and leads to the same, usual form of the Dirac equation--in special coordinates. To use the equation in the static-gravitational case, we need to rewrite it in more general coordinates. This can be done only if the usual, spinor transformation of the wave function is replaced by the 4-vector transformation. We show that the latter also makes the flat-space-time Dirac equation Lorentz-covariant, although the Dirac matrices are not invariant. Because the equation itself is left unchanged in the flat case, the 4-vector transformation does not alter the main physical consequences of that equation in that case. However, the equation derived in the ...
Stoll, Stefan; Breyer, Philippa; Tonkin, Jonathan D; Früh, Denise; Haase, Peter
2016-05-15
Although most stream restoration projects succeed in improving hydromorphological habitat quality, the ecological quality of the stream communities often remains unaffected. We hypothesize that this is because stream communities are largely determined by environmental properties at a larger-than-local spatial scale. Using benthic invertebrate community data as well as hydromorphological habitat quality data from 1087 stream sites, we investigated the role of local- (i.e. 100 m reach) and regional-scale (i.e. 5 km ring centered on each reach) stream hydromorphological habitat quality (LQ and RQ, respectively) on benthic invertebrate communities. The analyses showed that RQ had a greater individual effect on communities than LQ, but the effects of RQ and LQ interacted. Where RQ was either good or poor, communities were exclusively determined by RQ. Only in areas of intermediate RQ, LQ determined communities. Metacommunity analysis helped to explain these findings. Species pools in poor RQ areas were most depauperated, resulting in insufficient propagule pressure for species establishment even at high LQ (e.g. restored) sites. Conversely, higher alpha diversity and an indication of lower beta dispersion signals at mass effects occurring in high RQ areas. That is, abundant neighboring populations may help to maintain populations even at sites with low LQ. The strongest segregation in species co-occurrence was detected at intermediate RQ levels, suggesting that communities are structured to the highest degree by a habitat/environmental gradient. From these results, we conclude that when restoring riverine habitats at the reach scale, restoration projects situated in intermediate RQ settings will likely be the most successful in enhancing the naturalness of local communities. With a careful choice of sites for reach-scale restoration in settings of intermediate RQ and a strategy that aims to expand areas of high RQ, the success of reach-scale restoration in promoting the
Directory of Open Access Journals (Sweden)
Jaromír Baštinec
2010-01-01
without the usual assumption that the parameters ,ℎ,, and ℎ of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.
Kammann, Ulrike; Brinkmann, Markus; Freese, Marko; Pohlmann, Jan-Dag; Stoffels, Sandra; Hollert, Henner; Hanel, Reinhold
2014-02-01
The stock of the European eel (Anguilla anguilla L.) continues to decline and has reached a new minimum in 2011. Poor health status of the spawners due to organic contaminants is one of the possible causes for this dramatic situation. Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous contaminants, which are rapidly metabolized in vertebrates. EROD (ethoxyresorufin-O-deethylase) and GST (glutathione-S-transferase) are two enzymes involved in PAH detoxification in fish. In this study, PAH metabolites as well as EROD and GST activity in a large, comprising dataset of more than 260 migratory and pre-migratory eels from five large German river basin districts were used to describe PAH exposure and its metabolism as possible indicators for the habitat quality for eels. Eel from the river Elbe appear to be moderately contaminated with PAH. Highest mean values of PAH metabolites were analysed in fish from the river Rhine. However, the results suggest that contaminants such as PAH are metabolized in the fish and may have contributed to EROD activity in eels caught from the Elbe estuary to 600 km upstream. Since the eel's onset of cessation of feeding is closely linked to maturation and migration, we propose bile pigments as new indicators contributing to identify the proportion of migratory eel, which is crucial information for eel management plans. We showed that PAH metabolites normalized to bile pigments as well as EROD could be used to describe the habitat quality and might be suitable parameters in search for suitable stocking habitats.
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Enrique Castillo
2016-01-01
Full Text Available We first show that monomial ratio equations are not only very common in Physics and Engineering, but the natural type of equations in many practical problems. More precisely, in the case of models involving scale variables if the used formulas are not of this type they are not physically valid. The consequence is that when estimating the model parameters we are faced with systems of monomial ratio equations that are nonlinear and difficult to solve. In this paper, we provide an original algorithm to obtain the unique solutions of systems of equations made of linear combinations of monomial ratios whose coefficient matrix has a proper null space with low dimension that permits solving the problem in a simple way. Finally, we illustrate the proposed methods by their application to two practical problems from the hydraulic and structural fields.
Exact solution of Schroedinger equation in the case of reduction to Riccati type of ODE
Ershkov, Sergey V
2011-01-01
Here is presented a new type of exact solution of Schroedinger equation in the case of it's reduction to Riccati type of ordinary differential equations. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of the particle wavefunction (which is known to be determining a proper quantum state of the particle). It means a possibility of sudden transformation or transmutation of quantum state of the particle (from one meaning of wavefunction to another), at definite moment of parametrical time. Besides, in the case of spherical symmetry of particle potential V in position space, as well as spherical symmetry of quantum system E total energy, such a solution is proved to be a multiplying of Bessel function (for radial component) & Legendre spherical function (for angle component), in spherical coordinate system.
Regularity for the porous medium equation with variable exponent: The singular case
Henriques, Eurica
We extend to the singular case the results of [E. Henriques, J.M. Urbano, Intrinsic scaling for PDEs with an exponential nonlinearity, Indiana Univ. Math. J. 55 (5) (2006) 1701-1721] concerning the regularity of weak solutions of the porous medium equation with variable exponent. The method of intrinsic scaling is used to show that local weak solutions are locally continuous.
Sustainability in a Differential Equations Course: A Case Study of Easter Island
Koss, Lorelei
2011-01-01
Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in a first-semester ordinary differential equations course. This article describes curricular materials for a semester-long case study…
Sustainability in a Differential Equations Course: A Case Study of Easter Island
Koss, Lorelei
2011-01-01
Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in a first-semester ordinary differential equations course. This article describes curricular materials for a semester-long case study…
Crawford, John R.; Garthwaite, Paul H.; Denham, Annie K.; Chelune, Gordon J.
2012-01-01
Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because…
DEFF Research Database (Denmark)
Karpman, V.I.; Shagalov, A.G.; Juul Rasmussen, J.
2002-01-01
The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...
Phillips, D. R.; Afnan, I. R.; Henry-Edwards, A. G.
2000-04-01
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to renormalize the amplitude and produce a finite solution to the integral equation for all energies. This can be done either algebraically or numerically. In the latter case dimensional regularization can be implemented by solving the integral equation in a lower number of dimensions, fixing the potential strength, and computing the phase shifts, while taking the limit as the number of dimensions approaches three. We demonstrate that these steps can be carried out in a numerically stable way, and show that the results thereby obtained agree with those found when the renormalization is performed algebraically to four significant figures.
Energy Technology Data Exchange (ETDEWEB)
Phillips, D. R. [Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States); Afnan, I. R. [Department of Physics, The Flinders University of South Australia, G.P.O. Box 2100, Adelaide 5001, (Australia); Henry-Edwards, A. G. [Department of Physics, The Flinders University of South Australia, G.P.O. Box 2100, Adelaide 5001, (Australia)
2000-04-01
Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to renormalize the amplitude and produce a finite solution to the integral equation for all energies. This can be done either algebraically or numerically. In the latter case dimensional regularization can be implemented by solving the integral equation in a lower number of dimensions, fixing the potential strength, and computing the phase shifts, while taking the limit as the number of dimensions approaches three. We demonstrate that these steps can be carried out in a numerically stable way, and show that the results thereby obtained agree with those found when the renormalization is performed algebraically to four significant figures. (c) 2000 The American Physical Society.
Directory of Open Access Journals (Sweden)
E. P. Kubyshkin
2015-01-01
Full Text Available We consider a differential-difference equation of second order of delay type, containing the delay of the function and its derivatives. Such equations occur in the modeling of electronic devices. The nature of the loss of the zero solution stability is studied. The possibility of stability loss related to the passing of two pairs of purely imaginary roots, that are in resonance 1:3, through an imaginary axis is shown. In this case bifurcating oscillatory solutions are studied. It is noted the existence of a chaotic attractor for which Lyapunov exponents and Lyapunov dimension are calculated. As an investigation techniques we use the theory of integral manifolds and normal forms method for nonlinear differential equations.
Dealing with Dependent Uncertainty in Modelling: A Comparative Study Case through the Airy Equation
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J.-C. Cortés
2013-01-01
Full Text Available The consideration of uncertainty in differential equations leads to the emergent area of random differential equations. Under this approach, inputs become random variables and/or stochastic processes. Often one assumes that inputs are independent, a hypothesis that simplifies the mathematical treatment although it could not be met in applications. In this paper, we analyse, through the Airy equation, the influence of statistical dependence of inputs on the output, computing its expectation and standard deviation by Fröbenius and Polynomial Chaos methods. The results are compared with Monte Carlo sampling. The analysis is conducted by the Airy equation since, as in the deterministic scenario its solutions are highly oscillatory, it is expected that differences will be better highlighted. To illustrate our study, and motivated by the ubiquity of Gaussian random variables in numerous practical problems, we assume that inputs follow a multivariate Gaussian distribution throughout the paper. The application of Fröbenius method to solve Airy equation is based on an extension of the method to the case where inputs are dependent. The numerical results show that the existence of statistical dependence among the inputs and its magnitude entails changes on the variability of the output.
Coates, Peter S.; Casazza, Michael L.; Ricca, Mark A.; Brussee, Brianne E.; Blomberg, Erik J.; Gustafson, K. Benjamin; Overton, Cory T.; Davis, Dawn M.; Niell, Lara E.; Espinosa, Shawn P.; Gardner, Scott C.; Delehanty, David J.
2016-01-01
Predictive species distributional models are a cornerstone of wildlife conservation planning. Constructing such models requires robust underpinning science that integrates formerly disparate data types to achieve effective species management. Greater sage-grouse Centrocercus urophasianus, hereafter “sage-grouse” populations are declining throughout sagebrush-steppe ecosystems in North America, particularly within the Great Basin, which heightens the need for novel management tools that maximize use of available information. Herein, we improve upon existing species distribution models by combining information about sage-grouse habitat quality, distribution, and abundance from multiple data sources. To measure habitat, we created spatially explicit maps depicting habitat selection indices (HSI) informed by > 35 500 independent telemetry locations from > 1600 sage-grouse collected over 15 years across much of the Great Basin. These indices were derived from models that accounted for selection at different spatial scales and seasons. A region-wide HSI was calculated using the HSI surfaces modelled for 12 independent subregions and then demarcated into distinct habitat quality classes. We also employed a novel index to describe landscape patterns of sage-grouse abundance and space use (AUI). The AUI is a probabilistic composite of: (i) breeding density patterns based on the spatial configuration of breeding leks and associated trends in male attendance; and (ii) year-round patterns of space use indexed by the decreasing probability of use with increasing distance to leks. The continuous AUI surface was then reclassified into two classes representing high and low/no use and abundance. Synthesis and applications. Using the example of sage-grouse, we demonstrate how the joint application of indices of habitat selection, abundance, and space use derived from multiple data sources yields a composite map that can guide effective allocation of management intensity across
Spin-weighted spheroidal equation in the case of s = 1
Institute of Scientific and Technical Information of China (English)
Sun Yue; Tian Gui-Hua; Dong Kun
2011-01-01
We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of supersymmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s = 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigenfunctions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.
Agent-Based vs. Equation-based Epidemiological Models:A Model Selection Case Study
Energy Technology Data Exchange (ETDEWEB)
Sukumar, Sreenivas R [ORNL; Nutaro, James J [ORNL
2012-01-01
This paper is motivated by the need to design model validation strategies for epidemiological disease-spread models. We consider both agent-based and equation-based models of pandemic disease spread and study the nuances and complexities one has to consider from the perspective of model validation. For this purpose, we instantiate an equation based model and an agent based model of the 1918 Spanish flu and we leverage data published in the literature for our case- study. We present our observations from the perspective of each implementation and discuss the application of model-selection criteria to compare the risk in choosing one modeling paradigm to another. We conclude with a discussion of our experience and document future ideas for a model validation framework.
Dimakis, Aristophanes
2012-01-01
We present a general result within the bidifferential calculus approach to integrable partial differential and difference equations, which can be regarded as a quite universal formulation of a vectorial binary Darboux transformation. This is then applied to the non-autonomous chiral model, a certain reduction of which is known to appear in the case of the D-dimensional vacuum Einstein equations with D-2 commuting Killing vector fields. A large class of exact solutions is obtained, and the aforementioned reduction is implemented. This results in an alternative to the well-known Belinski-Zakharov formalism. We recover relevant examples of space-times in dimensions four (Kerr-NUT, Tomimatsu-Sato) and five (single and double Myers-Perry, black saturn, bicycling black rings).
Roche, Dylan V; Cardilini, Adam P A; Lees, Daniel; Maguire, Grainne S; Dann, Peter; Sherman, Craig D H; Weston, Michael A
2016-06-15
Wildlife living in the suburbs faces the challenge of dealing with human presence and yard management (including the occurrence of pets) which vary at the scale of the house block. This study examined the influence of ecological factors (e.g. extent of grass and food availability) and anthropogenic factors (e.g. human activity and garden usage) on breeding site choice and reproductive success of the ground-nesting masked lapwing Vanellus miles on Phillip Island, Australia. Lapwings nested less frequently in residential properties (high levels of human usage) compared with vacant blocks and holiday houses. They were also more likely to breed on properties with high food availability and larger areas of grass. None of these variables influenced clutch size or the probability of eggs hatching, although larger clutches and higher hatching rates tended to be associated with more food. This study shows that, for an urban exploiting species, habitat quality is not homogenous at the scale of the house block, and that human activity is avoided by a species generally considered highly tolerant of people.
Directory of Open Access Journals (Sweden)
Harold Exton
1996-05-01
Full Text Available A special case of the biconfluent Heun equation which is not reducible to a form of a hypergeometric equation is solved by means of a Laplace transform. The solutions are double series which exhibit a type of orthogonality comparable in some respects to that of Fourier-Bessel type.
Institute of Scientific and Technical Information of China (English)
Yan-ping Chen; Yun-qing Huang
2001-01-01
Improved L2-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higherorder spaces. A second paper will present the analysis of a fully discrete scheme (Numer.Math. J. Chinese Univ. vol.9, no.2, 2000, 181-192).
Atkinson, S F; Johnson, D R; Venables, B J; Slye, J L; Kennedy, J R; Dyer, S D; Price, B B; Ciarlo, M; Stanton, K; Sanderson, H; Nielsen, A
2009-06-15
Surfactants are high production volume chemicals that are used in a wide assortment of "down-the-drain" consumer products. Wastewater treatment plants (WWTPs) generally remove 85 to more than 99% of all surfactants from influents, but residual concentrations are discharged into receiving waters via wastewater treatment plant effluents. The Trinity River that flows through the Dallas-Fort Worth metropolitan area, Texas, is an ideal study site for surfactants due to the high ratio of wastewater treatment plant effluent to river flow (>95%) during late summer months, providing an interesting scenario for surfactant loading into the environment. The objective of this project was to determine whether surfactant concentrations, expressed as toxic units, in-stream water quality, and aquatic habitat in the upper Trinity River could be predicted based on easily accessible watershed characteristics. Surface water and pore water samples were collected in late summer 2005 at 11 sites on the Trinity River in and around the Dallas-Fort Worth metropolitan area. Effluents of 4 major waste water treatment plants that discharge effluents into the Trinity River were also sampled. General chemistries and individual surfactant concentrations were determined, and total surfactant toxic units were calculated. GIS models of geospatial, anthropogenic factors (e.g., population density) and natural factors (e.g., soil organic matter) were collected and analyzed according to subwatersheds. Multiple regression analyses using the stepwise maximum R(2) improvement method were performed to develop prediction models of surfactant risk, water quality, and aquatic habitat (dependent variables) using the geospatial parameters (independent variables) that characterized the upper Trinity River watershed. We show that GIS modeling has the potential to be a reliable and inexpensive method of predicting water and habitat quality in the upper Trinity River watershed and perhaps other highly urbanized
An†§ efficient code to solve the Kepler equation. Elliptic case.
Raposo Pulido, V.; Peláez, J.
2017-01-01
A new approach for solving Kepler equation for elliptical orbits is developed in this paper. This new approach takes advantage of the very good behavior of the modified Newton-Raphson method when the initial seed is close to the looked for solution. To determine a good initial seed the eccentric anomaly domain [0, π] is discretized in several intervals and for each one of these intervals a fifth degree interpolating polynomial is introduced. The six coefficients of the polynomial are obtained by requiring six conditions at both ends of the corresponding interval. Thus the real function and the polynomial have equal values at both ends of the interval. Similarly relations are imposed for the two first derivatives. In the singular corner of the Kepler equation, M ≪ 1 and 1 - e ≪ 0 an asymptotic expansion is developed. In most of the cases, the seed generated leads to reach machine error accuracy with the modified Newton-Raphson method with no iterations or just one iteration. This approach improves the computational time compared with other methods currently in use.
Noutchegueme, N; Noutchegueme, Norbert; Tetsadjio, Mesmin Erick
2003-01-01
We prove, for the relativistic Boltzmann equation in the homogeneous case, on the Minkowski space-time, a global in time existence and uniqueness theorem. The method we develop extends to the cases of some curved space-times such as the flat Robertson-Walker space-time and some Bianchi type I space-times.
Malkov, Ewgenij A.; Poleshkin, Sergey O.; Kudryavtsev, Alexey N.; Shershnev, Anton A.
2016-10-01
The paper presents the software implementation of the Boltzmann equation solver based on the deterministic finite-difference method. The solver allows one to carry out parallel computations of rarefied flows on a hybrid computational cluster with arbitrary number of central processor units (CPU) and graphical processor units (GPU). Employment of GPUs leads to a significant acceleration of the computations, which enables us to simulate two-dimensional flows with high resolution in a reasonable time. The developed numerical code was validated by comparing the obtained solutions with the Direct Simulation Monte Carlo (DSMC) data. For this purpose the supersonic flow past a flat plate at zero angle of attack is used as a test case.
Catry, Inês; Franco, Aldina M. A.; Rocha, Pedro; Alcazar, Rita; Reis, Susana; Cordeiro, Ana; Ventim, Rita; Teodósio, Joaquim; Moreira, Francisco
2013-01-01
Among birds, breeding numbers are mainly limited by two resources of major importance: food supply and nest-site availability. Here, we investigated how differences in land-use and nest-site availability affected the foraging behaviour, breeding success and population trends of the colonial cavity-dependent lesser kestrel Falco naumanni inhabiting two protected areas. Both areas were provided with artificial nests to increase nest-site availability. The first area is a pseudo-steppe characterized by traditional extensive cereal cultivation, whereas the second area is a previous agricultural zone now abandoned or replaced by forested areas. In both areas, lesser kestrels selected extensive agricultural habitats, such as fallows and cereal fields, and avoided scrubland and forests. In the second area, tracked birds from one colony travelled significantly farther distances (6.2 km ±1.7 vs. 1.8 km ±0.4 and 1.9 km ±0.6) and had significant larger foraging-ranges (144 km2 vs. 18.8 and 14.8 km2) when compared to the birds of two colonies in the extensive agricultural area. Longer foraging trips were reflected in lower chick feeding rates, lower fledging success and reduced chick fitness. Availability and occupation of artificial nests was high in both areas but population followed opposite trends, with a positive increment recorded exclusively in the first area with a large proportion of agricultural areas. Progressive habitat loss around the studied colony in the second area (suitable habitat decreased from 32% in 1990 to only 7% in 2002) is likely the main driver of the recorded population decline and suggests that the effectiveness of bird species conservation based on nest-site provisioning is highly constrained by habitat quality in the surrounding areas. Therefore, the conservation of cavity-dependent species may be enhanced firstly by finding the best areas of remaining habitat and secondly by increasing the carrying capacity of high-quality habitat areas
Directory of Open Access Journals (Sweden)
Alexandre Marco da Silva
2007-08-01
Full Text Available Soil loss expectation and possible relationships among soil erosion, riparian vegetation and water quality were studied in the São José dos Dourados River basin, State of São Paulo, Brazil. Through Geographic Information System (GIS resources and technology, Soil Loss Expectation (SLE data obtained using the Universal Soil Loss Equation (USLE model were analyzed. For the whole catchment area and for the 30 m buffer strips of the streams of 22 randomly selected catchments, the predominant land use and habitat quality were studied. Owing mainly to the high soil erodibility, the river basin is highly susceptible to erosive processes. Habitat quality analyses revealed that the superficial water from the catchments is not chemically impacted but suffers physical damage. A high chemical purity is observed since there are no urban areas along the catchments. The water is physically poor because of high rates of sediment delivery and the almost nonexistence of riparian vegetation.Expectativa de perda de solo e possíveis relações entre erosão, vegetação ripária e qualidade da água foram estudados na bacia do rio São José dos Dourados (SP. Através de recursos de geoprocessamento e da Equação Universal de Perda de Solos, os dados sobre expectativa de perda de solo foram levantados. Para a área de drenagem total e a faixa tampão dos corpos d'água de 22 sub-bacias aleatoriamente selecionadas, analisou-se a cobertura do solo predominante e qualidade do habitat. Devido principalmente à alta erodibilidade do solo, a área estudada é altamente suscetível ao processo erosivo. As análises de qualidade da água revelaram que as águas superficiais das sub-bacias estão quimicamente não impactadas, mas fisicamente degradadas. A alta pureza química deve-se, possivelmente, à ausência de áreas urbanizadas ao longo das sub-bacias e as alterações nas características físicas são, possivelmente, decorrentes das altas taxas de transfer
Experiments with the WDVV equations for the gluino-condensate prepotential the cubic (two-cut) case
Itoyama, H
2003-01-01
We demonstrate by explicit calculation that the first two terms in the CIV-DV prepotential for the two-cut case satisfy the generalized WDVV equations, just as in all other known examples of hyperelliptic Seiberg-Witten models. The WDVV equations are non-trivial in this situation, provided the set of moduli is extended as compared to the Dijkgraaf-Vafa suggestion and includes also moduli, associated with the positions of the cuts (not only with their lengths). Expression for the extra modulus dictated by WDVV equation, however, appears different from a naive expectation implied by the Whitham theory. Moreover, for every value of the "quantum-deformation parameter" 1/g_3, we actually find an entire one-parameter family of solutions to the WDVV equations, of which the conventional prepotential is just a single point.
Expert Strategies in Solving Algebraic Structure Sense Problems: The Case of Quadratic Equations
Jupri, Al; Sispiyati, R.
2017-02-01
Structure sense, an intuitive ability towards symbolic expressions, including skills to interpret, to manipulate, and to perceive symbols in different roles, is considered as a key success in learning algebra. In this article, we report results of three phases of a case study on solving algebraic structure sense problems aiming at testing the appropriateness of algebraic structure sense tasks and at investigating expert strategies dealing with the tasks. First, we developed three tasks on quadratic equations based on the characteristics of structure sense for high school algebra. Next, we validated the tasks to seven experts. In the validation process, we requested these experts to solve each task using two different strategies. Finally, we analyzing expert solution strategies in the light of structure sense characteristics. We found that even if eventual expert strategies are in line with the characteristics of structure sense; some of their initial solution strategies used standard procedures which might pay less attention to algebraic structures. This finding suggests that experts have reconsidered their procedural work and have provided more efficient solution strategies. For further investigation, we consider to test the tasks to high school algebra students and to see whether they produce similar results as experts.
On the third order wave equation in Duffin-Kemmer-Petiau theory. Massive case
Markov, Yu A; Bondarenko, A I
2015-01-01
Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [Phys.Lett.B 244 (1988) 329] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called $q$-commutator ($q$ is a primitive cubic root of unity) and a new set of matrices $\\eta_{\\mu}$ instead of the original matrices $\\beta_{\\mu}$ of the DKP algebra are introduced. It is shown that in terms of these $\\eta_{\\mu}$ matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit $z \\rightarrow q$, where $z$ is some complex parameter of deformation entering into the definition of the $\\eta$-matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced th...
The Darboux-like transform and some integrable cases of the q-Riccati equation
Energy Technology Data Exchange (ETDEWEB)
Odzijewicz, Anatol; Ryzko, Alina [Institute of Theoretical Physics, University in Bialystok, Bialystok (Poland)]. E-mails: aodzijew@labfiz.uwb.edu.pl; alaryzko@alpha.uwb.edu.pl
2002-01-25
Using the q-version of the Darboux transform we obtain the general solution of q-difference Riccati equation from a special one by the action of one-parameter group. This allows us to construct the solutions for the large class of q-difference Riccati equations as well as q-difference Schroedinger equations, which are different from those obtained by the standard Darboux transform. (author)
Marschall, Gosia; Andrews, Paul
2015-01-01
In this article we present an exploratory case study of six Polish teachers' perspectives on the teaching of linear equations to grade six students. Data, which derived from semi-structured interviews, were analysed against an extant framework and yielded a number of commonly held beliefs about what teachers aimed to achieve and how they would…
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
New solutions for two integrable cases of a generalized fifth-order nonlinear equation
Wazwaz, Abdul-Majid
2015-05-01
Multiple-complexiton solutions for a new generalized fifth-order nonlinear integrable equation are constructed with the help of the Hirota's method and the simplified Hirota's method. By extending the real parameters into complex parameters, nonsingular complexiton solutions are obtained for two specific coefficients of the new generalized equation.
Gilliers, C.; Le Pape, O.; Désaunay, Y.; Morin, J.; Guérault, D.; Amara, R.
2006-08-01
Bio-indicators were measured on juvenile fish to assess the quality of eight coastal and estuarine nursery grounds in the Eastern English Channel and in the Bay of Biscay during 3 years. Growth (size and otolith daily increment width), body condition (morphometric index) and abundance of juvenile common soles were analysed together with xenobiotic concentrations (heavy metals and organic contaminants). Condition indices displayed important variations and did not allow relevant estimation of environmental quality. On the contrary, growth and density indicators showed good steadiness above years but varied among sites. In spite of difficulties of interpreting these indicators on such a meso-scale approach, analyses highlighted the estuaries of Seine and Gironde. In these nursery areas, the levels of contamination were especially high, and the combination of fish growth performances and density was significantly lower than in other sites. The combination of these variables appears to provide reliable indicators of habitat quality and anthropogenic pressure on nursery grounds, especially highlighting contaminated areas. Such indicators may thus contribute to improve assessment of environmental quality of essential fish habitats with the aim of a sustainable management of fisheries resources. A study at a different scale, from this meso-scale nursery approach with more precise analyses, on local habitats, will nevertheless be necessary to optimize the relevance of these indicators for the assessment of essential fish habitat quality.
How Cumbersome is a Tenth Order Polynomial? The Case of Gravitational Triple Lens Equation
Rhie, S H
2002-01-01
Three point mass gravitational lens equation is a two-dimensional vector equation that can be embedded in a tenth order analytic polynomial equation of one complex variable, and we can solve the one variable equation on the source trajectories using recipies for Fortran or $C$ (portable for $C$++ or $C_{jj}$) in Numerical Recipes, or using packages such as Mathemetica, Matlab, etc. This ready solvability renders fitting microlensing light curves including triple lenses a normal process, and such was done in a circumbinary planet fit for MACHO-97-BLG-41. Subsequently, there was a claim that converting the triple lens equation into the analytic equation was rather cumbersome, and the impressionable judgement has caused an effect of mysterious impedance around the perfectly tractable lens equation. There are judgements. Then, there is nature. We looked up for one of the quantities of highest precision measurements: electron $g$-factor correction $a_e \\equiv g/2-1$. The current best experimental values of $a_e$ a...
Asymptotic Limit of a Singularly Perturbed Stationary Diffusion Equation: The Case of a Limit Cycle
Ge, Hao
2010-01-01
A limit cycle for a nonlinear ordinary differential equation has a sustained, stationary oscillation in time; Any non-trivial stationary stochastic process also exhibits stationary oscillations in time, though with randomness and a stationary probability density. A reconciliation of these two views of oscillatory dynamics has been elusive, although it becomes increasingly important in the biochemical modeling of cellular dynamics, where stochatic models based on the chemical master equation and the deterministic model based on the Law of Mass Action are routinely compared. Using a singularly perturbed stationary diffusion equation as a model for the chemical master equation with sufficiently large volume, $\\epsilon \\leftrightarrow 1/V$, we show that its stationary solution $u(\\vx)$ exhibits a clear separation of the exponentially and algebraic small contributions: $u(\\vx)=C_{\\epsilon}(\\vx) e^{-\\phi(\\vx)/\\epsilon}$, in which $\\phi(x)\\ge 0$ and $=0$ on the entire stable limit cycle. On the limit cycle, $C_0(\\vx...
Radiative transfer in plane-parallel media and Cauchy integral equations III. The finite case
Rutily, Bernard; Chevallier, Loïc
2006-01-01
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical scheme where a Cauchy integral equation is reduced to a couple of Fredholm integral equations. It is expressed in terms of two auxiliary functions $\\zeta_+$ and $\\zeta_-$ we introduce in this paper. These functions show remarkable analytical properties in the complex plane. They satisfy a simple algebraic relation which generalizes the factorization relation of semi-infinite media. They are regular in the domain of the Fredholm integral equations they satisfy, and thus can be computed accurately. As an illustration, the X- and Y-functions are calculated in the whole complex plane, together with the extension in this plane of the so-called Sobouti's functions.
Asinari, P.
2011-03-01
Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).
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Luiz Fernando Novack
2014-12-01
Full Text Available This study analyzed classical and developed novel mathematical models to predict body fat percentage (%BF in professional soccer players from the South Brazilian region using skinfold thicknesses measurement. Skinfolds of thirty one male professional soccer players (age of 21.48 ± 3.38 years, body mass of 79.05 ± 9.48 kg and height of 181.97 ± 8.11 cm were introduced into eight mathematical models from the literature for the prediction of %BF; these results were then compared to Dual-energy X-ray Absorptiometry (DXA. The classical equations were able to account from 65% to 79% of the variation of %BF in DXA. Statistical differences between most of the classical equations (seven of the eight classic equations and DXA were found, rendering their widespread use in this population useless. We developed three new equations for prediction of %BF with skinfolds from: axils, abdomen, thighs and calves. Theses equations accounted for 86.5% of the variation in %BF obtained with DXA.
Time-Domain Volume Integral Equation for TM-Case Scattering from Nonlinear Penetrable Objects
Institute of Scientific and Technical Information of China (English)
WANG Jianguo; Eric Michielssen
2001-01-01
This paper presents the time-domainvolume integral equation (TDVIE) method to analyzescattering from nonlinear penetrable objects, whichare illuminated by the transverse magnetic (TM) in-cident pulse. The time-domain volume integral equa-tion is formulated in terms of two-dimensional (2D)Green's function, and solved by using the march-on-in time (MOT) technique. Some numerical results aregiven to validate this method, and comparisons aremade with the results obtained by using the finite-difference time-domain (FDTD) method.
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Pigong Han
2012-01-01
Full Text Available The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: \\[i\\partial_t u = -\\Delta u -|u|^{\\frac{4}{N-2}}u,\\quad (x,0=u_0 \\in H^1 (\\mathbb{R}^N,\\quad N\\geq 3.\\] Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006, 645–675].
From Ordinary Differential Equations to Structural Causal Models: the deterministic case
Mooij, J.M.; Janzing, D.; Schölkopf, B.; Nicholson, A.; Smyth, P.
2013-01-01
We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept of causality as expressed within the framework of Structura
Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper studied spherical pulses of solutions of the system of semilinear wave equations with the pulses focusing at a point in three space variables. It is shown that there is no nonlinear effect at leading terms of pulses, when the initial data is subcritical.
O'Sullivan, N.; O'Dwyer, B.
2009-01-01
Purpose - The purpose of this paper is to present an in-depth, context rich, and stakeholder-focused perspective on the legitimation dynamics surrounding the initiation and evolution of one of the key financial sector environmental and social responsibility initiatives in recent years, the Equator P
O'Sullivan, N.A.
2010-01-01
In June 2003, the Equator Principles (EP) were launched by ten international commercial banks. The EP were designed as a set of voluntary environmental and social risk management guidelines for project finance. Whilst lauded as a revolutionary initiative by the financial sector, the Principles were
O'Sullivan, N.A.
2010-01-01
In June 2003, the Equator Principles (EP) were launched by ten international commercial banks. The EP were designed as a set of voluntary environmental and social risk management guidelines for project finance. Whilst lauded as a revolutionary initiative by the financial sector, the Principles were
Telegraph equations for the case of a waveguide with moving boundary
Baryshevsky, V G
2016-01-01
Telegraph equation describing the compression of electromagnetic waves in a waveguide (resonator) with moving boundary are derived. It is shown that the character of oscillations of the compressed electromagnetic field depends on the parameters of the resonator, and under certain conditions, the oscillations of voltage (current) yield the exponential growth, leading to a noticeable change in the radiation losses.
Remarks on the Regularity Criteria of Three-Dimensional Navier-Stokes Equations in Margin Case
Institute of Scientific and Technical Information of China (English)
ZHANG Xingwei; ZHANG Wenliang; DONG Bo-Qing
2011-01-01
In the study of the regularity criteria for Leray weak solutions to threedimensional Navier-Stokes equations, two sufficient conditions such that the horizontal velocity ú satisfies ú∈L2(0,T;BMO(R3)) or ú ∈ L2/1＋r(0,T;Br∞,∞(R3)) for 0 ＜ r ＜ 1 are considered.
Path Integral and Solutions of the Constraint Equations The Case of Reducible Gauge Theories
Ferraro, R; Puchin, M
1994-01-01
It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace.
Dafermos, Mihalis; Shlapentokh-Rothman, Yakov
2014-01-01
This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a| << M or axisymmetry, arXiv:1010.5132], providing the complete proof of definitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal |a| < M case without symmetry assumptions. The essential ideas of the proof (together with explicit constructions of the most difficult multiplier currents) have been announced in our survey [M. Dafermos and I. Rodnianski, The black hole stability problem for linear scalar perturbations, in Proceedings of the 12th Marcel Grossmann Meeting on General Relativity, T. Damour et al (ed.), World Scientific, Singapore, 2011, pp. 132-189, arXiv:1010.5137]. Our proof appeals also to the quantitative mode-stability proven in [Y. Shlapentokh-Rothman, Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime, arXiv:1302.6902, to appear, Ann. Henri Poincar...
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Sukjung Hwang
2015-11-01
Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1
Asinari, Pietro
2010-01-01
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains extremely challenging from the computational point of view, in particular by deterministic methods (free of stochastic noise). This work aims to improve a deterministic direct method recently proposed [V.V. Aristov, Kluwer Academic Publishers, 2001] for solving the HIBE with a generic collisional kernel and, in particular, for taking care of the late dynamics of the relaxation towards the equilibrium. Essentially (a) the original problem is reformulated in terms of particle kinetic energy (exact particle number and energy conservation during microscopic collisions) and (b) the computation of the relaxation rates is improved by the DVM-like correction, where DVM stands for Discrete Velocity Model (ensuring that the macroscopic conservation laws are exactly satisfied). Both ...
The heat equation source determination for the case of non-smooth boundary and initial conditions
Solovi’ev, V. V.; Tkachenko, D. S.
2017-01-01
An inverse problem of reconstructing the source of a special kind for parabolic equations in a bounded region with smooth boundary is considered. Solutions are sought in the Holder classes. We prove an uniqueness criterion for the solution and sufficient conditions of Fredholm property of the task at hand. As a consequence of the sufficient conditions for existence and uniqueness of solution of the inhomogeneous inverse problems are found.
The Difference Format of Landau-Lifshitz Equation in Two-dimensional Case
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Zhong Taiyong
2015-01-01
Full Text Available In this paper, the author considers a difference scheme of Laudau-Lifshitz equation (LL for short and modulus of unj which are constantly remaining equal to 1. Using this iteration format error which is ordered to t/2h2 , the author comes to a conclusion based on several initial simulations. According to some conditions, the author gives the numerical solution, the examples of exact solution and the error comparisons of the solutions.
The Blow-Up Rate for Strongly Perturbed Semilinear Wave Equations in the Conformal Case
Energy Technology Data Exchange (ETDEWEB)
Hamza, M. A., E-mail: ma.hamza@fst.rnu.tn; Saidi, O., E-mail: saidi.omar@hotmail.fr [Université de Tunis El Manar, Faculté des Sciences de Tunis, LR03ES04 Èquations aux dérivées partielles et applications (Tunisia)
2015-12-15
We consider in this work some class of strongly perturbed for the semilinear wave equation with conformal power nonlinearity. We obtain an optimal estimate for a radial blow-up solution and we have also obtained two less stronger estimates. These results are achieved in three-steps argument by the construction of a Lyapunov functional in similarity variables and the Pohozaev identity derived by multiplying (1.14) by y∂{sub y}w.
Gallo, Emanuel
2016-01-01
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. By construction, the model incorporates the back reaction due to gravitational radiation generated by the motion of the particle. Our approach differs from other constructions tackling the same kind of problem.
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Xiaohua Wang
2011-01-01
Full Text Available The Sauerbrey equation is a useful empirical model in material science to represent the dynamics of frequency change denoted by Δf in an area, denoted by A, of the electrode in terms of the increment of the mass, which is denoted by Δm, loaded on the surface of the crystal under a certain resonant frequency f0. For the purpose of studying Δf from the point of view of time series, we first propose two types of the modified representations of the Sauerbrey equation by taking time as an argument to represent Δf as a function expressed by x(t,f0,A,Δm, where t is time. Usually, Δf is studied experimentally for the performance evaluation of the tested quartz used in ammonia sensors. Its properties in time series, however, are rarely reported. This paper presents the fractal properties of Δf. We will show that Δf is long range dependent (LRD. Consequently, it is heavy tailed according to the Taqqu's theorem. The Hurst parameter (H of Δf approaches one, implying its strong long memory, providing a new explanation of the repeatability of the experiments and novel point of view of the dynamics of Δf relating to the Sauerbrey equation in material science.
Estimates for the Large Time Behavior of the Landau Equation in the Coulomb Case
Carrapatoso, Kleber; Desvillettes, Laurent; He, Lingbing
2017-05-01
This work deals with the large time behaviour of the spatially homogeneous Landau equation with Coulomb potential. Firstly, we obtain a bound from below of the entropy dissipation D( f) by weighted relative Fisher information of f with respect to the associated Maxwellian distribution, which leads to a variant of Cercignani's conjecture thanks to a logarithmic Sobolev inequality. Secondly, we prove the propagation of polynomial and stretched exponential moments with an at-most linearly growing in-time rate. As an application of these estimates, we show the convergence of any ( H- or weak) solution to the Landau equation with Coulomb potential to the associated Maxwellian equilibrium with an explicitly computable rate, assuming initial data with finite mass, energy, entropy and some higher L 1-moment. More precisely, if the initial data have some (large enough) polynomial L 1-moment, then we obtain an algebraic decay. If the initial data have a stretched exponential L 1-moment, then we recover a stretched exponential decay.
Galerkin boundary integral equation method for spontaneous rupture propagation problems: SH-case
Goto, Hiroyuki; Bielak, Jacobo
2008-03-01
We develop a Galerkin finite element boundary integral equation method (GaBIEM) for spontaneous rupture propagation problems for a planar fault embedded in a homogeneous full 2-D space. A 2-D antiplane rupture propagation problem, with a slip-weakening friction law, is simulated by the GaBIEM. This method allows one to eliminate the strong singularities from the integral representation of the traction, and to separate explicitly the expression for the traction into an instantaneous component; static and time-dependent components with weakly (logarithmic) singular kernels; and a dynamic component and a quasi-static component, with continuous, bounded, kernels. Simulated results throw light into the performance of the GaBIEM and highlight differences with respect to that of the traditional, collocation, boundary integral equation method (BIEM). Both methods converge with a power law with respect to grid size, with different exponents. There is no restriction on the CFL stability number for the GaBIEM since an implicit, unconditionally stable method is used for the time integration. The error of the approximation increases with the time step, as expected, and it can remain below that of the BIEM.
Shishkin, G. I.; Shishkina, L. P.
2009-05-01
The boundary value problem for the singularly perturbed reaction-diffusion parabolic equation in a ball in the case of spherical symmetry is considered. The derivatives with respect to the radial variable appearing in the equation are written in divergent form. The third kind boundary condition, which admits the Dirichlet and Neumann conditions, is specified on the boundary of the domain. The Laplace operator in the differential equation involves a perturbation parameter ɛ2, where ɛ takes arbitrary values in the half-open interval (0, 1]. When ɛ → 0, the solution of such a problem has a parabolic boundary layer in a neighborhood of the boundary. Using the integro-interpolational method and the condensing grid technique, conservative finite difference schemes on flux grids are constructed that converge ɛ-uniformly at a rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of the mesh points in the radial and time variables, respectively.
Energy Technology Data Exchange (ETDEWEB)
Anderson, Oscar A.
2006-08-06
The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain the second level. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope waveforms. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Energy Technology Data Exchange (ETDEWEB)
Anderson, O.A.
2007-01-31
The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed [Part. Accel. 52, 133 (1996)] how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain results of second-level accuracy. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope functions. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Students attitude towards calculus subject: A case-study using structural equation modeling
Awang, Noorehan; Hamid, Nur Nadiah Abd.
2015-10-01
This study was designed to assess the attitude of Bumiputera students towards mathematics. The instrument used to measure the attitude was Test of Mathematics Related Attitude (TOMRA). This test measures students' attitudes in four criteria: normality of mathematics (N), attitudes towards mathematics inquiry (I), adoption of mathematics attitude (A) and enjoyment of mathematics lessons (E). The target population of this study was all computer science and quantitative science students who enrolled in a Calculus subject at UiTM Negeri Sembilan. Confirmatory Factor Analysis was carried out and the inter-relationship among the four criteria was analyzed using Structural Equation Modeling. The students scored high in E, moderately in A and relatively low in N and I.
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Tenzin Doleck
2017-03-01
Full Text Available Although the last decade has witnessed social networking sites of varied flavors, Facebook’s user growth continues to balloon, and relatedly, Facebook remains popular among the college populace. While there has been a growing body of work on ascertaining antecedents of Facebook use among college students, Collège d'enseignement général et professionnel (CEGEP students’ acceptance of Facebook remains underexplored. The purpose of this study was to analyze CEGEP students’ acceptance of Facebook using the technology acceptance model (TAM. Structural equation modeling was conducted on data from a survey of 214 CEGEP students. We find that Facebook use is motivated by the core TAM constructs as well as the added factors of peer influence, perceived enjoyment, perceived self-efficacy, relative advantage, risk, and trust.
Parlongue, David
2010-01-01
We will give in this paper the proof of an integral breakdown criterion for Einstein vacuum equations. In a recent article of S.Klainerman and I.Rodnianski a new breakdown criterion was proved as a result of a sequence of articles involving new techniques. However, in this article, the authors mentioned that it was likely possible to prove a sharper result involving an integral condition instead of a pointwise one. This paper is concerned with giving the proof of this improvement. Moreover the proof of this breakdown criterion was written in the original article for a foliation of constant mean curvature, we will present it here for a maximal foliation which leads to some difficulties due to the non-compacity of the leaves of such a foliation and the use of weighted Sobolev norms.
Nakamura, Kouji
2010-01-01
We derived the second-order perturbations of the Einstein equations and the Klein-Gordon equation for a generic situation in terms of gauge-invariant variables. The consistency of all the equations is confirmed. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense. We also discuss the physical implication of these equations.
Existence of non-negative solutions for nonlinear equations in the semi-positone case
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Naji Yebari
2006-09-01
Full Text Available Using the fibring method we prove the existence of non-negative solution of the p-Laplacian boundary value problem $-Delta_pu=lambda f(u$, for any $lambda >0$ on any regular bounded domain of $mathbb{R}^N$, in the special case $f(t=t^q-1$.
Circular economy development phase research based on the IPAT equation: The case Shaanxi
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Fang Ying
2015-04-01
Full Text Available In recent years, the worsening of the quality of the air has urged more people to attach great importance to circular economy. Shaanxi, abundant in natural resources, maintained the GDP growth rate of 14.9% during the period of the twelfth five-year plan. However, the fast economic growth under the extensive traditional economic growth mode renders Shaanxi inadequate in resources supply and noticeably worse in ecological environment issues. With the method of the IPAT equation, this paper quantitatively analyzes the developmental stage and the developmental level of the circular economy of Shaanxi to cover the shortage of the previous studies having only been focused on the policy study and the practice mode. The result shows that Shaanxi is in the intermediate stage of circular economy and the advanced stage has an apparent advantage over the intermediate one by comparing their energy consumption and solid pollutant discharge. The development experience of Shaanxi, a typical province of China, has guidance and reference significance to China and other developing countries.
Alves, W de F; Mota, A S; Lima, R A A de; Bellezoni, R; Vasconcellos, A
2011-01-01
The composition of termite assemblages was analyzed in three caatinga sites of the Estação Ecológica do Seridó, located in the municipality of Serra Negra do Norte, in the state of Rio Grande do Norte, Brazil. These sites have been subjected to selective logging, and cleared for pasture and farming. A standardized sampling protocol for termite assemblages (30h/person/site) was conducted between September 2007 and February 2009. At each site we measured environmental variables, such as soil pH and organic matter, necromass stock, vegetation height, stem diameter at ankle height (DAH) and the largest and the smallest crown width. Ten species of termites, belonging to eight genera and three families, were found at the three experimental sites. Four feeding groups were sampled: wood-feeders, soil-feeders, wood-soil interface feeders and leaf-feeders. The wood-feeders were dominant in number of species and number of encounters at all sites. In general, the sites were not significantly different in relation to the environmental variables measured. The same pattern was observed for termite assemblages, where no significant differences in species richness, relative abundance and taxonomic and functional composition were observed between the three sites. The agreement between composition of assemblages and environmental variables reinforces the potential of termites as biological indicators of habitat quality.
Feldhaus, J.W.; Heppell, S.A.; Li, H.; Mesa, M.G.
2010-01-01
We examined tissue-specific levels of heat shock protein 70 (hsp70) and whole body lipid levels in juvenile redband trout (Oncorhynchus mykiss gairdneri) from the South Fork of the John Day River (SFJD), Oregon, with the goal of determining if these measures could be used as physiological indicators of thermal habitat quality for juvenile redband trout. Our objectives were to determine the hsp70 induction temperature in liver, fin, and white muscle tissue and characterize the relation between whole body lipids and hsp70 for fish in the SFJD. We found significant increases in hsp70 levels between 19 and 22??C in fin, liver, and white muscle tissue. Maximum hsp70 levels in liver, fin, and white muscle tissue occurred when mean weekly maximum temperatures (MWMT) exceeded 20-22??C. In general, the estimated hsp70 induction temperature for fin and white muscle tissue was higher than liver tissue. Whole body lipid levels began to decrease when MWMT exceeded 20. 4??C. There was a significant interaction between temperature and hsp70 in fin and white muscle tissue, but not liver tissue. Collectively, these results suggest that increased hsp70 levels in juvenile redband trout are symptomatic of thermal stress, and that energy storage capacity decreases with this stress. The possible decrease in growth potential and fitness for thermally stressed individuals emphasizes the physiological justification for thermal management criteria in salmon-bearing streams. ?? Springer Science+Business Media B.V. 2010.
Mathematical modelling with case studies a differential equations approach using Maple and Matlab
Barnes, B
2011-01-01
""The book is written in a very lucid manner, with numerous case studies and examples thoroughly discussed. The material is very well organized, generously illustrated, and delightfully presented. All chapters, except the first one, conclude with scores of nicely designed exercises that can be used for independent study. The book contains enough material to organize a new well-structured one-semester course or to complement the existing one with additional examples and problems and is highly recommended for either purpose""-Zentralblatt MATH, 1168""… The book can be useful for students of math
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Liudan Jiao
2016-09-01
Full Text Available The rapid urbanization process has brought problems to China, such as traffic congestion, air pollution, water pollution and resources scarcity. Sustainable urbanization is commonly appreciated as an effective way to promote the sustainable development. The proper understanding of the sustainable urbanization performance is critical to provide governments with support in making urban development strategies and policies for guiding the sustainable development. This paper utilizes the method of Structural equation modeling (SEM to establish an assessment model for measuring sustainable urbanization performance. Four unobserved endogenous variables, economic variable, social variable, environment variable and resource variable, and 21 observed endogenous variables comprise the SEM model. A case study of the 31 provinces in China demonstrates the validity of the SEM model and the analysis results indicated that the assessment model could help make more effective policies and strategies for improving urban sustainability by recognizing the statue of sustainable urbanization.
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Peng Wei
2016-01-01
Full Text Available Tight schedules, multifunctional scopes, and colossal sizes usually characterize transportation megaprojects as challenging tasks for completion. In order to address these situations, a schedule risk management method was developed in this paper based on the structural equation model. In the proposed method, risk identification, evaluation and response were arranged as a sequence, and the expert elicitation technique was adopted in order to quantify the schedule risk status. To demonstrate the applicability of the proposed model, a megaproject case in China, the Shanghai Hongqiao Integrated Transport Hub (SHITH, was chosen. Information within the expanded risk register was collected including the probability and consequence of risk events, the complexity of risk responsible owners, the reaction time, and the time lasting for risk countermeasures. Final risk control results showed that the method could not only address the schedule risks correlations effectively, but also maintained the simplicity for construction management practices.
Habitat quality and fish population
Tafesse Tirkaso, Wondmagegn; Gren, Ing-Marie
2016-01-01
Degradation of marine ecosystem due to, among others, eutrophication and climate change, has been of concern for sustainable fishery management worldwide, but studies on associated impacts on fish populations are rare. The purpose of this study is to estimate effects of nutrient loads, which cause eutrophication, on the perch population at the Swedish east coast. To this end, we use a modified Gordon-Schaefer logistic growth model for econometric estimation of perch population on the Swedish ...
Rijmen, Frank; Manalo, Jonathan R.; von Davier, Alina A.
2009-01-01
This article describes two methods for obtaining the standard errors of two commonly used population invariance measures of equating functions: the root mean square difference of the subpopulation equating functions from the overall equating function and the root expected mean square difference. The delta method relies on an analytical…
Vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow
Bardos, Claude; Wiedemann, Emil
2012-01-01
We show that for a certain family of initial data, there exist non-unique weak solutions to the 3D incompressible Euler equations satisfying the weak energy inequality, whereas the weak limit of every sequence of Leray-Hopf weak solutions for the Navier-Stokes equations, with the same initial data, and as the viscosity tends to zero, is uniquely determined and equals the shear flow solution of the Euler equations. This simple example suggests that, also in more general situations, the vanishing viscosity limit of the Navier-Stokes equations could serve as a uniqueness criterion for weak solutions of the Euler equations.
Li, Bingtuan; Bewick, Sharon; Barnard, Michael R; Fagan, William F
2016-07-01
We study an integro-difference equation model that describes the spatial dynamics of a species in an expanding or contracting habitat. We give conditions under which the species disperses to a region of poor quality where the species eventually becomes extinct. We show that when the species persists in the habitat, the rightward and leftward spreading speeds are determined by c, the speed at which the habitat quality increases or decreases in time, as well as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which are formulated in terms of the dispersal kernel and species growth rates in both directions. We demonstrate that in the case that the species grows everywhere in space, the rightward spreading speed is [Formula: see text] if c is relatively small and is [Formula: see text] if c is large, and the leftward spreading speed is one of [Formula: see text], [Formula: see text], or [Formula: see text]. We also show that it is possible for a solution to form a two-layer wave, with the propagation speeds of the two layers analytically determined.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
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N. N. Nefedov
2016-01-01
Full Text Available Parabolic singularly perturbed problems have been actively studied in recent years in connection with a large number of practical applications: chemical kinetics, synergetics, astrophysics, biology, and so on. In this work a singularly perturbed periodic problem for a parabolic reaction-diﬀusion equation is studied in the two-dimensional case. The case when there is an internal transition layer under unbalanced nonlinearity is considered. The internal layer is localised near the so called transitional curve. An asymptotic expansion of the solution is constructed and an asymptotics for the transitional curve is determined. The asymptotical expansion consists of a regular part, an interior layer part and a boundary part. In this work we focus on the interior layer part. In order to describe it in the neighborhood of the transition curve the local coordinate system is introduced and the stretched variables are used. To substantiate the asymptotics thus constructed, the asymptotic method of diﬀerential inequalities is used. The upper and lower solutions are constructed by suﬃciently complicated modiﬁcation of the asymptotic expansion of the solution. The Lyapunov asymptotical stability of the solution was proved by using the method of contracting barriers. This method is based on the asymptotic comparison principle and uses the upper and lower solutions which are exponentially tending to the solution to the problem. As a result, the solution is locally unique.The article is published in the authors’ wording.
Millar, C. I.; Smith, A. T.; Hik, D. S.
2009-12-01
Patterned-ground and related periglacial features such as rock-glaciers and fractured-rock talus are emblematic of cold and dry arctic environments. The freeze-thaw processes that cause these features were first systematically investigated in the pioneering work of Linc Washburn. Unusual internal and autonomous micro-climatic and hydrologic processes of these features, however, are only beginning to be understood. Such features occur also in temperate latitude mountains, often in surprising abundance in regions such as the Great Basin (NV, USA) and San Juan Mtns (CO, USA), where they occur as active as well as relict (neoglacial or Pleistocene) features. Rock-dwelling species of pikas (Ochotona) in temperate North American and Asian mountains and in North American high-latitudes have long been known for their preference for talus habitats. We are investigating geomorphic, climatic, and hydrologic attributes of these periglacial features for their role in habitat quality and thermal environment of pikas. PRISM-modeled and observed climatic conditions from a range of talus types for Ochotona princeps in California and the western Great Basin (USA) indicate that, 1) thermal conditions of intra-talus-matrix in summer are significantly colder than talus-surface temperatures and colder than adjacent slopes and forefield wetlands where pika forage; 2) near-talus-surface locations (where haypiles are situated) are warmer in winter than intra-talus-matrix temperatures; 3) high-quality wetland vegetation in talus forefields is promoted by year-round persistence of outlet springs, seeps, and streams characteristic of active taluses. The importance of snowpack to winter thermal conditions is highlighted from these observations, suggesting a greater sensitivity of habitat in dry temperate regions such as eastern California and Nevada USA to warming winter minimum temperatures than in regions or elevations where snowpacks are more persistent. In regions where warming air
Povstenko, Y. Z.
2010-11-01
In the case of time-fractional diffusion-wave equation considered in the spatial domain -∞Mainardi [F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals 7 (1996) 1461-1477]. In the present paper, we supplement Mainardi’s results with additional numerical calculations illustrating the behavior of the solution and solve the corresponding problems for axisymmetric and central symmetric cases. The obtained results show an unusual behavior of solutions.
Institute of Scientific and Technical Information of China (English)
ZONG Hong-Shi; SUN Wei-Min; PING Jia-Lun; L(U) Xiao-Fu; WANG Fan
2005-01-01
@@ It is shown on general ground that there exist two qualitatively distinct solutions of the Dyson-Schwinger equation for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the "NambuGoldstone" phase and the other one corresponds to the "Wigner" phase in the chiral limit.
Fabra, M. Eugenia; Camison, Cesar
2009-01-01
Empirical literature has traditionally analyzed the effect of education on job satisfaction with single-equation models that ignore interrelationships between theoretical explanatory variables. Their results are somewhat inconclusive. We propose estimating a structural equation model to obtain both the direct effects and the set of indirect…
Gicquaud, Romain
2014-01-01
We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced by Dahl, Humbert and the first author. We focus on solutions over compact 3-manifolds admitting a $\\bS^1$-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.
Zyskin, M
1995-01-01
We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field O(k) and the regularization .
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
Zhang, Jiwei; Xu, Zhenli; Wu, Xiaonan
2009-04-01
This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and accurate LABCs on the artificial boundaries. In the corners, we use the (1,1)-Padé approximation to the kinetic term and also unite it with the nonlinear term to give some local corner boundary conditions. Numerical tests are given to verify the stable and tractable advantages of the method.
Use of Identification Equations for a Model of the Black-Box Type in the Case of its Instability
Moshinskii, A. I.; Markova, A. V.; Rubtsova, L. N.; Sorokin, V. V.; Ganin, P. G.
2016-11-01
A chemical-engineering system represented in the form of a black box with an input and an output is considered. The heat and mass transfer in this system was defined with the use of ordinary differential equations with constant coefficients of definite order. A method of use of "unstable" equations for the description of practical problems is proposed. The term instability was taken to mean that a differential operator has eigenvalues with a positive real part. The coefficients of an equation were determined on the basis of an analysis of the curve of response of the system to a disturbance in the form of a step. A concrete example of realization of the algorithm proposed is considered.
Di Francesco, Romolo
2013-01-01
Terzaghi's one-dimensional consolidation equation simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for example, when foundation are laid and start carrying the weight of the structure. Its application is traditionally based on Taylor's solution that approximates experimental results by introducing non-theoretical variables that, however, contradict the actual behaviou of soils. After careful examination of the theoretical and experimental aspects connected with consolidation, the proposal of this research is a solution consisting in a non-linear equation that can be considered correct as it meets both mathematical and experimental requirements. The solution proposed is extended to include differential equations relating to two/three dimensional consolidation by adopting a transversally isotropic model more consistent with the inner structure of soils. Finally, this essay is complete with application examples that give more reliable results than the traditional solut...
Kofroň, David
2016-01-01
We present the separation of the Teukolsky master equation for the test field of arbitrary spin on the background of the rotating C-metric. We also summarize and simplify some known results about Debye potentials of these fields on type D background. The equation for the Debye potential is also separated. Solving for the Debye potential of the electromagnetic field we show that on the extremely rotating C-metric no magnetic field can penetrate through the outer black hole horizon --- we thus recover the Meissner effect for the C-metric.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if \\emph{the absorption is small enough}, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
Dratman, Ezequiel
2011-01-01
We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if the absorption is large enough, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the "continuous" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the number of nodes involved in the discretization and the logarithm of the number of digits of approximation required.
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U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Institute of Scientific and Technical Information of China (English)
DUAN Huoyuan; LIANG Guoping
2001-01-01
Following Part I., we study the stabilized finite element method for the incom pressible Navier-Stokes equations. It is shown that this new methodology is stable and has an optimal error estimates for all mesh Peclet number, allowing any combination of velocity and pressure interpolation.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
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A. A. Makarova
2014-01-01
Full Text Available Sweeping scanning scheme of a hot gas in the task of infrared tomography is formulated. Two diagnosis regimes are used: the active one (ON – with included source and the passive one (OFF – without it. Two integral equations are deduced concerning the absorption coefficient k and the Planck function B of a medium (by which it is possible to calculate the temperature profile of a medium T.
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Julio Alfonso Piña López
2016-09-01
Full Text Available In this article, a research paper is analysed, which was justified based on the theory of developmental psychopathology, the protective factors, self-regulation, resilience, and quality of life among individuals who lived with type 2 diabetes and hypertension. Structural equation modelling (SEM was used for the data analysis. Although the authors conclude that the data are adequate to the theory tested, they commit errors of logic, concept, methodology and interpretation which, taken together, demonstrate a flagrant rupture between the theory and the data.
Arisawa, M
2010-01-01
A comparison principle for the integro-differential equation with the L{\\'e}vy operator corresponding to the spacial depending jump process is presented in this paper. The jump $\\beta(x,z)$ at a point $x$ and the L{\\'e}vy measure $dq(z)$ satisfy conditions given independently for each of them, which is a major difference from other works. Moreover, a useful form of the viscosity solution is presented, which is equivalent to more "classical" definitions, and is used to prove the comparison principle easily.
Cheng, Xing; Miao, Changxing; Zhao, Lifeng
2016-09-01
We consider the Cauchy problem for the nonlinear Schrödinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in H1 (Rd) and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in H1 (Rd) below the threshold for radial data when d ≤ 4.
Parand, K.; Rad, J. A.; Ahmadi, M.
2016-09-01
Natural convective heat transfer in porous media which is of importance in the design of canisters for nuclear waste disposal has received considerable attention during the past few decades. This paper presents a comparison between two different analytical and numerical methods, i.e. pseudospectral and Adomian decomposition methods. The pseudospectral approach makes use of the orthogonal rational Jacobi functions; this method reduces the solution of the problem to a solution of a system of algebraic equations. Numerical results are compared with each other, showing that the pseudospectral method leads to more accurate results and is applicable on similar problems.
Vitali, P; Tettamanti, M; Abutalebi, J; Ansaldo, A-I; Perani, D; Cappa, S F; Joanette, Y
2010-04-01
Structural Equation Modelling analysis of three longitudinal er-fMRI sessions was used to test the impact of phonological training and of the generalization process on the pattern of brain connectivity during overt picture naming in two chronic anomic patients. Phonological training yielded a positive effect on the trained material. Six months after the training, a generalization of the positive impact on the untrained items was also observed. Connectivity analysis showed that training and generalization effects shared paralleled cortical patterns of functional integration. These findings may represent the neurophysiological correlate of the training-induced cognitive strategies for the compensation of anomia.
Gili, Juan Antonio; Poletta, Fernando Adrián; Campaña, Hebe; Comas, Belén; Pawluk, Mariela; Rittler, Monica; López-Camelo, Jorge Santiago
2013-09-01
Background : There is disagreement about the association between cleft lip with or without cleft palate and multigravidity, which could be explained by differences of adjusting for maternal age, Amerindian ancestry, and socioeconomic status. Objective : The aim was to evaluate gravidity 4+ (four or more gestations) as a risk factor for cleft lip with or without cleft palate in South America. Design : We used a matched (1:1) case-control study with structural equation modeling for related causes. Data were obtained from 1,371,575 consecutive newborn infants weighing ≥500 g who were born in the hospitals of the Estudio Colaborativo Latinoamericano de Malformaciones Congénitas (ECLAMC) network between 1982 and 1999. There were a total of 1,271 cases with cleft lip with or without cleft palate (excluding midline and atypical cleft lip with or without cleft palate). A total of 1,227 case-control pairs were obtained, matched by maternal age, newborn gender, and year and place of birth. Potential confounders and intermediary variables were analyzed with structural equation modeling. Results : The crude risk of gravidity 4+ was 1.41 and the 95% confidence interval was 1.14 to 1.61. When applying structural equation modeling, the effect of multigravidity on the risk of cleft lip with or without cleft palate was 1.22 and the 95% confidence interval was 0.91 to 1.39. Conclusions : Multigravid mothers (more than four gestations) showed no greater risk of bearing children who had cleft lip with or without cleft palate than mothers with two or three births. Therefore, the often observed and reported association between multigravidity and oral clefts likely reflects the effect of other risk factors related to low socioeconomic status in South American populations.
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Camille Gilliers
2006-06-01
Full Text Available Indicators of growth and condition were used to compare the habitat quality of nurseries of juvenile sole (Solea solea L. in the Bay of Biscay, based on one survey in 2000. The four biological indicators are poorly correlated with each other, suggesting that no single measure may give an adequate description of fish health and of its habitat’s quality. Growth indicators showed significant differences between northern and southern areas. Juveniles from the two southernmost nurseries, the Gironde estuary and the Pertuis Antioche, displayed significant lower otolith increment widths and mean sizes. These differences were inversely related to water temperature and unrelated to genetic or age differences, and are unlikely to be due to limiting trophic conditions in the nurseries. Hence, they may be considered in terms of differences in habitat quality and potential anthropogenic impacts. Condition indices do not show this north-south pattern but highlight low condition values in the Pertuis Antioche. Short-term and fluctuating biochemical indicators such as RNA/DNA ratios appeared to be unreliable over a long-term study, while morphometric indices seemed to be relevant, complementary indicators as they integrate the whole juvenile life-history of sole in the nurseries. The growth and condition indices of juveniles in September 2000 from nursery grounds exposed to the Erika oil spill in December 1999 were relatively high. These results lead us to suggest that there was no obvious impact of this event on the health of juvenile sole and on the quality of the exposed nursery grounds a few months after the event.
Benard, P; Vivoda, J; Smolikova, P; Benard, Pierre; Laprise, Rene; Vivoda, Jozef; Smolikova, Petra
2003-01-01
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of thermal and baric residual terms (metric residual terms linked to the orography are not considered here). It is shown that conversely to what occurs with Hydrostatic Primitive Equations, the choice of the prognostic variables used to solve the system in time is of primary importance for the robustness with Euler Equations. For an optimal choice of prognostic variables, unconditionnally stable schemes can be obtained (with respect to the length of the time-step), but only for a smaller range of reference states than in the case of Hydrostatic Primitive Equations. This study also indicates that: (i) vertical coordinates based on geometrical height and on mass behave similarly in terms of stability for the problems examined here, and (ii) hybrid coordinates induce an intrinsic inst...
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
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Seid Mehdi Veiseh
2014-06-01
Full Text Available Psychological empowerment refers to the process of increase of internal motivation proportional to the performance of delivered duties, including recognition aspects such as being affective, worthiness, meaningfulness and right of choice. This study is Objective to investigate the relationship between psychological empowerment of the devotees and the variables work life quality, organizational justice, social support and social health. Methodology research: This is a descriptive – correlation study in which the structural equation modeling is used. The populations include all devotees of Ilam who were selected by use of Cochrane's formula. From the results, it became clear that psychological empowerment of the devotees is directly affected by the factors such as social health, social support, work life quality and organizational justice. Moreover, the variable work life quality has more influence on the psychological empowerment of the devotees.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Ravangard, Ramin; Yasami, Shamim; Shokrpour, Nasrin; Sajjadnia, Zahra; Farhadi, Payam
2015-01-01
Nurses are the largest group and an important part of the providers in the health care systems that who a key role in hospitals. Any defect and deficiency in their work can result in irreversible outcomes. This study aimed to determine the effect of supervisors' support and mediating factors on the job performance (JOBPER) of 400 nurses working in the teaching hospitals affiliated to Shiraz University of Medical Sciences, using structural equation modeling. The results showed that the supervisor's support had a significant negative effect on work-family conflict (t = -2.57) and a positive effect on organizational commitment (t = 4.03); Work-family conflict had a significant positive effect on job stress (t = 11.24) and a negative effect on organizational commitment (t = -3.35) and JOBPER (t = -2.29). Family-work conflict had a positive effect on job stress (t = 4.48) and a negative effect on organizational commitment (t = -2.54). Finally, job stress had a negative effect (t = -3.30), and organizational commitment showed a positive effect (t = 5.96) on the studied nurses' JOBPER. According to the results, supervisor's support could influence JOBPER through reducing work-family conflict and increasing organizational commitment. Therefore, to improve the nurses' JOBPER in the hospitals, some strategies are recommended.
Ravangard, Ramin; Karimi, Sakine; Farhadi, Payam; Sajjadnia, Zahra; Shokrpour, Nasrin
This study was undertaken to determine the effects of transformational leadership (TL) and mediating factors on organizational success (OS) from the administrative, financial, and support employees' perspective in teaching hospitals affiliated with Shiraz University of Medical Sciences using structural equation modeling. Three hundred administrative and financial employees were selected, using stratified sampling proportional to size and simple random sampling. Data were collected using 5 questionnaires and analyzed using SPSS 21.0 and Lisrel 8.5 through Pearson correlation coefficient and path analysis and confirmatory factor analysis methods. Results showed that TL had significant positive effects on the 3 mediating factors, including organizational culture (t = 15.31), organizational citizenship behavior (OCB) (t = 10.06), and social capital (t = 10.25). Also, the organizational culture (t = 2.26), OCB (t = 3.48), and social capital (t = 7.41) had significant positive effects on OS. According to the results, TL had an indirect effect on OS. Therefore, organizations can achieve more success by strengthening organizational culture, OCB, and social capital through using transformational leadership style. Therefore, in order to increase OS, the following recommendations are made: supporting and encouraging new ideas in the organization, promoting teamwork, strengthening intergroup and intragroup relationships, planning to strengthen and enrich the social and organizational culture, considering the promotion of social capital in the employee training, establishing a system to give rewards to the employees performing extra-role activities, providing a suitable environment for creative employees, and so on.
Vasileva, D.
2014-11-01
We investigate numerically the time evolution and stability of some known 1D soliton solutions of Boussinesq paradigm equation in 1D and in a 2D setting. A moving frame coordinate system helps us to keep the structures in the center of the computational domain, where the grid is much finer. The numerical experiments show that the stable 1D solutions preserve themselves for very large times. The corresponding solutions of the 2D problem for the same parameters and in narrow in the y-direction domains also preserve their shape for very large times. But the solutions of the 2D problem in wide in the y-direction domains seem to be not stable - the waves preserve their shape in relatively long intervals of time (depending on the parameters), but after that the waves lose their constant profile in the y-direction. The number of the maxima, which appear in the y-direction, strongly depends on the size of the domain in this direction, as well as on the problem's parameters.
Machfudiyanto, Rossy Armyn; Latief, Yusuf; Yogiswara, Yoko; Setiawan, R. Mahendra Fitra
2017-06-01
In facing the ASEAN Economic Community, the level of prevailing working accidents becomes one of the competitiveness factors among the companies. A construction industry is one of the industries prone to high level of accidents. Improving the safety record will not be completely effective unless the occupational safety and healthy culture is enhanced. The aim of this research was to develop a model and to conduct empirical investigation on the relationships among the dimensions of construction occupational safety culture. This research used the structural equation model as a means to examine the hypothesis of positive relationships between dimensions and objectives. The method used in this research was questionnaire survey which was distributed to the respondents from construction companies in a state-owned enterprise in Indonesia. Moreover, there were dimensions of occupational safety culture that was established, such as leadership, behavior, value, strategy, policy, process, employee, safety cost, and contract system. The results of this study indicated that all dimensions were significant and inter-related in forming the safety culture. The result of R2 yielded the safety performance was 54%, which means it was in low category and evaluation of policies on construction companies was required in addressing the issue of working accidents.
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Eka Arista Anggorowati
2015-05-01
Full Text Available Train system is one of the transportation modes with some special characteristics that make it becomes an effective and efficient transportation system to increase the service quality. Although the AC economy class of Majapahit Railway has been officially opened by the government, it has not been able to fulfill the people’s need. It is proved with the decrease of number of passenger, and the increase of critics related to the service quality. This research aims to analyze the principal elements and the effect of service qualities towards the customer’s loyalty. The research was conducted through survey on the Majapahit railway users consisting of 200 respondents. The used sampling technique was non probability sampling with purposive sampling method. It applied Structural Equation Modelling in which the previous test was the classical assumptions. Based on the calculations, it is indicated that the variables of service quality in customer satisfaction and loyalty is significant. The principal elements that influence satisfaction and loyalty are the operational schedule, the rolling stock condition, station’s comfort and security, safety, ticket price, and how the passengers enjoy the travelling. Adjusted R square of 0.8246 shows that 82 percent of consumer’ loyalty can give impact on service quality and customer satisfaction.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 曾庆存; 谢正辉
2004-01-01
An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.
Giraldi, Loïc
2014-01-01
In parametric equations---stochastic equations are a special case---one may want to approximate the solution such that it is easy to evaluate its dependence on the parameters. Interpolation in the parameters is an obvious possibility---in this context often labeled as a collocation method. In the frequent situation where one has a “solver” for a given fixed parameter value, this may be used “nonintrusively” as a black-box component to compute the solution at all the interpolation points independently of each other. By extension, all other methods, and especially simple Galerkin methods, which produce some kind of coupled system, are often classed as “intrusive.” We show how, for such “plain vanilla” Galerkin formulations, one may solve the coupled system in a nonintrusive way, and even the simplest form of block-solver has comparable efficiency. This opens at least two avenues for possible speed-up: first, to benefit from the coupling in the iteration by using more sophisticated block-solvers and, second, the possibility of nonintrusive successive rank-one updates as in the proper generalized decomposition (PGD).
Institute of Scientific and Technical Information of China (English)
黄虎; 丁平兴; 吕秀红
2001-01-01
The Hamiltonian formalism for surface waves and the mild-slope approximation were empolyed in handling the case of slowly varying three-dimensional currents and an uneven bottom, thus leading to an extended mild-slope equation. The bottom topography consists of two components: the slowly varying component whose horizontal length scale is longer than the surface wave length, and the fast varying component with the amplitude being smaller than that of the surface wave. The frequency of the fast varying depth component is, however, comparable to that of the surface waves. The extended mild- slope equation is more widely applicable and contains as special cases famous mild-slope equations below: the classical mild-slope equation of Berkhoff , Kirby' s mild-slope equation with current, and Dingemans' s mild-slope equation for rippled bed. The extended shallow water equations for ambient currents and rapidly varying topography are also obtained.
Quasi self-adjoint nonlinear wave equations
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Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
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Taha Aziz
2013-01-01
Full Text Available The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.
Coupled Nonlinear Schr\\"{o}dinger equation and Toda equation (the Root of Integrability)
Hisakado, Masato
1997-01-01
We consider the relation between the discrete coupled nonlinear Schr\\"{o}dinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\\"{o}dinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.
Reduction of infinite dimensional equations
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Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 曾庆存; 谢正辉
2004-01-01
The mixed finite element (MFE) methods for a shallow water equation system consisting of water dynamics equations, silt transport equation, and the equation of bottom topography change were derived. A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established. The existence and convergence of MFE solution of the discrete current velocity, elevation of the bottom topography, thickness of fluid column, and mass rate of sediment is demonstrated.
Porru, Stefano; Pavanello, Sofia; Carta, Angela; Arici, Cecilia; Simeone, Claudio; Izzotti, Alberto; Mastrangelo, Giuseppe
2014-01-01
DNA adducts are considered an integrate measure of carcinogen exposure and the initial step of carcinogenesis. Their levels in more accessible peripheral blood lymphocytes (PBLs) mirror that in the bladder tissue. In this study we explore whether the formation of PBL DNA adducts may be associated with bladder cancer (BC) risk, and how this relationship is modulated by genetic polymorphisms, environmental and occupational risk factors for BC. These complex interrelationships, including direct and indirect effects of each variable, were appraised using the structural equation modeling (SEM) analysis. Within the framework of a hospital-based case/control study, study population included 199 BC cases and 213 non-cancer controls, all Caucasian males. Data were collected on lifetime smoking, coffee drinking, dietary habits and lifetime occupation, with particular reference to exposure to aromatic amines (AAs) and polycyclic aromatic hydrocarbons (PAHs). No indirect paths were found, disproving hypothesis on association between PBL DNA adducts and BC risk. DNA adducts were instead positively associated with occupational cumulative exposure to AAs (p = 0.028), whereas XRCC1 Arg 399 (poccupational cumulative exposure to AAs with DNA adducts and BC risk, strengthening the central role of AAs in bladder carcinogenesis. However the lack of an association between PBL DNA adducts and BC risk advises that these snapshot measurements are not representative of relevant exposures. This would envisage new scenarios for biomarker discovery and new challenges such as repeated measurements at different critical life stages.
The Riccati Differential Equation and a Diffusion-Type Equation
Suazo, Erwin; Vega-Guzman, Jose M
2008-01-01
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equation with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary functions and certain integrals involving a characteristic function, which should be found as an analytic or numerical solution of the second order linear differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding nonhomogeneous equation is also found.
Nonlocal electrical diffusion equation
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 0numerical 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.
Directory of Open Access Journals (Sweden)
Stefano Porru
Full Text Available DNA adducts are considered an integrate measure of carcinogen exposure and the initial step of carcinogenesis. Their levels in more accessible peripheral blood lymphocytes (PBLs mirror that in the bladder tissue. In this study we explore whether the formation of PBL DNA adducts may be associated with bladder cancer (BC risk, and how this relationship is modulated by genetic polymorphisms, environmental and occupational risk factors for BC. These complex interrelationships, including direct and indirect effects of each variable, were appraised using the structural equation modeling (SEM analysis. Within the framework of a hospital-based case/control study, study population included 199 BC cases and 213 non-cancer controls, all Caucasian males. Data were collected on lifetime smoking, coffee drinking, dietary habits and lifetime occupation, with particular reference to exposure to aromatic amines (AAs and polycyclic aromatic hydrocarbons (PAHs. No indirect paths were found, disproving hypothesis on association between PBL DNA adducts and BC risk. DNA adducts were instead positively associated with occupational cumulative exposure to AAs (p = 0.028, whereas XRCC1 Arg 399 (p<0.006 was related with a decreased adduct levels, but with no impact on BC risk. Previous findings on increased BC risk by packyears (p<0.001, coffee (p<0.001, cumulative AAs exposure (p = 0.041 and MnSOD (p = 0.009 and a decreased risk by MPO (p<0.008 were also confirmed by SEM analysis. Our results for the first time make evident an association between occupational cumulative exposure to AAs with DNA adducts and BC risk, strengthening the central role of AAs in bladder carcinogenesis. However the lack of an association between PBL DNA adducts and BC risk advises that these snapshot measurements are not representative of relevant exposures. This would envisage new scenarios for biomarker discovery and new challenges such as repeated measurements at different
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Soliton states of Maxwell’s equations and nonlinear Schrodinger equation
Institute of Scientific and Technical Information of China (English)
陈翼强
1997-01-01
Similarities and fundamental differences between Maxwell’s equations and nonlinear Schrodinger equation in predicting a soliton evolution in a uniform nonlinear anisotropic medium are analyzed.It is found that in some cases,the soliton solutions to the nonlinear Schrodinger equation cannot be recovered from Maxwell’s equations while in others the soliton solutions to Maxwell’s equations are lost from the nonlinear Schrodinger equation through approximation,although there are cases where the soliton solutions to the two sets of the equations demonstrate only quantitative difference.The origin of the differences is also discussed.
Trzetrzelewski, Maciej
2016-11-01
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
Gerhardt, Claus
2016-01-01
In a recent paper we quantized the interaction of gravity with a Yang-Mills and Higgs field and obtained as a result a gravitational wave equation in a globally hyperbolic spacetime. Assuming that the Cauchy hypersurfaces are compact we proved a spectral resolution for the wave equation by applying the method of separation of variables. In this paper we extend the results to the case when the Cauchy hypersurfaces are non-compact by considering a Gelfand triplet and applying the nuclear spectral theorem.
Directory of Open Access Journals (Sweden)
Ramzi N. Nasser
2010-01-01
Full Text Available Problem statement: Mathematically little is known of college admission criteria as in school grade point average, admission test scores or rank in class and weighting of the criteria into a composite equation. Approach: This study presented a method to obtain weights on composite admission equation. The method uses an iterative procedure to build a prediction equation for an optimal weighted admission composite score. The three-predictor variables, high school average, entrance exam scores and rank in class, were regressed on college Grade Point Average (GPA. The weights for the composite equation were determined through regression coefficients and numerical approach that correlate the composite score with college GPA. Results: A set of composite equations were determined with the weights on each criteria in a composite equation. Conclusion: This study detailed a substantiated algorithm and based on an optimal composite score, comes out with an original and unique structured composite score equation for admissions, which can be used by admission officers at colleges and universities.
Conditions of the Classical Transmission Line Equations at High Frequency
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
New transmission line equations are deduced applying Maxwell's equations in this paper. The conditions of the classical transmission line equations have been discussed, which is important to solve the EM problems in high frequency case.
Homographic scheme for Riccati equation
Dubois, François
2011-01-01
In this paper we present a numerical scheme for the resolution of matrix Riccati equation, usualy used in control problems. The scheme is unconditionnaly stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.
Lattice Boltzmann solver of Rossler equation
Institute of Scientific and Technical Information of China (English)
GuangwuYAN; LiRUAN
2000-01-01
We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the diffusion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numerical results show the method can be used to simulate Rossler equation.
On a Equation in Finite Algebraically Structures
Valcan, Dumitru
2013-01-01
Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…
Stochastic Evolution Equations with Adapted Drift
Pronk, M.
2013-01-01
In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
function, apparently previously unknown and dubbed "Maccone distribution" by Paul Davies. DATA ENRICHMENT PRINCIPLE. It should be noticed that ANY positive number of random variables in the Statistical Drake Equation is compatible with the CLT. So, our generalization allows for many more factors to be added in the future as long as more refined scientific knowledge about each factor will be known to the scientists. This capability to make room for more future factors in the statistical Drake equation, we call the "Data Enrichment Principle," and we regard it as the key to more profound future results in the fields of Astrobiology and SETI. Finally, a practical example is given of how our statistical Drake equation works numerically. We work out in detail the case, where each of the seven random variables is uniformly distributed around its own mean value and has a given standard deviation. For instance, the number of stars in the Galaxy is assumed to be uniformly distributed around (say) 350 billions with a standard deviation of (say) 1 billion. Then, the resulting lognormal distribution of N is computed numerically by virtue of a MathCad file that the author has written. This shows that the mean value of the lognormal random variable N is actually of the same order as the classical N given by the ordinary Drake equation, as one might expect from a good statistical generalization.
Bilinear approach to the supersymmetric Gardner equation
Babalic, C. N.; Carstea, A. S.
2016-08-01
We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from the supersymmetric modified Korteweg-de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.
Some Aspects of Extended Kinetic Equation
Directory of Open Access Journals (Sweden)
Dilip Kumar
2015-09-01
Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.
All General Solutions of Post Equations
Institute of Scientific and Technical Information of China (English)
Dragi(c) BANKOVI(C)
2007-01-01
In a previous paper, we have described all reproductive general solutions of a Post equation, supposing that a general solution is known. In this paper we describe all general solutions of Post equation, supposing that a general solution of this equation is known (Theorem 6). As a special case we get the previous characterization of reproductive solutions and a similar result for Boolean equations (Theorem 9).
Covariant Hamilton equations for field theory
Energy Technology Data Exchange (ETDEWEB)
Giachetta, Giovanni [Department of Mathematics and Physics, University of Camerino, Camerino (Italy); Mangiarotti, Luigi [Department of Mathematics and Physics, University of Camerino, Camerino (Italy)]. E-mail: mangiaro@camserv.unicam.it; Sardanashvily, Gennadi [Department of Theoretical Physics, Physics Faculty, Moscow State University, Moscow (Russian Federation)]. E-mail: sard@grav.phys.msu.su
1999-09-24
We study the relations between the equations of first-order Lagrangian field theory on fibre bundles and the covariant Hamilton equations on the finite-dimensional polysymplectic phase space of covariant Hamiltonian field theory. If a Lagrangian is hyperregular, these equations are equivalent. A degenerate Lagrangian requires a set of associated Hamiltonian forms in order to exhaust all solutions of the Euler-Lagrange equations. The case of quadratic degenerate Lagrangians is studied in detail. (author)
Institute of Scientific and Technical Information of China (English)
Yao Lei; Wang Wenjun
2008-01-01
This is a continuation of the article (Comm. Partial Differential Equations 26 (2001) 965). In this article, the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force, fixed boundary condition, a general pressure and the density-dependent viscosity coefficient when the viscous gas con-nects to vacuum state with a jump in density. Precisely, the viscosity coefficient u is proportional to pθ and 0 < θ < 1/2, where p is the density, and the pressure P =P(p) is a general pressure. The global existence and the uniqueness of weak solution are proved.
Anisovich, A V; Markov, V N; Matveev, M A; Sarantsev, A V
2004-01-01
The Bethe--Salpeter equations for the quark-antiquark composite systems with different quark masses, such as $q\\bar s$ (with $q=u$,$d$), $q\\bar Q$ and $s \\bar Q$ (with $Q=c$,$b$), are written in terms of spectral integrals. For the mesons characterized by the mass $M$, spin $J$ and radial quantum number $n$, the equations are presented for the $(n,M^2)$-trajectories with fixed $J$. In the spectral-integral technique one can use the energy-dependent forces and get beyond instantaneous approximation. The mixing between states with different quark spin $S$ and angular momentum $L$ are also discussed.
Institute of Scientific and Technical Information of China (English)
高玲; 赵智杰; 张浩; 关学斌; 肖明
2012-01-01
通过市场价格法、机会成本法、影子工程法等常用生态服务价值评估方法计算出自然、农业和城市生态系统的生态服务基准价值,利用生境质量系数和生态区位系数对海口市1998,2004和2008年生态系统服务基准价值进行空间调整,得到3个时期海口市生态系统服务价值的空间分布情况.结果显示,单位面积服务价值除针叶林、红树林和橡胶林2008年较1998年减少外,其他生态系统呈增加趋势.3期生态系统服务价值分别为58.09,83.40和106.02亿元,比相应年份基准价值增加-2.82％,21.62％和30.59％;价值构成中农业生态系统服务价值所占比例最高,1998、2004和2008年分别占总价值的78.60％,80.07％和81.89％,自然和城市生态系统服务价值增加趋势相对缓慢.%This paper consulted basic ecosystem services value research of natural ecosystem, agricultural ecosystem and city ecosystem with market value method, opportunity cost approach and shadow engineering method, and then adjusted ecosystem services value of Haikou in 1998, 2004 and 2008 based on habitat quality and ecological location in space, obtained the spatial distribution of ecosystem services value. The result turned out that the adjusted unit area value of ecosystem functions in Haikou was increasing in the three periods, except for coniferous forests, mangrove wetlands and rubber plantation ecosystem decreased in 2008 compared to 1998. The total economic value of the ecosystem in the three periods was estimated as 58.09><108 RMB yuan, 83.40* 10s RMB yuan and 106.02xl08 RMB yuan respectively, increased by -2.82%, 21.62% and 30.59% compared to the corresponding benchmark value of total ecosystem services. The ecosystem services value of agricultural ecosystem dominated the whole ecosystem services value with the proportion of 78.60%, 80.07% and 81.89% in 1998, 2004 and 2008 respectively, the growth of natural ecosystem and city ecosystem slowed down
Energy Technology Data Exchange (ETDEWEB)
Goto, H. [Dept. of Mathematics and Physical Science, Graduate School of Science and Technology, Chiba Univ. (Japan); Natsume, Y. [Chiba Univ. (Japan). Dept. of Physics
1995-04-01
The estimation of Tc for the superconducting phase under the ultra-high magnetic feild is discussed on the basis of numerical calculation by the use of the expression of Eliashberg equations for strong coupling theory. The essenthial effect of the retardation of the interaction by phonons on making the gap is pointed out in comparison between 2 and 3 dimensinal systems. (orig.)
Samuel, Koji; Mulenga, H. M.; Angel, Mukuka
2016-01-01
This paper investigates the challenges faced by secondary school teachers and pupils in the teaching and learning of algebraic linear equations. The study involved 80 grade 11 pupils and 15 teachers of mathematics, drawn from 4 selected secondary schools in Mufulira district, Zambia in Central Africa. A descriptive survey method was employed to…
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Priimak, Dmitri
2014-01-01
We present finite differences numerical algorithm for solving 2D spatially homogeneous Boltzmann transport equation for semiconductor superlattices (SL) subject to time dependant electric field along SL axis and constant perpendicular magnetic field. Algorithm is implemented in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPUs. We compare performance and merits of one implementation versus another and discuss various methods of optimization.
Dembinski, S. T.; Wolniewicz, L.
1996-01-01
It is shown that the 1D Hamiltonian, which is a sum of operators which generate a finite nilpotent Lie algebra and depends explicitly on time existing closed form solutions of the time-dependent Schrödinger equation, cannot fulfil in general boundary and normalization conditions on a positive semi-axis. An explanation of the controversy surrounding the solutions of the quantum bouncer model, which appeared recently in the literature, is given.
Energy Technology Data Exchange (ETDEWEB)
Dembinski, S.T.; Wolniewicz, L. [Institute of Physics, Nicholas Copernicus University, Torun (Poland)
1996-01-21
It is shown that the 1 D Hamiltonian, which is a sum of operators which generate a finite nilpotent Lie algebra and depends explicitly on time existing closed form solutions of the time-dependent Schroedinger equation, cannot fulfil in general boundary and normalization conditions on a positive semi-axis. An explanation of the controversy surrounding the solutions of the quantum bouncer model, which appeared recently in the literature, is given. (author)
Energy Technology Data Exchange (ETDEWEB)
Simoens, S.; Michelot, C.; Ayrault, M. [Ecole Centrale de Lyon, 69 - Ecully (France). Lab. de Mecanique des Fluides et d`Acoustique; Sabelnikov, V. [Institut Vaktsin i Syvorotok, Moscow (Russian Federation)
1997-12-31
This note presents the results obtained from the theoretical analysis of the continuous stochastic mixing model (CSM model) and its discretized counterpart. The CSM model contains an unspecified coefficient {xi}. When {xi} is a random variable uniformly distributed in the range [0, 1], the CSM model is reduced to the Hsu and Chen (1991) model. Differential approximation of the concentration pdf equation corresponding to the discretized CSM model for homogeneous turbulence is derived. The analysis shows that the pdf shape tends to a Gaussian shape only in the case when {xi} is a deterministic variable. The model is then in agreement with experimental data (Jayesh and Warhaft, 1992). (author)
Universal solutions for the classical dynamical Yang-Baxter equation and the Maurer-Cartan equations
Energy Technology Data Exchange (ETDEWEB)
Petracci, Emanuela [Universite de Cergy-Pontoise, Departement de Mathematiques, UFR Sciences et Tecniques, 2 av. A Chauvin, 95302 Cergy-Pontoise Cedex (France)
2004-01-16
Using functional equations we solve the Maurer-Cartan equations and a special version of the classical dynamical Yang-Baxter equation (vCDYBE). Our solutions are valid for any Lie algebra over a base ring containing Q, and in the case of vCDYBE for any quadratic Lie algebra. Our method applies also to Lie superalgebras.
Sparse dynamics for partial differential equations.
Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley
2013-04-23
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.
Generalized Euclidean stars with equation of state
Abebe, G Z; Govinder, K S
2014-01-01
We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and find the Lie algebra corresponding to the optimal system of the symmetries. The symmetries in the optimal system allow us to transform the boundary condition to ordinary differential equations. The various cases for which the resulting systems of equations can be solved are identified. For each of these cases the boundary condition is integrated and the gravitational potentials are found explicitly. A particular group invariant solution produces a class of models which contains Euclidean stars as a special case. Our generalized model satisfies a linear equation of state in general. We thus establish a group theoretic basis for our generalized model with an equation of state. By considering a particular example we show that the weak, dominant and strong energy conditions are sa...
On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
Zygalakis, K. C.
2011-01-01
In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.
Directory of Open Access Journals (Sweden)
Hichem Dkhili
2013-01-01
Full Text Available This study aims to the behavior of management control; it is providing a model to the behavior of integration of social responsibility in the management control tools. This model was validated with 306 Tunisian companies in the industrial sector. Through a questionnaire, the data collected are processed using exploratory and confirmatory analysis by the methods of structural equations. The results revealed that the management control system in industrial Tunisia is facing economic responsibility. This is in response to emerging pressures of uncertainty related to the environment, and in enrolling a strategy of domination by cost. In addition, the management control system is designed as a guidance tool actions and behaviors.
Parand, K; Kazem, S; Rezaei, A R; 10.1016/j.cnsns.2010.07.011
2010-01-01
In this paper two common collocation approaches based on radial basis functions have been considered; one be computed through the integration process (IRBF) and one be computed through the differentiation process (DRBF). We investigated the two approaches on natural convection heat transfer equations embedded in porous medium which are of great importance in the design of canisters for nuclear wastes disposal. Numerical results show that the IRBF be performed much better than the common DRBF, and show good accuracy and high rate of convergence of IRBF process.
Complex Transforms for Systems of Fractional Differential Equations
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Rabha W. Ibrahim
2012-01-01
Full Text Available We provide a complex transform that maps the complex fractional differential equation into a system of fractional differential equations. The homogeneous and nonhomogeneous cases for equivalence equations are discussed and also nonequivalence equations are studied. Moreover, the existence and uniqueness of solutions are established and applications are illustrated.
Kinetic energy equations for the average-passage equation system
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.
Kinetic energy equations for the average-passage equation system
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.
Fredholm's equations for subwavelength focusing
Velázquez-Arcos, J. M.
2012-10-01
Subwavelength focusing (SF) is a very useful tool that can be carried out with the use of left hand materials for optics that involve the range of the microwaves. Many recent works have described a successful alternative procedure using time reversal methods. The advantage is that we do not need devices which require the complicated manufacture of left-hand materials; nevertheless, the theoretical mathematical bases are far from complete because before now we lacked an adequate easy-to-apply frame. In this work we give, for a broad class of discrete systems, a solid support for the theory of electromagnetic SF that can be applied to communications and nanotechnology. The very central procedure is the development of vector-matrix formalism (VMF) based on exploiting both the inhomogeneous and homogeneous Fredholm's integral equations in cases where the last two kinds of integral equations are applied to some selected discrete systems. To this end, we first establish a generalized Newmann series for the Fourier transform of the Green's function in the inhomogeneous Fredholm's equation of the problem. Then we go from an integral operator equation to a vector-matrix algebraic one. In this way we explore the inhomogeneous case and later on also the very interesting one about the homogeneous equation. Thus, on the one hand we can relate in a simple manner the arriving electromagnetic signals with those at their sources and we can use them to perform a SF. On the other hand, we analyze the homogeneous version of the equations, finding resonant solutions that have analogous properties to their counterparts in quantum mechanical scattering, that can be used in a proposed very powerful way in communications. Also we recover quantum mechanical operator relations that are identical for classical electromagnetics. Finally, we prove two theorems that formalize the relation between the theory of Fredholm's integral equations and the VMF we present here.
Global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations
Wan, Renhui; Chen, Jiecheng
2016-08-01
In this paper, we obtain global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations. Our works are consistent with the corresponding works by Elgindi-Widmayer (SIAM J Math Anal 47:4672-4684, 2015) in the special case {A=κ=1}. In addition, our result concerning the SQG equation can be regarded as the borderline case of the work by Cannone et al. (Proc Lond Math Soc 106:650-674, 2013).
Shen, Y.; Kevrekidis, P. G.; Sen, S.; Hoffman, A.
2014-08-01
Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.
Euler integral symmetries for a deformed Heun equation and symmetries of the Painlevé PVI equation
Kazakov, A. Ya.; Slavyanov, S. Yu.
2008-05-01
Euler integral transformations relate solutions of ordinary linear differential equations and generate integral representations of the solutions in a number of cases or relations between solutions of constrained equations (Euler symmetries) in some other cases. These relations lead to the corresponding symmetries of the monodromy matrices. We discuss Euler symmetries in the case of the simplest Fuchsian system that is equivalent to a deformed Heun equation, which is in turn related to the Painlevé PVI equation. The existence of integral symmetries of the deformed Heun equation leads to the corresponding symmetries of the PVI equation.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Isomorphism of Intransitive Linear Lie Equations
Directory of Open Access Journals (Sweden)
Jose Miguel Martins Veloso
2009-11-01
Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.
Solutions to the Optical Cascading Equations
Lafortune, S; Menyuk, C R
1998-01-01
Group theoretical methods are used to study the equations describing by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtained
The Nonlinear Convection—Reaction—Diffusion Equation
Institute of Scientific and Technical Information of China (English)
ShiminTANG; MaochangCUI; 等
1996-01-01
A nonlinear convection-reaction-diffusion equation is used as a model equation of the El Nino events.In this model,the effects of convection,turbulent diffusion,linear feed-back and nolinear radiation on the anomaly of Sea Surface Temperature(SST) are considered.In the case of constant convection,this equation has exact kink-like travelling wave solutions,which can be used to explain the history of an El Nino event.
Einstein equations with fluctuating volume
Dzhunushaliev, Vladimir; Quevedo, Hernando
2017-07-01
We develop a simple model to study classical fields on the background of a fluctuating spacetime volume. It is applied to formulate the stochastic Einstein equations with a perfect-fluid source. We investigate the particular case of a stochastic Friedmann-Lema\\^itre-Robertson-Walker cosmology, and show that the resulting field equations can lead to solutions which avoid the initial big bang singularity. By interpreting the fluctuations as the result of the presence of a quantum spacetime, we conclude that classical singularities can be avoided even within a stochastic model that include quantum effects in a very simple manner.
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Time-dependent exact solutions of the nonlinear Kompaneets equation
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H, E-mail: nib@bth.s [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)
2010-12-17
Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions. (fast track communication)
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
On the periodic "good" Boussinesq equation
Farah, Luiz Gustavo
2009-01-01
We study the well-posedness of the initial-value problem for the periodic nonlinear "good" Boussinesq equation. We prove that this equation is local well-posed for initial data in Sobolev spaces \\textit{$H^s(\\T)$} for $s>-1/4$, the same range of the real case obtained in Farah \\cite{LG4}.
ON ALGEBRICO-DIFFERENTIAL EQUATIONS-SOLVING
Institute of Scientific and Technical Information of China (English)
WU Wenjun(Wu Wen-tsun)
2004-01-01
The char-set method of polynomial equations-solving is naturally extended to the differential case which gives rise to an algorithmic method of solving arbitrary systems of algebrico-differential equations. As an illustration of the method, the Devil's Problem of Pommaret is solved in details.
Anekawati, Anik; Widjanarko Otok, Bambang; Purhadi; Sutikno
2017-06-01
Research in education often involves a latent variable. Statistical analysis technique that has the ability to analyze the pattern of relationship among latent variables as well as between latent variables and their indicators is Structural Equation Modeling (SEM). SEM partial least square (PLS) was developed as an alternative if these conditions are met: the theory that underlying the design of the model is weak, does not assume a certain scale measurement, the sample size should not be large and the data does not have the multivariate normal distribution. The purpose of this paper is to compare the results of modeling of the educational quality in high school level (SMA/MA) in Sumenep Regency with structural equation modeling approach partial least square with three schemes estimation of score factors. This paper is a result of explanatory research using secondary data from Sumenep Education Department and Badan Pusat Statistik (BPS) Sumenep which was data of Sumenep in the Figures and the District of Sumenep in the Figures for the year 2015. The unit of observation in this study were districts in Sumenep that consists of 18 districts on the mainland and 9 districts in the islands. There were two endogenous variables and one exogenous variable. Endogenous variables are the quality of education level of SMA/MA (Y1) and school infrastructure (Y2), whereas exogenous variable is socio-economic condition (X1). In this study, There is one improved model which represented by model from path scheme because this model is a consistent, all of its indicators are valid and its the value of R-square increased which is: Y1=0.651Y2. In this model, the quality of education influenced only by the school infrastructure (0.651). The socio-economic condition did not affect neither the school infrastructure nor the quality of education. If the school infrastructure increased 1 point, then the quality of education increased 0.651 point. The quality of education had an R2 of 0
On the Monotone Iterative Method for Set Valued Equation
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This paper deals with the monotone iterative method for set- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.
Nonrelativistic limit of solution of radial quasipotential equations
Energy Technology Data Exchange (ETDEWEB)
Minh, Vu.X.; Kadyshevskii, V.G.; Zhidkov, E.P.
1986-10-01
For the S-wave case, solutions of relativistic radial quasipotential equations that degenerate in the limit c ..-->.. infinity into the Jost solutions of the corresponding nonrelativistic radial Schrodinger equations are found.
Lie symmetries for equations in conformal geometries
Hansraj, S; Msomi, A M; Govinder, K S
2005-01-01
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.
Indian Academy of Sciences (India)
George F R Ellis
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowi......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
The example of modeling of logistics processes using differential equations
Ryczyński, Jacek
2017-07-01
The article describes the use of differential calculus to determine the form of differential equations family of curves. Form of differential equations obtained by eliminating the parameters of the equations describing the different family of curves. Elimination of the parameters has been performed several times by differentiation starting equations. Received appropriate form of differential equations for the case of family circles, family of curves of the second degree and the families of the logistic function.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
The periodic b-equation and Euler equations on the circle
Escher, J
2010-01-01
In this note we show that the periodic b-equation can only be realized as an Euler equation on the Lie group Diff(S^1) of all smooth and orientiation preserving diffeomorphisms on the cirlce if b=2, i.e. for the Camassa-Holm equation. In this case the inertia operator generating the metric on Diff(S^1) is given by A=1-d^2/dx^2. In contrast, the Degasperis-Procesi equation, for which b=3, is not an Euler equation on Diff(S^1) for any inertia operator. Our result generalizes a recent result of B. Kolev.
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
On implicit abstract neutral nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br [Universidade de São Paulo, Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto (Brazil); O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie [National University of Ireland, School of Mathematics, Statistics and Applied Mathematics (Ireland)
2016-04-15
In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Logarithmic diffusion and porous media equations: a unified description.
Pedron, I T; Mendes, R S; Buratta, T J; Malacarne, L C; Lenzi, E K
2005-09-01
In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a Lorentzian form, consequently this equation characterizes a superdiffusion like a Lévy kind. In addition an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension, is obtained. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.
Decoherent Histories and Hydrodynamic Equations
Halliwell, J J
1998-01-01
For a system consisting of a large collection of particles, a set of variables that will generally become effectively classical are the local densities (number, momentum, energy). That is, in the context of the decoherent histories approach to quantum theory, it is expected that histories of these variables will be approximately decoherent, and that their probabilites will be strongly peaked about hydrodynamic equations. This possibility is explored for the case of the diffusion of the number density of a dilute concentration of foreign particles in a fluid. It is shown that, for certain physically reasonable initial states, the probabilities for histories of number density are strongly peaked about evolution according to the diffusion equation. Decoherence of these histories is also shown for a class of initial states which includes non-trivial superpositions of number density. Histories of phase space densities are also discussed. The case of histories of number, momentum and energy density for more general...
Discrete and Continuous Linearizable Equations
Lafortune, S; Ramani, A
1998-01-01
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one and reduce the system to a single differential equation. This equation is of the form of those singled-out by Painlevé in his quest for integrable forms. In the discrete case, we extend previous results of ours showing that, again by elimination of variables, the general projective system can be written as a mapping for a single variable. We show that this mapping is a member of the family of multilinear systems (which is not integrable in general). The continuous limit of multilinear mappings is also discussed.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean
2015-02-03
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Static gravitational equations of general relativity and "the fifth force"
Das, A.
2015-10-01
Einstein's static field equations are investigated in various coordinate charts. After comparing Newtonian gravitational theory (in a curvilinear coordinate chart) with various charts of Einstein's static gravitational equations, the most appropriate choice of the coordinate chart for Einstein's static field equations is made. As a consequence, Einstein's equations imply the non-linear potential equation instead of the usual Poisson's equation of the Newtonian theory. Investigating the non-linear potential equation above in the spherically symmetric cases, the corresponding potentials yield scenarios comparable to "the fifth force". Next, static gravitational and electric fields generated by an incoherent charged dust are investigated. The corresponding non-linear potential equation is derived. Finally, the static Einstein-Maxwell-Klein-Gordon equations are explored and again, the corresponding non-linear potential equation is obtained. This potential resembles the static Higgs boson field.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Solving Operator Equation Based on Expansion Approach
Directory of Open Access Journals (Sweden)
A. Aminataei
2014-01-01
Full Text Available To date, researchers usually use spectral and pseudospectral methods for only numerical approximation of ordinary and partial differential equations and also based on polynomial basis. But the principal importance of this paper is to develop the expansion approach based on general basis functions (in particular case polynomial basis for solving general operator equations, wherein the particular cases of our development are integral equations, ordinary differential equations, difference equations, partial differential equations, and fractional differential equations. In other words, this paper presents the expansion approach for solving general operator equations in the form Lu+Nu=g(x,x∈Γ, with respect to boundary condition Bu=λ, where L, N and B are linear, nonlinear, and boundary operators, respectively, related to a suitable Hilbert space, Γ is the domain of approximation, λ is an arbitrary constant, and g(x∈L2(Γ is an arbitrary function. Also the other importance of this paper is to introduce the general version of pseudospectral method based on general interpolation problem. Finally some experiments show the accuracy of our development and the error analysis is presented in L2(Γ norm.
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Ramsey, Scott; Baty, Roy
2015-11-01
This work considers the group invariance properties of the inviscid compressible flow equations (Euler equations) under the assumptions of one-dimensional symmetry and a modified Tait equation of state (EOS) closure model. When written in terms of an adiabatic bulk modulus, a transformed version of these equations is found to be identical to that for an ideal gas EOS. As a result, the Lie group invariance structure of these equations - and their subsequent reduction to a lower-order system - is identical to the published results for the ideal gas case. Following the reduction of the Euler equations to a system of ordinary differential equations, a variety of elementary closed-form solutions are derived. These solutions are then used in conjunction with the Rankine-Hugoniot conditions to construct discontinuous shock wave and free surface solutions that are analogous to the classical Noh, Sedov, Guderley, and Hunter similarity solutions of the Euler equations for an ideal gas EOS. The versions of these problems for the modified Tait EOS are found to be semi-analytic in that a transcendental root extraction (and in some cases numerical integration of ordinary differential equations) enables solution of the relevant equations.
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Unconditionnally stable scheme for Riccati equation
Dubois, François; 10.1051/proc:2000003
2011-01-01
We present a numerical scheme for the resolution of matrix Riccati equation used in control problems. The scheme is unconditionnally stable and the solution is definite positive at each time step of the resolution. We prove the convergence in the scalar case and present several numerical experiments for classical test cases.
ON PROPERTIES OF q-DIFFERENCE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zheng Xiumin; Chen Zongxuan
2012-01-01
In this article,we consider some type of q-difference equations,which have meromorphic solutions with Borel exceptional zeros and poles.We also give a precise result in the finite order case and some further results in a particular case where qi =qi.
Adomian Method for Solving Fuzzy Fredholm-Volterra Integral Equations
Directory of Open Access Journals (Sweden)
M. Barkhordari Ahmadi
2013-09-01
Full Text Available In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.
Upper bounds on the solution of coupled algebraic riccati equation
Directory of Open Access Journals (Sweden)
Czornik Adam
2001-01-01
Full Text Available Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE and discrete time coupled algebraic Riccati equation (DCARE are developed as special cases of bounds for the unified coupled algebraic Riccati equation (UCARE. They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.
Approximate Solution Methods for Linear Stochastic Difference Equations. I. Moments
Roerdink, J.B.T.M.
1983-01-01
The cumulant expansion for linear stochastic differential equations is extended to the case of linear stochastic difference equations. We consider a vector difference equation, which contains a deterministic matrix A0 and a random perturbation matrix A1(t). The expansion proceeds in powers of ατc, w
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Directory of Open Access Journals (Sweden)
Guojun Shi
2000-01-01
Full Text Available In this paper we consider the Finite Signal-to-Noise ratio model for linear stochastic systems. It is assumed that the intensity of noise corrupting a signal is proportional to the variance of the signal. Hence, the signal-to-noise ratio of each sensor and actuator is finite – as opposed to the infinite signal-to-noise ratio assumed in LQG theory. Computational errors in the controller implementation are treated similarly. The objective is to design a state feedback control law such that the closed loop system is mean square asymptotically stable and the output variance is minimized. The main result is a controller which achieves its maximal accuracy with finite control gains – as opposed to the infinite controls required to achieve maximal accuracy in LQG controllers. Necessary and sufficient conditions for optimality are derived. An optimal control law which involves the positive definite solution of a Riccati-like equation is derived. An algorithm for solving the Riccati-like equation is given and its convergence is guaranteed if a solution exists.
Hazewinkel, M.
1995-01-01
Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
than the classical method in the solution of the aforementioned differential equation. Keywords: ... present a successful approximation of shell ... displacement function. .... only applicable to cylindrical shell subject to ..... (cos. 4. 4. 4. 3 β. + β. + β. -. = β. - β x x e ex. AL. xA w. Substituting equations (29); (30) and (31) into.
Nonlinear elliptic equations of the second order
Han, Qing
2016-01-01
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...
On the experimental foundations of the Maxwell equations
Haugan, Mark P
2000-01-01
We begin by reviewing the derivation of generalized Maxwell equations from anoperational definition of the electromagnetic field and the most basic notionsof what constitutes a dynamical field theory. These equations encompass thefamiliar Maxwell equations as a special case but, in other cases, can predictbirefringence, charge non-conservation, wave damping and other effects that thefamiliar Maxwell equations do not. It follows that observational constraints onsuch effects can restrict the dynamics of the electromagnetic field to be verylike the familiar Maxwellian dynamics, thus, providing an empirical foundationfor the Maxwell equations. We discuss some specific observational results thatcontribute to that foundation.
Symmetries and (Related Recursion Operators of Linear Evolution Equations
Directory of Open Access Journals (Sweden)
Giampaolo Cicogna
2010-02-01
Full Text Available Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these equations in their initial and their simplified form are compared, showing in particular that this transformation partially prevents a clear understanding and a full application of the (physically relevant notion of the so-called step up/down operators. These operators are shown to be recursion operators, related to the Lie point symmetries of the equations, which are also carefully discussed.
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Symmetries of the Euler compressible flow equations for general equation of state
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-10-15
The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.
On fictitious domain formulations for Maxwell's equations
DEFF Research Database (Denmark)
Dahmen, W.; Jensen, Torben Klint; Urban, K.
2003-01-01
We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic...... formulations of the Maxwell's equations are considered. and we derive well-posed formulations for both cases. The variational problem that arises can be discretized by functions that do not satisfy an a-priori divergence constraint....
Linear causal modeling with structural equations
Mulaik, Stanley A
2009-01-01
Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal
Bilinear approach to N=2 supersymmetric KdV equations
Institute of Scientific and Technical Information of China (English)
2009-01-01
The N=2 supersymmetric KdV equations are studied within the framework of Hirota bilinear method. For two such equations, namely N=2, a=4 and N=2, a=1 supersymmetric KdV equations, we obtain the corresponding bilinear formulations. Using them, we construct particular solutions for both cases. In particular, a bilinear Bcklund transformation is given for the N=2, a=1 supersymmetric KdV equation.
Soliton solutions of a generalized discrete KdV equation
Kanki, Masataka; Tokihiro, Tetsuji
2012-01-01
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This phenomenon is intuitively understood from its ultradiscrete limit, where the system turns to the box ball system with a carrier. KEYWORDS: soliton, integrable equation, nonlinear system, discrete KdV equation, cellular automaton
Stochastic nonhomogeneous incompressible Navier-Stokes equations
Cutland, Nigel J.; Enright, Brendan
We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.
Stochastic Differential Equations and Kondratiev Spaces
Energy Technology Data Exchange (ETDEWEB)
Vaage, G.
1995-05-01
The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.
Schrodinger Equation for an Open System
Institute of Scientific and Technical Information of China (English)
毕桥; H.E.Ruda
2002-01-01
We present a Schrodinger (Liouville) type of equation for a quantum open system. It has a correlated part, and various master equations may be its special cases. It also has significant applications for constructing decoherencefree subspace for quantum computation. It is related to the original Schrodinger (Liouville) equation for the total system through a non-unitary similarity transformation. It is unnecessary for its correlated part to be self-adjoint,so there is a complex spectrum for the corresponding Hamiltonian (Liouvillian), which enables the time evolution of states to be asymmetric. This shows just the correlation to produce evolution of world.
Minimal String Theory and the Douglas Equation
Belavin, A. A.; Belavin, V. A.
We use the connection between the Frobenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search for a solution of the Douglas string equation and simultaneously a proper transformation from the KdV to the Liouville frame which ensures the fulfilment of the conformal and fusion selection rules. We find that the desired solution of the string equation has an explicit and simple form in the flat coordinates on the Frobenius manifold in the general case of (p,q) Minimal Liouville gravity.
A Riccati equation in radiative stellar collapse
Rajah, S S
2008-01-01
We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special cases. A significant feature of our solutions is the general spatial dependence in the metric functions which allows for a wider study of the physical features of the model, such as the behaviour of the causal temperature in inhomogeneous spacetimes.
Stochastic equations of evolution of channeled particles
Koshcheev, V P
2001-01-01
The stochastic equations of evolution of lateral energy of the fast charged channeled particles is obtained from the condition of nonpreservation of the adiabatic invariant. The electric potential of the crystal is presented in form of the sum of its average value and the potential fluctuation, caused by the thermal oscillations of the atomic nuclei and the quantum fluctuations of the atomic electrons. The problem is solved for the cases of the planar and axial channeling of the fast charged particles. The Fokker-Planck equation may easily plotted on the basis of the stochastic equation for evolution of the lateral energy
State-dependent neutral delay equations from population dynamics.
Barbarossa, M V; Hadeler, K P; Kuttler, C
2014-10-01
A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.
Averaging Einstein's equations : The linearized case
Stoeger, William R.; Helmi, Amina; Torres, Diego F.
2007-01-01
We introduce a simple and straightforward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general relativity and cosmology for weak-field and perturbed FLRW situ
Averaging Einstein's equations : The linearized case
Stoeger, William R.; Helmi, Amina; Torres, Diego F.
We introduce a simple and straightforward averaging procedure, which is a generalization of one which is commonly used in electrodynamics, and show that it possesses all the characteristics we require for linearized averaging in general relativity and cosmology for weak-field and perturbed FLRW
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
A Comparison of IRT Equating and Beta 4 Equating.
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
Advanced lab on Fresnel equations
Petrova-Mayor, Anna; Gimbal, Scott
2015-11-01
This experimental and theoretical exercise is designed to promote students' understanding of polarization and thin-film coatings for the practical case of a scanning protected-metal coated mirror. We present results obtained with a laboratory scanner and a polarimeter and propose an affordable and student-friendly experimental arrangement for the undergraduate laboratory. This experiment will allow students to apply basic knowledge of the polarization of light and thin-film coatings, develop hands-on skills with the use of phase retarders, apply the Fresnel equations for metallic coating with complex index of refraction, and compute the polarization state of the reflected light.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
Institute of Scientific and Technical Information of China (English)
A.I.Arbab
2013-01-01
A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Singular Renormalization Group Equations
Minoru, HIRAYAMA; Department of Physics, Toyama University
1984-01-01
The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Equations for the Filled Inelastic Membrane: A More General Derivation
Deakin, Michael A. B.
2011-01-01
An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.
Collapse in a forced three-dimensional nonlinear Schrodinger equation
DEFF Research Database (Denmark)
Lushnikov, P.M.; Saffman, M.
2000-01-01
We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation.......We derive sufficient conditions for the occurrence of collapse in a forced three-dimensional nonlinear Schrodinger equation without dissipation. Numerical studies continue the results to the case of finite dissipation....
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Geometric Implications of Maxwell's Equations
Smith, Felix T.
2015-03-01
Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Functional Equations and Fourier Analysis
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
Multiplicative equations over commuting matrices
Energy Technology Data Exchange (ETDEWEB)
Babai, L. [Univ. of Chicago, IL (United States)]|[Eotvos Univ., Budapest (Hungary); Beals, R. [Rutgers Univ., Piscataway, NJ (United States); Cai, Jin-Yi [SUNY, Buffalo, NY (United States)] [and others
1996-12-31
We consider the solvability of the equation and generalizations, where the A{sub i} and B are given commuting matrices over an algebraic number field F. In the semigroup membership problem, the variables x{sub i} are constrained to be nonnegative integers. While this problem is NP-complete for variable k, we give a polynomial time algorithm if k is fixed. In the group membership problem, the matrices are assumed to be invertible, and the variables x{sub i} may take on negative values. In this case we give a polynomial time algorithm for variable k and give an explicit description of the set of all solutions (as an affine lattice). The special case of 1 x 1 matrices was recently solved by Guoqiang Ge; we heavily rely on his results.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Painlevé analysis for nonlinear partial differential equations
Musette, M
1998-01-01
The Painlevé analysis introduced by Weiss, Tabor and Carnevale (WTC) in 1983 for nonlinear partial differential equations (PDE's) is an extension of the method initiated by Painlevé and Gambier at the beginning of this century for the classification of algebraic nonlinear differential equations (ODE's) without movable critical points. In these lectures we explain the WTC method in its invariant version introduced by Conte in 1989 and its application to solitonic equations in order to find algorithmically their associated so-called ``integrable'' equations but they are generically no more valid for equations modelising physical phenomema. Belonging to this second class, some equations called ``partially integrable'' sometimes keep remnants of integrability. In that case, the singularity analysis may also be useful for building closed form analytic solutions, which necessarily % Conte agree with the singularity structure of the equations. We display the privileged role played by the Riccati equation and syste...
The Explicit Solutions of Riccati Equation by Integral Series
Yan, Yimin
2010-01-01
The paper aims at exactly solving the linear differential equation and the matrix Riccati equation with variable coefficients. Starting with the simplest structure of them, this article promotes the exponential function by introducing two maps with integral series: $\\mathcal{E}(X)$ and $\\mathcal{F}(X)$, which extend the important properties of exponential function: convergence, reversibility, and the relationship of determinant. Then,the article shows two approaches to the Riccati equation solving: (1)one is the Simplified Way: summed up the Riccati equation into the simplest form $\\frac{\\partial}{\\partial x}W+WPW-Q=0$, and gets the accurate solution;(2) the other is Matrix Way: directly deal with the general Riccati equation, and transform into the matrix linear differential equation. And then the solution could be further expresses with the elementary form with the particular solution. At the end, we can see that Riccati equation solving is somehow a particular case of linear differential equation when view...
Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields
Lindner, Manfred; Lindner, Manfred; Muller, Markus Michael
2006-01-01
Boltzmann equations are often used to study the thermal evolution of particle reaction networks. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equations are only a classical approximation of the quantum thermalization process which is described by the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the full Kadanoff-Baym equations. Therefore, we present in this paper a detailed comparison between the Kadanoff-Baym and Boltzmann equations in the framework of a scalar Phi^4 quantum field theory in 3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Most notably, apart from quantitative discrepancies, on a qualitative level the universality observed for the Kadanoff-Baym equations is severely restricted in the case o...
Directory of Open Access Journals (Sweden)
Florian Ion Tiberiu Petrescu
2015-09-01
Full Text Available This paper presents the dynamic, original, machine motion equations. The equation of motion of the machine that generates angular speed of the shaft (which varies with position and rotation speed is deduced by conservation kinetic energy of the machine. An additional variation of angular speed is added by multiplying by the coefficient dynamic D (generated by the forces out of mechanism and or by the forces generated by the elasticity of the system. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses, while the dynamic coefficient introduces the variation of w with forces acting in the mechanism. Deriving the first equation of motion of the machine one can obtain the second equation of motion dynamic. From the second equation of motion of the machine it determines the angular acceleration of the shaft. It shows the distribution of the forces on the mechanism to the internal combustion heat engines. Dynamic, the velocities can be distributed in the same way as forces. Practically, in the dynamic regimes, the velocities have the same timing as the forces. Calculations should be made for an engine with a single cylinder. Originally exemplification is done for a classic distribution mechanism, and then even the module B distribution mechanism of an Otto engine type.
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation
Rui, Wenjuan; Zhang, Xiangzhi
2016-05-01
This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.
Generalization of Hopf Functional Equation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
This paper generalizes the Hopf functional equation in order to apply it to a wider class of not necessarily incompressible fluid flows. We start by defining characteristic functionals of the velocity field, the density field and the temperature field of a compressible field. Using the continuity equation, the Navier-Stokes equations and the equation of energy we derive a functional equation governing the motion of an ideal gas flow and a van der Waals gas flow, and then give some general methods of deriving a functional equation governing the motion of any compressible fluid flow. These functional equations can be considered as the generalization of the Hopf functional equation.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Exact Closed Master Equation for Gaussian Non-Markovian Dynamics.
Ferialdi, L
2016-03-25
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.
Transform of Riccati equation of constant coefficients through fractional procedure
Rosu, H C; Socorro, J
2003-01-01
We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by Faraoni.
Transform of Riccati equation of constant coefficients through fractional procedure
Energy Technology Data Exchange (ETDEWEB)
Rosu, H C [Department of Applied Mathematics, IPICyT, Apdo Postal 3-74 Tangamanga, San Luis Potosi (Mexico); Madueno, A L [Instituto de Fisica, Universidad de Guanajuato, Apdo Postal E-143, Leon (Mexico); Socorro, J [Instituto de Fisica, Universidad de Guanajuato, Apdo Postal E-143, Leon (Mexico)
2003-01-31
We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by Faraoni.
Generalization of the Majorana equation for real spinors
Teruel, Ginés R Pérez
2016-01-01
We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation by means of two algebraic differential operators, allowing to describe real spinors in any representation of the Dirac matrices maintaining the reality condition $\\tilde{\\Psi}=\\tilde{\\Psi}^{*}$ unaltered. In addition, it is shown that the Majorana wave equation is a particular case of the relativistic system of equations deduced in this paper. We also briefly discuss how the formalism can be extended to deal with complex (charged) spinors.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Gas Dynamics Equations: Computation
Chen, Gui-Qiang G
2012-01-01
Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. In this paper, we discuss some historic and recent developments, as well as mathematical challenges, in designing and formulating efficient numerical methods and algorithms to compute weak entropy solutions for the Euler equations for gas dynamics.
Theory of differential equations
Gel'fand, I M
1967-01-01
Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations.This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cau
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Institute of Scientific and Technical Information of China (English)
Ding Yi
2009-01-01
In this article, the author derives a functional equation η(s)=［(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.
Comparison of Kernel Equating and Item Response Theory Equating Methods
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…
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Indian Academy of Sciences (India)
Zehra Pinar; Abhishek Dutta; Guido Bény; Turgut Öziş
2015-01-01
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation of a nonlinear PBE with appropriately chosen parameters is taken to be analogous to the description of the dynamic behaviour of the particulate processes. For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation and breakage, (2) when aggregation can dominate and (3) breakage can dominate, are selected and solved for their corresponding analytical solutions. The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the solution approach proposed via AEM is flexible and therefore more efficient than the analytical approach used in the literature.
Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation
Institute of Scientific and Technical Information of China (English)
LIU Yan-hong; ZHANG Hui-ming
2007-01-01
Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
Footballs, Conical Singularities and the Liouville Equation
Redi, M
2004-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.
Zakharov equations in quantum dusty plasmas
Energy Technology Data Exchange (ETDEWEB)
Sayed, F. [Center for Risk Management and Safety Sciences, Yokohama National University, Yokohama 240-8501 (Japan); Vladimirov, S. V. [Center for Risk Management and Safety Sciences, Yokohama National University, Yokohama 240-8501 (Japan); Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya st. 13 Bld. 2, Moscow 125412 (Russian Federation); Metamaterials Laboratory, National Research University of Information Technology, Mechanics, and Optics, St. Petersburg 199034 (Russian Federation); Ishihara, O. [Center for Risk Management and Safety Sciences, Yokohama National University, Yokohama 240-8501 (Japan); Institute of Science and Technology Research, Chubu University, Kasugai 487-8501 (Japan)
2015-08-15
By generalizing the formalism of modulational interactions in quantum dusty plasmas, we derive the kinetic quantum Zakharov equations in dusty plasmas that describe nonlinear coupling of high frequency Langmuir waves to low frequency plasma density variations, for cases of non-degenerate and degenerate plasma electrons.
Twisting singular solutions of Bethe's equations
Nepomechie, Rafael I
2014-01-01
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
Advanced structural equation modeling issues and techniques
Marcoulides, George A
2013-01-01
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
Reduced Magnetohydrodynamic Equations in Toroidal Geometry
Institute of Scientific and Technical Information of China (English)
REN Shen-Ming; YU Guo-Yang
2001-01-01
By applying a new assumption of density, I.e. R2 p = const, the continuity equation is satisfied to the order ofe2`+with e being the inverse aspect ratio. In the case of large aspect ratio, a set of reduced magnetohydrodynamicequations in toroidal geometry are obtained. The new assumption about the density is supported by experimentalobservation to some extent.
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Standardized Referente Evapotranspiration Equation
Directory of Open Access Journals (Sweden)
M.D. Mundo–Molina
2009-04-01
Full Text Available In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude it was selected tomake comparisons. The compared equations we re: a CIANO weat her station, b Penman–Monteith ASCE (PMA, Penman–Monteith FAO 56 (PM FAO 56, Penman–Monteith estandarizado ASCE (PM Std. ASCE. The results were: a There are important differences between PMA and CIANO weather station. The differences are attributed to the nonstandardization of the equation CIANO weather station, b The coefficient of correlation between both methods was of 0,92, with a standard deviation of 1,63 mm, an average quadratic error of 0,60 mm and one efficiency in the estimation of ETo with respect to the method pattern of 87%.
Modified differential equations
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007-01-01
Motivated by the theory of modified differential equations (backward error analysis) an approach for the construction of high order numerical integrators that preserve geometric properties of the exact flow is developed. This summarises a talk presented in honour of Michel Crouzeix.
Equational binary decision diagrams
Groote, J.F.; Pol, J.C. van de
2000-01-01
We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checkin
Directory of Open Access Journals (Sweden)
Garkavenko A. S.
2011-08-01
Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Structural Equation Model Trees
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…
Generalized reduced magnetohydrodynamic equations
Energy Technology Data Exchange (ETDEWEB)
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tauto
Universal solutions for the classical dynamical Yang Baxter equation and the Maurer Cartan equations
Petracci, Emanuela
2004-01-01
Using functional equations we solve the Maurer-Cartan equations and a special version of the classical dynamical Yang-Baxter equation (vCDYBE). Our solutions are valid for any Lie algebra over a base ring containing {\\bb Q} , and in the case of vCDYBE for any quadratic Lie algebra. Our method applies also to Lie superalgebras. This research was done during a visit to the 'Institut de Mathématiques de Jussieu' in Paris, and completed during a visit—supported by the Swiss National Science Foundation—to the 'Section de Mathématiques' of the University of Geneva.
Effect of habitat quality on diet flexibility in Barbary macaques.
Ménard, Nelly; Motsch, Peggy; Delahaye, Alexia; Saintvanne, Alice; Le Flohic, Guillaume; Dupé, Sandrine; Vallet, Dominique; Qarro, Mohamed; Tattou, Mohamed Ibn; Pierre, Jean-Sébastien
2014-07-01
Barbary macaques live in extreme temperate environments characterized by strongly seasonal resource availability. They are mainly terrestrial while foraging, harvesting food from the herbaceous layer. These monkeys are threatened mainly because of anthropogenic habitat degradation. We studied the adaptive capacities of wild groups of Barbary macaques that lived in different cedar forests undergoing varying extents of grazing pressure from domestic livestock. In all three sites, diet varied seasonally. Heavy grazing led to a significant decrease in herbaceous production and species richness. As a consequence, the monkeys' diet in this poor habitat showed a decreased plant species richness. Moreover, it incorporated fewer above-ground herbaceous resources, and a greater proportion of subterranean resources (especially hypogeous fungi and subterranean invertebrates such as earthworms, eggs and adults of earwigs, and ant's larvae) than the diet of monkeys inhabiting ungrazed forest. Cedar bark, cedar strobiles, earthworms, and earwigs were part of the monkeys' diet only in grazed forest. Monkeys in heavily grazed forest compensated for a lack of herbaceous foods by eating subterranean foods preferentially to tree and shrub products. The foods they consumed take longer to harvest and process than the seeds or leaves consumed by Barbary macaques in less heavily grazed forest habitats. Our results suggest that monkeys do differ in their diets according to the degree of habitat change induced by human activities. They also highlight the dietary flexibility of Barbary macaques as a key element that allows them to cope with degraded habitats. We later compare the dietary adjustments of Barbary macaques facing environmental change to dietary strategies of other macaques and temperate-zone primates. © 2014 Wiley Periodicals, Inc.
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Elements of partial differential equations
Sneddon, Ian N
2006-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Energy Technology Data Exchange (ETDEWEB)
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Concentration phenomena in the semilinear parabolic equation
Institute of Scientific and Technical Information of China (English)
TAN; Zhong
2001-01-01
［1］Fujita, H., On the blowing up of solutions of the Chauch problem for u=Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I, 966, 3: 09.［2］Ni, W. -M., Sacks, P. E., Tavantzis, J., On the asymptotic behavior of solutions of certain quasilinear equations of parabolic type, J. Differential Equations, 984, 54: 97.［3］Cazenave, T., Lions, P. L., Solutions globales d'equations de la chaleur semilineaires, Comm. in Partial Differential Equations, 984, 9(0): 955.［4］Giga, Y., A bound for global solutions of semilinear heat equations, Commun. Math. Phys., 986, 03: 45.［5］Galaktionov, V., Vazquez, J. L., Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math., 997, 50: .［6］Rey, O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Func. Anal., 990, 89: .［7］Wei Juncheng, Asymptotic behavior of least energy solution to a semilinear Dirichlet problem near the critical exponent, J. Math. Soc. Japan, 998, 50(): 39.［8］Lions, P. L., The concentration-compactness principle in the calculus of variations, The limit case ,2, Rev. Mat. Iberoamerioana, 985, : 45, 45.［9］Brezis, H., Elliptic equations with limiting Sobolev exponents——the impact of topology, Commun. Pure and Appl. Math., 986, XXXXIX: S7.［10］Sacks, J., Uhlenbeck, K., The existence of minimal immersions of 2-spheres, Ann. Math., 98, 3: .［11］Zhu Xiping, Nontrivial solutions of quasilinear elliptic equation involving critical growth, Science in China (in Chinese), Ser. A, 988, (3): 225.［12］Pohozaev, S. I., Eigenfunctions of the equation -Δu+λf(u)=0, Soviet. Math. Dold., 965, 6: 408.［13］Gidas, B., Ni, W. -M., Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys., 979, 68: 209.［14］Ni, W. -M., Sacks, P. E., Singular behaviour in nonlinear parabolic equations, Tran. of the AMS, 985, 287(2): 657.［15］Ni, W. -M., Sacks, P. E
On the full Boltzmann equations for Leptogenesis
Garayoa, J; Pinto, T; Rius, N; Vives, O
2009-01-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T=0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ~< 1) the final lepton asymmetry can change up to a factor four with respect to previous...
On the full Boltzmann equations for leptogenesis
Energy Technology Data Exchange (ETDEWEB)
Garayoa, J.; Pastor, S.; Pinto, T.; Rius, N.; Vives, O., E-mail: garayoa@ific.uv.es, E-mail: pastor@ific.uv.es, E-mail: teguayco@gmail.com, E-mail: nuria@ific.uv.es, E-mail: vives@ific.uv.es [Depto. de Física Teórica and IFIC, Universidad de Valencia-CSIC, Edificio de Institutos de Paterna, Apt. 22085, 46071 Valencia (Spain)
2009-09-01
We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T = 0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ∼< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Differential Equations with Linear Algebra
Boelkins, Matthew R; Potter, Merle C
2009-01-01
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, t
SPECIFIC SOLUTIONS GROUNDWATER FLOW EQUATION
Syahruddin, Muhammad Hamzah
2014-01-01
Geophysic publication Groundwater flow under surface, its usually slow moving, so that in laminer flow condition can find analisys using the Darcy???s law. The combination between Darcy law and continuity equation can find differential Laplace equation as general equation groundwater flow in sub surface. Based on Differential Laplace Equation is the equation that can be used to describe hydraulic head and velocity flow distribution in porous media as groundwater. In the modeling Laplace e...
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
G. Dziuk; C.M. Elliott
2007-01-01
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Chen Zhongying; Wu Bin; Xu Yuesheng
2005-01-01
We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.
Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics
Ratliff, Daniel J.; Bridges, Thomas J.
2016-10-01
Whitham modulation theory with degeneracy in wave action is considered. The case where all components of the wave action conservation law, when evaluated on a family of periodic travelling waves, have vanishing derivative with respect to wavenumber is considered. It is shown that Whitham modulation equations morph, on a slower time scale, into the two way Boussinesq equation. Both the 1 + 1 and 2 + 1 cases are considered. The resulting Boussinesq equation arises in a universal form, in that the coefficients are determined from the abstract properties of the Lagrangian and do not depend on particular equations. One curious by-product of the analysis is that the theory can be used to confirm that the two-way Boussinesq equation is not a valid model in shallow water hydrodynamics. Modulation of nonlinear travelling waves of the complex Klein-Gordon equation is used to illustrate the theory.
Quantization of Equations of Motion
Directory of Open Access Journals (Sweden)
D. Kochan
2007-01-01
Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail.
Solving equations through particle dynamics
Edvardsson, S.; Neuman, M.; Edström, P.; Olin, H.
2015-12-01
The present work evaluates a recently developed particle method (DFPM). The basic idea behind this method is to utilize a Newtonian system of interacting particles that through dissipation solves mathematical problems. We find that this second order dynamical system results in an algorithm that is among the best methods known. The present work studies large systems of linear equations. Of special interest is the wide eigenvalue spectrum. This case is common as the discretization of the continuous problem becomes dense. The convergence rate of DFPM is shown to be in parity with that of the conjugate gradient method, both analytically and through numerical examples. However, an advantage with DFPM is that it is cheaper per iteration. Another advantage is that it is not restricted to symmetric matrices only, as is the case for the conjugate gradient method. The convergence properties of DFPM are shown to be superior to the closely related approach utilizing only a first order dynamical system, and also to several other iterative methods in numerical linear algebra. The performance properties are understood and optimized by taking advantage of critically damped oscillators in classical mechanics. Just as in the case of the conjugate gradient method, a limitation is that all eigenvalues (spring constants) are required to be of the same sign. DFPM has no other limitation such as matrix structure or a spectral radius as is common among iterative methods. Examples are provided to test the particle algorithm's merits and also various performance comparisons with existent numerical algorithms are provided.
The effect of nonlinearity on unstable zones of Mathieu equation
Indian Academy of Sciences (India)
M GH SARYAZDI
2017-03-01
Mathieu equation is a well-known ordinary differential equation in which the excitation term appears as the non-constant coefficient. The mathematical modelling of many dynamic systems leads to Mathieu equation. The determination of the locus of unstable zone is important for the control of dynamic systems. In this paper, the stable and unstable regions of Mathieu equation are determined for three cases of linear and nonlinear equations using the homotopy perturbation method. The effect of nonlinearity is examined in the unstable zone. The results show that the transition curves of linear Mathieu equation depend on the frequency of the excitation term. However, for nonlinear equations, the curves depend also on initial conditions. In addition, increasing the amplitude of response leads to an increase in the unstable zone.
Darboux transformations and linear parabolic partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Arrigo, Daniel J.; Hickling, Fred [Department of Mathematics, University of Central Arkansas, Conway, AR (United States)
2002-07-19
Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor.
THE INVERSE PROBLEM FOR BOOLEAN EQUATIONS
Directory of Open Access Journals (Sweden)
Hussain Mobarak Albarakati
2012-01-01
Full Text Available The Forward Problem (FB of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X = 0 where f(X: Bn â B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB of Boolean equations aims to reconstruct the equation f (X = 0 given the set of solutions and hence to verify the correctness of this set. This study derives methods that handle this inverse problem for the main types of solutions of Boolean equations. These include: (a Subsumptive general solutions, in which each of the variables is expressed as an interval by deriving successive conjunctive or disjunctive eliminants of the original function, (b Parametric general solutions, in which each of the variables is expressed via arbitrary parameters which are freely chosen elements of the underlying Boolean algebra and (c Particular solutions, each of which is an assignment from the underlying Boolean algebra to every pertinent variable that makes the Boolean equation an identity. The reconstructed function f(X in every case is set in a canonical form, such as the complete-sum form, to facilitate proving its equivalence to the original function. The methods presented herein are demonstrated with carefully-chosen illustrative examples over big Boolean algebras of various sizes. Among the methods utilized in handling the inverse problem for Boolean equations, the ones utilizing the variable-entered Karnaugh map offered pictorial insight and exhibited an efficient divide-and-conquer strategy.
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Symmetries of the Continuous and Discrete Krichever-Novikov Equation
Directory of Open Access Journals (Sweden)
Decio Levi
2011-10-01
Full Text Available A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever-Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1≤n≤5. The highest dimensions, namely n=5 and n=4 occur only in the integrable cases.
The Swift-Hohenberg equation with a nonlocal nonlinearity
2013-01-01
It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This paper extends these multiple scales analyses to cases where an additional nonlinear integral term, in the form of a convolution, is present. The presence of a kernel function introduces a new lengthscale into the problem, and this results in additional complexity in both the derivation of envelope equations and in ...
Convergence analysis of Strang splitting for Vlasov-type equations
Einkemmer, Lukas
2012-01-01
A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that under suitable assumptions the convergence is of second order in the time step h. As an example, it is verified that the Vlasov-Poisson equation in 1+1 dimensions fits into the framework of this analysis. Also, numerical experiments for the latter case are presented.
Weak solutions of the Landau-Lifshitz-Bloch equation
Le, Kim Ngan
2016-12-01
The Landau-Lifshitz-Bloch (LLB) equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. We study LLB equation in case the temperature raised higher than the Curie temperature. The existence of weak solution is showed and its regularity properties are also discussed. In this way, we lay foundations for the rigorous theory of LLB equation that is currently not available.
The Hamiltonian Structure of the Maxwell-Vlasov Equations.
1981-02-01
principle of Percival [1979). 4. By using an appropriate Darboux theorem, (see Marsden [1981], lecture 1), one can show that Of admits canonically...get the Vlasov-Poisson equation. It would also be of interest to realize both the Vlasov-Maxwell and MHD equations as limiting cases of a grand...de Vries equation, Springer Lecture Notes, #755, 1-15 and Inv. Math. 50, 219-248. J. Arms (1979]. Linearization stability of gravitational and gauge
Difference equations versus differential equations, a possible equivalence for the Rössler system?
Letellier, Christophe; Elaydi, Saber; Aguirre, Luis A.; Alaoui, Aziz
2004-08-01
When a set of nonlinear differential equations is investigated, most of time there is no analytical solution and only numerical integration techniques can provide accurate numerical solutions. In a general way the process of numerical integration is the replacement of a set of differential equations with a continuous dependence on the time by a model for which the time variable is discrete. In numerical investigations a fourth-order Runge-Kutta integration scheme is usually sufficient. Nevertheless, sometimes a set of difference equations may be required and, in this case, standard schemes like the forward Euler, backward Euler or central difference schemes are used. The major problem encountered with these schemes is that they offer numerical solutions equivalent to those of the set of differential equations only for sufficiently small integration time steps. In some cases, it may be of interest to obtain difference equations with the same type of solutions as for the differential equations but with significantly large time steps. Nonstandard schemes as introduced by Mickens [Nonstandard Finite Difference Models of Differential Equations, World Scientific, 1994] allow to obtain more robust difference equations. In this paper, using such nonstandard scheme, we propose some difference equations as discrete analogues of the Rössler system for which it is shown that the dynamics is less dependent on the time step size than when a nonstandard scheme is used. In particular, it has been observed that the solutions to the discrete models are topologically equivalent to the solutions to the Rössler system as long as the time step is less than the threshold value associated with the Nyquist criterion.
Dissipative Boussinesq equations
2007-01-01
40 pages, 15 figures, published in C. R. Mecanique 335 (2007) Other author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutykh; International audience; The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water fr...
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Arithmetic partial differential equations
Buium, Alexandru; Simanca, Santiago R.
2006-01-01
We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave...
Stability in Neutral Equations
1976-02-04
Martinez-Amores Division of Applied Mathematics Brown University Providence, Rhode Island 02912 and Universidad de Granada, Seccion de Matematicas , Spain S...XG w)1- 0 ~t)- >~~~ 0 suc ht j~<kIp, Ii 2 ~ o ~~~ X~ G (t) , y’ip X= 0 y 20 since equation (3.16) is satisfied. Since F = col(f,0), only the col
Quantum molecular master equations
Brechet, Sylvain D.; Reuse, Francois A.; Maschke, Klaus; Ansermet, Jean-Philippe
2016-10-01
We present the quantum master equations for midsize molecules in the presence of an external magnetic field. The Hamiltonian describing the dynamics of a molecule accounts for the molecular deformation and orientation properties, as well as for the electronic properties. In order to establish the master equations governing the relaxation of free-standing molecules, we have to split the molecule into two weakly interacting parts, a bath and a bathed system. The adequate choice of these systems depends on the specific physical system under consideration. Here we consider a first system consisting of the molecular deformation and orientation properties and the electronic spin properties and a second system composed of the remaining electronic spatial properties. If the characteristic time scale associated with the second system is small with respect to that of the first, the second may be considered as a bath for the first. Assuming that both systems are weakly coupled and initially weakly correlated, we obtain the corresponding master equations. They describe notably the relaxation of magnetic properties of midsize molecules, where the change of the statistical properties of the electronic orbitals is expected to be slow with respect to the evolution time scale of the bathed system.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
A simple deduction of the Lindblad equation
Brasil, Carlos Alexandre; Napolitano, Reginaldo de Jesus
2011-01-01
We present a deduction of the Lindblad equation that is accessible to students with a basic background on quantum mechanics. We consider a specific case, corresponding to a very simple situation, where a primary system interacts with a bath of harmonic oscillators at zero temperature, with an interaction Hamiltonian that resembles the Jaynes-Cummings format. We start with the Born-Markov equation and, tracing out the bath degrees of freedom, we obtain an equation in the Lindblad form. The speci?c situation is very instructive, for it makes it easy to realize that the Lindblads represent the e?ect on the main system caused by the interaction with the bath, and that the Markov approximation is a fundamental condition for the emergence of the Lindbladian operator. The formal derivation of the Lindblad equation for a more general case requires broader considerations regarding the environment, the temperature, and the use of quantum dynamical semi-groups than we have considered in the particular case treated here.
Nonlinear Biharmonic Equations with Critical Potential
Institute of Scientific and Technical Information of China (English)
Hui XIONG; Yao Tian SHEN
2005-01-01
In this paper, we study two semilinear singular biharmonic equations: one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile,we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian
2014-10-08
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
Modification of Ordinary Differential Equations MATLAB Solver
Directory of Open Access Journals (Sweden)
E. Cocherova
2003-12-01
Full Text Available Various linear or nonlinear electronic circuits can be described bythe set of ordinary differential equations (ODEs. The ordinarydifferential equations can be solved in the MATLAB environment inanalytical (symbolic toolbox or numerical way. The set of nonlinearODEs with high complexity can be usually solved only by use ofnumerical integrator (solver. The modification of ode23 MATLABnumerical solver has been suggested in this article for the applicationin solution of some special cases of ODEs. The main feature of thismodification is that the solution is found at every prescribed point,in which the special behavior of system is anticipated. Theextrapolation of solution is not allowed in those points.
Stochastic Einstein equations with fluctuating volume
Dzhunushaliev, Vladimir
2016-01-01
We develop a simple model to study classical fields on the background of a fluctuating spacetime volume. It is applied to formulate the stochastic Einstein equations with a perfect-fluid source. We investigate the particular case of a stochastic Friedmann-Lema\\^itre-Robertson-Walker cosmology, and show that the resulting field equations can lead to solutions which avoid the initial big bang singularity. By interpreting the fluctuations as the result of the presence of a quantum spacetime, we conclude that classical singularities can be avoided even within a stochastic model that include quantum effects in a very simple manner.
Multicomponent integrable wave equations: II. Soliton solutions
Energy Technology Data Exchange (ETDEWEB)
Degasperis, A [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Lombardo, S [School of Mathematics, University of Manchester, Alan Turing Building, Upper Brook Street, Manchester M13 9EP (United Kingdom)], E-mail: antonio.degasperis@roma1.infn.it, E-mail: sara.lombardo@manchester.ac.uk, E-mail: sara@few.vu.nl
2009-09-25
The Darboux-dressing transformations developed in Degasperis and Lombardo (2007 J. Phys. A: Math. Theor. 40 961-77) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.
The Pullback Equation for Differential Forms
Csató, Gyula
2012-01-01
An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map I so that it satisfies the pullback equation: I *(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ae k ae n-1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differe
Global identifiability of linear structural equation models
Drton, Mathias; Sullivant, Seth
2010-01-01
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology.
Zero temperature quark matter equation of state
Energy Technology Data Exchange (ETDEWEB)
Grassi, F.
1987-09-01
An equation of state is computed for a plasma of one flavor quarks interacting through some phenomenological potential, in the Hartree approximation, at zero temperature. Assuming that the confining potential is scalar and color-independent, it is shown that the quarks undergo a first-order mass phase transition. In addition, due to the way screening is introduced, all the thermodynamic quantities computed are independent of the actual shape of the interquark potential. This equation of state is then generalized to a potential with scalar and vector components, Fock corrections are discussed and the case of a several quark flavor plasma is studied. 19 refs., 2 figs.
Langevin equation path integral ground state.
Constable, Steve; Schmidt, Matthew; Ing, Christopher; Zeng, Tao; Roy, Pierre-Nicholas
2013-08-15
We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.
Relativistic wave equations: an operational approach
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
The Jeffcott equations in nonlinear rotordynamics
Zalik, R. A.
1989-01-01
The solutions of the Jeffcott equations describing the behavior of a rotating shaft are investigated analytically, with a focus on the case where deadband is taken into account. Bounds on the solutions are obtained from those for the linearized equations, and the onset of destructive vibrations is predicted by analyzing the Fourier transforms of the solutions; good agreement with numerical solutions and power-spectrum density plots is demonstrated. It is suggested that the present analytical approach could be applied to determine cryogenic-pump stability margins in flight and hot-fire ground testing of launch vehicles such as the Space Shuttle.
Integrable version of Burgers equation in magnetohydrodynamics.
Olesen, P
2003-07-01
It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields v(y)(y,t) and Bx(y,t), one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the propagation of the nonlinear effects is governed by the initial velocity (as in Burgers case) as well as by the initial Alfvén velocity. Many results previously obtained for the Burgers equation can be transferred to the MHD case. We also discuss equipartition v(y)=+/-Bx. It is shown that an initial localized small scale magnetic field will end up in fields moving to the left and the right, thus transporting energy from smaller to larger distances.
Rebelo, Raphaël; Winternitz, Pavel
2017-01-01
This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers...
Lie Symmetries of (1+2 Nonautonomous Evolution Equations in Financial Mathematics
Directory of Open Access Journals (Sweden)
Andronikos Paliathanasis
2016-05-01
Full Text Available We analyse two classes of ( 1 + 2 evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the ( 1 + 2 Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a ( 1 + 1 equation, the resulting equation is of maximal symmetry and so equivalent to the ( 1 + 1 Classical Heat Equation.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
New application to Riccati equation
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
An Internal Observability Estimate for Stochastic Hyperbolic Equations
2015-01-01
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the $L^2$-space. Different from the deterministic case, a delicate analysis of the adaptedness for some stochastic processes is required in the stochastic setting.
Kelvin Equation for a Non-Ideal Multicomponent Mixture
DEFF Research Database (Denmark)
Shapiro, Alexander; Stenby, Erling Halfdan
1997-01-01
The Kelvin equation is generalized by application to a case of a multicomponent non-ideal mixture. Such a generalization is necessary in order to describe the two-phase equilibrium in a capillary medium with respect to both normal and retrograde condensation. The equation obtained is applied...... to the equilibrium state of a hydrocarbon mixture ina gas-condensate reservoir....
Conservation laws for Ablowitz-Kaup-Newell-Segur equation
Mothibi, Dimpho Millicent
2016-06-01
In this paper we study the Ablowitz-Kaup-Newell-Segur equation, which has many applications in several physical phenomena. We perform the Noether symmetries analysis for this equation. Thereafter we construct the conservation laws for those cases which admit the Noether operators.
On nonlocal symmetries of some shallow water equations
Energy Technology Data Exchange (ETDEWEB)
Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2 Santiago (Chile)
2007-04-27
A recent construction of nonlocal symmetries for the Korteweg-de Vries, Camassa-Holm and Hunter-Saxton equations is reviewed, and it is pointed out that-in the Camassa-Holm and Hunter-Saxton case-these symmetries can be considered as (nonlocal) symmetries of integro-differential equations.
On the fractional counterpart of the higher-order equations
D'Ovidio, Mirko
2011-01-01
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be expressed by means of the transition laws of stable subordinators and their inverse processes. In particular we establish connections between fractional and higher-order equations.
Speed ot travelling waves in reaction-diffusion equations
Benguria, R D; Méndez, V
2002-01-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency
Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake
2014-01-01
This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…
Finite Volume Multilevel Approximation of the Shallow Water Equations
Institute of Scientific and Technical Information of China (English)
Arthur BOUSQUET; Martine MARION; Roger TEMAM
2013-01-01
The authors consider a simple transport equation in one-dimensional space and the linearized shallow water equations in two-dimensional space,and describe and implement a multilevel finite-volume discretization in the context of the utilization of the incremental unknowns.The numerical stability of the method is proved in both cases.
Speed ot travelling waves in reaction-diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Benguria, R.D.; Depassier, M.C. [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Avda. Vicuna Mackenna 4860, Santiago (Chile); Mendez, V. [Facultat de Ciencies de la Salut, Universidad Internacional de Catalunya, Gomera s/n 08190 Sant Cugat del Valles, Barcelona (Spain)
2002-07-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
Propagation and interaction of solitons for nonintegrable equations
Omel'yanov, G.
2016-04-01
We describe an approach to the construction of multi-soliton asymptotic solutions for nonintegrable equations. The general idea is realized in the case of N waves, N = 1, 2, 3, and for the KdV-type equation with nonlinearity u 4. A brief review of asymptotic methods as well as results of numerical simulation are included.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
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…
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
New Exact Solutions to NLS Equation and Coupled NLS Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2004-01-01
A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrodinger (NLS) equation and coupled NLS equations. Many kinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some are found for the first time.
The compressible adjoint equations in geodynamics: equations and numerical assessment
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Stochastic partial differential equations an introduction
Liu, Wei
2015-01-01
This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...
SuperDARN scalar radar equations
Berngardt, O I; Potekhin, A P
2016-01-01
The quadratic scalar radar equations are obtained for SuperDARN radars that are suitable for the analysis and interpretation of experimental data. The paper is based on a unified approach to the obtaining radar equations for the monostatic and bistatic sounding with use of hamiltonian optics and ray representation of scalar Green's function and without taking into account the polarization effects. The radar equation obtained is the sum of several terms corresponding to the propagation and scattering over the different kinds of trajectories, depending on their smoothness and the possibility of reflection from the ionosphere. It is shown that the monostatic sounding in the media with significant refraction, unlike the case of refraction-free media, should be analyzed as a combination of monostatic and bistatic scattering. This leads to strong dependence of scattering amplitude on background ionospheric density due to focusing mechanism and appearance of new (bistatic) areas of effective scattering with signific...
Pdf - Transport equations for chemically reacting flows
Kollmann, W.
1989-01-01
The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.
Genuinely Multidimensional Kinetic Scheme For Euler Equations
Tiwari, Praveer
2015-01-01
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using polar coordinates. The aim is to develop a framework which is genuinely multidimensional and can be implemented with different methodologies, no matter whether it is in finite difference, finite volume or finite element form. There is a considerable improvement in capturing shocks and other discontinuities. Also, since the method is multidimensional, the flow features are captured isotropically. The method is further extended to second order using 'Arc of Approach' concept. The framework is developed as a finite difference method (called as GINEUS) and is tested on the benchmark test cases. The results are compared against Kinetic Flux Vector Splitting Method.
Equations in mathematical physics a practical course
Pikulin, Victor P
2001-01-01
This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular ...
Relativistic diffusion equation from stochastic quantization
Kazinski, P O
2007-01-01
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck constant). We apply this method to the models of nonrelativistic and relativistic particles interacting with an electromagnetic field. In the first case we establish the equivalence of such a quantization to the Fokker-Planck equation with a special force. The application of the proposed quantization procedure to the model of a relativistic particle results in a relativistic generalization of the Fokker-Planck equation in the coordinate space, which in the absence of the electromagnetic field reduces to the relativistic diffusion (heat) equation. The stationary probability distribution functions for a stochastically quantized particle diffusing under a barrier and a particle in the potential of a harmonic oscillator are derived.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Free geometric equations for higher spins
Francia, D
2002-01-01
We show how allowing non-local terms in the field equations of symmetric tensors uncovers a neat geometry that naturally generalizes the Maxwell and Einstein cases. The end results can be related to multiple traces of the generalized Riemann curvatures ${\\cal R}_{\\alpha_1 ... \\alpha_{s}; \\beta_1 >... \\beta_{s}}$ introduced by de Wit and Freedman, divided by suitable powers of the D'Alembertian operator $\\Box$. The conventional local equations can be recovered by a partial gauge fixing involving the trace of the gauge parameters $\\Lambda_{\\alpha_1 ... \\alpha_{s-1}}$, absent in the Fronsdal formulation. The same geometry underlies the fermionic equations, that, for all spins $s+1/2$, can be linked via the operator $\\frac{\
On the Well-Posedness of the Vacuum Einstein's Equations
Karp, Lavi
2009-01-01
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\\alpha\\beta}$ of a spacetime with vanishing Ricci curvature $R_{\\alpha,\\beta}$ and prescribed initial data. Under the harmonic gauge condition, the equations $R_{\\alpha,\\beta}=0$ are transferred into a system of quasi-linear wave equations which are called the reduced Einstein equations. The initial data for Einstein's equations are a proper Riemannian metric $h_{ab}$ and a second fundamental form $K_{ab}$. A necessary condition for the reduced Einstein equation to satisfy the vacuum equations is that the initial data satisfy Einstein constraint equations. Hence the data $(h_{ab},K_{ab})$ cannot serve as initial data for the reduced Einstein equations. Previous results in the case of asymptotically flat spacetimes provide a solution to the constraint equations in one type of Sobolev spaces, while initial data for the evolution equations belong to a different type of Sobolev spaces. The goal of our work is to resolve this inco...
Shiryaeva, E V
2014-01-01
In paper [S.I. Senashov, A. Yakhno. 2012. SIGMA. Vol.8. 071] the variant of the hodograph method based on the conservation laws for two hyperbolic quasilinear equations of the first order is described. Using these results we propose a method which allows to reduce the Cauchy problem for the two quasilinear PDE's to the Cauchy problem for ODE's. The proposed method is actually some similar method of characteristics for a system of two hyperbolic quasilinear equations. The method can be used effectively in all cases, when the linear hyperbolic equation in partial derivatives of the second order with variable coefficients, resulting from the application of the hodograph method, has an explicit expression for the Riemann-Green function. One of the method's features is the possibility to construct a multi-valued solutions. In this paper we present examples of method application for solving the classical shallow water equations.
Gardas, Bartlomiej
2010-01-01
The problem of decoherence viewed from a block operator matrix perspective is revisited. We study an algebraic Riccati equation associate with the Hamiltonian modeling the process of decoherence. We proof that if the environment responsible for decoherence process is an invariant under transformation of an antilinear involution, then this operator (a symmetry of the system) is a solution of the Riccati equation in question. We also argue the later solution leads to neither linear not antilinear similarity operator matrix and therefore cause the problem with the standard procedure of solving linear differential equation, like for instance Schrodinger one. Finally, we give an explicit formula for the solution of the Riccati equation in the case when the operators defining the environment commute with each other. We also discuses a connection between our results and the standard Kraus representation approach of the completely positive map. We show that reduced dynamics we obtained dose not posses the Kraus repre...
A complex Noether approach for variational partial differential equations
Naz, R.; Mahomed, F. M.
2015-10-01
Scalar complex partial differential equations which admit variational formulations are studied. Such a complex partial differential equation, via a complex dependent variable, splits into a system of two real partial differential equations. The decomposition of the Lagrangian of the complex partial differential equation in the real domain is shown to yield two real Lagrangians for the split system. The complex Maxwellian distribution, transonic gas flow, Maxwellian tails, dissipative wave and Klein-Gordon equations are considered. The Noether symmetries and gauge terms of the split system that correspond to both the Lagrangians are constructed by the Noether approach. In the case of coupled split systems, the same Noether symmetries are obtained. The Noether symmetries for the uncoupled split systems are different. The conserved vectors of the split system which correspond to both the Lagrangians are compared to the split conserved vectors of the complex partial differential equation for the examples. The split conserved vectors of the complex partial differential equation are the same as the conserved vectors of the split system of real partial differential equations in the case of coupled systems. Moreover a Noether-like theorem for the split system is proved which provides the Noether-like conserved quantities of the split system from knowledge of the Noether-like operators. An interesting result on the split characteristics and the conservation laws is shown as well. The Noether symmetries and gauge terms of the Lagrangian of the split system with the split Noether-like operators and gauge terms of the Lagrangian of the given complex partial differential equation are compared. Folklore suggests that the split Noether-like operators of a Lagrangian of a complex Euler-Lagrange partial differential equation are symmetries of the Lagrangian of the split system of real partial differential equations. This is not the case. They are proved to be the same if the
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Savvidy, G K
1998-01-01
We discuss the basic properties of the gonihedric string and the problem of its formulation in continuum. We propose a generalization of the Dirac equation and of the corresponding gamma matrices in order to describe the gonihedric string. The wave function and the Dirac matrices are infinite-dimensional. The spectrum of the theory consists of particles and antiparticles of increasing half-integer spin lying on quasilinear trajectories of different slope. Explicit formulas for the mass spectrum allow to compute the string tension and thus demonstrate the string character of the theory.
Generalized estimating equations
Hardin, James W
2013-01-01
Generalized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, along with the software code used to create, run, and evaluate the models being examined. Stata is used as the primary software for running and displaying modeling output; associated R code is also given to allow R users to replicat
The Arrhenius equation revisited.
Peleg, Micha; Normand, Mark D; Corradini, Maria G
2012-01-01
The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
OSCILLATION THEOREMS FOR SECOND ORDER QUASILINEAR PERTURBED DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
New oscillation criteria for the second order perturbed differential equation are presented. The special case of the results includes the corresponding results in previous papers,extends and unifies a number of known results.
Quasiconformal mappings and degenerate elliptic and parabolic equations
Directory of Open Access Journals (Sweden)
Filippo Chiarenza
1987-11-01
Full Text Available In this paper two Harnak inequalities are proved concerning a degenerate elliptic and a degenerate parabolic equation. In both cases the weight giving the degeneracy is a power of the jacobian of a quasiconformal mapping.
Conservational PDF Equations of Turbulence
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
Program Transformation by Solving Equations
Institute of Scientific and Technical Information of China (English)
朱鸿
1991-01-01
Based on the theory of orthogonal program expansion[8-10],the paper proposes a method to transform programs by solving program equations.By the method,transformation goals are expressed in program equations,and achieved by solving these equations.Although such equations are usually too complicated to be solved directly,the orthogonal expansion of programs makes it possible to reduce such equations into systems of equations only containing simple constructors of programs.Then,the solutions of such equations can be derived by a system of solving and simplifying rules,and algebraic laws of programs.The paper discusses the methods to simplify and solve equations and gives some examples.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
The equivalence between B-W and K-G and R-S equations
Institute of Scientific and Technical Information of China (English)
黄时中; 阮图南; 吴宁; 郑志鹏
2003-01-01
The equivalence between the Bargmann-Wigner (B-W) equations and the Klein-Gordon (K-G) equations for integral spin, and the Rarita-Schwinger (R-S) equations for half integral spin is established by explicit derivation, starting from the lowest spin cases. It is demonstrated that all the constraints or subsidiary conditions imposed on the K-G or R-S equations are included in the B-W equations.
Nonlinear unified equations for water waves propagating over uneven bottoms in the nearshore region
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Considering the continuous characteristics for water waves propagating over complex topography in the nearshore region, the unified nonlinear equations, based on the hypothesis for a typical uneven bottom, are presented by employing the Hamiltonian variational principle for water waves. It is verified that the equations include the following special cases: the extension of Airy's nonlinear shallow-water equations, the generalized mild-slope equation, the dispersion relation for the second-order Stokes waves and the higher order Boussinesq-type equations.
Explicit solution of the problem of equivalence for some Painleve equations
Kartak, V V
2009-01-01
For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it is true then in case the Painleve equations I and II an explicite change of variables is given that is written using the differential invariants of the equation.
Scattering integral equations for distorted transition operators
Energy Technology Data Exchange (ETDEWEB)
Kowalski, K.L.; Siciliano, E.R.; Thaler, R.M.
1978-11-01
Methods for embedding phenomenological distorted-wave techniques for rearrangement and inelastic scattering within well-defined theories of multiparticle scattering are developed. The essential point of contact between the two approaches is in the definition and choice of distorting potential. It is shown that the concept of a channel coupling scheme allows a comparative freedom of choice for these potentials; if they are connected operators, such as optical potentials, then it is possible to obtain connected-kernel equations for the distorted transition operators. The latter are introduced in the course of exploiting the two-potential formula for the full transition operator and have the property that their matrix elements with respect to distorted waves are the physical scattering amplitudes. It is found that the distorted counterparts of the Kouri, Levin, and Tobocman and the Bencze-Redish integral equations maintain their connected-kernel and minimally coupled properties. These equations can be used to derive other integral equations with the same properties for the distorted-wave operators which consist of the product of the distorted transition operators and the wave operators corresponding to distorted waves. These simplifications are not realized for arbitrary channel coupling schemes. In order to deal with the general situation an alternative approach employing a subtraction technique which involves projections on the bound two-cluster channel states is introduced. When the distorting potentials are essentially the optical potentials in the entrance and exit channels a set of multichannel two-particle Lippmann-Schwinger integral equations for the two-cluster distorted-wave transition operators are obtained. Input into these two-particle integral equations involves the solution of a modified N-particle equation. Approximations to the latter are discussed in the particular cases of the Kouri, Levin, and Tobocman and Bencze-Redish channel coupling schemes.
``Riemann equations'' in bidifferential calculus
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
Residual power series method for fractional Burger types equations
Kumar, Amit; Kumar, Sunil
2016-12-01
We present an analytic algorithm to solve the generalized Berger-Fisher (B-F) equation, B-F equation, generalized Fisher equation and Fisher equation by using residual power series method (RPSM), which is based on the generalized Taylor's series formula together with the residual error function. In all the cases obtained results are verified through the different graphical representation. Comparison of the results obtained by the present method with exact solution reveals that the accuracy and fast convergence of the proposed method.
Maxwell's equations and their consequences elementary electromagnetic theory
Chirgwin, B H; Kilmister, C W 0
2013-01-01
Elementary Electromagnetic Theory Volume 3: Maxwell's Equations and their Consequences is the third of three volumes that intend to cover electromagnetism and its potential theory. The third volume considers the implications of Maxwell's equations, such as electromagnetic radiation in simple cases, and its relation between Maxwell's equation and the Lorenz transformation. Included in this volume are chapters 11-14, which contain an in-depth discussion of the following topics: Electromagnetic Waves The Lorentz Invariance of Maxwell's Equation Radiation Motion of Charged Particles Intended
On the hierarchy of partially invariant submodels of differential equations
Golovin, Sergey V
2007-01-01
It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given.
On the hierarchy of partially invariant submodels of differential equations
Energy Technology Data Exchange (ETDEWEB)
Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru
2008-07-04
It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.
Cnoidal waves governed by the Kudryashov–Sinelshchikov equation
Energy Technology Data Exchange (ETDEWEB)
Randrüüt, Merle, E-mail: merler@cens.ioc.ee [Tallinn University of Technology, Faculty of Mechanical Engineering, Department of Mechatronics, Ehitajate tee 5, 19086 Tallinn (Estonia); Braun, Manfred [University of Duisburg–Essen, Chair of Mechanics and Robotics, Lotharstraße 1, 47057 Duisburg (Germany)
2013-10-30
The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech{sup 2} type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.
Discretization of partial differential equations preserving their physical symmetries
Energy Technology Data Exchange (ETDEWEB)
Valiquette, F; Winternitz, P [Centre de Recherches Mathematiques, Universite de Montreal, C.P. 6128, succ. Centre-ville, Montreal, QC, H3C 3J7 (Canada)
2005-11-11
A procedure for obtaining a 'minimal' discretization of a partial differential equation, preserving all of its Lie point symmetries, is presented. 'Minimal' in this case means that the differential equation is replaced by a partial difference scheme involving N difference equations, where N is the number of independent and dependent variables. We restrict ourselves to one scalar function of two independent variables. As examples, invariant discretizations of the heat, Burgers and Korteweg-de Vries equations are presented. Some exact solutions of the discrete schemes are obtained.
Generalized multitime expansions for equations with slowly varying coefficients
Directory of Open Access Journals (Sweden)
L. E. Levine
1984-01-01
Full Text Available The successive terms in a uniformly valid multitime expansion of the solutions of constant coefficient differential equations containing a small parameter ϵ may be obtained without resorting to secularity conditions if the time scales ti=ϵit(i=0,1,… are used. Similar results have been achieved in some cases for equations with variable coefficients by using nonlinear time scales generated from the equations themselves. This paper extends the latter approach to the general second order ordinary differential equation with slowly varying coefficients and examines the restrictions imposed by the method.
On The Ladder Bethe-Salpeter Equation
Efimov, G V
2003-01-01
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass $m$ interacting via an exchange of a scalar field (tieon) with mass $\\mu$. The BS equation is written in the form of an integral equation in the configuration Euclidean $x$-space with the kernel which for stable bound states $M<2m$ is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed. The analytical form of test functions for which the accuracy of calculations of bound state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents. As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound...
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; LI Chao
2004-01-01
We extend the approach of solving master equations for density matrices by projecting it onto the thermal entangled state representation (Hong-Yi Fan and Jun-Hua Chen, J. Phys. A35 (2002) 6873) to two-mode case. In this approach the two-photon master equations can be directly and conveniently converted into c-number partial differential equations. As an example, we solve the typical master equation for two-photon process in some limiting cases.
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
An Extented Wave Action Equation
Institute of Scientific and Technical Information of China (English)
左其华
2003-01-01
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Lie group analysis method for two classes of fractional partial differential equations
Chen, Cheng; Jiang, Yao-Lin
2015-09-01
In this paper we deal with two classes of fractional partial differential equation: n order linear fractional partial differential equation and nonlinear fractional reaction diffusion convection equation, by using the Lie group analysis method. The infinitesimal generators general formula of n order linear fractional partial differential equation is obtained. For nonlinear fractional reaction diffusion convection equation, the properties of their infinitesimal generators are considered. The four special cases are exhaustively investigated respectively. At the same time some examples of the corresponding case are also given. So it is very convenient to solve the infinitesimal generator of some fractional partial differential equation.
Modified Van der Waals equation and law of corresponding states
Zhong, Wei; Xiao, Changming; Zhu, Yongkai
2017-04-01
It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.
Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation
Li, Xiang-Zheng; Zhang, Jin-Liang; Wang, Ming-Liang
2017-02-01
Three (2+1)-dimensional equations-KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully. Supported by the National Natural Science Foundation of China under Grant No. 11301153 and the Doctoral Foundation of Henan University of Science and Technology under Grant No. 09001562, and the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No. 2015XPT001
A Riemann-Hilbert Approach for the Novikov Equation
Boutet de Monvel, Anne; Shepelsky, Dmitry; Zielinski, Lech
2016-09-01
We develop the inverse scattering transform method for the Novikov equation u_t-u_{txx}+4u^2u_x=3u u_xu_{xx}+u^2u_{xxx} considered on the line xin(-∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann-Hilbert (RH) problem, which in this case is a 3× 3 matrix problem. The structure of this RH problem shares many common features with the case of the Degasperis-Procesi (DP) equation having quadratic nonlinear terms (see [Boutet de Monvel A., Shepelsky D., Nonlinearity 26 (2013), 2081-2107, arXiv:1107.5995]) and thus the Novikov equation can be viewed as a ''modified DP equation'', in analogy with the relationship between the Korteweg-de Vries (KdV) equation and the modified Korteweg-de Vries (mKdV) equation. We present parametric formulas giving the solution of the Cauchy problem for the Novikov equation in terms of the solution of the RH problem and discuss the possibilities to use the developed formalism for further studying of the Novikov equation.
Solutions of the Wheeler-Feynman equations with discontinuous velocities
de Souza, Daniel Câmara
2014-01-01
We generalize Wheeler-Feynman electrodynamics with a variational boundary-value problem having boundary conditions in past and future. The extended variational problem accepts trajectories with discontinuous velocities as critical points of the action functional. Critical-point trajectories must satisfy the Euler-Lagrange equations of the action functional, which are neutral-differential delay equations of motion. Moreover, at velocity discontinuity points critical-point orbits must satisfy the Weierstrass-Erdmann corner conditions of continuity of the partial momenta and partial energies. We study a special class of boundary data having the shortest time-separation between boundary segments, for which case the Wheeler-Feynman equations reduce to a two-point boundary problem for an ordinary differential equation. For this simple case we prove that solutions of the Wheeler-Feynman equations can have discontinuous velocities. We construct a numerical method to find critical-point orbits with a shooting method f...
Compressible turbulence transport equations for generalized second order closure
Energy Technology Data Exchange (ETDEWEB)
Cloutman, L D
1999-05-01
Progress on the theory of second order closure in turbulence models of various types requires knowledge of the transport equations for various turbulence correlations. This report documents a procedure that provides such equations for a wide variety of turbulence averages for compressible flows of a multicomponent fluid. Generalizing some work by Germano for incompressible flows, we introduce an appropriate extension of his generalized second order correlations and use a generalized mass-weighted averaging procedure to derive transport equations for the correlations. The averaging procedure includes all of the commonly used averages as special cases. The resulting equations provide an internally consistent starting point for future work in developing single-point statistical turbulence transport models for fluid flows. The form invariance of the in-compressible equations also holds for the compressible case, and we discuss some of the closure issues and frequently ignored complications of statistical turbulence models of compressible flows.
Numerical solution of large Lyapunov equations
Saad, Youcef
1989-01-01
A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Abdon Atangana
2014-02-01
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of in
Differential equations extended to superspace
Energy Technology Data Exchange (ETDEWEB)
Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)
2003-07-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
Symmetry classification of time-fractional diffusion equation
Naeem, I.; Khan, M. D.
2017-01-01
In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.
LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
Cao LUO
2013-01-01
The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt +ut =uxx-V'(u) on R.The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut =uxx-V'(u).Whereas a lot is known about the local stability of travelling fronts in parabolic systems,for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type.However,for the combustion or monostable type of V,the problem is much more complicated.In this paper,a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established.And then,the result is extended to the damped wave equation with a case of monostable pushed front.
On fractional partial differential equations related to quantum mechanics
Purohit, S. D.; Kalla, S. L.
2011-01-01
In this paper, we investigate the solutions of generalized fractional partial differential equations involving the Caputo time-fractional derivative and the Liouville space-fractional derivatives. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms. Several special cases as solutions of one-dimensional non-homogeneous fractional equations occurring in quantum mechanics are presented in the concluding section. The results given earlier by Debnath (2003 Fract. Calc. Appl. Anal. 6 119-55), Saxena et al (2010 Appl. Math. Comput. 216 1412-7) and Pagnini and Mainardi (2010 J. Comput. Appl. Math. 233 1590-5) follow as special cases of our findings.
On fractional partial differential equations related to quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Purohit, S D [Department of Basic-Sciences (Mathematics), College of Technology and Engineering, M.P. University of Agriculture and Technology, Udaipur-313001 (India); Kalla, S L, E-mail: sunil_a_purohit@yahoo.com, E-mail: shyamkalla@gmail.com [Institute of Mathematics, VIHE, 15 B, Pal-Link Road, Jodhpur-342008 (India)
2011-01-28
In this paper, we investigate the solutions of generalized fractional partial differential equations involving the Caputo time-fractional derivative and the Liouville space-fractional derivatives. The solutions of these equations are obtained by employing the joint Laplace and Fourier transforms. Several special cases as solutions of one-dimensional non-homogeneous fractional equations occurring in quantum mechanics are presented in the concluding section. The results given earlier by Debnath (2003 Fract. Calc. Appl. Anal. 6 119-55), Saxena et al (2010 Appl. Math. Comput. 216 1412-7) and Pagnini and Mainardi (2010 J. Comput. Appl. Math. 233 1590-5) follow as special cases of our findings.
Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators
Alpomishev, E X
2016-01-01
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
On integrable rational potentials of the Dirac equation
Stachowiak, Tomasz
2012-01-01
The Dirac equation, when reducible to an ordinary second order linear equation, exhibits a form of quasi-integrability, i.e. exact solutions exist only for a particular subset of energies. The differential Galois theory can be used to identify the integrable cases, recover integrable rational potentials, explicit solutions and strictly rule out the remaining cases as non-integrable. The effectiveness of this approach is demonstrated by providing a new class of potentials for which the equation in question can be transformed to the Whittaker form.
Existence of solutions for the dynamic equation of ferrimagnets
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.
Yehorchenko, Irina
2010-01-01
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.