We study a stochastic Landau-Lifschitz-Gilbert Equations with non-zero anisotrophy energy and multidimensional noise. We prove the existence and some regularities of weak solution proved. Our paper is motivated by finite-dimensional study of stochastic LLGEs or general stochasric differential equations with constraints studied by Kohn et al cite{Kohn_2005} and Leli{`e}vre et al cite{LeBris_2008}.
{"title":"Weak solutions of the Stochastic Landau–Lifshitz–Gilbert Equations with nonzero anisotrophy energy","authors":"Z. Brzeźniak, B. Goldys","doi":"10.1093/AMRX/ABW003","DOIUrl":"https://doi.org/10.1093/AMRX/ABW003","url":null,"abstract":"We study a stochastic Landau-Lifschitz-Gilbert Equations with non-zero anisotrophy energy and multidimensional noise. We prove the existence and some regularities of weak solution proved. Our paper is motivated by finite-dimensional study of stochastic LLGEs or general stochasric differential equations with constraints studied by Kohn et al cite{Kohn_2005} and Leli{`e}vre et al cite{LeBris_2008}.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"13 1","pages":"334-375"},"PeriodicalIF":0.0,"publicationDate":"2008-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89669323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (Boltzmann) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering an extended ensemble where the control parameter is a dynamical variable, conditional expectations of a nonlinear stochastic process are used to determine the right value of the control variable. A single trajectory discretization is proposed. As an application, we consider the computation of points along the Hugoniot curve, which are equilibrium states obtained after equilibration of a material heated and compressed by a shock wave.
{"title":"Sampling Constraints in Average: The Example of Hugoniot Curves","authors":"J. Maillet, G. Stoltz","doi":"10.1093/AMRX/ABN004","DOIUrl":"https://doi.org/10.1093/AMRX/ABN004","url":null,"abstract":"We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (Boltzmann) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering an extended ensemble where the control parameter is a dynamical variable, conditional expectations of a nonlinear stochastic process are used to determine the right value of the control variable. A single trajectory discretization is proposed. As an application, we consider the computation of points along the Hugoniot curve, which are equilibrium states obtained after equilibration of a material heated and compressed by a shock wave.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76042999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. I also give some other examples showing that the main results are reasonably sharp.
{"title":"Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation","authors":"A. Davie","doi":"10.1093/AMRX/ABM009","DOIUrl":"https://doi.org/10.1093/AMRX/ABM009","url":null,"abstract":"driving path x(t) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. I also give some other examples showing that the main results are reasonably sharp.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88038677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding the movement of drops and bubbles in microchannels is increasingly important in the design and operation of microfluidic devices that involve two-phase flows. Thus, Bretherton’s analysis of the motion of long bubbles in tubes and the associated profile of the wetting film around it are relevant. In this work, steady motion of a long bubble through a cylindrical tube is revisited in the case where the wetting film between the bubble interface and the capillary wall is non-Newtonian and described by the power-law constitutive relation. Using the standard lubrication analysis, the equation for the thickness of the wetting film as a function of axial distance is derived and integrated to find the film thickness. The film thickness and pressure drop across the bubble are found to scale with the capillary number as Ca 2/3 , with a proportionality fac
{"title":"Confined motion of a long bubble through a power-law fluid","authors":"A. Nadim, A. Borhan","doi":"10.1155/AMRX/2006/36283","DOIUrl":"https://doi.org/10.1155/AMRX/2006/36283","url":null,"abstract":"Understanding the movement of drops and bubbles in microchannels is increasingly important in the design and operation of microfluidic devices that involve two-phase flows. Thus, Bretherton’s analysis of the motion of long bubbles in tubes and the associated profile of the wetting film around it are relevant. In this work, steady motion of a long bubble through a cylindrical tube is revisited in the case where the wetting film between the bubble interface and the capillary wall is non-Newtonian and described by the power-law constitutive relation. Using the standard lubrication analysis, the equation for the thickness of the wetting film as a function of axial distance is derived and integrated to find the film thickness. The film thickness and pressure drop across the bubble are found to scale with the capillary number as Ca 2/3 , with a proportionality fac","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"3 1","pages":"36283"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88783682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The papers presented in this issue are selected contributions from participants of a workshop on “thin films and fluid interfaces” held at the Institute for Pure and Applied Mathematics at the University of California, Los Angeles, January 30–February 2, 2006. The workshop was organized by Andrea L. Bertozzi, Robert Behringer, Michael Shearer, Dejan Slepcev, and Tom Witelski. The purpose of the workshop was to bring together an international group of researchers working on experimental, analytical, and computational problems related to thin films and fluid interfaces. The workshop featured current research progress in this area including moving contact lines, solid-liquid-vapor interfaces, and surface tension effects. Funding for this workshop was made possible by the National Science Foundation through a Focused Research Group grant in the Mathematical Sciences. The workshop was attended by speakers from six countries: France, Germany, Israel, Italy, the United Kingdom, and the United States. Over fifty people in total participated during the four days of the workshop. This issue contains six papers illustratingmany of the topics of interest from the workshop. All papers are research articles contributed by speakers at the workshop, and their collaborators. Here we summarize the papers in regards to their connection to the current literature. The works include a blend of new experimental results (two papers) mathematical models, asymptotics, numerical simulations, and analysis. Typically, the
本刊中发表的论文是2006年1月30日至2月2日在洛杉矶加利福尼亚大学纯粹与应用数学研究所举行的“薄膜和流体界面”研讨会的参与者所作的论文。研讨会由Andrea L. Bertozzi、Robert Behringer、Michael Shearer、Dejan Slepcev和Tom Witelski组织。研讨会的目的是汇集一个国际研究小组，研究与薄膜和流体界面有关的实验、分析和计算问题。研讨会介绍了该领域的最新研究进展，包括移动接触线，固体-液体-蒸汽界面和表面张力效应。本次研讨会的资金是由美国国家科学基金会通过数学科学重点研究小组拨款提供的。来自六个国家的发言者出席了讲习班:法国、德国、以色列、意大利、联合王国和美国。总共有五十多人参加了为期四天的研讨会。本期包含六篇论文，阐述了研讨会中许多感兴趣的主题。所有的论文都是由研讨会上的演讲者及其合作者贡献的研究文章。在这里，我们总结了这些论文与当前文献的联系。作品包括新的实验结果(两篇论文)，数学模型，渐近，数值模拟和分析的混合。通常,
{"title":"Editorial to “UCLA-IPAM-NSF workshop on thin films and fluid interfaces”","authors":"A. Bertozzi","doi":"10.1155/AMRX/2006/34149","DOIUrl":"https://doi.org/10.1155/AMRX/2006/34149","url":null,"abstract":"The papers presented in this issue are selected contributions from participants of a workshop on “thin films and fluid interfaces” held at the Institute for Pure and Applied Mathematics at the University of California, Los Angeles, January 30–February 2, 2006. The workshop was organized by Andrea L. Bertozzi, Robert Behringer, Michael Shearer, Dejan Slepcev, and Tom Witelski. The purpose of the workshop was to bring together an international group of researchers working on experimental, analytical, and computational problems related to thin films and fluid interfaces. The workshop featured current research progress in this area including moving contact lines, solid-liquid-vapor interfaces, and surface tension effects. Funding for this workshop was made possible by the National Science Foundation through a Focused Research Group grant in the Mathematical Sciences. The workshop was attended by speakers from six countries: France, Germany, Israel, Italy, the United Kingdom, and the United States. Over fifty people in total participated during the four days of the workshop. This issue contains six papers illustratingmany of the topics of interest from the workshop. All papers are research articles contributed by speakers at the workshop, and their collaborators. Here we summarize the papers in regards to their connection to the current literature. The works include a blend of new experimental results (two papers) mathematical models, asymptotics, numerical simulations, and analysis. Typically, the","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"203 1","pages":"34149"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89805888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Experiments on sessile drops evaporating in normal atmosphere in the situation of complete wetting are reported and compared with a theoretical model by Ben Amar and Boudaoud. For alkanes and water, the model accounts very well for the behavior of radius and contact angle, which scale like power laws of the time interval to drop vanishing. However, the range where these power laws are obeyed is significantly wider in experiments, especially for small contact angles, as it is the case for polydimethylsiloxane oligomers. The reason why is the need of an intermediate length scale between the macroscopic wedge and the microscopic contact line which leads us to reconsider the mere definition of the contact angle in that case.
{"title":"The contact angle of droplets evaporating at ambient temperature","authors":"Geoffroy Guéna, C. Poulard, A. Cazabat","doi":"10.1155/AMRX/2006/23465","DOIUrl":"https://doi.org/10.1155/AMRX/2006/23465","url":null,"abstract":"Experiments on sessile drops evaporating in normal atmosphere in the situation of complete wetting are reported and compared with a theoretical model by Ben Amar and Boudaoud. For alkanes and water, the model accounts very well for the behavior of radius and contact angle, which scale like power laws of the time interval to drop vanishing. However, the range where these power laws are obeyed is significantly wider in experiments, especially for small contact angles, as it is the case for polydimethylsiloxane oligomers. The reason why is the need of an intermediate length scale between the macroscopic wedge and the microscopic contact line which leads us to reconsider the mere definition of the contact angle in that case.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"3 1","pages":"23465"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73545604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This research is devoted to a study of stability problem of linearly elastic isotropic thin rectangular plate resting on linearly elastic foundation (of Winkler type). The plate is simply supported along all four edges and is subjected to a compressive loading of magnitude λ > 0 evenly distributed along two parallel edges, see Figure 1.1. If the loading parameter λ has a small value, then the plate is not deformed and flat (compared to Euler problem of elastic rod). If the loading parameter λ increases to the critical value λ1 (“Euler critical load,” “buckling load”), the plate bifurcation holds,which means that the plate buckles to the bent form. The main purpose of this paper is to give a precise mathematical description of the plate bifurcation. Let us consider corresponding mathematical model. The Cartesian coordinates system (u, v,w) presented in Figure 1.1 is assumed. Themiddle surface of the not buckled thin plate is presented in Cartesian coordinates (u, v,w) by the rectangle
{"title":"Bifurcations in von Kármán problem for rectangular, thin, elastic plate resting on elastic foundation of Winkler type","authors":"A. Borisovich, Jolanta Dymkowska, C. Szymczak","doi":"10.1155/AMRX/2006/82959","DOIUrl":"https://doi.org/10.1155/AMRX/2006/82959","url":null,"abstract":"This research is devoted to a study of stability problem of linearly elastic isotropic thin rectangular plate resting on linearly elastic foundation (of Winkler type). The plate is simply supported along all four edges and is subjected to a compressive loading of magnitude λ > 0 evenly distributed along two parallel edges, see Figure 1.1. If the loading parameter λ has a small value, then the plate is not deformed and flat (compared to Euler problem of elastic rod). If the loading parameter λ increases to the critical value λ1 (“Euler critical load,” “buckling load”), the plate bifurcation holds,which means that the plate buckles to the bent form. The main purpose of this paper is to give a precise mathematical description of the plate bifurcation. Let us consider corresponding mathematical model. The Cartesian coordinates system (u, v,w) presented in Figure 1.1 is assumed. Themiddle surface of the not buckled thin plate is presented in Cartesian coordinates (u, v,w) by the rectangle","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"1 1","pages":"82959"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89753083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Firstly, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented, and then pointing out the drawbacks of these definitions, a new approach is proposed in the context of decision maker’s (optimistic and pessimistic) point of view. Secondly, an interval technique is proposed to solve unconstrained multimodal optimization problems with continuous variables. In this proposed method, the search region is divided into two equal subregions successively and in each subregion, the lower and upper bounds of the objective function are computed with the help of interval arithmetic. Then, by comparing these two interval objective values and considering the subregion containing the better objective value, the global optimal value of the objective function or close to it is obtained. Finally, the proposed method is applied to solve several number of test problems of global optimization with lower as well as higher dimension and is compared with the existing methods with respect to the number of function evaluations.
{"title":"Interval-Arithmetic-Oriented Interval Computing Technique for Global Optimization","authors":"S. Mahato, A. Bhunia","doi":"10.1155/AMRX/2006/69642","DOIUrl":"https://doi.org/10.1155/AMRX/2006/69642","url":null,"abstract":"Firstly, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented, and then pointing out the drawbacks of these definitions, a new approach is proposed in the context of decision maker’s (optimistic and pessimistic) point of view. Secondly, an interval technique is proposed to solve unconstrained multimodal optimization problems with continuous variables. In this proposed method, the search region is divided into two equal subregions successively and in each subregion, the lower and upper bounds of the objective function are computed with the help of interval arithmetic. Then, by comparing these two interval objective values and considering the subregion containing the better objective value, the global optimal value of the objective function or close to it is obtained. Finally, the proposed method is applied to solve several number of test problems of global optimization with lower as well as higher dimension and is compared with the existing methods with respect to the number of function evaluations.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"6 1","pages":"69642"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88817396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We obtain sufficient conditions for conditional stability of the zero solution of impulsive functional differential equations with impulse perturbations at fixed moments of time. The main results are found by means of piecewise continuous functions, which are analogues of the classical Lyapunov functions and via the comparison method.
{"title":"On the conditional stability of impulsive functional differential equations","authors":"I. Stamova, G. Stamov","doi":"10.1155/AMRX/2006/94865","DOIUrl":"https://doi.org/10.1155/AMRX/2006/94865","url":null,"abstract":"We obtain sufficient conditions for conditional stability of the zero solution of impulsive functional differential equations with impulse perturbations at fixed moments of time. The main results are found by means of piecewise continuous functions, which are analogues of the classical Lyapunov functions and via the comparison method.","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"3 1","pages":"94865"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85747376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the structure of detonation waves in magnetohydrodynamics","authors":"A. Aghajani, M. Hesaaraki","doi":"10.1155/AMRX/2006/96131","DOIUrl":"https://doi.org/10.1155/AMRX/2006/96131","url":null,"abstract":"","PeriodicalId":89656,"journal":{"name":"Applied mathematics research express : AMRX","volume":"22 1","pages":"96131"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74639961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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