Article
Mathematics
Md. Sahidul Islam, Masato Kimura, Hisanori Miyata
Summary: In this paper, a generalized moment method with a continuous weight function is developed to study the mass conservation property of the Smoluchowski coagulation equation in its continuous form. Basic inequalities for the generalized moment are established and used to prove the mass conservation property under certain conditions on the kernel and initial condition. Concrete examples of coagulation kernels that exhibit mass conservation properties and demonstrate polynomial or exponential growth along specific curves are provided.
Article
Mathematics
Sebastian Throm
Summary: This article addresses the uniqueness of self-similar profiles for Smoluchowski's coagulation equation with algebraic decay (fat tails) at infinity. By considering a rate kernel and perturbation, it shows that under certain regularity assumptions, there exists at most one self-similar profile for sufficiently small perturbations. This is the first statement of uniqueness for a non-solvable kernel in the context of fat-tailed self-similar profiles.
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Physics, Multidisciplinary
Koji Ohkitani
Summary: After studying the source-type solution of the standard dissipative Burgers equation, this paper investigates the hypoviscous version of the equation. An equation governing the near-identity transformation of its self-similar solution is determined and an approximation scheme is developed. The source-type solution is obtained numerically using the Newton-Raphson iteration scheme and found to agree well with the first-order approximation. Implications of the source-type solution for linearization of the hypoviscous Burgers equation are discussed. Lastly, the problems of the incompressible fluid equations in two dimensions, specifically the surface quasi-geostrophic equation with standard and hypoviscous dissipativity, are addressed.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Chemistry, Analytical
Chuhang Zhang
Summary: The growth mechanism of size-selected silver nanoclusters generated by modulated pulsed power magnetron sputtering was investigated, and a temperature-dependent fragmentation coefficient was proposed. The results showed that the recombination of cation and anion species is the dominant mechanism for nanocluster growth at lower power, while fragmentation becomes more impactful at higher power.
Article
Mathematics, Applied
S. A. Matveev, A. P. Smirnov, I. Timokhin, E. E. Tyrtyshnikov
Summary: The paper investigates the structure of linear spaces and proposes a model reduction method to reduce high-dimensional problems. The research discovers the possibility of applying higher dimensional bases to lower dimensional problems without significant decrease in the accuracy of numeric solutions.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Reine Gladys Noucheun, Jean Louis Woukeng
Summary: In this study, we conducted a multiscale analysis of Smoluchowski's diffusion-coagulation equations in a thin heterogeneous porous layer. We obtained an upscaled model in the lower space dimension and proved a corrector-type result that is valuable for numerical computations.
Article
Mathematics, Interdisciplinary Applications
Wei Tang, Sze-Man Ngai
Summary: We study the heat equation on a bounded open set U subset of R-d supporting a Borel measure. We obtain asymptotic bounds for the solution and prove the weak parabolic maximum principle. We mainly consider self-similar measures defined by iterated function systems with overlaps. Important information about the structure of these measures can be obtained for a class of measures that we call essentially of finite type. We make use of this information to set up a framework to study the associated heat equations in one dimension. We discretize the heat equation and apply the finite element method to yield a system of linear differential equations. We show the convergence of numerical solutions to the actual solution and provide the rate of convergence. We also investigate the propagation speed problem.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Dongho Chae, Jorg Wolf
Summary: This study focuses on the (alpha, lambda)-discretely self-similar blow up for solutions to the Euler equations for alpha >= 3/2, where sublinear growth is allowed for the profile. It is shown that there are only spatial constant (alpha, lambda)-discretely self-similar solutions with sublinear growth at infinity. A new a priori L-loc(2)(R-3) estimate for the 3D Euler equations is established as part of the proof.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Chemistry, Physical
Kaori Fujii, Tomoaki Yagi, Hiroshi Nakano, Hirofumi Sato, Yoshifumi Kimura
Summary: The recombination dynamics of geminate PAPT radicals produced in ionic liquids were investigated using transient absorption spectroscopy, showing that the recombination yields and dynamics were virtually independent of the cation species. A theoretical analysis model incorporating a square well potential was used to simulate the experimentally obtained time profiles and final yield successfully. The optimized parameters for the fit, including the mutual diffusion coefficient, cage radius, and well depth, were discussed in terms of conventional diffusion theory and potential mean force estimated from molecular dynamics simulation.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Mathematics
Yi Han
Summary: This article constructs unique martingale solutions to the damped stochastic wave equation and shows their applicability to a wider class of SPDEs. It also demonstrates the validity of the Smoluchowski-Kramers approximation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2024)
Article
Physics, Multidisciplinary
Pavel Castro-Villarreal, Cesar O. Solano-Cabrera, Ramon Castaneda-Priego
Summary: Brownian motion is a universal characteristic in physics and other fields, and its understanding is crucial for various applications. The study of colloidal dynamics in curved spaces can provide insights into phenomena such as spinodal decomposition and thermodynamics, as well as the role of geometry in complex transport processes.
FRONTIERS IN PHYSICS
(2023)
Article
Mathematics
James A. McCoy
Summary: The article discusses the fully nonlinear contraction of convex hypersurfaces by nonhomogeneous functions of curvature, and explores self-similar solutions to curvature flows that are not homogeneous in principle curvatures, revealing situations where curvature-pinched hypersurfaces contracting self-similarly must necessarily be spheres.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Materials Science, Multidisciplinary
Koen Heijmans, Bern Klein Holkenborg, Silvia Gaastra-Nedea, David Smeulders
Summary: Through simulation and analysis of the diffusion behavior of water in crystalline CaCl2.2H(2)O, it was found that crystal imperfections such as cracks and pores can significantly enhance the diffusion performance of salt hydrates, thereby improving their characteristics for thermochemical heat storage applications.
COMPUTATIONAL MATERIALS SCIENCE
(2022)
Article
Astronomy & Astrophysics
Raquel Galazo-Garcia, Philippe Brax, Patrick Valageas
Summary: Fuzzy dark matter (FDM) models have self-similar solutions that differ greatly from the self-similar solutions of standard cold dark matter (CDM) models and do not converge to the latter in the semiclassical limit. These self-similar solutions in FDM models exhibit an inverse-hierarchy blowup, where larger masses become linear first, in contrast to the familiar CDM hierarchical collapse. This blowup process roughly follows the Hubble expansion and maintains a constant central density contrast over time, although the width of the self-similar profile shrinks in comoving coordinates.
Article
Chemistry, Physical
Vladimir D. Sobolev, Anatoly N. Filippov, Victor M. Starov
Summary: In the measurements of membranes with high porosity and permeability, it is necessary to introduce a correction that accounts for the influence of fluid flow and charge transfer inside the membrane. Equations for modified zeta potential calculations were derived for both streaming potential and streaming current measurements considering flow and charge transfer inside the membrane.
JOURNAL OF MOLECULAR LIQUIDS
(2021)
Article
Mathematics, Applied
Miguel Escobedo, Minh-Binh Tran
KINETIC AND RELATED MODELS
(2015)
Article
Mathematics
M. Escobedo, J. J. L. Velazquez
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY
(2015)
Article
Mathematics, Applied
Hind Al Baba, Cherif Amrouche, Miguel Escobedo
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2017)
Article
Mathematics, Applied
Marie Doumic, Miguel Escobedo
KINETIC AND RELATED MODELS
(2016)
Article
Mathematics, Applied
Marie Doumic, Miguel Escobedo, Magali Tournus
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2018)
Article
Physics, Mathematical
M. Escobedo, J. J. L. Velazquez
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2014)
Article
Mathematics
M. Escobedo, J. J. L. Velazquez
INVENTIONES MATHEMATICAE
(2015)
Article
Mathematics, Applied
Thibault Bourgeron, Marie Doumic, Miguel Escobedo
Article
Mathematics
L. Corrias, M. Escobedo, J. Matos
JOURNAL OF DIFFERENTIAL EQUATIONS
(2014)
Article
Physics, Mathematical
E. Cortes, M. Escobedo
JOURNAL OF STATISTICAL PHYSICS
(2019)
Article
Biochemical Research Methods
Magali Tournus, Miguel Escobedo, Wei-Feng Xue, Marie Doumic, Philip K. Maini, Mark Alber, Philip K. Maini, Mark Alber, Philip K. Maini, Mark Alber
Summary: The study discovered mathematical formulae to extract fibril division characteristics from experimental data and discussed the impact of small errors in measurements on division rate. It also suggested new experimental designs to improve estimates of division patterns.
PLOS COMPUTATIONAL BIOLOGY
(2021)
Article
Mathematics
M. Escobedo
Summary: The purpose of this work is to solve the Cauchy problem for the classical approximation of a linearized three waves kinetic equation that appears in the kinetic theory of a condensed gas of bosons near the critical temperature. The fundamental solution is obtained, proved to be unique in a suitable space of distributions, and some of its regularity and integrability properties are described. The initial value problem for integrable and locally bounded initial data is then solved. Classical solutions are obtained as functions, whose regularity depends on time and that satisfy the expected conservation of energy.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
M. Escobedo
Summary: We study the linearization of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas at very low temperature and small condensate density, around one of its equilibrium points. Using a simple and transparent argument, we give a necessary and sufficient condition for the existence of global solutions that satisfy the conservation of the total number of particles and energy. The global solutions describe the time evolution of the density of the thermal cloud and the condensate's density, unlike previous work, and we also demonstrate the convergence of these global solutions to a suitable stationary state, obtaining convergence rates for the normal fluid and superfluid components.
STUDIES IN APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
M. Escobedo
Summary: The Cauchy problem for the linearization around one of its equilibria of a non linear system of equations arising in the kinetic theory of a condensed gas of bosons near the critical temperature is solved for radially symmetric initial data. As time tends to infinity, the solutions are proved to converge to an equilibrium of the same linear system determined by the conservation of total mass and energy. The asymptotic limit of the condensate's density is proved to be larger or smaller than its initial value under a simple and explicit criteria on the initial data. For a large set of initial data and for values of the momentum variable near the origin, the linear approximation n(t) of the density of the normal fluid behaves instantaneously as the equilibria of the non linear system.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2023)
Article
Mathematics
Miguel Escobedo
COMPTES RENDUS MATHEMATIQUE
(2017)
