Article
Mathematics, Applied
Yanlin Liu, Li Xu
Summary: In this paper, we study the global existence of a unique strong solution to the 3-D Navier-Stokes equations with almost axisymmetric initial data. We establish refined estimates for the integral average in the θ variable and consider the expansion of the initial data into Fourier series. The asymptotic expansion of the solution is also studied, along with the influence between different profiles.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2023)
Article
Chemistry, Physical
R. T. van Gaalen, C. Diddens, H. M. A. Wijshoff, J. G. M. Kuerten
Summary: The study shows that stronger evaporation, slower adsorption kinetics, and lower solubility of surfactants tend to suppress the Marangoni circulation. Diffusion and the formation of micelles also have an impact on Marangoni flow, with micelles sometimes enhancing circulatory behavior.
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2021)
Article
Mathematics, Applied
Arnold Reusken
Summary: This paper studies the finite element discretizations of a surface vector-Laplace eigenproblem. Two known classes of finite element methods are considered, with a focus on the penalization method used to enforce tangentiality of the vector field. The paper presents a general abstract framework for such nonconforming discretizations of eigenproblems, and derives error bounds and convergence properties through numerical experiments.
MATHEMATICS OF COMPUTATION
(2022)
Article
Mathematics, Applied
Luan T. Hoang, Edriss S. Titi
Summary: In this study, the three-dimensional Navier-Stokes equations for rotating incompressible viscous fluids with periodic boundary conditions are investigated. Asymptotic expansions in all Gevrey spaces are derived for Leray-Hopf weak solutions, using oscillating, exponentially decaying functions. The results are applicable for all non-zero rotation speeds, with and without zero spatial average of the solutions.
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2021)
Article
Computer Science, Interdisciplinary Applications
Takuji Ishikawa
Summary: This study proposes a novel hybrid method combining lubrication theory (LT) and boundary element method (BEM) called LT-BEM, which can accurately calculate the rheological and diffusion properties of small particle suspensions. The LT-BEM successfully captures the asymptotic nature of forces and torques acting on two spheres and dramatically improves the accuracy of squeezing force, preventing particle overlap. It is applicable to various shapes of particles and demonstrated advantages in applications involving pairwise microswimmers and bacteria interactions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
He-Wei Du, Peng Gao
Summary: In this study, an asymptotic theory of gas film thickness selection based on lubrication approximations is presented. It is found that the gas film thickness primarily depends on the curvature of the meniscus, determined by the balance between capillary force and gravity. The influence of plate speed on gas film thickness follows the classical 2/3 power law, with a mild correction from the gas-liquid viscosity ratio.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2022)
Article
Mathematics, Applied
Thomas G. Anderson, Marc Bonnet, Shravan Veerapaneni
Summary: This study focuses on the mixing of passive tracers by an incompressible viscous fluid. A physically inspired surrogate norm, the negative index Sobolev norm, is used to quantify mixing in the complex fluid mixing domain. The computation of the norm requires the computation of an eigenbasis for L-2(Omega). Instead, a representative of the scalar concentration field in an appropriate Sobolev space is computed to obtain an equivalent definition of the norm. Fast and accurate potential theoretic methods are used to efficiently solve the elliptic problems related to the concentration field, and numerical results demonstrate the convergence of the approach.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics
Carmela Scalone
Summary: In this work, a numerical method for discretizing linear stochastic oscillators is proposed, which is compared with a standard approach through theoretical considerations and numerical experiments.
Article
Mathematical & Computational Biology
Aline Lefebvre-Lepot, Flore Nabet
Summary: This research focuses on the numerical simulation of suspensions of rigid particles in Stokes flow, with particular emphasis on including singular short range interaction effects without introducing new hypotheses or models. By decomposing the velocity and pressure flows into singular and regular parts, and utilizing explicit asymptotic expansions for calculating the singular part, accurate results can be obtained with minimal degrees of freedom. Testing in 2D scenarios demonstrates the method's effectiveness for various particle clusters.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2021)
Article
Chemistry, Physical
R. T. van Gaalen, H. M. A. Wijshoff, J. G. M. Kuerten, C. Diddens
Summary: The study investigates the relationship between thermal Marangoni flow and surfactant dynamics using two numerical models. It is found that insoluble surfactants can suppress the thermal Marangoni flow if their concentration is sufficiently large and evaporation and diffusion are slow. Soluble surfactants, on the other hand, can either reduce or increase interfacial velocity depending on their sorption kinetics. The study also shows that a small concentration of insoluble surfactants can significantly decrease the tangential flow velocity at the interface. The numerical models are validated through comparison in cases where both are applicable.
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2022)
Article
Mathematics
Shuya Kanagawa
Summary: This study investigates asymptotic expansions for U-statistics and V-statistics with degenerate kernels, showing remainder terms of O(n(1-p/2)) in both cases. The results also suggest that asymptotic expansions for the Cramer-von Mises statistics of the uniform distribution U(0,1) are valid with the remainder term O(n(1-p/2) for any p >= 4. The proof scheme is based on three steps: almost sure convergence in a Fourier series expansion, representation of statistics by single sums of Hilbert space valued random variables, and application of asymptotic expansions for single sums of Hilbert space valued random variables.
Article
Mathematics, Applied
Sourav Das, A. Swaminathan
Summary: In this work, we focus on establishing asymptotic expansions for the triple gamma function using the triple Bernoulli polynomials. We also obtain an asymptotic expansion for the hyperfactorial function as an application. Additionally, we derive Pade approximants related to the triple gamma function using these asymptotic expansions, and demonstrate the importance of the results by deducing interesting remarks and corollaries.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Huijie Zhang
Summary: This paper discusses the Omega function and related quantities, and presents asymptotic expansions and new bounds. The effectiveness and feasibility of the proposed method are demonstrated through a numerical example.
RESULTS IN MATHEMATICS
(2022)
Article
Mathematics, Applied
A. Gil, J. Segura, N. M. Temme
Summary: This paper presents new and complete asymptotic expansions for the relativistic Fermi-Dirac integral, which can be applied in nuclear astrophysics, solid state physics, and semiconductor modeling to help achieve a correct qualitative understanding of Fermi systems. The performance of the expansions is demonstrated through numerical examples.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Peter Opsomer, Daan Huybrechs
Summary: Gaussian quadrature rules are effective in numerically approximating integrals with smooth integrands and positive weight functions. In this study, we derive and list asymptotic expressions for the points and weights of Gaussian quadrature rules for three general classes of positive weight functions. These rules cover various situations including classical orthogonal polynomials. Additionally, we provide experimental evidence for the precision achieved by these expressions and present an algorithm to compute the expansions for classical and generalized cases.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
