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The low Mach number limit for one-dimensional non-isentropic compressible Navier-Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the…

Analysis of PDEs · Mathematics 2017-05-23 Yechi Liu

In the dynamics of linear structures, the impulse response function is of fundamental interest. In some cases one examines the short term response wherein the disturbance is still local and the boundaries have not yet come into play, and…

Computational Engineering, Finance, and Science · Computer Science 2023-10-03 Bidhayak Goswami , K. R. Jayaprakash , Anindya Chatterjee

We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are…

Analysis of PDEs · Mathematics 2010-11-04 Bin Cheng

We consider generalised versions of the spin-boson model at small coupling. We assume the spin (or atom) to sit at the origin $0 \in \mathbb{R}^d$ and the propagation speed $v_p$ of free bosons to be constant, i.e.\ independent of momentum.…

Mathematical Physics · Physics 2014-02-21 W. De Roeck , A. Kupiainen

We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…

Soft Condensed Matter · Physics 2016-08-31 J. M. Skotheim , L. Mahadevan

A novel method for the numerical prediction of the slowly varying dynamics of nonlinear mechanical systems has been developed. The method is restricted to the regime of an isolated nonlinear mode and consists of a two-step procedure: In the…

Computational Engineering, Finance, and Science · Computer Science 2021-01-01 Malte Krack , Lars Panning-von Scheidt , Jörg Wallaschek

In spite of recent progress, soft robotics still suffers from a lack of unified modeling framework. Nowadays, the most adopted model for the design and control of soft robots is the piece-wise constant curvature model, with its consolidated…

Robotics · Computer Science 2018-10-25 Federico Renda , Frederic Boyer , Jorge Dias , Lakmal Seneviratne

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2$\epsilon$) tends to zero. Using a novel asymptotic expansion we determine the behavior of the…

Numerical Analysis · Mathematics 2017-11-23 Marie Chaussade-Beaudouin , Monique Dauge , Erwan Faou , Zohar Yosibash

In this paper, we explore the low Mach number singular limit of the local-in-time strong solutions to the compressible primitive equations with gravity for general adiabatic coefficient. First we construct the uniform estimate for the…

Analysis of PDEs · Mathematics 2023-10-03 Pengcheng Mu

This is the less technical half of a two-part work in which we introduce a robust microlocal framework for analyzing the non-relativistic limit of relativistic wave equations with time-dependent coefficients, focusing on the Klein--Gordon…

Analysis of PDEs · Mathematics 2025-11-13 Andrew Hassell , Qiuye Jia , Ethan Sussman , Andras Vasy

We study a superlinear and subcritical Kirchhoff type equation which is variational and depends upon a real parameter $\lambda$. The nonlocal term forces some of the fiber maps associated with the energy functional to have two critical…

Analysis of PDEs · Mathematics 2019-06-12 Kaye Silva

The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…

Soft Condensed Matter · Physics 2024-09-19 Alessandro Cazzolli , Francesco Dal Corso

We derive asymptotic expansions for the displacement at the boundary of a smooth, elastic body in the presence of small inhomogeneities. Both the body and the inclusions are allowed to be anisotropic. This work extends prior work of…

Analysis of PDEs · Mathematics 2011-05-23 Elena Beretta , Eric Bonnetier , Elisa Francini , And Anna L Mazzucato

We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter $\varepsilon \to 0$, the Froude number proportional to $\sqrt{\varepsilon}$ and when the fluid…

Analysis of PDEs · Mathematics 2022-11-10 Aneta Wróblewska-Kamińska

We investigate 3-dimensional flagellar swimming in a fluid with a sparse network of stationary obstacles or fibers. The Brinkman equation is used to model the average fluid flow where a flow-dependent term, including a resistance parameter…

Fluid Dynamics · Physics 2019-03-27 Nguyenho Ho , Karin Leiderman , Sarah Olson

This review presents the elastic theory of low-dimensional (one- and two-dimensional) continua and its applications in bio- and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional…

Soft Condensed Matter · Physics 2015-01-20 Z. C. Tu , Z. C. Ou-Yang

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not…

Differential Geometry · Mathematics 2014-09-09 Raz Kupferman , Jake P. Solomon

The paper presents a constraint-based collision model for Cosserat rods, able to handle dynamic or static contact between a large number of highly flexible structures. The model provides the required collision impulses prior to updating the…

Soft Condensed Matter · Physics 2025-04-30 Bastian Löhrer , Rolf Krause , Jochen Fröhlich

We investigate various versions of multi-dimensional systems involving many species, modeling aggregation phenomena through nonlocal interaction terms. We establish a rigorous connection between kinetic and macroscopic descriptions by…

Analysis of PDEs · Mathematics 2024-02-06 Young-Pil Choi , Simone Fagioli , Valeria Iorio

Starting from a three-dimensional model based on the Ciarlet-Geymonat energy, we derive nonlinear shell models within the classical elasticity theory of compressible isotropic materials. The Neo-Hookean term involving the norm of the…

Analysis of PDEs · Mathematics 2026-03-20 Ionel-Dumitrel Ghiba , Trung Hieu Giang , Catalina Ureche