相关论文: Stable determination of the Winkler subgrade coeff…

Nanoindentation is a widely used method for sensitive exploration of the mechanical properties of micromechanical systems. We derived an empirical analysis technique to extract stress-strain field gradient and divergence representations…

In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…

A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a…

The variational static formulation contributed in [International Journal of Engineering Science 143, 73-91 (2019)] is generalized in the present paper to model axial and flexural dynamic behaviors of elastic nano-beams by nonlocal strain…

We are concerned with the Calder\'on problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the…

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for the inverse problem of determining smooth cavities inside a thin isotropic cylinder {}from a single…

We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of K\"ahler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) to compute the stability thresholds…

The rotation of a nanoparticle in a quantum system has many applications, from theory to experiments. This paper will treat nanoparticle rotational dynamics for spin-embedded nanorotors. We will model it as a rigid body that properly treats…

We analyze the stability of the Von K\'arm\'an model for thin plates subject to pure Neumann conditions and to dead loads, with no restriction on their direction. We prove a stability alternative, which extends previous results by…

In this paper, we consider the Kirchhoff plate equation with delay terms on the boundary control are added (see system \eqref{p5-2.1} below). we give some instability examples of system \eqref{p5-2.1} for some choices of delays. Finally, we…

We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack.…

Dynamical stability is a prerequisite for control and functioning of desired nano-machines. We utilize the Caldeira-Leggett master equation to investigate dynamical stability of molecular cogwheels modeled as a rigid, propeller-shaped…

This work presents a generalized Kirchhoff-Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for…

Self-assembling novel ordered structures with nanoparticles has recently received much attention. Here we use computer simulations to study a two-dimensional model system characterized by a simple isotropic interaction that could be…

We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…

We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove H{\"o}lder stability with…

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier-Stokes equations, from a single measurement of force and velocity on a portion of the…

In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts. In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality:…