相关论文: One-dimensional von K\'arm\'an models for elastic …
A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter h of the cross-section goes to zero. More precisely, we show that stationary points of the nonlinear elastic…
We investigate codimension-one vacua arising from low energy effective actions inspired by string theory, with an eye to their consistency when localized sources are allowed in the equations of motion. We draw some inspiration from…
We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and…
We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost…
We put forward a variational framework suitable for the study of curves whose energies depend on their bend and twist degrees of freedom. By employing the material curvatures to describe such elastic deformation modes, we derive the…
We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…
We consider the dynamics of an electrostatically actuated thin elastic plate being clamped at its boundary above a rigid plate. The model includes the harmonic electrostatic potential in the three-dimensional time-varying region between the…
This paper derives a finite-strain plate theory consistent with the principle of stationary three-dimensional (3-D) potential energy under general loadings with a third-order error. Staring from the 3-D nonlinear elasticity (with both…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the cross-section. We use the approach analogous to the one for rods and curved rods and start from the…
The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as $\Gamma$-limits of 3D atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness $h$ and…
We analyze a recent experiment on a Tonks-Girardeau gas of $^{87}$Rb atoms (T. Kinoshita, T. Wenger, and D.S. Weiss, Science {\bf 305}, 1125 (2004)). We find that the experimental data are compatible with the one-dimensional theory of Lieb,…
The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a…
Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the…
Three-dimensional two-layer incompressible Euler fluids are studied from a Hamiltonian perspective. A natural Hamiltonian structure for the effective 2D model described by the interface-value of the field variables is obtained by means of a…
We present one-dimensional KKR method with the aim to elucidate its linear features, particularly important in optimizing the numerical algorithms in energy bands computations. The conventional KKR equations based on the multiple scattering…
A slender-thread model is derived to explore the Rayleigh-Plateau instability of a filament of elasto-viscoplastic fluid. Without elasticity, a finite yield stress suppresses any linear instability for a filament of constant radius.…
This work is devoted so show the appearance of different cracking modes in linearly elastic thin film systems by means of an asymptotic analysis as the thickness tends to zero. By superposing two thin plates, and upon suitable scaling law…
In this paper we derive the one-dimensional bending-torsion equilibrium model modeling the junction of straight rods. The starting point is a three-dimensional nonlinear elasticity equilibrium problem written as a minimization problem for a…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain, which is theoretically well understood. Here and in the companion paper, we extend this…