Related papers: Non-trivial solution to a simple problem
The non-equilibrium structural and dynamical properties of a flexible polymer tethered to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
Given finitely many pointed forces in the plane. Suppose that these forces sum up to zero and their net torques also sum up to zero. One can show that there exists a system of springs whose boundary forces exactly counter-balance these…
Within the context of linear elasticity we show that a two-terminal network of springs and masses, can respond exactly the same as a normal spring, but with a frequency dependent spring constant. As a consequence a network of such springs…
This work investigates the dynamics of a one-dimensional homogeneous harmonic chain on a horizontal table. One end is anchored to a wall, the other (free) end is pulled by external force. A Green's function is derived to calculate the…
In this paper, we consider a mass-spring-friction oscillator with the friction modelled by a regularized stiction model in the limit where the ratio of the natural spring frequency and the forcing frequency is on the same order of magnitude…
A thin infinitely long elastic shell is stiffened by $J$ in number identical lengthwise ribs distributed uniformly around the circumference and joined to a rod in the center. The 2D model of the substructure is a rigid central mass…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
A system of equations consisting of an infinite string coupled to a nonlinear oscillator is considered. The Cauchy problem for the system with the periodic initial data is studied. The main goal is to prove the convergence of the solutions…
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…
We consider the (in)stability problem of the inviscid 2D Boussinesq equations near a combination of a shear flow $v=(y,0)$ and a stratified temperature $\theta=\alpha y$ with $\alpha>\frac{1}{4}$. We show that for any $\epsilon>0$ there…
We consider the stability of periodic gravity-capillary waves of finite amplitude for small values of the surface tension. Linear stability with respect to both superharmonic and subharmonic perturbations is calculated for each solution,…
In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
Using dynamic simulations and analytic methods, we study the elastic response of a helical filament subject to uniaxial tension over a wide range of bend and twist persistence length. A low-pitch helix at low temperatures exhibits a…
In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stress-strain law close to the linear case. We consider…
The rheological properties of soft materials often exhibit surprisingly universal linear and non-linear features. Here we show that these properties can be unified by considering the effect of the strain-rate amplitude on the structural…
A simple two charge system, one charge being suspended on a spring, exhibits complex behavior including bistability, hysteresis and catastrophic response to gradual variation of the external parameters. We discuss these complex features…
The free motion of balls is investigated experimentally in continously stratified fluid in a finite container. The oscillation frequency is found to be very close to the local Brunt-Vaisala frequency. The effect of added mass proves to be…
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…