Related papers: Non-trivial solution to a simple problem
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…
We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged…
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear…
We study a simple micro-mechanical device that does not lose its snap-through behavior in an environment dominated by fluctuations. The main idea is to have several degrees of freedom that can cooperatively resist the de-synchronizing…
Implant placement under soft tissues operation is described. In this operation tissues can reach such deformations that nonlinear properties are appeared. A mass-spring model modification for modeling nonlinear tissue operation is…
The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body).…
Using a one-dimensional jellium model and standard beam theory we calculate the spring constant of a vibrating nanowire cantilever. By using the asymptotic energy eigenvalues of the standing electron waves over the nanometer-sized…
Nonlinear effects were observed in a forced vibrating string. The motion of the string becomes elliptic as the amplitude of the vibration increases. The fundamental resonance frequency depends on the amplitude of the vibration. At…
Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size.…
This study is on small oscillations of a heavy symmetric top. A different method than previous works is applied, and differently from previous works, the explicit formulas for the amplitudes for oscillations are given. This method can be…
We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We…
By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary…
Using the short-wavelength instability method, we investigate the linear instability of an exact solution describing upward-propagating mountain waves, derived in A. Constantin, \emph{J. Phys. A: Math. Theor.} (2023), under the assumption…
We consider two dimensional nonstationary scattering of plane waves by a NN-wedge. We prove the existence and uniqueness of a solution to the corresponding mixed problem and we give an explicit formula for the solution. Also the Limiting…
The classical problem of the brachistochrone asks for the curve down which a body sliding from rest and accelerated by gravity will slip (without friction) from one point to another in least time. In undergraduate courses on classical…
Stochastic physics is a central pillar of modern research in many fields, but is rarely presented to undergrad students in a hands-on experiment. Here, we demonstrate how a human-scale, simple, and affordable experimental setup can be used…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
Two surfaces are "sticky" if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or…
The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains. Existence and uniqueness of the problem can be proved…
A popular problem asks for the equilibrium separation between two identical (mutually repelling) charges suspended by strings fastened to a common point. We slightly modify this problem by considering two opposite (mutually attracting)…