This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain hardening and strain softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving, are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a nonlinear Schrödinger equation to construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.
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http://dx.doi.org/10.1103/PhysRevE.107.054208 | DOI Listing |
J Biomech Eng
January 2025
Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093-0411.
Design and analysis are presented for a new device to test the response of endothelial cells to the simultaneous action of cyclic shear stresses and pressure fluctuations. The design consists of four pulsatile-flow chambers connected in series, where shear stress is identical in all four chambers and pressure amplitude decreases in successive chambers. Each flow chamber is bounded above and below by two parallel plates separated by a small gap.
View Article and Find Full Text PDFChaos
July 2024
School of Mathematics, Jilin University, 2699 Qianjin Street, Changchun, Jilin Province, China.
In this study, we perform an extensive numerical study of the one-dimensional Kuramoto-Sivashinsky equation under time-periodic forces. We examine the statistics of chaotic solutions and the behaviors from turbulent solutions to steady periodic solutions as the period of the forces increases. When the period is small, global turbulent characteristics associated with local oscillations are found, and the forces are considered not to influence the turbulent dynamics.
View Article and Find Full Text PDFChaos
April 2024
Institut für Mathematik, Universität Oldenburg, D26111 Oldenburg, Germany.
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie-Gower type. Two regimes are studied in detail. In the first, the homogeneous state loses stability to supercritical spatially uniform oscillations, followed by a subcritical steady state bifurcation of Turing type.
View Article and Find Full Text PDFMath Ann
March 2023
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zurich, Switzerland.
Being driven by the goal of finding edge modes and of explaining the occurrence of edge modes in the case of time-modulated metamaterials in the high-contrast and subwavelength regime, we analyse the topological properties of Floquet normal forms of periodically parameterized time-periodic linear ordinary differential equations . In fact, our main goal being the question whether an analogous principle as the bulk-boundary correspondence of solid-state physics is possible in the case of Floquet metamaterials, i.e.
View Article and Find Full Text PDFPhys Rev E
December 2023
Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.
We consider a system of globally coupled phase-only oscillators with distributed intrinsic frequencies and evolving in the presence of distributed Gaussian white noise, namely, a Gaussian white noise whose strength for every oscillator is a specified function of its intrinsic frequency. In the absence of noise, the model reduces to the celebrated Kuramoto model of spontaneous synchronization. For two specific forms of the mentioned functional dependence and for a symmetric and unimodal distribution of the intrinsic frequencies, we unveil the rich long-time behavior that the system exhibits, which stands in stark contrast to the case in which the noise strength is the same for all the oscillators, namely, in the studied dynamics, the system may exist in either a synchronized, or an incoherent, or a time-periodic state; interestingly, all these states also appear as long-time solutions of the Kuramoto dynamics for the case of bimodal frequency distributions, but in the absence of any noise in the dynamics.
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