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Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant…
The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important ``topological" transitions are…
A diagnostics method based on a continuous wavelet transform is proposed. This method makes it possible to diagnose the presence of synchronization of the oscillations of a self-excited oscillator locked by an external force with a linearly…
We consider the impact of stochastic perturbations on otherwise coherent oscillations of classical pulsators. The resulting dynamics are modelled by a driven damped harmonic oscillator subject to either an external or an internal forcing…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state…
We discuss the origin of the leg factors appearing in 2D string theory. Computing in the world sheet framework we use the semiclassical method to study string amplitudes at high energy. We show that in the case of a simplest 2-point…
Internal activity can fundamentally reshape the mechanical behavior of solids, yet its role in softening and failure remains incompletely understood. In this study, we investigate spontaneous deformations in activated solids via non-affine…
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes…
The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
Synchronization is ubiquitous in nature at various scales and fields. This phenomenon not only offers a window into the intrinsic harmony of complex systems, but also serves as a robust probe for many-body quantum systems. One such system…
We study a class of fourth-order quasilinear degenerate parabolic equations under both time-and space-dependent and time-and space-independent forces, modeling non-Newtonian thin-film flow over a solid surface in the "complete wetting"…
Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensed-matter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin…
When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the…
Gravity-induced buoyancy, inevitable in most solidification processes, substantially alters the dynamics of crystal growth, such that incorporating fluid flow in solidification models is crucial to understand and predict key aspects of…
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional…
As a prototype of systems bearing a localization-delocalization transition, the strand-separation (melting) process in a double-stranded biopolymer is studied by a mapping to a quantum-mechanical problem with short-ranged potentials. Both…
We experimentally study a one-dimensional uncompressed granular chain composed of a finite number of identical spherical beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary…
The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental…
This work investigates the effect of nonlinearities on topologically protected edge states in one and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are…