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Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an…
An analytical method is proposed for computing the low-Reynolds-number hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with…
We introduce a relativistic splitting structure as a means to map fields and equations of electromagnetism from curved four-dimensional space-time to three-dimensional observer's space. We focus on a minimal set of mathematical structures…
Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a…
Hierarchical dynamics in glass-forming systems span multiple timescales, from fast vibrations to slow structural rearrangements, appearing in both supercooled fluids and glassy states. Understanding how these diverse processes interact…
Liquid crystal elastomers represent a novel class of programmable shape-transforming materials whose shape change trajectory is encoded in the material's nematic director field. Using three-dimensional nonlinear finite element…
We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we…
This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…
This paper investigates the flow past a flexible splitter plate attached to the rear of a fixed circular cylinder at a low Reynolds number of 150. A systematic exploration of the plate length ($L/D$), flexibility coefficient ($S^{*}$), and…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the electromagnetic resonators share a common property:…
We present a detailed derivation of the renormalization group equations for two dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between…
The equilibrium behavior of a system of elastic layers under tension in the presence of correlated disorder is studied using functional renormalization group techniques. The model exhibits many of the features of the Bose glass phase of…
We investigate the elastic normal modes of two-dimensional media with broken time-reversal and parity symmetries due to a Lorentz term. Our starting point is an elasticity theory that captures the low-energy physics of a diverse range of…
According to the principle of relativity, the equations describing the laws of physics should have the same forms in all admissible frames of reference, i.e., form-invariance is an intrinsic property of correct wave equations. However, so…
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in…
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless…