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Geometric phases in particle diffusion systems, an intriguing aspect enlightened from thermal systems, offer a different understanding beyond traditional Brownian motion and Fick's laws. This concept introduces a phase factor with…
We propose a mathematical model for describing propagating confined modes in domain walls of intermediate angle between domains. The proposed model is derived from the linearised Bloch equations of motion and after reasonable assumptions,…
We study analytically how noninteracting weakly active particles, for which passive Brownian diffusion cannot be neglected and activity can be treated perturbatively, distribute and behave near boundaries in various geometries. In…
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically…
A systematic study of small, time-dependent, perturbations to geometric wave-equation domains is hardly existent. Acoustic enclosures are typical examples featuring locally reacting surfaces that respond to a pressure gradient or a pressure…
A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
Periodic fluidization of solids in a gas medium can generate structured bubbling patterns. This phenomenon has been successfully reproduced in fluidized bed systems called pulsed-fluidized beds, known for their efficient mixing and…
Femtosecond high-intensity laser pulses at intensities surpassing $10^{14} \,\text{W}/\text{cm}^2$ can generate a diverse range of functional surface nanostructures. Achieving precise control over the production of these functional…
Morphological change of bilayer membrane in vivo is not a spontaneous procedure but modulated by various types of proteins in general. Most of these modulations are associated with the localization of related proteins in the crowded lipid…
We solve a hydrodynamic model of active chromatin dynamics, within a confined geometry simulating the cell nucleus. Using both analytical and numerical methods, we describe the behavior of the chromatin polymer driven by the activity of…
We investigate the dynamics of fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2. We introduce a two-dimensional perturbation method, which generalizes the perturbation method…
Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which…
We expand upon previous work that examined behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations: that of a line and an ellipse and that of a line together with a $p$-sphere. With…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and…
We derive a simple expression for the photon helicity and polarisation-flip probabilities in arbitrary background fields, in the low energy regime. Taking the background to model a focused laser beam, we study the impact of pulse shape and…
Magnetohydrodynamic waves interact with structured plasmas and reveal the internal magnetic and thermal structures therein, thereby having seismological applications in the solar atmosphere. We investigate the evolution of fast…
Fine-grain patterns produced by juxtacrine signalling, have been studied using static monolayers as cellular domains. Unfortunately, analytical results are restricted to a few cells due to the algebraic complexity of nonlinear dynamical…
We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…