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We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…

In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure…

Epithelial-Mesenchymal Transition (EMT), and the corresponding reverse process, Mesenchymal-Epithelial Transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at biochemical and morphological levels. A…

A reformulation of Maxwell equations for an inhomogeneous, anisotropic, passive and non-dispersive medium results in a quantum-like Dirac equation that admits unitary time evolution. In contrast to other approaches, there is no a-priori…

Maxwell equations provide a complete description of the electromagnetic (EM) phenomena, which have been one of the key fundamental-theories of modern physics, such as electromagnetism, optics, quantum theories, etc. The vacuum permittivity…

Moore-Gibson-Thompson (MGT) equations, which describe acoustic waves in a heterogeneous medium, are considered. These are the third order in time evolutions of a predominantly hyperbolic type. MGT models account for a finite speed…

In the recent work~\cite{Wang:2021p2}, the author proposed the expanded Maxwell's equations for moving charged media system, which seems subtle. Considering a very short time, we can approximately define the inertial frame of reference. If…

Eco-evolutionary dynamics, or eco-evolution for short, are thought to involve rapid demography (ecology) and equally rapid phenotypic changes (evolution) leading to novel, emergent system behaviours. This focus on contemporary dynamics is…

We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d > 1, whose quench and Floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for…

Observations of the CMB today allow us to answer detailed questions about the properties of our Universe, targeting both standard and non-standard physics. In this paper, we study the effects of varying fundamental constants (i.e., the…

This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are…

Extreme-mass-ratio inspirals are one of the most exciting and promising target sources for space-based interferometers (such as LISA, TianQin). The observation of their emitted gravitational waves will offer stringent tests on general…

Mass transfer (MT) is a fundamental process in stellar evolution. While MT in circular orbits is well studied, observations indicate that it also occurs in eccentric ones, where theoretical models are limited. We present a new semi-analytic…

The Hamiltonian of a linearly driven two-level system, or qubit, in the standard rotating frame contains non-commuting terms that oscillate at twice the drive frequency, $\omega$, rendering the task of analytically finding the qubit's time…

The striking success of the Standard Model in explaining precision data and, at the same time, its lack of explanations for various fundamental phenomena, such as dark matter or the baryon asymmetry of the universe, suggests new physics at…

An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…

Continual Model Merging (CMM) sequentially integrates task-specific models into a unified architecture without intensive retraining. However, existing CMM methods are hindered by a fundamental saturation-redundancy dilemma: backbone-centric…

The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…

A method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories (EFT) which are non-perturbative at leading order is presented. The Renormalisation Group evolution of an observable predicts the…

Effective theory framework based on symmetry has recently gained widespread interest in the field of cosmology. In this paper, we apply the same idea on the genesis of the primordial magnetic field and its evolution throughout the…