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We revisit the interaction of an initially uniform near-inertial wave (NIW) field with a steady background flow, with the goal of predicting the subsequent organization of the wave field. To wit, we introduce an exact analogy between the…
In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic…
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is…
A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
From particle lifting in atmospheric boundary layers to dust ingestion in jet engines, the transport and deposition of inertial particles in wall-bounded turbulent flows are prevalent in both nature and industry. Due to triboelectrification…
Optimization of quantum states using the variational principle has recently seen an upsurge due to developments of increasingly expressive wave functions. In order to improve on the accuracy of the ans\"atze, it is a time-honored strategy…
We reinvestigate numerically the classic problem of two-dimensional superfluid flow past an obstacle. Taking the obstacle to be elongated (perpendicular to the flow), rather than the usual circular form, is shown to promote the nucleation…
A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and…
This article is devoted to the study of local well-posedness for deep water waves with constant vorticity in two space dimensions on the real line. The water waves can be paralinearized and written as a quasilinear dispersive system of…
The problems with an emergent approach to quantum statistical mechanics are discussed and shown to follow from some of the same sources as those of quantum measurement. A wavefunction of an N atom solid is described in the ground and…
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modelled theoretically using a mass-imbalanced homogeneous two component Gross-Pitaevskii equation where each…
A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source…
We describe kinetic simulations of transient problems in partially ionized weakly-collisional plasma around spherical bodies absorbing or emitting charged particles. Numerical solutions of kinetic equations for electrons and ions in 1D2V…
In this paper, we formulate, analyse and implement the discrete formulation of the Brinkman problem with mixed boundary conditions, including slip boundary condition, using the Nitsche's technique for virtual element methods. The divergence…
Artificial electrostatic potentials can be present in supercells constructed for atomistic simulations of surfaces and interfaces in ionic crystals. Treating the ions as point charges, we systematically derive an electrostatic formalism for…
The nodal structure of bound-state wave functions for one-dimensional quantum systems with quartic energy-momentum dispersion and polynomial potentials is analysed by using the semiclassical approximation and variational approach. For…
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems,…
The $n+1$ vortex filament problem has explicit solutions consisting of $n$ parallel filaments of equal circulation in the form of nested polygons uniformly rotating around a central filament which has circulation of opposite sign. We show…
We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb…