Related papers: Adiabatic stability under semi-strong interactions…
We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system, and argue that it offers lessons for real molecular collisions in…
We study the problem of stability of the catenoid, which is an asymptotically flat rotationally symmetric minimal surface in Euclidean space, viewed as a stationary solution to the hyperbolic vanishing mean curvature equation in Minkowski…
The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions.…
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
This paper is concerned with the existence and stability of phase transition steady states to a quasi-linear hyperbolic-parabolic system of chemotactic aggregation, which was proposed in \cite{ambrosi2005review, gamba2003percolation} to…
The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…
High levels of penetration of distributed generation and aggressive reactive power compensation with modern power electronics may result in the reversal of active and reactive power flows in future distribution grids. The voltage stability…
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is…
A system of N classical particles in a 2D periodic cell interacting via long-range attractive potential is studied. For low energy density $U$ a collapsed phase is identified, while in the high energy limit the particles are homogeneously…
We use the invariant-based inverse engineering subject to the quasiadiabatic condition to produce robust and high fidelity coherent superposition of quantum states. The inverse engineering provides shortcuts to the desired quantum-state…
We investigate the asymptotic stability of standing waves for a model of Schr\"odinger equation with spatially concentrated nonlinearity in space dimension three. The nonlinearity studied is a power nonlinearity concentrated at the point…
We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…
Recent real-time TDDFT calculations have reported an unexpected delayed growth of molecular dipole oscillations some time after an extreme-ultraviolet (XUV) pulse is applied. We show that numerical and analytical arguments suggest that this…
We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well controlled numerical method based on the tensor network algorithm, we calculate…
We provide a rigorous justication of nonlinear geometric optics expansions for reflecting \emph{pulses} in space dimensions $n>1$. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The…
We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations, that is to nonlinear Schroedinger equations in which either the nonlinear coupling constant or, equivalently, the…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
A novel, compact, quasi-axisymmetric configuration is presented which exhibits low fast-particle losses and is stable to ideal MHD instabilities. The design has fast-particle loss rates below 8\% for flux surfaces within the half-radius,…
Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…