相关论文: Resonances and Eigenvalues for the Constant Mean C…

This research investigates the formation and stability of localized states, known as quantum droplets and bubbles, in the quadratic-cubic discrete nonlinear Schr\"odinger equation. Near a Maxwell point, these states emerge from two fronts…

We investigate the Neumann problem for the critical semilinear elliptic equation in cones. The standard bubble provides a family of radial solutions, which are known to be the only positive solutions in convex cones. For nonconvex cones,…

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry…

We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process.…

Motivated by the desire to understand complex transient behaviour in fluid flows, we study the dynamics of an air bubble driven by the steady motion of a suspending viscous fluid within a Hele-Shaw channel with a centred depth perturbation.…

The square-gradient density-functional model with triple-parabolic free energy, that was used previously to study the homogeneous bubble nucleation [J. Chem. Phys. 129, 104508 (2008)], is used to study the stability of the critical bubble…

We study the formation of generic singularities of mean curvature flow by combining the different approaches, specifically the methods in studying blowup of nonlinear heat equations, the techniques used by the author and the collaborators…

We study the perturbation of bound states embedded in the continuous spectrum which are unstable by the Fermi Golden Rule. The approach to resonance theory based on spectral deformation is extended to a more general class of quantum systems…

In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to…

Recent studies have raised doubts about the occurrence of r modes in Newtonian stars with a large degree of differential rotation. To assess the validity of this conjecture we have solved the eigenvalue problem for Rossby-Haurwitz waves…

Following ideas of Gromov we prove scalar and mean curvature comparison results for Riemannian bands with lower scalar curvature bounds in dimension $n\leq7$. The model spaces we use are warped products over scalar-flat manifolds with…

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being…

The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…

We calculate analytically the distributions of "level curvatures" (LC) (the second derivatives of eigenvalues with respect to a magnetic flux) for a particle moving in a white-noise random potential. We find that the Zakrzewski-Delande…

Circumstellar dust particles can be captured in a mean motion resonance with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the mean motion…

We show that the rotating Rayleigh-Benard convection, where a rotating fluid is heated from below, exhibits non-Hermitian topological states. Recently, Favier and Knobloch (JFM 2020) hypothesized that the robust wall modes in rapidly…

The Thouless conjecture states that the average conductance of a disordered metallic sample in the diffusive regime can be related to the sensitivity of the sample's spectrum to a change in the boundary conditions. Here we present results…

Context: The Circular Restricted Three-Body Problem provides a fundamental framework for understanding resonant dynamics in binary star systems. Aims: We develop a unified Hamiltonian formulation for mean-motion resonances that encompasses…

Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n \geq 25$ with positive Yamabe invariant $Y(M,g_0)>0$ and positive fourth-order invariant $Y_4(M,g_0)>0$. We show that, arbitrarily $C^1$-close to $g_0$, there exists a Riemannian…

We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…