Related papers: Nonlocal interactions by repulsive-attractive pote…
Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types…
We study two interacting identical run and tumble particles (RTP's) in one dimension. Each particle is driven by a telegraphic noise, and in some cases, also subjected to a thermal white noise with a corresponding diffusion constant $D$. We…
We investigate the emergent interactions between two active Brownian particles coupled by an attractive harmonic potential and in contact with a thermal reservoir. By analyzing the stationary distribution of their separation, we demonstrate…
We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the…
This article extends the previous paper in "M.W. Yuen, \textit{Stabilities for Euler-Poisson Equations in Some Special Dimensions}, J. Math. Anal. Appl. \textbf{344} (2008), no. 1, 145--156.", from the Euler-Poisson equations for attractive…
We consider the one-dimensional Schroedinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the…
We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or…
A model of a particle in finite space is developed and the properties that the particle may possess under this model are studied. The possibility that particles attract each other due to their own wave nature is discussed. The assumption…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
We investigate stationary solutions of a non-local aggregation equation with degenerate power-law diffusion and bounded attractive potential in arbitrary dimensions. Compact stationary solutions are characterized and compactness…
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are…
We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show…
The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the…
We study one-dimensional hardcore lattice gases, with nearest-neighbor interactions, in the presence of an external potential barrier, that moves on the periodic lattice with a constant speed. We investigate how the nature of the…
In this paper, we consider radial standing waves to a nonlinear Klein-Gordon equation with a repulsive inverse-square potential. It is known that existence of a "radial" ground state to the stationary problem of the nonlinear Klein-Gordon…
Throughout physics, stable composite objects are usually formed via attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured…
Soft, repulsive run-and-tumble particles display emergent effective interactions as they appear to stick to each other in spite of the absence of attractive forces. This effective attraction emerges at strong enough repulsion and large…
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
We analyze the dynamics of one-dimensional quantum gases with strongly attractive contact interactions. We specify a class of initial states for which attractive forces effectively act as strongly repulsive ones during the time evolution.…
We show that it is possible to obtain credible static anisotropic spherically symmetric matter configurations starting from known density profiles and satisfying a nonlocal equation of state. These particular types of equation of state…