Related papers: Shock-type singularity of the hyperbolic-parabolic…
We consider self-similar solutions describing intermittent bursts in shell models of turbulence, and study their relationship with blowup phenomena in continuous hydrodynamic models. First, we show that these solutions are very close to…
We theoretically investigate the gap function, superfluid density and the transition temperature of the superconductivity (SC) on semi-periodic Penrose lattice, where an attractive Hubbard model is adopted as an example. Firstly, we clarify…
Finite time blow up vs global regularity question for 3D Euler equation of fluid mechanics is a major open problem. Several years ago, Luo and Hou \cite{HouLuo14} proposed a new finite time blow up scenario based on extensive numerical…
This is the first in a series of papers devoted to the blow up analysis for the quenching phenomena in a parabolic MEMS equation. In this paper, we first give an optimal H\"{o}lder estimate for solutions to this equation by using the blow…
The existence of travelling waves for a coupled system of hyperbolic/ parabolic equations is established in the case of a finite number of velocities in the kinetic equation. This finds application in collective motion of chemotactic…
We present a hypersurface singularity in positive characteristic which is defined by a purely inseparable power series, and a sequence of point blowups so that, after applying the blowups to the singularity, the same type of singularity…
In this paper a diffuse-interface model featuring phase change, transition to supercritical conditions, thermal conduction, compressibility effects and shock wave propagation is exploited to deal with the dynamics of a cavitation bubble. At…
We propose a charge crystal model that captures all the essential physics of the high temperature superconductivity (HTS) in the long wavelength limit. Based on the recent transport and the far-infrared (far-IR) experiments, we argue that…
Expansion dynamics of single-species, non-neutral clouds, such as electron bunches used in ultrafast electron microscopy, show novel behavior due to high acceleration of particles in the cloud interior. This often leads to electron bunching…
We investigate singularity formation in the regularized Saint--Venant (rSV) equations, a conservative, non-dispersive shallow water system that is formally regarded as a Hamiltonian regularization of the isentropic Euler equations. While it…
The onset of pattern formation in a spatially homogeneous system subjected to external driving is an important topic in various scientific fields. A celebrated classical example is the Faraday instability, where a vertically oscillated…
We present a model of a hypersonic, collimated, "single pulse" outflow, produced by an event with an ejection velocity that first grows, reaches a peak, and then decreases again to zero velocity in a finite time (simultaneously, the…
We considered the structure of steady-state plane-parallel radiative shock waves propagating through the partially ionized hydrogen gas of temperature T_1 = 3000K and density 1e-12 gm/cm^3 <= \rho_1 <= 1e-9 gm/cm^3. The upstream Mach…
We consider the parabolic-elliptic Keller-Segel system in dimensions $d \geq 3$, which is the mass supercritical case. This system is known to exhibit rich dynamical behavior including singularity formation via self-similar solutions. An…
Density Functional Theory calculations using the quasi-harmonic approximation have been used to calculate the solid Hugoniot of two polytypes of boron carbide up to 100 GPa. Under the assumption that segregation into the elemental phases…
In this paper we study the geometry of first time singularities of the mean curvature flow. By the curvature pinching estimate of Huisken and Sinestrari, we prove that a mean curvature flow of hypersurfaces in the Euclidean space $\R^{n+1}$…
The breakup of a spherical droplet in a decaying homogeneous isotropic turbulence is studied by solving the Cahn-Hilliard-Navier-Stokes equations, using the discrete unified gas kinetic scheme combined with the free-energy-based phase-field…
A molecular solid C$_{50}$Cl$_{10}$ with possible crystalline structures, including the hexagonal-close-packed (hcp) phase, the face-centered cubic (fcc) phase, and a hexagonal monolayer, is predicted in terms of first-principles…
We combine experiments, large scale simulations and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant…
In this paper, we shall study the parabolic-elliptic Keller-Segel system on the Poincar{\'e} disk model of the 2D-hyperbolic space. We shall investigate how the negative curvature of this Riemannian manifold influences the solutions of this…