Related papers: Shock-type singularity of the hyperbolic-parabolic…
We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an…
In this work the systematic theory of discharge structure is built for highly electronegative plasma, by means of self-consistent fluid model simulation that is based on the finite element method. The highly electronegative plasma is…
The shock formation process in shock tubes has been extensively studied; however, significant gaps remain in understanding the effects of the diaphragm rupture process on the resulting flow non-uniformities. Existing models predicting the…
The level set flow of a mean-convex closed hypersurface is stable off singularities, in the sense that the level set flow of the perturbed hypersurface would be close in the smooth topology to the original flow wherever the latter is…
We consider the focusing nonlinear Schr\"odinger equations $i\partial_t u+\Delta u +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities $p_c<p<(1+\e)p_c$ with $p_c=1+\frac{4}{N}$ and $0<\e\ll 1$.…
The high-pressure phases of solid hydrogen are of fundamental interest and relevant to the interior of giant planets; however, knowledge of these phases is far from complete. Particle swarm optimization (PSO) techniques were applied to a…
An initially planar shock wave propagating into a medium of non-uniform density will be perturbed, leading to the generation of post-shock velocity perturbations. Using numerical simulations we study this phenomenon in the case of…
Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self energy of the two dimensional Hubbard model. From these the evolution of the superconducting gap and the momentum dependent…
In this paper, we obtain upper bounds for the critical time $T^*$ of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment condition or/and entropy condition are required on the initial data;…
We consider an initial boundary value problem for a 2x2 system of conservation laws modeling heatless adsorption of a gaseous mixture with two species and instantaneous exchange kinetics, close to the system of Chromatography. In this model…
We obtain estimates on both size and dimensions of the singular set at the first blow-up time of the mean curvature flow of hypersurfaces whose initial data is $\sigma_k$-convex.
In this paper we study the singularity formation for two nonlocal 1D active scalar equations, focusing on the hyperbolic flow scenario. Those 1D equations can be regarded as simplified models of some 2D fluid equations.
We study liquid-vapor phase separation under shear via the Shan-Chen lattice Boltzmann model. Besides the rheological characteristics, we analyze the Kelvin-Helmholtz(K-H) instability resulting from the tangential velocity difference of the…
The presence of slight azimuthal asymmetry in the initial shape of an underwater bubble entirely alters the final breakup dynamics. Here I examine the influence of initial asymmetry on the final breakup by simulating the bubble surface…
We consider the 3D isentropic compressible Euler equations with the ideal gas law. We provide a constructive proof of shock formation from smooth initial datum of finite energy, with no vacuum regions, with nontrivial vorticity present at…
A comprehensive, semi-quantitative model for the thermodynamics of hydrophobic solvation is presented. The model is based on a very simple premise suggested by the scaled particle theory and treats both solute and solvent molecules as hard…
Aims: The physical structure of a shock wave may take a form unique to its shock type, implying that the chemistry of each shock type is unique as well. We aim to investigate the different chemistries of J-type and C-type shocks in order to…
The synthesis of the high-$T_c$ superhydride CaH$_6$ has stimulated significant interest in understanding synthesis pathways for metastable hydrides. However, the microscopic mechanisms governing such hydrogenation reactions remain poorly…
It is well-known that shock will form in finite time for hyperbolic conservation laws from initial nonlinear compression no matter how small and smooth the data are. Classical results, including Lax [14], Liu [22], Li-Zhou-Kong [16],…
For the first order 1D $n\times n$ quasilinear strictly hyperbolic system $\partial_tu+F(u)\partial_xu=0$ with $u(x, 0)=\varepsilon u_0(x)$, where $\varepsilon>0$ is small, $u_0(x)\not\equiv 0$ and $u_0(x)\in C_0^2(\mathbb R)$, when at…