Related papers: A Two Species Thomas-Fermi Model for Stellar Groun…
We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of configurational energies featuring two-body short-ranged…
The Kondo-Heisenberg model is used for a microscopic demonstration of existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a…
We consider a model composed of Landau quasiparticle states with patched Fermi surfaces (FS) sandwiched by states with flat FS to simulate the ``cold'' spot regions in cuprates. We calculate the one particle irreducible function and the…
We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from the mass and momentum…
We study the flow of two immiscible fluids located on a solid bottom, where the lower fluid is Newtonian and the upper fluid is a non-Newtonian Ellis fluid. Neglecting gravitational effects, we consider the formal asymptotic limit of small…
We consider the mass-critical nonlinear Schr\"odinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass…
We prove existence and uniqueness of strong solutions to the Cucker--Smale flocking model coupled with an incompressible viscous non-Newtonian fluid, with the stress tensor of a power--law structure for $p\geq\frac{11}{5}$. The coupling is…
In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins…
We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we…
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…
A new variational principle - extremizing the fixed frame kinetic energy under constant relative enstrophy - for a coupled barotropic flow - rotating solid sphere system is introduced with the following consequences. In particular, angular…
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some…
We study a lattice model for Marginal Fermi liquid behavior, involving a gas of electrons coupled to a dense lattice of three-body bound-states. The bound-states change the phase space for electron-electron scattering and induce a marginal…
We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes…
We study the ionization problem in the Thomas-Fermi-Dirac-von Weizs\"acker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge…
For the stationary Gross-Pitaevskii equation with harmonic real and linear imaginary potentials in the space of one dimension, we study the ground state in the limit of large densities (large chemical potentials), where the solution…
Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we theoretically and numerically investigate a Hartree…
We consider an exchange model describing two isotropic spin-1/2 Heisenberg antiferromagnets coupled by a quartic term on the square lattice. The model is relevant for systems with orbital degeneracy and strong electron-vibron coupling in…
We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the existence of a critical mass such that minimizers do exist for…
We analyze the particle-hole symmetric two-dimensional Hubbard model on a square lattice starting from weak-to-moderate couplings by means of the field-theoretical renormalization group (RG) approach up to two-loop order. This method is…