Related papers: Which electric fields are realizable in conducting…
We study the fillability (or embeddability) of 3-dimensional $CR$ structures under the geometric flows. Suppose we can solve a certain second order equation for the geometric quantity associated to the flow. Then we prove that if the…
Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…
This paper concerns the reconstruction of an anisotropic conductivity tensor $\gamma$ from internal current densities of the form $J = \gamma\nabla u$, where $u$ solves a second-order elliptic equation $\nabla\cdot(\gamma\nabla u) = 0$ on a…
For a cylindrical superconductor surrounded by a normal material, we discuss transition to the normal phase of stable, locally stable and critical configurations. Associated with those phase transitions, we define critical magnetic fields…
Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that…
In search of novel, improved materials for magnetic data storage and spintronic devices, compounds that allow a tailoring of magnetic domain shapes and sizes are essential. Good candidates are materials with intrinsic anisotropies or…
We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\phi$ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we…
We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the…
This paper concerns the existence of critical points for solutions to second order elliptic equations of the form $\nabla\cdot \sigma(x)\nabla u=0$ posed on a bounded domain $X$ with prescribed boundary conditions. In spatial dimension…
This paper investigates the irreducibility of certain representations for the Lie algebra of divergence zero vector fields on a torus. In "Irreducible Representations of the Lie-Algebra of the Diffeomorphisms of a d-Dimensional Torus," S.…
We study the higher gradient integrability of distributional solutions $u$ to the equation $div(\sigma \nabla u) = 0$ in dimension two, in the case when the essential range of $\sigma$ consists of only two elliptic matrices, i.e.,…
We consider a class of invariant measures for a passive scalar $f$ driven by an incompressible velocity field $\boldsymbol{u}$, on a $d$-dimensional periodic domain, satisfying $$ \partial_t f + \boldsymbol{u} \cdot \nabla f = 0, \qquad…
Recent experiments on amorphous materials have established the existence of surface states similar to those of crystalline three-dimensional topological insulators (TIs). Amorphous topological insulators are also independently of interest…
We consider gradient fields on $\mathbb{Z}^d$ for potentials $V$ that can be expressed as $$e^{-V(x)}=pe^{-\frac{qx^2}{2}}+(1-p)e^{-\frac{x^2}{2}}.$$ This representation allows us to associate a random conductance type model to the gradient…
We show continuity of solutions $u \in W^{1,n}(B^n,\mathbb{R}^N)$ to the system \[ -{\rm div} (|\nabla u|^{n-2} \nabla u) = \Omega \cdot |\nabla u|^{n-2} \nabla u \] when $\Omega$ is an $L^n$-antisymmetric potential -- and additionally…
In this work, we mainly explore the possibility of charged rho superconductor (CRS) in the presence of parallel magnetic field and rotation within three-flavor Nambu--Jona-Lasino model. By following similar schemes as in the previous…
We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for nonzero external magnetic field, $H$. Exact results are given for the phase diagram in the…
The anomalous conducting phase that has been shown to exist in zero field in dilute two-dimensional electron systems in silicon MOSFETs is driven into a strongly insulating state by a magnetic field of about 20 kOe applied parallel to the…
An exact expression for the Drude conductivity in one dimension is derived under the presence of an arbitrary potential. In getting the conductivity the influence of the electric field on the crystal potential is taken into account. This…
We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a…