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We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are…
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties convergence results for sequences of distribution functions \phi_n=|s_N| / |s_N|_{L^2} for sections s_N\in…
We study the localization of gravity on string-like defects in codimension two. We point out that the gravity-localizing `local cosmic string' spacetime has an orbifold singularity at the horizon. The supergravity embedding and the AdS/CFT…
Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material…
Turbulent flow restricted to two dimensions can spontaneously develop order on large scales, defying entropy expectations and in sharp contrast with turbulence in three dimensions where nonlinear turbulent processes act to destroy…
We investigate the nitrogen substitutional impurity in semiconducting zigzag and metallic armchair single-wall carbon nanotubes using ab initio density functional theory. At low concentrations (less than 1 atomic %), the defect state in a…
We investigate the matching of eigenvalue densities of Wilson loops in SU(N) lattice gauge theory: the eigenvalue densities in 1+1, 2+1 and 3+1 dimensions are nearly identical when the traces of the loops are equal. We show that the…
We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range density-density interaction, and they encounter a general…
We consider a 2-1 electrolyte in contact with a narrow nanotube, which only allows one-dimensional storage along the axis. The asymmetry does not allow an a priori definition of the potential of zero charge; instead, the natural reference…
We discuss fluctuations near the second order phase transition where the free energy has an additional non-Hermitian term. The spectrum of the fluctuations changes when the odd-parity potential amplitude exceeds the critical value…
The electronic and vibrational density of states of a semiconducting carbon nanotube in a crossed junction was investigated by elastic and inelastic scanning tunneling spectroscopy. The strong radial compression of the nanotube at the…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…
For a power series which converges in some neighborhood of the origin in the complex plane, it turns out that the zeros of its partial sums---its sections---often behave in a controlled manner, producing intricate patterns as they converge…
We discuss the evolution of the local quasiparticle spectral density and the related tunneling conductance measurable by the scanning tunneling microscope, as a function of distance r and angle \theta from the vortex core in a d_{x^2-y^2}…
First we investigate the evolutions of the radius function and its gradient along the volume-preserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line C, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new…
We investigate the asymptotic behavior, as t goes to infinity, for a semilinear hyperbolic equation with asymptotically smal dissipation and convex potential. We prove that if the damping term behaves like K/t^\alpha for t large enough, k>0…
We give the first rigorous construction of complete, embedded self-shrinking hypersurfaces under mean curvature flow, since Angenent's torus in 1989. The surfaces exist for any sufficiently large prescribed genus $g$, and are non-compact…
A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase…