We consider 2D localized rotating patterns which solve a parabolic system of PDEs on the spatial domain R2. Under suitable assumptions, we prove nonlinear stability with asymptotic phase with respect to the norm in the Sobolev space H2. The stability result is obtained by a combination of energy and resolvent estimates, after the dynamics is decomposed into an evolution within a three–dimension...

Superconductivity is a fascinating quantum phenomenon characterized by zero electrical resistance and the Meissner effect. To date, several distinct families of superconductors (SCs) have been discovered. These include three-dimensional (3D) bulk SCs in both inorganic and organic materials as well as two-dimensional (2D) thin film SCs but only in inorganic materials. Here we predict superconduc...

We introduce a model of a two-dimensional (2D) optical waveguide with Kerr nonlinearity, linear and quintic losses, cubic gain, and temporal-domain filtering. In the general case, temporal dispersion is also included, although it is not necessary. The model provides for description of a nonlinear planar waveguide incorporated into a closed optical cavity. It takes the form of a 2D cubic-quintic...

We report on the Fermi surfaces and superconducting parameters of CaSb$_2$ single crystals (superconducting below $T_{\text{c}}\sim 1.8~\text{K}$) grown by self-flux method. The frequency de-Haas-van-Alphen Shubnikov-de-Haas oscillations evidences a quasi-two-dimensional (quasi-2D) surface, consistent with one forming Dirac lines predicted first-principles calculations. Measurements in state re...

Broadening the knowledge and understanding on magnetic correlations in van der Waals layered magnets is critical realizing their potential next-generation magneto-electronic applications. In this study, we employ high-frequency (? = 240 GHz) electron spin resonance (ESR) spectroscopy plate-like quasi two-dimensional (2D) CrBr3 to gain insight into interactions as a function of temperature (4–20...

The complex Ginzburg-Landau model appears in the mathematical description of wave propagation nonlinear optics. In this paper, fractional is investigated using generalized exponential rational function method. Kerr law and parabolic are considered to discuss nonlinearity proposed model. effects also included a novel local derivative order <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"...

A formal asymptotic expansion is used to simplify the Ginzburg-Landau model of superconductivity in the limit of large values of the Ginzburg-Landau parameter and high applied magnetic field strengths. The convergence of solutions of the full Ginzburg-Landau equations to solutions of the leading order equations in the hierarchy is demonstrated for both boundary value and periodic problems. The ...

In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e. nonlinear sigma models on nontrivial noncompact manifolds with superpotential, generalizing old computations in Landau-Ginzburg models over (orbifolds of) vector spaces. For Landau-Ginzburg models in the same universality class as nonlinear sigma models, we explicitly ...

ion and Ontology: questions as propositional abstracts in type theory with records Jonathan Ginzburg∗ Department of Computer Science King’s College, London The Strand, London WC2R 2LS [email protected] http://www.dcs.kcl.ac.uk/staff/ginzburg/papers

Let Ω be a 2D domain with a hole ω. In the domain A = Ω \ ω consider a class J of complex valued maps having degrees 1 and 1 on ∂Ω, ∂ω respectively. In a joint work with P. Mironescu we show that if cap(A) ≥ π (subcritical domain), minimizers of the Ginzburg-Landau energy E κ exist for each κ. They are vortexless and converge in H(A) to a minimizing S-valued harmonic map as the coherency length...