相关论文: On radial stochastic Loewner evolution in multiply…
This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…
We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains…
We present a discretization of the linear advection of differential forms on bounded domains. The framework previously established is extended to incorporate the Lie derivative, $\mathcal L$, by means of Cartan's homotopy formula. The…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
The Brownian loop measure is a conformally invariant measure on loops in the plane that arises when studying the Schramm-Loewner evolution (SLE). When an SLE curve in a domain evolves from an interior point, it is natural to consider the…
Given a bounded n-connected domain in the plane bounded by non-intersecting Jordan curves, and given one point on each boundary curve, L. Bieberbach proved that there exists a proper holomorphic mapping of the domain onto the unit disc that…
We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with…
We study the moduli space of the spectral curves $y^2=W'(z)^2+f(z)$ which characterize the vacua of $\mathcal{N}=1$ U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential $W(z)$. It is shown…
Consider a random planar point process whose law is invariant under planar isometries. We think of the process as a random distribution of point charges and consider the electric field generated by the charge distribution. In Part I of this…
We consider Calder{\'o}n's problem on a class of Sobolev extension domains containing non-Lipschitz and fractal shapes. We generalize the notion of Poincar{\'e}-Steklov (Dirichlet-to-Neumann) operator for the conductivity problem on such…
We review the recently developed relation between the traditional algebraic approach to conformal field theories and the more recent probabilistic approach based on stochastic Loewner evolutions. It is based on implementing random conformal…
The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The…
Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…
We propose a mathematical model for describing propagating confined modes in domain walls of intermediate angle between domains. The proposed model is derived from the linearised Bloch equations of motion and after reasonable assumptions,…
We consider families of mappings with moduli inequalities, having different definition domains. Under some additional assumptions we have proved that such families are uniformly equicontinuous. We have considered four main cases: when…
We consider the parabolic polyharmonic diffusion and $L^2$-gradient flows of the $m$-th arclength derivative of curvature for regular closed curves evolving with generalised Neumann boundary conditions. In the polyharmonic case, we prove…
This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from fractional quantum mechanics and more…