相关论文: Skeleton Integral Equations for Acoustic Transmiss…

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…

In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to…

We study theoretically the noise-assisted quantum exciton (electron) transfer (ET) in bio-complexes consisting of a single-level electron donor and an acceptor which has a complicated internal structure, and is modeled by many electron…

We extend the theory of non-thermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field…

We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the…

Nonlocal MEMS equations exhibit finite-time quenching, or touchdown, which is difficult to capture numerically. We study a stagewise rescaling algorithm for a two-dimensional nonlocal MEMS equation in an asymptotically constant-feedback…

We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture…

We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is strongly non-local due to the long range character of the magnetic interaction. We develop a systematic…

We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the…

Layered media have been studied extensively both for their importance in imaging technologies and as an example of a hyperbolic PDE with discontinuous coefficients. From the perspective of acoustic imaging, the time limited impulse response…

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…

We derive an alternative representation for the relativistic non--local kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and…

In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…

We consider a semilinear elliptic equation with a nonsmooth, locally \hbox{Lipschitz} potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our…

Inspired by medical applications of high-intensity ultrasound, we study a coupled elasto-acoustic problem with general acoustic nonlinearities of quadratic type as they arise, for example, in the Westervelt and Kuznetsov equations of…

We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

We study an elliptic equation with measurable coefficients arising from photo-acoustic imaging in inhomogeneous media. We establish Holder continuity of weak solutions and obtain pointwise bounds for Green's functions subject to Dirichlet…

A covariant non-local extention if the stationary Schr\"odinger equation is presented and it's solution in terms of Heisenbergs's matrix quantum mechanics is proposed. For the special case of the Riesz fractional derivative, the calculation…