We study the renormalization problem for the Hartree–Fock approximation of the O(N)−invariant φ model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct renormalization properties of the effective field equations, including Renormalization–Group invariance with the one–loop beta function. These new Hartree–Fock dynamic...

Talk Abstract A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the surface elevation which is obtained from the Euler formulation of the water-wave problem without approximation. This new approach is compared with o...

Here the path integral is over real metrics modulo coordinate transformations, G denotes a renormalized Newton constant and the · · · indicate higher derivative terms like R, etc. There may also be nonlocal terms related to the conformal anomaly [2]. The integral over μ produces the volume fixing delta function δ( ∫ dx √ g − V ). If this integral were done in the saddle point approximation, the...

Nonlocal nonlinear Schrödinger equations are considered as models of liquid helium II. The models contain a nonlocal interaction potential that leads to a phonon–roton-like dispersion relation. Also, a higher-order term in the local density approximation for the correlation energy is introduced into the model to overcome nonphysical mass concentrations. These equations are solved for straight-l...

We study the validity of the recently proposed universal plasmon ruler in the present work using a combination of numerical techniques based on the finite difference time domain (FDTD) method, and semianalytical theories based on the coupled dipole approximation. By incorporating nonlocal effects for closely spaced two-dimensional gold nanocylinder dimers, we find using both the FDTD and semian...

We have applied the technique of evaluating a nonlocal pseudopotential with a trial function to give an approximate, local many-body pseudopotential which was used in a valence-only diffusion Monte Carlo (DMC) calculation. The pair and triple correlation terms in the trial function have been carefully optimized to minimize the effect of the locality approximation. We discuss the accuracy and co...

A vectorial nonlocal and nonlinear parabolic problem on a bounded domain for an intermediate state between type-I and type-II superconductivity is proposed. The domain is for instance a multiband superconductor that combines the characteristics of both types. The nonlocal term is represented by a (space) convolution with a singular kernel arising in Eringen’s model. The nonlinearity is coming f...

Helium Natalia G. Berloff and Paul H. Roberts Department of Mathematics University of California, Los Angeles, CA, 90095-1555 [email protected], [email protected], Abstract. Nonlocal nonlinear Schrödinger equations are considered as models of superfluid helium. The models contain a nonlocal interaction potential that leads to a phonon-roton-like dispersion relation. It is shown that fo...

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (M...

We exploit a recently developed nonlocal vector calculus to provide a variational analysis for a general class of nonlocal diffusion problems given by a linear integral equation on bounded domains in R. The ubiquity of the nonlocal operator is illustrated by a number of applications ranging from continuum mechanics to graph theory. These applications elucidate different interpretations of the o...