Related papers: Calculation of higher-twist evolution kernels for …

We discuss the expansion of interaction kernels between anisotropic rigid molecules. The expansion decouples the correlated orientational variables so that it can be utilized to derive macroscopic models. Symmetries of two types are…

We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous…

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term.

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…

This paper introduces a directional multiscale algorithm for the two dimensional $N$-body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal…

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…

Calculating dynamical spin correlations is essential for matching model magnetic exchange Hamiltonians to momentum-resolved spectroscopic measurements. A major numerical bottleneck is the diagonalization of the dynamical matrix, especially…

This paper continues the systematic investigation of diffusive shear instabilities initiated in Part I of this series. In this work, we primarily focus on quantifying the impact of non-local mixing, which is not taken into account in Zahn's…

We consider the numerical evolution of dynamic black hole initial data sets with a full 3D, nonlinear evolution code. These data sets consist of single black holes distorted by strong gravitational waves, and mimic the late stages of…

We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical…

In this paper we discuss non-local operators with killing potentials, which may not be in the standard Kato class. We first discuss factorization of their Dirichlet heat kernels in metric measure spaces. Then we establish explicit estimates…

We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative $d$-torus using multiple operator integrals. We derive a recursive formula that easily produces an explicit expression for the…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

The most general bound binary black hole (BBH) system has an eccentric orbit and precessing spins. The detection of such a system with significant eccentricity close to the merger would be a clear signature of dynamical formation. In order…

We combine high-resolution resonant inelastic x-ray scattering with cluster calculations utilizing a recently derived effective magnetic scattering operator to analyze the polarization, excitation energy, and momentum dependent excitation…

It is shown in this paper that the QCD equations for dipole density have the natural solution: the 'fan' diagrams of the Pomeron calculus. We found the dipole densities comparing the analytic solution to the Balitsky-Kovchegov (BK) equation…

This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations. The…