Related papers: Approximation of anisotropic pair potentials using…
The binary potential technique of interpolation (by M. Riesz, Acta Math. 81, 1 (1949)) is applied to some well-known metrics of general relativity. These include Schwarzschild, de Sitter and 2+1-dimensional BTZ spacetimes. In particular,…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
Accurate interaction potentials between microscopic components such as colloidal particles or cells are crucial to understanding a range of processes, including colloidal crystallization, bacterial colony formation, and cancer metastasis.…
The excitonic behavior of anisotropic two-dimensional crystals is investigated using numerical methods. We employ a screened potential arising due to the system polarizability to solve the central-potential problem using the Numerov…
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…
Dipolar interactions govern the structure and dynamics of many soft-matter systems, from molecular to colloids assemblies. When dipole moments are induced by an external field, mutual interactions lead to a many-body magnetization response…
Creating accurate, analytic atom--atom potentials for small organic molecules from first principles can be a time-consuming and computationally intensive task, particularly if we also require them to include explicit polarization terms,…
Anharmonic oscillators with the sextic and decatic potentials are studied employing the refinable interpolating scale functions. This method yields highly accurate values of both energy eigenvalues and eigenfunctions for the sextic and…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
We study the bias-variance tradeoff within a multiscale approximation framework. Our approach uses a given quasi-interpolation operator, which is repeatedly applied within an error-correction scheme over a hierarchical data structure. We…
The intricate interplay between colloidal particle shape and precisely engineered interaction potentials has paved the way for the discovery of unprecedented crystal structures in both two and three dimensions. Here, we make use of…
We calculate the second and third virial coefficients of the effective sphere-sphere interaction due to polymer depletion. By utilizing the anisotropy of a typical polymer conformation, we can consider polymers that are roughly the same…
We show that multichannel quantum defect theory (MQDT) can be applied successfully as an efficient computational method for cold molecular collisions in Li+NH, which has a deep and strongly anisotropic interaction potential. In this…
In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation…
An isotropic interaction potential for classical particles is devised in such a way that the crystalline ground state of the system changes discontinuously when some parameter of the potential is varied. Using this potential we model…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of…
We propose a method to tune interactions between absorptionless colloidal particle pairs. This is achieved via optimization of the spectral energy density of a homogeneous random optical field. Several standard and more exotic interaction…