Related papers: Construction of effective interpolating equation o…
We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines…
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical…
This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode…
The charge reduction effect, produced by the nonlinear Debye screening of high-Z charges occuring in strongly-coupled plasmas, is investigated. An analytic asymptotic expression is obtained for the charge reduction factor which determines…
We have developed a simple analytic formula that well describes quadrupole $l$-changing collisions of the form $nl \rightarrow nl'$, as confirmed by comparison with numerical quantal Born calculations obtained with the program autostructure…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
Equivalence criteria are established for an effective Yukawa-type theory of composite fields representing two-particle fermion bound states with the original "microscopic" theory of interacting fermions based on the spectral decomposition…
We present a model reduction approach for the real-time solution of time-dependent nonlinear partial differential equations (PDEs) with parametric dependencies. The approach integrates several ingredients to develop efficient and accurate…
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus $\mathsf{S^2IC}$,…
We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe…
We develop a unifying framework for interpolatory $\mathcal{L}_2$-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally…
Interpolating functional method is a powerful tool for studying the behavior of a quantity in the intermediate region of the parameter space of interest by using its perturbative expansions at both ends. Recently several interpolating…
Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term…
We reconsider the naturalness from the viewpoint of effective field theories, motivated by the alternative scenario that the standard model holds until a high-energy scale such as the Planck scale. We propose a calculation scheme of…
Studies of charge-charge (ion-ion, ion-electron, and electron-electron) coupling properties for ion impurities in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential without…
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of…