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A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
A universal relationship between scaled size and scaled energy is explored in five-body self-bound quantum systems. The ground-state binding energy and structure properties are obtained by means of the diffusion Monte Carlo method. We use…
Surface albedo is an important parameter in radiative-transfer simulations of the Earth's system as it is fundamental for correctly calculating the energy budget of the planet. The Moderate Resolution Imaging Spectroradiometer (MODIS)…
Surface morphology of size-selected silver nanocluster films grown by dc magnetron sputtering has been investigated by means of an atomic force microscopy (AFM). From the height-height correlation functions ( HHCF) obtained from…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
We use the Profile numerical method to calculate the spectral line width, or half width at half maximum (HWHM) of the absorption peaks of multi-photon absorption processes in a two-dimensional graphene system (2DGS) according to important…
Using Quantum Monte Carlo we compute thermodynamics and spectra for the orbitally degenerate Hubbard model in infinite spatial dimensions. With increasing orbital degeneracy we find in the one-particle spectra: broader Hubbard bands…
We prove that smooth Wigner-Weyl spectral sums at an energy level $E$ exhibit Airy scaling asymptotics across the classical energy surface $\Sigma_E$. This was proved earlier by the authors for the isotropic harmonic oscillator and the…
The dynamics and thermodynamics of melting in two-dimensional Coulomb clusters is revisited using molecular dynamics and Monte Carlo simulations. Several parameters are considered, including the Lindemann index, the largest Lyapunov…
The photon Doppler velocimetry (PDV) spectrum is investigated in an attempt to reveal the particle parameters of ejecta from shock-loaded samples in a vacuum. A GPU-accelerated Monte-Carlo algorithm, which considers the multiple-scattering…
The scaling properties of the maximal height of a growing self-affine surface with a lateral extent $L$ are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: $h^{*}_{L}…
Quantum Monte Carlo methods have proven to predict atomic and bulk properties of light and non-light elements with high accuracy. Here we report on the first variational quantum Monte Carlo (VMC) calculations for solid surfaces. Taking the…
Thin film deposition on weakly interacting substrates exhibits a unique growth mode characterized by initially strong island formation and rapidly increasing roughness, which reaches a maximum and subsequently decreases as the film returns…
In this paper, we study a novel behavior developed by certain tree-level scalar scattering amplitudes, including the biadjoint, NLSM, and special Galileon, when a subset of kinematic invariants vanishes without producing a singularity. This…
Fluctuations of isolated and pairs of ascending steps of monoatomic height are studied in the framework of SOS models, using mainly Monte Carlo techniques. Below the roughening transistion of the surface, the profiles of long steps show the…
We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an…
The two-dimensional Hubbard model is studied using the variational quantum Monte Carlo technique with Gutzwiller-type variational wave functions. In addition to the simple one-site correlated Gutzwiller wave function, we use a form with…
This work analyzes singular-value spectra of weight matrices in pretrained transformer models to understand how information is stored at both ends of the spectrum. Using Random Matrix Theory (RMT) as a zero information hypothesis, we…
Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their…
We introduce an approach to study homogenisation of a large class of singular SPDEs of the form $$ \partial_t u_\varepsilon - \nabla\cdot {A}(x/\varepsilon,t/\varepsilon^2) \nabla u_\varepsilon = F(x/\varepsilon , t/\varepsilon^2,…