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We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…
We generalize a simple Monte Carlo (MC) model for dilute gases to consider the transport behavior of positrons and electrons in Percus-Yevick model liquids under highly non-equilibrium conditions, accounting rigorously for coherent…
We have recently shown that by using a scaling approach for randomly distributed topological defects in graphene, reliable estimates for transmission properties of macroscopic samples can be calculated based even on single-defect…
For a broad class of random walks with anisotropic scattering kernel and absorption, we derive explicit formulas that allow expressing the moments of the collision number $n_V$ performed in a volume $V$ as a function of the particle…
This work continues the development of the raytracing method of [1] for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the…
A recently introduced particle-based model for fluid flow, called Stochastic Rotation Dynamics, can be made Galilean invariant by introducing a random shift of the computational grid before collisions. In this paper, it is shown how the…
Radiative transfer (RT) simulations are a powerful tool that enables the calculation of synthetic images of a wide range of astrophysical objects. These simulations are often based on the Monte Carlo (MC) method, as it provides the needed…
Electron transport within nanostructures can be important to varied engineering applications, such as thermoelectrics and nanoelectronics. In theoretical studies, electron Monte Carlo simulations are widely used as an alternative approach…
The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…
We study the propogation and diffusion of electric charge fluctuations in high energy heavy ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form…
A kinetic Monte Carlo method was used to simulate the diffusion of reptating polymer chains across the interface. A time-resolved fluorescence technique conjunction with direct energy transfer method was used to measure the extend of…
The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach, which does not rely on the diffusion approximation, becomes asymptotically exact in the regime of most…
The solutions of the radiative transfer equation, known for the energy density, do not satisfy the fundamental transitivity property for Green's functions expressed by Chapman-Kolmogorov's relation. I show that this property is retrieved by…
In this work we compare numerically exact Quantum Monte Carlo (QMC) calculations and Green function theory (GFT) calculations of thin ferromagnetic films including second order anisotropies. Thereby we concentrate on easy plane systems,…
We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…
We study the similarities and differences between different models concerning subdiffusion. More particularly, we calculate first passage time (FPT) distributions for subdiffusion, derived from Greens' functions of nonlinear equations…
Two methods are developed for solving the steady-state spherically symmetric radiative transfer equation for resonance line radiation emitted by a point source in the Intergalactic Medium. One method is based on solving the ray and moment…
We rederive the Green-Kubo relation establishing a connection between the near- and far-field heat transfer between two objects out of equilibrium to the equilibrium fluctuations of these objects in an arbitrary environment. Employing the…
The transport and gain properties of quantum cascade (QC) structures are investigated using a nonequilibrium Green's function (NGF) theory which includes quantum effects beyond a Boltzmann transport description. In the NGF theory, we…
The analytical treatment of the Greens function in the convergent close-coupling method [Bray et al. Comp. Phys. Comm. 203 147 (2016)] has been extended to charged targets. Furthermore, we show that this approach allows for calculation of…