Related papers: Analytic expressions for the moving infinite line …
To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on dominant runoff generating mechanisms. Acceptable model runs, defined as total simulated flow with similar (and minimal)…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
This work applies resolvent analysis to incompressible flow through a rectangular duct, in order to identify dominant linear energy-amplification mechanisms present in such flows. In particular, we formulate the resolvent operator from…
In this paper we show how a two dimensional fluid model can be used to interpret data obtained from an inclined Mach-probe or a Gundestrup probe. We use an analytical approximation of the solution of the differential equations describing…
Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…
We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…
This work introduces a generalized characteristic mapping method designed to handle non-linear advection with source terms. The semi-Lagrangian approach advances the flow map, incorporating the source term via the Duhamel integral. We…
We study the dynamics of a nonlinear two-level crossing model with a cubic modification of the linear Landau-Zener diabatic energies. The solutions are expressed in terms of the bi-confluent Heun functions --- the generalization of the…
We derive the formula of energy flux for the hierarchical equations of motion (HEOM) method with the help of stochastic decoupling technique. The resulting expression is a combination of the terms in the first two layers of the hierarchy.…
It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz-Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential, for…
First derivatives of the Whittaker function $\mathrm{M}_{\kappa ,\mu }\left(x\right) $ with respect to the parameters are calculated. Using the confluent hypergeometric function, these derivarives can be expressed as infinite sums of…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
Recently developed series representations of the Boltzmann operator are used to obtain Quantum Mechanical results for the matrix elements, <x| exp(-{\beta} H)|x>, of the imaginary time propagator. The calculations are done for two different…
The flow of an ideal fluid possesses a remarkable property: despite limited regularity of the velocity field, its particle trajectories are analytic curves. In our previous work, this fact was used to introduce the structure of an analytic…
A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…