Related papers: New Solutions of the Inflationary Flow Equations
A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the…
A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3+1) dimensions. We focus on those types of…
A high-order method to evolve in time electromagnetic and velocity fields in conducting fluids with non-periodic boundaries is presented. The method has a small overhead compared with fast FFT-based pseudospectral methods in periodic…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
We examine inflationary universe models driven by scalar fields with logarithmic potentials of the form $V(\phi) = V_0 \phi^p(\ln \phi)^q$. Combining the slow-roll approximation with asymptotic techniques, we identify regions of the…
An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow,…
We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation…
The usual description of inflationary fluctuations uses the framework of quantum field theory (QFT) in curved spacetime, in which quantum fluctuations are superimposed on a classical background spacetime. Even for large fluctuations, such…
We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
Usually inflation ends either by a slow rolling of the inflaton field, which gradually becomes faster and faster, or by a first-order phase transition. We describe a model where inflation ends in a different way, due to a very rapid rolling…
We propose a hierarchical asynchronous iterative method that differs from the traditional synchronous iterative method used across the entire flow field in conventional Computational Fluid Dynamics applications. This method forcibly divides…
We develop a stochastic approach to a non de Sitter Universe in a gauge-invariant way and obtain a system of Langevin-type equations which may be considered to be renormalization group equations for the long wave parts of the scalar fields…
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…
A first order inflation model where a gauge coupling constant runs as the universe inflates is investigated. This model can solve the graceful-exit problem within Einstein gravity by varying the bubble formation rate. The sufficient…
In recent years, the power system research community has seen an explosion of novel methods for formulating and solving power network optimization problems. These emerging methods range from new power flow approximations, which go beyond…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
A method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the $\curly{L}_2$ norm of perturbations from a notional laminar…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear…