相关论文: Minimal solutions to generalized Lambda-semiflows …
A classical problem of free-space Green's function $G_{0\Lambda}$ representations of the Helmholtz equation is studied in various quasi-periodic cases, i.e., when an underlying periodicity is imposed in less dimensions than is the dimension…
Many fluctuation-driven phenomena in fluids can be analysed effectively using the generalised Lagrangian mean (GLM) theory of Andrews & McIntyre (1978). This theory relies on particle-following averaging to incorporate the constraints…
A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a…
We review some recent results on the mean curvature flows of Lagrangian submanifolds from the perspective of geometric partial differential equations. These include global existence and convergence results, characterizations of first-time…
A generic theory of a single real scalar field is considered, and a simple method is presented for obtaining a class of solutions to the equation of motion. These solutions are obtained from a simpler equation of motion that is generated by…
Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is…
We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by…
Generalized empirical likelihood and generalized method of moments are well spread methods of resolution of inverse problems in econometrics. Each method defines a specific semiparametric model for which it is possible to calculate…
We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savar\'e, to CAT(1)-spaces. The key tool is the so-called "commutativity" representing a Riemannian nature of the…
We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…
Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the…
"Generalized Hydrodynamics" (GHD) stands for a model that describes one-dimensional \textit{integrable} systems in quantum physics, such as ultra-cold atoms or spin chains. Mathematically, GHD corresponds to nonlinear equations of kinetic…
The complexity of comprehensive ocean models poses an important question for parameterisations: is there a minimum set of equations that should be parameterised, on the one hand, to reduce the development to a minimum, and, on the other…
We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
We present semi-analytic techniques for finding bubble wall profiles during first order phase transitions with multiple scalar fields. Our method involves reducing the problem to an equation with a single field, finding an analytic solution…
When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…