Related papers: Derivation of exact flow equations from the self-c…
We consider bipartite quantum systems that are described completely by a state vector $|\Psi(t)>$ and the fully deterministic Schr\"odinger equation. Under weak constraints and without any artificially introduced decoherence or…
We obtain the Maxwell-J\"uttner distribution function at first order in the post-Newtonian approximation within the framework of general relativity. Taking into account the aforesaid distribution function, we compute the particle four-flow…
Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics with Maxwell's equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing…
It is well known that some quantum and statistical fluctuations of a quantum field may be recovered by adding suitable stochastic sources to the mean field equations derived from the Schwinger-Keldysh (Closed-time-path) effective action. In…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced…
Starting from the Liouville equation, we derive the exact hierarchy of equations satisfied by the reduced distribution functions of the single species point vortex gas in two dimensions. Considering an expansion of the solution in powers of…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
The multicomponent 2D Toda hierarchy is analyzed through a factorization problem associated to an infinite-dimensional group. A new set of discrete flows is considered and the corresponding Lax and Zakharov--Shabat equations are…
We study a 2D potential flow of an ideal fluid with a free surface with decaying conditions at infinity. By using the conformal variables approach, we study a particular solution of Euler equations having a pair of square-root branch points…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
We consider a dissipative flow network that obeys the standard linear nodal flow conservation, and where flows on edges are driven by potential difference between adjacent nodes. We show that in the case when the flow is a monotonically…
We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…
The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential…
This paper aims to systematically and comprehensively initiate a foundation for using concepts from computational differential geometry as instruments for power flow computing and research. At this point we focus our discussion on the…
Several theories for weakly damped free-surface flows have been formulated. In this paper we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to…
Exact renormalization group techniques are applied to mass deformed N=4 supersymmetric Yang-Mills theory, viewed as a regularised N=2 model. The solution of the flow equation, in the local potential approximation, reproduces the one-loop…
The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…
This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The class includes, for example, gas pipe network systems described by barotropic…
Using a modified WKB approach, we present a rigorous semi-classical analysis for solutions of nonlinear Schroedinger equations with rotational forcing. This yields a rigorous justification for the hydrodynamical system of rotating…