Related papers: A universal equation for calculating the energy gr…
The study rederives the fundamental equations of fluid flow and examines the inherent relationship between momentum conservation and mechanical energy conservation. It is shown that the material derivative of velocity is to depict the…
We report on generic relations between fractional flow and pressure in steady two-phase flow in porous media. The main result is a differential equation for fractional flow as a function of phase saturation. We infer this result from two…
A popular method of forcing the fluid in Direct Numerical Simulations of turbulence is to take the body force proportional to the projection of the velocity of the fluid onto its lowest Fourier modes, while keeping the injected external…
Using the Lagrangian transport of momentum, the Reynolds stress can be expressed in terms of basic turbulence parameters. The Reynolds stress gradient represents the lateral transport of stream-wise momentum, balanced by the u2 transport,…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
Using a dynamical density functional theory we analyze the density profile of a colloidal liquid near a wall under shear flow. Due to the symmetries of the system considered, the naive application of dynamical density functional theory does…
We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow…
We consider a gradient flow related to the mean field type equation. First, we show that this flow exists for all time. Next, we prove a compactness result for this flow allowing us to get, under suitable hypothesis on its energy, the…
Turbulent plane Poiseuille and Couette flows share the same geometry, but produce their flow rate owing to different external drivers, pressure gradient and shear respectively. By looking at integral energy fluxes, we pose and answer the…
Unsteady flow fields over a circular cylinder are trained and predicted using four different deep learning networks: convolutional neural networks with and without consideration of conservation laws, generative adversarial networks with and…
In this article, we introduce a new mathematical framework that can describe the budget of turbulence kinetic energy and heat transfer in both physical space and scale space of turbulence. We derived two exact transport equations for…
The shallow water equations without shear effects are similar to the gas dynamics equations with a polytropic equation of state. When the shear effects are taken into account, the equations contain additional evolution equations…
Polymeric turbulence, flows of fluids with dilute polymer additives at high Reynolds numbers, exhibits striking deviations from the Kolmogorovean behaviour of Newtonian turbulence. Recent experiments as well as simulations have uncovered a…
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is achieved by first conditioning the underlying stochastic…
The dynamics of systems out of thermal equilibrium is usually treated on a case-by-case basis without knowledge of fundamental and universal principles. We address this problem for a class of driven steady states, namely those mechanically…
We study the energy loss of a heavy quark slowly moving through an evolving strongly coupled plasma. We use the linearized fluid/gravity correspondence to describe small perturbations of the medium flow with general spacetime dependence.…
The electrostatic shear-flow-driven ion cyclotron instability of magnetic field aligned sheared plasma flow is investigated analytically. It is shown that the shear-flow-driven electrostatic ion cyclotron instability can be considered as a…
We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general,…
We study the flow of a shear-thinning, chemically-reacting fluid that could be used to model the flow of the synovial fluid. The actual geometry where the flow of the synovial fluid takes place is very complicated, and therefore the…
Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational…