Related papers: Revisiting interpolating flows in $(1+1)$ hydrodyn…
We consider a (d+2)-dimensional class of Lorentzian geometries holographically dual to a relativistic fluid flow in (d+1) dimensions. The fluid is defined on a (d+1)-dimensional time-like surface which is embedded in the (d+2)-dimensional…
Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing…
We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks…
A general thermodynamic treatment of dissipative relativistic fluids is introduced, where the temperature four vector is not parallel to the velocity field of the fluid. Generic stability and kinetic equilibrium points out a particular…
We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial subvariety is irreducible. We also show various symmetries in…
In this work we provide analytic and numerical solutions for the Bjorken flow, a standard benchmark in relativistic hydrodynamics providing a simple model for the bulk evolution of matter created in collisions between heavy nuclei. We…
In the framework of the variational principle the canonical variables describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with spatially varying entropy and nonzero values of all topological invariants) are introduced.…
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…
We consider a family of exact boost invariant solutions of the transport equation for free streaming massless particles, where the one particle distribution function is defined in terms of a function of a single variable. The evolution of…
We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of…
Analytical solutions to the microscopic Boltzmann equation are useful in testing the applicability and accuracy of macroscopic hydrodynamic theory. In this work, we present exact solutions of the relativistic Boltzmann equation, based on a…
We study the (local) propagation of plane waves in a relativistic, non-dissipative, two-fluid system, allowing for a relative velocity in the "background" configuration. The main aim is to analyze relativistic two-stream instability. This…
We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via…
For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a…
Molecules at the air-water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through the competition of short- and long-range…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
We consider the hydrodynamic regime of a 2+1 dimensions QFT with the parity anomaly. Beyond the known constraints from positivity of entropy production, we show that the anomaly inflow mechanism, from a corresponding bulk SPT phase,…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.
A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…