Related papers: Geometric microcanonical theory of two-dimensional…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…
We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…
We introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps, equipped with the L2 metric, which as observed by Arnold solve Euler's equations of inviscid incompressible fluids. The method…
We discuss invariant measures of partial differential equations such as the 2D Euler or Vlasov equations. For the 2D Euler equations, starting from the Liouville theorem, valid for N-dimensional approximations of the dynamics, we define the…
In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…
We consider dry granular flow down an inclined chute with a localised contraction theoretically and numerically. The flow regimes are predicted through a novel extended one-dimensional hydraulic theory. A discrete particle method validated…
We investigate the emergence of finite-amplitude non-zonal flows on the sphere $\mathbb{S}^2$ arising from stationary solutions to the 2D Euler equations. By restricting the Laplace-Beltrami eigenspace to the invariant subspace of the…
We study geometric modular flows in two-dimensional conformal field theories. We explore which states exhibit a geometric modular flow with respect to a causally complete subregion and, conversely, how to construct a state from a given…
The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different…
Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be…
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from…
A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…
In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…
Models that describe two-fluid flow in porous media suffer from a widely-recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are non-unique, thus requiring a…
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…
We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the initial datum, exponential convergence towards single "diffused…