相关论文: Remarks on the waterbag model of dispersionless To…

We present an accurate free-energy functional for liquid water written in terms of a set of effective potential fields in which fictitious noninteracting water molecules move. The functional contains an \emph{exact} expression of the…

Classical density-functional theory is the most direct approach to equilibrium structures and free energies of inhomogeneous liquids, but requires the construction of an approximate free-energy functional for each liquid of interest. We…

This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of "Landau-Ginzburg potentials" that play the role of reduced Lax…

We study the dispersionless limit of the recently introduced Toda lattice hierarchy with constraint of type B (the B-Toda hierarchy) and compare it with that of the DKP and C-Toda hierarchies. The dispersionless limits of the B-Toda and…

We formulate an energy-storage concept based on the free energy associated with metastable magnetic configurations. Despite the active, magnetic region of the battery being electrically insulating, it can sustain effective hydrodynamics of…

We develop a model free energy from an expansion that basically includes graphs without loops. From this calculation, we derive the temperature dependence of the density (or specific volume), the typical time scale of the…

We study uncharged Rindler hydrodynamics at second order in the derivative expansion. The equation of state of the theory is given by a vanishing equilibrium energy density. We derive relations among the transport coefficients by employing…

We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its…

We quantize Hamiltonian structures with hydrodynamic leading terms using the Heisenberg vertex algebra. As an application, we construct the quantum dispersionless KdV hierarchy via a non-associative Weyl quantization procedure and compute…

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…

The Laplace sequence of the discrete conjugate nets is constructed. The invariants of the nets satisfy, in full analogy to the continuous case, the system of difference equations equivalent to the discrete version of the generalized Toda…

Using diffeomorphism group vector fields on $\mathbb{C}$-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of…

We present a study of a quasi-integrable deformation of the three-particle open Toda chain, constructed by introducing a translation-invariant three-body interaction terms. Although this modification explicitly breaks the exact…

This paper is a short review of the connection between certain types of growth processes and the integrable systems theory, written from the viewpoint of the latter. Starting from the dispersionless Lax equations for the 2D Toda hierarchy,…

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…

The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual based pore scale network modeling method…

The vacuum structure is probed by boundary conditions. The behaviour of thermodynamical quantities like free energy, boundary entropy and entanglement entropy under the boundary renormalization group flow are analysed in 2D conformal field…

We construct a new class of positive solutions for a classical semilinear elliptic problem in the plane which arise for instance as the standing-wave problem for the standard nonlinear Schr\"odinger equation or in nonlinear models in…

We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…