相关论文: Flow Equations and Normal Ordering

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

A novel flow instability emerging during a rheometric flow of a phase change material sheared in the vicinity of the solid-fluid transition is reported. Right above the onset of the flow induced crystallisation, the presence of the crystals…

A study of elliptical flow is presented with respect to the asymmetry of colliding nuclei using the reactions of 24Cr50 +44 Ru102, 16S32 +50 Sn120 and 8O16 +54 Xe136 at incident energies between 50 and 250 MeV/nucleon within the framework…

The problem of a travelling wave over an arbitrary quasi-flat bathymetry in a semi infinite channel is studied in the shallow-water formulation. It is shown how the streamfunction can be cast, in the vicinity of an elliptic equilibrium for…

In this paper, we first establish regularity of the heat flow of biharmonic maps into the unit sphere $S^L\subset\mathbb R^{L+1}$ under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of…

We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the…

In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.

Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…

The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…

We study the effect of correlation on the direction of particle exchange between local thermal sub-systems where the total system is isolated. Our focus is the situation where both sub-systems have the same temperature but different…

Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular,…

The practical focus of this work is the dynamical simulation of polarization transport processes in quantum spin microscopy and spectroscopy. The simulation framework is built-up progressively, beginning with state-spaces (configuration…

For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the…

The possibility that particle production in high-energy collisions is a result of two asymmetric hydrodynamic flows is investigated, using the Khalatnikov form of the 1+1-dimensional approximation of hydrodynamic equations. The general…

The nucleation process of polyethylene under quiescent and shear flow conditions are comparatively studied with all_atom molecular dynamical simulations. At both conditions, nucleation are demonstrated to be two_step processes, which,…

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases the…

The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the…

Starting from the linear sigma model with constituent quarks we derive the chiral fluid dynamics where hydrodynamic equations for the quark fluid are coupled to the equation of motion for the order-parameter field. In a static system at…

We show uniqueness of classical solutions of the normalised two-dimensional Hamilton-Ricci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural…