Related papers: Minimal Modification to Nos\'e-Hoover Barostat Ena…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
The Biot-Savart law is relevant in physical contexts including electromagnetism and fluid dynamics. In the latter case, when the rotation of a fluid is confined to a set of very thin vortex filaments, this law describes the velocity field…
Efficient and accurate estimation of multivariate empirical probability distributions is fundamental to the calculation of information-theoretic measures such as mutual information and transfer entropy. Common techniques include variations…
For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the…
We present in this paper a pressure correction scheme for barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the…
Reservoir computing is a powerful framework for modeling dynamical systems due to its universality and computational efficiency. However, a major challenge is achieving a forecast with accurate long-time statistics, or climate, which is…
In the paper we prove the existence results for initial-value boundary value problems for compressible isothermal Navier-Stokes equations. We restrict ourselves to 2D case of a problem with no-slip condition for nonstationary motion of…
A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "macrostates" (e.g. sets of "microstates"), the consequence on…
This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…
Transitions out of the ground space limit the performance of quantum adiabatic algorithms, while hardware imperfections impose stringent limitations on the circuit depth. We propose an adiabatic echo verification protocol which mitigates…
We introduce a three independent functions variational formalism for stationary and non-stationary barotropic flows. This is less than the four variables which appear in the standard equations of fluid dynamics which are the velocity field…
In applying Vibration-Transit (V-T) theory of liquid dynamics to the thermodynamic properties of monatomic liquids, the point has been reached where an improved model is needed for the small (approx. 10%) transit contribution. Toward this…
We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary…
We consider barotropic motions described by the compressible Navier-Stokes equations in a box with periodic boundary conditions. We are looking for density $\varrho$ in the form $\varrho=a+\eta$, where $a$ is a constant and $\eta|_{t=0}$ is…
We study the nonparametric Nadaraya-Watson estimator of the drift function for ergodic stochastic processes driven by fractional Brownian motion of Hurst parameter H > 1/2. The estimator is based on the discretely observed stochastic…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density…
When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the…