A parameter identification problem in stochastic homogenization

In porous media physics, calibrating model parameters through experiments is a challenge. This process is plagued with errors that come from modelling, measurement and computation of the macroscopic observables through random homogenization -- the forward problem -- as well as errors coming from the parameters fitting procedure -- the inverse problem. In this work, we address these issues by considering a least-square formulation to identify parameters of the microscopic model on the basis on macroscopic observables. In particular, we discuss the selection of the macroscopic observables which we need to know in order to uniquely determine these parameters. To gain a better intuition and explore the problem without a too high computational load, we mostly focus on the one-dimensional case. We show that the Newton algorithm can be efficiently used to robustly determine optimal parameters, even if some small statistical noise is present in the system

Negative thermal conductivity of chains of rotors with mechanical forcing

We consider chains of rotors subjected to both thermal and mechanical forcings,in a nonequilibrium steady-state. Unusual nonlinear profiles of temperature and velocities are observed in the system. In particular, the temperature is maximal in the center, which is an indication of the nonlocal behavior of the system. In spite of that, local equilibrium holds for long enough chains. Our numerical results also show that, when the mechanical forcing is strong enough, the energy current can be increased by an inverse temperature gradient. This counterintuitive result again reveals the complexity of nonequilibrium states

Thermal conductivity of the Toda lattice with conservative noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$

A weak characterization of slow variables in stochastic dynamical systems

We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a key role in system analysis and coarse graining. The defining characteristics of these slow variables is that they parametrize a so-called transition manifold, a low-dimensional manifold in a certain density function space that emerges with progressive equilibration of the system's fast variables. The existence of said manifold was previously predicted for certain classes of metastable and slow-fast systems. However, in the original work, the existence of the manifold hinges on the pointwise convergence of the system's transition density functions towards it. We show in this work that a convergence in average with respect to the system's stationary measure is sufficient to yield reaction coordinates with the same key qualities. This allows one to accurately predict the timescale preservation in systems where the old theory is not applicable or would give overly pessimistic results. Moreover, the new characterization is still constructive, in that it allows for the algorithmic identification of a good slow variable. The improved characterization, the error prediction and the variable construction are demonstrated by a small metastable system

Simple quantitative tests to validate sampling from thermodynamic ensembles

It is often difficult to quantitatively determine if a new molecular simulation algorithm or software properly implements sampling of the desired thermodynamic ensemble. We present some simple statistical analysis procedures to allow sensitive determination of whether a de- sired thermodynamic ensemble is properly sampled. We demonstrate the utility of these tests for model systems and for molecular dynamics simulations in a range of situations, includ- ing constant volume and constant pressure simulations, and describe an implementation of the tests designed for end users.Comment: 48 pages, 4 figure