Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals

Variational approach to coarse-graining of generalized gradient flows

In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (A) a natural interaction between the duality structure and the coarse-graining, (B) application to systems with non-dissipative effects, and (C) application to coarse-graining of approximate solutions which solve the equation only to some error. As examples, we use this technique to solve three limit problems, the overdamped limit of the Vlasov-Fokker-Planck equation and the small-noise limit of randomly perturbed Hamiltonian systems with one and with many degrees of freedom

Homogenization of the one-dimensional wave equation

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high frequency waves and especially on the boundary conditions of the homogenized equation. Numerical simulations are reported

Steam reforming of different biomass tar model compounds over Ni/Al2O3 catalysts

This work focuses on the removal of the tar derived from biomass gasification by catalytic steam reforming on Ni/Al2O3 catalysts. Different tar model compounds (phenol, toluene, methyl naphthalene, indene, anisole and furfural) were individually steam reformed (after dissolving each one in methanol), as well as a mixture of all of them, at 700 °C under a steam/carbon (S/C) ratio of 3 and 60 min on stream. The highest conversions and H2 potential were attained for anisole and furfural, while methyl naphthalene presented the lowest reactivity. Nevertheless, the higher reactivity of oxygenates compared to aromatic hydrocarbons promoted carbon deposition on the catalyst (in the 1.5–2.8 wt.% range). When the concentration of methanol is decreased in the feedstock and that of toluene or anisole is increased, the selectivity to CO is favoured in the gaseous products, thus increasing coke deposition on the catalyst and decreasing catalyst activity for the steam reforming reaction. Moreover, an increase in Ni loading in the catalyst from 5 to 20% enhances carbon conversion and H2 formation in the steam reforming of a mixture of all the model compounds studied, but these values decrease for a Ni content of 40%. Coke formation also increased by increasing Ni loading, attaining its maximum value for 40% Ni (6.5 wt.%)

Pathogenesis of peroxisomal deficiency disorders (Zellweger syndrome) may be mediated by misregulation of the GABAergic system via the diazepam binding inhibitor

BACKGROUND: Zellweger syndrome (ZS) is a fatal inherited disease caused by peroxisome biogenesis deficiency. Patients are characterized by multiple disturbances of lipid metabolism, profound hypotonia and neonatal seizures, and distinct craniofacial malformations. Median live expectancy of ZS patients is less than one year. While the molecular basis of peroxisome biogenesis and metabolism is known in considerable detail, it is unclear how peroxisome deficiency leads to the most severe neurological symptoms. Recent analysis of ZS mouse models has all but invalidated previous hypotheses. HYPOTHESIS: We suggest that a regulatory rather than a metabolic defect is responsible for the drastic impairment of brain function in ZS patients. TESTING THE HYPOTHESIS: Using microarray analysis we identify diazepam binding inhibitor/acyl-CoA binding protein (DBI) as a candidate protein that might be involved in the pathogenic mechanism of ZS. DBI has a dual role as a neuropeptide antagonist of GABA(A) receptor signaling in the brain and as a regulator of lipid metabolism. Repression of DBI in ZS patients could result in an overactivation of GABAergic signaling, thus eventually leading to the characteristic hypotonia and seizures. The most important argument for a misregulation of GABA(A) in ZS is, however, provided by the striking similarity between ZS and "benzodiazepine embryofetopathy", a malformation syndrome observed after the abuse of GABA(A) agonists during pregnancy. IMPLICATIONS OF THE HYPOTHESIS: We present a tentative mechanistic model of the effect of DBI misregulation on neuronal function that could explain some of the aspects of the pathology of Zellweger syndrome

Variational approach to coarse-graining of generalized gradient flows

In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational evolutions, and which often arises from a large-deviations principle. It has three main features: (a) a natural interaction between the duality structure and the coarse-graining, (b) application to systems with non-dissipative effects, and (c) application to coarse-graining of approximate solutions which solve the equation only to some error. As examples, we use this technique to solve three limit problems, the overdamped limit of the Vlasov–Fokker–Planck equation and the small-noise limit of randomly perturbed Hamiltonian systems with one and with many degrees of freedom

Natural convection in horizontal annuli: Evaluation of the error for two approximations

We consider convection inside annuli, driven by a uniform temperature gap on the boundaries and gravitation as outer force. It takes place for any Rayleigh number while steady convective motions are observed only for small ones (but any Prandtl number and gap width). We provide estimates for the relative error of two popular approximations to the full Navier–Stokes–Fourier equations. For this we propose a new method. In particular we have to derive a lower bound for the norm of the velocity and the temperature both for steady nonlinear coupled and decoupled approximations in two space dimensions

Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

\u3cp\u3eIn molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals.\u3c/p\u3