Correctors for some asymptotic problems

In the theory of anisotropic singular perturbation boundary value problems, the solution u ɛ does not converge, in the H 1-norm on the whole domain, towards some u 0. In this paper we construct correctors to have good approximations of u ɛ in the H 1-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problems

Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation

Nonequilibrium, ``fast switching'' estimates of equilibrium free energy differences, Delta F, are often plagued by poor convergence due to dissipation. We propose a method to improve these estimates by generating trajectories with reduced dissipation. Introducing an artificial flow field that couples the system coordinates to the external parameter driving the simulation, we derive an identity for Delta F in terms of the resulting trajectories. When the flow field effectively escorts the system along a near-equilibrium path, the free energy estimate converges efficiently and accurately. We illustrate our method on a model system, and discuss the general applicability of our approach.Comment: 4 pages, including 2 figures, accepted for publication in Phys Rev Let

Differential Dynamics at Glycosidic Linkages of an Oligosaccharide as Revealed by 13C NMR Spin Relaxation and Stochastic Modeling

Among biomolecules, carbohydrates are unique in that not only can linkages be formed through different positions but the structures may also be branched. The trisaccharide \uf062-D-Glcp-(1\uf0ae3)[\uf062-D-Glcp-(1\uf0ae2)]-\uf061-D-Manp-OMe represents a model of a branched vicinally disubstituted structure. A 13C site-specific isotopologue with labeling in each of the two terminal glucosyl residues enabled acquisition of high-quality 13C NMR relaxation parameters T1, T2 and heteronuclear NOE, with standard deviations of \uf0a3 0.5%. For interpretation of the experimental NMR data a diffusive chain model was used in which the dynamics of the glycosidic linkages is coupled to the global reorientation motion of the trisaccharide. Brownian dynamics simulations relying on the potential of mean force at the glycosidic linkages were employed to evaluate spectral densities of the spin probes. Calculated NMR relaxation parameters showed very good agreement with experimental data, deviating < 3%. The resulting dynamics is described by correlation times of 196 ps and 174 ps for the \uf062-(1\uf0ae2)- and \uf062-(1\uf0ae3)-linked glucosyl residues, respectively, i.e., different and linkage dependent. Notably, the devised computational protocol was performed without any fitting of parameters

Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback

We extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback. Within this framework, we derive a generalization of the detailed fluctuation theorem, which is modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback. As an application, we extend two nonequilibrium work relations: the nonequilibrium work fluctuation theorem and the relative-entropy work relation.Comment: 7 pages, 3 figure

Origin of Native Driving Force in Protein Folding

We derive an expression with four adjustable parameters that reproduces well the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein structures. The numerical values of the parameters can be approximately computed from the surface tension of water, water-screened dipole interactions between residues and water and among residues, and average exposures of residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table

Ice Formation on Kaolinite: Insights from Molecular Dynamics Simulations

The formation of ice affects many aspects of our everyday life as well as technologies such as cryotherapy and cryopreservation. Foreign substances almost always aid water freezing through heterogeneous ice nucleation, but the molecular details of this process remain largely unknown. In fact, insight into the microscopic mechanism of ice formation on different substrates is difficult to obtain even via state-of-the-art experimental techniques. At the same time, atomistic simulations of heterogeneous ice nucleation frequently face extraordinary challenges due to the complexity of the water-substrate interaction and the long timescales that characterize nucleation events. Here, we have investigated several aspects of molecular dynamics simulations of heterogeneous ice nucleation considering as a prototypical ice nucleating material the clay mineral kaolinite, which is of relevance in atmospheric science. We show via seeded molecular dynamics simulations that ice nucleation on the hydroxylated (001) face of kaolinite proceeds exclusively via the formation of the hexagonal ice polytype. The critical nucleus size is two times smaller than that obtained for homogeneous nucleation at the same supercooling. Previous findings suggested that the flexibility of the kaolinite surface can alter the time scale for ice nucleation within molecular dynamics simulations. However, we here demonstrate that equally flexible (or non flexible) kaolinite surfaces can lead to very different outcomes in terms of ice formation, according to whether or not the surface relaxation of the clay is taken into account. We show that very small structural changes upon relaxation dramatically alter the ability of kaolinite to provide a template for the formation of a hexagonal overlayer of water molecules at the water-kaolinite interface, and that this relaxation therefore determines the nucleation ability of this mineral

Quasivariational solutions for first order quasilinear equations with gradient constraint

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable {\em a priori} estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

Time-independent free energies from metadynamics via Mean Force Integration

Inspired by thermodynamic integration, we propose a method for the calculation of time-independent free energy profiles from history-dependent biased simulations via Mean Force Integration (MFI). MFI circumvents the need for computing the ensemble average of the bias acting on the system c(t) and can be applied to different variants of metadynamics. Moreover, MFI naturally extends to aggregate information obtained from independent metadynamics simulations, allowing to converge free energy surfaces without the need to sample recrossing events in a single continuous trajectory. We validate MFI against one- and two-dimensional analytical potentials and by computing the conformational free energy landscape of ibuprofen in the bulk of its most common crystal phase.Comment: 8 pages, 4 figure