Langlands duality for representations of quantum groups

We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of semi-simple Lie algebras. To explain this duality, we introduce an "interpolating quantum group" depending on two parameters which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending on two parameters, which interpolate between representations of two Langlands dual quantum groups.Comment: 37 pages. References added. Accepted for publication in Mathematische Annale

Rate of Homogeneous Crystal Nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute-force" Molecular Dynamics simulations. The melting temperature of ("Tosi-Fumi") NaCl is $\sim 1060$K. We studied crystal nucleation at $T$=800K and 825K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted: the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the Forward Flux Sampling and Transition Interface Sampling (FFS-TIS) methods. We find that the two methods yield the same result to within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly 5 orders of magnitude. We discuss the possible causes for this discrepancy

Dissipative particle dynamics for interacting systems

We introduce a dissipative particle dynamics scheme for the dynamics of non-ideal fluids. Given a free-energy density that determines the thermodynamics of the system, we derive consistent conservative forces. The use of these effective, density dependent forces reduces the local structure as compared to previously proposed models. This is an important feature in mesoscopic modeling, since it ensures a realistic length and time scale separation in coarse-grained models. We consider in detail the behavior of a van der Waals fluid and a binary mixture with a miscibility gap. We discuss the physical implications of having a single length scale characterizing the interaction range, in particular for the interfacial properties.Comment: 25 pages, 12 figure

Gas-solid coexistence of adhesive spheres

In this note we investigate using basic free energy considerations the location of the gas-liquid critical point with respect to solidification for narrow attractive interactions down to the Baxter limit. Possible experimental and simulation realizations leading to a stable critical point are briefly discussed.Comment: 2 pages, 2 figures, submitte

Replica exchange Monte Carlo applied to Hard Spheres

In this work a replica exchange Monte Carlo scheme which considers an extended isobaric-isothermal ensemble with respect to pressure is applied to study hard spheres (HS). The idea behind the proposal is expanding volume instead of increasing temperature to let crowded systems characterized by dominant repulsive interactions to unblock, and so, to produce sampling from disjoint configurations. The method produces, in a single parallel run, the complete HS equation of state. Thus, the first order fluid-solid transition is captured. The obtained results well agree with previous calculations. This approach seems particularly useful to treat purely entropy-driven systems such as hard body and non-additive hard mixtures, where temperature plays a trivial role

Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids with small bond angles: Effects of steric hindrance and ring formation

In this paper we develop a thermodynamic perturbation theory for two site associating fluids which exhibit bond cooperativity. We include both steric hindrance and ring formation such that the equation of state is bond angle dependent. Here the bond angle is the angle separating the centers of the two association sites. As a test, new Monte Carlo simulations are performed, and the theory is found to accurately predict the internal energy as well as the distribution of associated clusters as a function of bond angle and bond cooperativity.Comment: To appear in The Journal of Chemical Physic

Adaptively Biased Molecular Dynamics for Free Energy Calculations

We present an Adaptively Biased Molecular Dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using non-equilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential, and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters, and an $O(t)$ numerical cost with molecular dynamics time $t$. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.Comment: Revised version to appear in Journal of Chemical Physic