Multisymplectic Lie group variational integrator for a geometrically exact beam in R3

In this paper we develop, study, and test a Lie group multisymplectic integra- tor for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions.Comment: Article in press. 22 pages, 18 figures. Received 20 November 2013, Received in revised form 26 February 2014, Accepted 27 February 2014. Communications in Nonlinear Science and Numerical Simulation. 201

Reduced Joule heating in nanowires

The temperature distribution in nanowires due to Joule heating is studied analytically using a continuum model and a Green's function approach. We show that the temperatures reached in nanowires can be much lower than that predicted by bulk models of Joule heating, due to heat loss at the nanowire surface that is important at nanoscopic dimensions, even when the thermal conductivity of the environment is relatively low. In addition, we find that the maximum temperature in the nanowire scales weakly with length, in contrast to the bulk system. A simple criterion is presented to assess the importance of these effects. The results have implications for the experimental measurements of nanowire thermal properties, for thermoelectric applications, and for controlling thermal effects in nanowire electronic devices.Comment: 4 pages, 3 figures. To appear in Applied Physics Letter

The Geometric Structure of Complex Fluids

This paper develops the theory of affine Euler-Poincar\'e and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microfluids, and liquid crystals. As a consequence of the Lagrangian approach, the variational formulation of the equations is determined. On the Hamiltonian side, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin-Noether circulation theorem is presented and is applied to these examples

Affine Lie-Poisson Reduction, Yang-Mills magnetohydrodynamics, and superfluids

This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin-Noether circulation theorem is presented and is applied to these examples

Probing an nonequilibrium Einstein relation in an aging colloidal glass

We present a direct experimental measurement of an effective temperature in a colloidal glass of Laponite, using a micrometric bead as a thermometer. The nonequilibrium fluctuation-dissipation relation, in the particular form of a modified Einstein relation, is investigated with diffusion and mobility measurements of the bead embedded in the glass. We observe an unusual non-monotonic behavior of the effective temperature : starting from the bath temperature, it is found to increase up to a maximum value, and then decreases back, as the system ages. We show that the observed deviation from the Einstein relation is related to the relaxation times previously measured in dynamic light scattering experiments.Comment: 4 pages, 4 figures, corrected references, published in Phys. Rev. Lette

Reconstructing the free-energy landscape of Met-enkephalin using dihedral Principal Component Analysis and Well-tempered Metadynamics

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers however from the same limitation, i.e. the non trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachadran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates. We illustrate the robustness of this method in the case of the small and very diffusive Metenkephalin pentapeptide, and highlight a criterion to limit the number of CVs necessary to biased the metadynamics simulation. The free-energy landscape (FEL) of Met-enkephalin built on CVs generated from dPCA is found rugged compared with the FEL built on CVs extracted from PCA of the Cartesian coordinates of the atoms.Comment: 17 pages, 9 figures (4 in color