Campuses:

<span class=strong>Reception and Poster Session</span>

Tuesday, July 24, 2007 - 5:00pm - 6:30pm
Lind 400
  • Method for determination of Hubbard model phase diagram from

    optical lattice experiments by two parameter scaling

    Vivaldo Campo (University of Minnesota, Twin Cities)
    We propose[1] an experimental scheme to obtain the phase diagram
    of the Hubbard model using cold atoms in optical lattices.[2] The
    scheme is based on measuring the total energy for a sequence of
    trapping potentials with different profile and is independent of di-
    mensionality. Its essential ingredient is a two-parameter scaling pro-
    cedure that combines a variant of the familiar finite-size scaling with
    a nontrivial additional ’finite-curvature scaling’ necessary to reach
    the homogeneous limit. We illustrate the viability of the scheme
    in the one-dimensional case, using simulations based on the Bethe
    Ansatz local-density approximation as a substitute for experimental
    data, and show that the filling corresponding to the Mott transition
    can be determined with better than 3% accuracy.

  • Numerical method for solving stochastic differential equations with non-Gaussian noise
    Changho Kim (Korea Advanced Institute of Science and Technology (KAIST))
    We propose numerical integration schemes to solve stochastic differential equations driven by two important non-Gaussian noises – dichotomous Markov noise and Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if these noises approach the Gaussian white noise. We further propose a simplified weak scheme that significantly reduces the computation time, while still satisfying the moment properties up to the required order. Our approach is readily applicable to dynamical systems driven by arbitrary types of noise, provided there exists a way to describe the random increment of the noise accumulated during each integration time step. The accuracy and efficiency of the proposed algorithms are numerically examined.
  • Molecular modelling the structure and dynamics of alginate

    oligosaccharides

    Hoda Abdel-Aal Bettley (University of Manchester)
    Joint work with Richard A. Bryce.

    Alginate copolymers are a key component of the extracellular polymeric
    substances (EPS) matrix of bacterial microorganisms such as P. aeruginosa, and
    occur in high abundance in nature. Alginate heteropolysaccharides comprise
    alternating blocks of alpha-(1->4)-linked L-guluronate and beta-(1->4)-linked
    D-mannuronate. To understand the microscopic behaviour and interactions of
    these flexible acidic sugars within the EPS matrix, a suitable molecular-level
    model is required. We derive a molecular mechanical force field for the two
    uronic acids, with validation against available experimental data. We then
    construct a detailed study of the structure and dynamics of alginate chains. We
    explore alginate models of increasing complexity, from disaccharides to single-
    and double-stranded oligomer helices, employing the techniques of molecular
    dynamics and replica-exchange molecular dynamics. The condensed phase behaviour
    of these systems is discussed, including the role of counterions and the
    implications for interaction with other constituents of the EPS matrix.
  • Objective structures and their applications
    Kaushik Dayal (University of Minnesota, Twin Cities)
    Objective structures [1] are a recent classification of atomic and
    molecular structures that includes numerous systems of current
    interest. Examples are nanotubes and biological virus components.
    While these structures are not crystalline, there are many strong
    analogies to crystals. These analogies can be exploited to generalize
    computational techniques developed in the context of crystals to these
    new systems. Further, they may provide strategies for self-assembly
    and structure determination.

    Some examples of current work exploiting these ideas will be
    presented. These include finding the normal modes of these structures
    (in analogy with phonons), Objective Molecular Dynamics in analogy
    with conventional MD, and DFT and other first-principles techniques in
    the Objective setting. Recent work on finding all possible objective
    structures will be described.

    [1] R. D. James, Objective Structures, J. Mech. Phys. Solids, 54,
    2354-2390 (2006).
  • Uniqueness of the density-to-potential mapping in excited-state

    density-functional theory

    Prasanjit Samal (University of Minnesota, Twin Cities)
    Jont work with Manoj K. Harbola (Department of Physics, Indian Institute of Technology, Kanpur 208016, India).

    The question of whether there exists a mapping from
    an excited-state density to a potential is central to performing density-functional calculation for excited states. The motivation of the present work is to establish a unique way of selecting a system (potential) for a given excited-state density. The issue of density – to – potential mapping has been addressed in a series of work by Sahni et al [1], Harbola [2] and Gaudoin et al [3]. In the work of [1] and [2], it was shown that ground- or excited-state density can be generated by configuration of one’s choice. In the work [3], they have shown that even with a fixed configuration, one could reproduce same excited-state density from more than one potentials as shown in Fig.1. This implies in addition to the excited-state density one requires some extra information to establish such a unique mapping. This has been done by comparison of ground state densities in Levy-Nagy [4] theory. Following the earlier attempts we have further explored the density-to-potential mapping based on the work of Levy-Nagy [4] and Gorling [5] for excited-states [6]. We have proposed a new criterion [7], which uniquely establishes such mapping.


    href=/2006-2007/SP7.23-8.3.07/activities/Samal-Prasanjit/samal-full.gif>
    src=/2006-2007/SP7.23-8.3.07/activities/Samal-Prasanjit/samal.gif>



    Fig.1: Two potentials (middle panel) giving the same excited-state density (upper panel)
    along with their corresponding ground-state densities (lower panel) for an excited-state
    of the three electron 1D infinitely deep well model system.

    References:

    [1] V. Sahni, L. Massa, R. Singh and M. Slamet, Phys. Rev. Lett. 87, 113002 (2001).

    [2] M. K. Harbola, Phys. Rev. A 69, 042512 (2004).

    [3] R. Gaudoin and K. Burke, Phys. Rev. Lett. 93, 173001 (2004).

    [4] M. Levy and A. Nagy, Phys. Rev. Lett. 83, 4361 (1999).

    [5] A. Gorling, Phys. Rev. A 59, 3359 (1999).

    [6] P. Samal, M. K. Harbola and A. Holas, Chem. Phys. Lett. 419, 217 (2006)

    [7] P. Samal and M. K. Harbola, J. Phys. B 39, 4065 (2006).
  • Particle-Scaling function (P3S) algorithm for electrostatic problems in free

    boundary conditions

    Alexey Neelov (Universität Basel)
    A simple algorithm for fast calculation of the Coulombic forces and energies of
    point particles with free boundary conditions will be presented. Its
    calculation time scales as N log N for N particles. This novel method has lower
    crossover point with the full O(N^2) direct summation than the Fast Multipole
    Method. The forces obtained by our algorithm are analytical derivatives of the
    energy which guarantees energy conservation during a molecular dynamics
    simulation. Our method is based on the Poisson solver [2] for continuous
    charge distribution that uses the Deslaurier-Dubuc (interpolating) wavelets.

    [1] L. Genovese, T. Deutsch, A. Neelov, S. Goedecker, and G. Beylkin, Efficient
    solution of Poisson's equation with free boundary conditions, J. Chem. Phys.
    125, 007415 (2006).

    [2] A. Neelov, S. A. Ghasemi, S. Goedecker, Particle-Particle, Particle-Scaling
    function (P3S) algorithm for electrostatic problems in free boundary
    conditions, J. Chem. Phys., 2007 (to appear)
  • An ab initio molecular dynamics simulation of solid CL-20:

    mechanism and kinetics of thermal decomposition

    Olexandr Isayev (Jackson State University)
    Joint work with Leonid Gorb,(1
    and 2)
    Mo. Qasim,(2) and
    Jerzy Leszczynski. (1)

    CL-20
    (Octahydro-1,3,4,7,8,10-hexanitro-5,2,6-(iminomethenimino)-1H-imidazo[4,5-b]-pyrazin)
    is one of the most important high energetic nitramines which
    are used as explosives and propellants. The decomposition of
    CL-20 is very complicated and involves hundreds of elementary
    reactions. Accurate knowledge of these reactions and
    predictions of their kinetic parameters are important for
    modeling these complex processes in combustion and explosion.
    However, due to the energetic nature of these materials and the
    rapid rates of the intermediate reactions, it is difficult to
    monitor these individual reactions experimentally. Recent
    advances in first principles modeling have led to enormous
    progress toward understanding complex condensed phase chemical
    phenomena. Theoretical methods, especially accurate ab initio
    molecular dynamics method, provide a viable alternative to
    study the dynamics of these reactions. Electronic properties
    and the dynamics of the initial thermal decomposition step of
    gas-, and e-crystal phases of CL-20 are investigated using the
    Car-Parrinello molecular dynamics (CPMD) approach. The
    difference in the reaction pathways between gas- and crystal
    phases has been accounted for the strong intermolecular
    interaction into crystal lattice. The thermal rate constants
    have been also estimated.


    1) Computational Center of Molecular Structure and Interactions,
    Jackson State University, Jackson, MS 39217

    2) US Army ERDC, Vicksburg, MS, 39180.
  • Temperature-regulated microcanonical dynamics
    Emad Noorizadeh (University of Edinburgh)
    Joint work with Ben Leimkuhler (School of Mathematics, University of Edinburgh) and Frederic Legoll (LAMI, Ecole Nationale des Ponts et Chaussees, France).

    We describe a new dynamical technique for the equilibration of molecular dynamics. Temperature is moderated by a control law and an additional variable, as in Nose dynamics,
    but whose influence on the system decreases as the system approaches equilibrium. This device enables approximation of microcanonical averages and autocorrelation functions consistent with given target temperature. Moreover, we demonstrate that the suggested technique is effective for the regulation of heat production in a nonequilibrium setting.
  • New numerical algorithms and software for minimizing

    biomolecular potential energy functions

    Dexuan Xie (University of Wisconsin)
    This poster reports some progresses we made recently in developing numerical algorithms and program packages for minimizing large scale biomolecular potential energy functions, which is one of the fundamental tasks in biomolecular simulations.

    The new algorithms are designed from a sparse incomplete Hessian matrix constructed by a spherical cutoff strategy according to the problem size and computer capability. They are called the incomplete Hessian Newton method (IHN), the truncated-IHN method (T-IHN), and the refined T-IHN method (RT-IHN), respectively. The program package of RT-IHN for solving the biomolecular potential energy minimization problem is developed based on a widely-used biomolecular simulation packages, CHARMM. This poster will give RT-IHN a detailed description, and present its numerical performances for some large scale protein systems.



    In theory, these new algorithms are defined and analyzed for a general unconstrained minimization problem with a target function having a dense Hessian matrix. They are proved to be convergent globally. While IHN and T-IHN are shown to have a linear rate of convergence, RT-IHN is proved to have a super-linear rate of convergence. Hence, these new algorithms can be applied to other large scale scientific and engineering applications. For this purpose, we develop a general program package of RT-IHN in C++ based on the optimization program package TAO (http://www-unix.mcs.anl.gov/tao/index.html), and apply it to solve the chemical database optimal projection mapping problem.

    This is the joint work with Mazen G. Zarrouk and Jun Wang.
  • A Bell-Evans-Polanyi principle for molecular dynamics trajectories and

    its implications for global optimization

    Shantanu Roy (Universität Basel)
    Joint work with Waldemar Hellmann and Stefan Goedecker (Institute of Physics, University of Basel).

    The Bell-Evans-Polanyi principle that is valid for a chemical reaction that
    proceeds along the reaction coordinate over the transition state is extended to
    molecular dynamics trajectories that in general do not cross the dividing
    surface between the initial and the final local minimum at the exact transition
    state. Our molecular dynamics Bell-Evans-Polanyi principle states that low
    energy molecular dynamics trajectories are more likely to lead into the basin
    of attraction of a low energy local minimum than high energy trajectories. In
    the context of global optimization schemes based on molecular dynamics our
    molecular dynamics Bell-Evans-Polanyi principle implies that using low energy
    trajectories one needs to visit a smaller number of distinguishable local
    minima before finding the global minimum than when using high energy
    trajectories.
  • Absolute entropy and free energy of free and bound states of a mobile

    loop of alpha-amylase using the

    hypothetical scanning method

    Srinath Cheluvaraja (University of Pittsburgh)
    A new simulation method is studied which is capable of calculating the
    absolute entropy and free energy of a microstate. The method is based on
    calculating the probability of a member in the statistical ensemble by
    growing the configuration in a step-by-step manner and expressing it as
    a product of conditional probabilities, each of which is calculated by
    performing
    simulations at every step. This is a potentially exact method with the errors
    arising only from inadequate sampling. The method is applied to a small protein loop in
    implicit solvent and the results obtained agree quite well with those
    obtained from other (approximate) methods. Unlike other
    methods, all long range interactions are taken into account in the
    reconstruction procedure.
  • Precision problems in density functional development

    for better molecular modeling

    Michael Teter (Cornell University)
    Classical modeling depends upon Density Functional Theory (DFT)
    for its potential parameters, and quantum modeling usually uses DFT directly. The only significant
    improvement in DFT in the last 40 years has been the gradient corrections by Perdew et al., and they
    only improved the gross energy errors without improving molecular geometries or forces. Indeed, many
    of the talks in the second week address this problem. If we are to get better modeling, we need DFT
    functional development.

    The primary problem with DFT functional development is that the total energy errors are quadratic in electron
    density errors while the force errors are linear, so that further improvements must get the electron densities
    right. The differences between the electron densities predicted by the various theories is at the 1-2% level.
    So, in order to get the differences right, one must actually have a numerical method which resolves the
    density to 1/10% or the energies to a part per million. Easy-to-use methods which can achieve this accuracy
    regularly do not exist, hence my work.
  • Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures
    Erkan Tüzel (North Dakota State University)
    Joint work with Guoai Pan (National Institute for Nanotechnology, Canada),
    Thomas Ihle and Daniel M. Kroll (Department of Physics,
    North Dakota State University).

    A recently introduced particle-based model for fluid dynamics
    with continuous velocities is generalized to model
    immiscible binary mixtures. Excluded volume interactions
    between the two components are modeled by stochastic
    multiparticle collisions which depend on the local velocities
    and densities. Momentum and energy are conserved
    locally, and entropically driven phase separation occurs for
    high collision rates. An explicit expression for the equation
    of state is derived, and the concentration dependence of the
    bulk free energy is shown to be the same as that of the
    Widom-Rowlinson model. Analytic results for the phase diagram
    are in excellent agreement with simulation data.
    Results for the line tension obtained from the analysis of the
    capillary wave spectrum of a droplet agree with measurements
    based on the Laplace's equation. The dispersion relation for
    the capillary waves is derived and compared with the
    numerical measurements of the time correlations of the radial
    fluctuations in the damped and over-damped limits.
    The introduction of amphiphilic dimers makes it possible to
    model the phase behavior of ternary surfactant mixtures.
  • Multilevel summation method for Coulomb interactions
    David Hardy (University of Illinois at Urbana-Champaign)
    The multilevel summation method (MSM) computes an approximation to
    the pairwise interaction potential and its gradient with an amount of
    work that scales linearly as the size of the system. The potential
    is smoothly split into a sum of partial potentials of increasing
    range and decreasing variability with the longest-range parts
    interpolated from grids of increasing coarseness. Multilevel
    summation is especially appropriate for dynamical simulations,
    because it can produce continuous forces for both nonperiodic and
    periodic boundary conditions. A small correction to the grid-based
    force approximation can be used to conserve both energy and momentum.
  • Conformational reinvestigation of two cyclic pentapeptides: to

    a generic approach in drug development

    Pieter Hendrickx (University of Ghent (UG))
    Joint work with I. Van den Eynde2, J.C. Martins1 and D. Tourwé2

    As part of a bigger research effort which consists of the
    development of a generic approach for drug development, two
    cyclic peptides based on the active sequence of somatostatin
    were characterized using nuclear magnetic resonance
    spectroscopy (NMR). In order to obtain the 3D conformation of
    these molecules, conformational relevant parameters (eg. nOe,
    scalar couplings and amide temperature coefficients) were
    recorded. A simulated annealing protocol using distance
    restraints was used to obtain a set of conformations which were
    validated by analysis of the hydrogen bridges present and by
    recalculating the measured scalar couplings.
    Future efforts will consist of generating mathematical
    descriptions (templates) of this kind of small peptide chains
    as well as creating templates of non-peptidic small molecules.
    This must allow for an intelligent choice for drug templates
    upon positive screening results of the small peptide molecules.


    1NMR and Structure Analysis Unit, Department of Organic
    Chemistry, Ghent University, Krijgslaan 281 S4 B-9000 Gent,
    Belgium


    2Unit for Organic Studies, Department of Organic
    Chemistry, Vrije Universiteit Brussel, Pleinlaan 2 9G616 B-1050
    Elsene, Belgium
  • Modelling of local defects in crystals
    Amélie Deleurence (École Nationale des Ponts-et-Chaussées (ENPC))
    Work in collaboration with Eric Cancès (CERMICS-ENPC, France) and Mathieu Lewin (Department of Mathematics, Université de Cergy, France)

    We present mathematical results obtained for a new mean-field model
    dedicated to the description of interacting electrons in crystals with local
    defects. We work with a reduced Hartree-Fock model, obtained from the
    usual Hartree-Fock model by neglecting the exchange term. Then we
    deduce a new variational model for computing the perturbation in a
    basis of precomputed maximally localized Wannier functions of the
    reference perfect crystal. Finally we show some numerical results in
    which we have applied the variational approximation and used a
    one-dimensional model with Yukawa interaction potential.
  • A comparison of maximum likelihood and weighted

    residual approximations to the potential of mean force

    Eric Cyr (University of Illinois at Urbana-Champaign)
    The potential of mean force (PMF) describes the change in free energy
    along a reaction coordinate and determines the strength and likelihood
    of association in molecular systems. Current methods, like Thermodynamic
    Integration (TI) and WHAM, use piecewise linear and piecewise constant
    approximations of the PMF. We propose two methods that allow the use
    of arbitrary basis functions, one based on maximum likelihood
    estimation and another on the method of weighted residuals. Numerical
    comparisons with TI and WHAM are performed.
  • A systematic method to explore possible silicon tip structures used in AFM
    Seyed-Alireza Ghasemi (Universität Basel)
    We present a systematic way to construct silicon tips by using
    the minima hopping method(MHM) with limited temperature.
    In Molecular Dynamics part of the MHM we limit the temperature to
    some value used in experiments. We used Tight-Binding
    scheme to evaluate energy and forces of silicon and hydrogen atoms
    in MHM. Structures with lowest energy obtained with this method
    are used in AFM simulation and force between tip and surface is
    calculated in terms of distance and some of obtained results
    are presented in this poster.