Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session X32: Theoretical and Multiscale Modeling Methods |
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Sponsoring Units: DCOMP Chair: Daryl Hess, NSF Room: LACC 507 |
Friday, March 25, 2005 8:00AM - 8:12AM |
X32.00001: Distribution and Other Properties of Zeros of Mittag-Leffler Functions John W. Hanneken, B. N. Narahari Achar, Raymond Puzio The zeros of the Mittag-Leffler function play a significant role in the solutions of dynamic problems in fractional calculus. For example see the book Fractional Differential Equations by Podlubny, or for a specific application see the fractional oscillator by Achar et. al. Physica A297 (2001) 361-367; A309 (2002) 275-288; A339 (2204) 311-319. Very little, however, is known about these zeros. A summary of the available information about the zeros of Mittag-Leffler functions will be given and new results pertaining to their distribution will be presented. [Preview Abstract] |
Friday, March 25, 2005 8:12AM - 8:24AM |
X32.00002: Electric-field dependent quantum dynamics in a delta-function potential system ILki Kim, Gerald J. Iafrate The quantum dynamics for a single electron interacting with a general superposition of delta-function potentials subject to a spatially homogeneous electric field of arbitrary strength and time dependence is presented. The delta-function model system has been utilized heuristically to represent a short range atom or optically active defect, and in more complex combinations, in representing resonant tunneling junctions, molecular switches, and Dirac comb lattices. In the formalism, the electric field is described through the use of the vector potential gauge. The time dependent Schr\"{o}dinger equation for this problem is solved exactly in quadrature form; specific detailed analysis is performed for constant and oscillatory electric fields, and for a single attractive delta-function. For this case, when the electron is initially in the bound state, the exact ionization probability is determined and discussed for both constant and oscillatory electric fields of varying strengths. [Preview Abstract] |
Friday, March 25, 2005 8:24AM - 8:36AM |
X32.00003: Dynamics of Coupled Fractional Oscillators B.N. Narahari Achar, John W. Hanneken The theory of fractional oscillators (Achar et al. Physica A 297(2001) 361-367; A 309 (2002) 275-288; A 339 (2004) 311-339) has been extended to the study of coupled fractional oscillators. The response characteristics and energy flow are analyzed in the frame work of fractional integral equations of motion and the Greens function obtained by Laplace transform technique. The continuum limit is also studied. [Preview Abstract] |
Friday, March 25, 2005 8:36AM - 8:48AM |
X32.00004: XQED(3) : Non-compact QED(3) with an added four-fermi interaction Ioannis Tziligakis Non-compact QED with an extra weak four-fermion term (aka XQED) is simulated in 2+1 dimensions. Approaches based on Schwinger- Dyson studies, arguments based on thermodynamic inequalities and numerical studies lead to estimates of the critical number of fermion flavors (below which chiral symmetry is broken) ranging from $N_{fc}=1$ to $N_{fc}=4$. The weak four-fermion coupling is irrelevant in the continuum thus it provides the framework for an improved algorithm, allowing us to simulate the chiral limit of massless fermions. We present results of a first round of simulations. [Preview Abstract] |
Friday, March 25, 2005 8:48AM - 9:00AM |
X32.00005: Optical properties of a spherical 2D electron gas in the presence of a uniform magnetic field Ali Goker, Peter Nordlander Using the RPA, we calculate the plasmon frequencies of an electron gas on a two-dimensional spherical surface in the presence of a weak magnetic field[1]. We show that the magnetic field results in a coupling between electronic states with different angular momentum numbers. This coupling results in a blueshift of the dipolar plasmon resonance with increasing magnetic field. We also investigate how the plasmon energies vary as a function of the number of electrons and radius of the sphere. We discuss how the calculation can be generalized to an electron liquid confined in a spherical shell of finite thickness. [1] A. Goker and P. Nordlander, J. Phys.: Cond. Mat. 16(2004) 8233 [Preview Abstract] |
Friday, March 25, 2005 9:00AM - 9:12AM |
X32.00006: Mott transition in a two-band model Federico Becca, Michel Ferrero, Michele Fabrizio We investigate the properties of the Mott transition in a two-band Hubbard model with different bandwidths. Using a Gutzwiller approximation, we show that below a critical ratio of the bandwidths, the bands undergo separate Mott transitions, both is the presence or in the absence of a Hund's coupling between the two orbitals. The validity of the approximation is studied within dynamical mean-field theory. In addition, we use a projective self-consistent technique to examine the low-energy part of the spectrum. All our results are in good agreement with the Gutzwiller approximation. [Preview Abstract] |
Friday, March 25, 2005 9:12AM - 9:24AM |
X32.00007: Process, Pattern and Prediction in Avalanche Models of Driven Threshold Systems, with Applications to Earthquakes John Rundle, James Holliday, William Klein, Paul Rundle, Donald Turcotte Forecasting the onset and severity of extreme avalanche events in driven threshold systems, including neural networks, earthquakes, charge density waves, sandpiles and magnetic de-pinning transitions is complicated by the inability to directly observe many of the fundamental dynamical processes, together with the wide range of scales that characterize these systems. With respect to earthquakes, the economic damages from the most severe of these events amount to annualized economic costs of many billions of dollars, and are also associated with great suffering associated with the loss of many thousands of human lives each year. In systems such as these, we can only observe the space-time \textit{patterns} of extreme events, the largest earthquakes. Using these space-time patterns, and whatever is known about the dynamics of these high-dimensional nonlinear earth systems, it often possible to construct numerical simulations that can be used to make \textit {predictions} about the future space-time evolution of the system and the possible occurrence of extreme events. The accuracy of these predictions and forecasts is limited by the proximity and similarity of the model trajectory through state space, to that of the actual system. In this talk we summarize current methods that are being developed based on space-time pattern recognition techniques, together with numerical simulation of the underlying dynamics. We also discuss how these techniques may be tested, together with the current results. [Preview Abstract] |
Friday, March 25, 2005 9:24AM - 9:36AM |
X32.00008: Hamiltonian QM/MM scheme based on a plane-wave DFT approach Angelo Bongiorno, Seung Bum Suh, Robert Barnett, Uzi Landman We present an Hamiltonian quantum mechanical (QM)/molecular mechanical (MM), QM/MM, scheme for investigating large biological systems. The QM region is described through a plane-wave density-functional theory approach, while for the MM region we use the AMBER force field. The QM and MM regions are merged in our scheme across C-C bonds. These bonds are saturated by using hydrogen-like pseudopotentials. Charge consistency across the QM/MM interface is achieved by generating norm-conserving pseudopotentials accounting for the values of the MM effective charge. The interaction between the QM region and non-bonded MM ions includes van der Waals and coulomb interactions. Spill-out effects and spurious large electrostatic interactions at the frontier between the QM and MM regions are avoided by smearing the MM effective ionic charges according to a gaussian distribution. Our QM/MM scheme well reproduces the properties of the water dimer, water, small organic molecules, and large oligomers, as compared to either full MM and QM calculations. [Preview Abstract] |
Friday, March 25, 2005 9:36AM - 9:48AM |
X32.00009: Multiscale modeling of singular cavity flow and moving contact lines Xiaobo Nie, Mark O. Robbins, Shiyi Chen We have extended our previous continuum-atomistic hybrid method [1] to simulate macro-scale (millimeter and larger) quasistatic flows while retaining atomistic structure in key spatial regions. The method uses local refinement to handle the wide range of spatial scales. The separation in time scales is addressed by iterating the solution at each spatial scale to steady state using smaller time steps at smaller length scales. Speedups of more than 10 orders of magnitude have been obtained compared to pure atomistic simulations. The method has been applied to study wall driven cavity flows with different Reynolds numbers (up to $\sim$7000) and driving velocities. Singular stresses at the corner lead to an infinite total force on the moving wall in continuum theory. Our hybrid approach allows this force to be investigated for the first time. The method has also has been used to examine similar singularities in motion of the contact line between a fluid interface and a solid wall. The dependence of the dynamic contact angle is evaluated as a function of surface tension, viscosity, system size, and molecular scale slip length and compared to analytic models [2]. 1. X. B. Nie et al, J. Fluid Mech. {\bf 500}, 55 (2004); Phys. Fluids {\bf 16}, 3579 (2004). 2. R. G. Cox, J. Fluid Mech. {\bf 168}, 169 (1886). [Preview Abstract] |
Friday, March 25, 2005 9:48AM - 10:00AM |
X32.00010: Texture and Microstructure evolution in PVD films of fcc metals using Molecular Dynamics Asit Rairkar, James Adams Metallic polycrystalline thin films are used in a plethora of applications including especially metallic interconnects for the microelectronic industry. Numerous researchers have attempted to investigate both theoretical and experimental aspects of grain growth, texture competition and microstructure evolution. However the exact atomistic mechanisms behind these phenomena are still unknown. We attempt to study atomic level mechanisms behind polycrystalline thin film growth using Molecular dynamics techniques. The basic idea is to deposit Aluminum atoms on an fcc Lennard-Jones type of substrate with varying interaction energies with the Aluminum atoms. This will enhance the understanding of mechanisms behind island formation, substrate wetting, facetting in nuclei. We also report the results of similar depositions on Bicrystals of $<$110$>$ and $<$111$>$ oriented Aluminum slabs which result in dominance of the $<$111$>$ grains by twinning mechanisms. All the MD simulations will be carried out at elevated temperatures and high deposition rates. This helps compensate the surface diffusion rates for the atomsThe goal of this study is to provide input to our multi-scale film growth model called FACET and the future 3D version of it called FACET-3D. [Preview Abstract] |
Friday, March 25, 2005 10:00AM - 10:12AM |
X32.00011: Speed-Up of Dynamic Observables in Coarse-Grained Molecular Dynamics Simulations of Polymer Melts Praveen Depa, Janna Maranas We provide a prediction for the ``indirect speed-up'' observed in Coarse-Grained Molecular Dynamics (CGMD) simulations of chain molecules, including those of biological significance. The indirect speed-up can be advantageous in that it provides reduction in computation time, in addition to the direct speed-up obtained by coarse-graining. By moving to a coarser description of the system, the interaction energies between the particles decrease (the potential energy surface becomes shallower), leading to an apparent increase in the time-step of the CGMD simulation. We borrow from the framework of Accelerated Molecular Dynamics method to predict the time-step i.e., the observed indirect speed-up. With this prediction of indirect speed-up, we are able to accurately reproduce both static and dynamic properties from CGMD simulations. [Preview Abstract] |
Friday, March 25, 2005 10:12AM - 10:24AM |
X32.00012: Reflection-free atomistic-continuum coupling for solid mechanics employing spacetime discontinuous finite element method B. Kraczek, D.D. Johnson, R.B. Haber We present a means for coupling dynamic atomistic and continuum simulations via a spacetime discontinuous Galerkin (SDG) finite element method. Our scheme allows the SDG method to couple a general MD simulation using Verlet time-stepping through the flux conditions on the element boundaries at the interface. These flux conditions ensure weak balance of momentum and energy to achieve reflection-free transfer of disturbance across the interface. Our work is supported by the National Science Foundation (ITR grant DMR-0121695) on Process Simulation and Design and, in part, by the Materials Computation Center (FRG grant DMR-99-76550) [Preview Abstract] |
Friday, March 25, 2005 10:24AM - 10:36AM |
X32.00013: Comparison between united atom and explicit atom models for simulation of poly(ethylene oxide) Chunxia Chen, Janna Maranas, Victoria Garc\'ia Sakai, Jeffrey Lynn, Inmaculada Peral, John Copley We compare static and dynamic properties obtained from three simulation models with neutron scattering data for poly(ethylene oxide). The three models are a united atom (UA) model [CH$_{2}$ and CH$_{3}$ groups are considered as a single unit], the UA model with hydrogen atoms replaced afterwards (UA+H) and an explicit atom (EA) model [all the hydrogens are taken into account explicitly]. Both EA and UA+H models accurately describe the structure as measured via neutron diffraction. If the hydrogen atoms are not replaced in the UA model, the intermolecular peak is still modeled accurately, while the intensity for the intramolecular peak is much weaker than experiments. Dynamically, hydrogen motion in the EA model closely follow the experimental results. The mobility on the UA model is greater than that of carbon and oxygen atoms in the EA model. Since the size of the increase is comparable to the difference in mobility between hydrogen and carbon oxygen atoms in the EA model, the mobility of united atom is approximately equal to that of hydrogen in EA model. [Preview Abstract] |
Friday, March 25, 2005 10:36AM - 10:48AM |
X32.00014: Numerical studies on some unsteady motion of a falling Young-Ju Lee, Andrew Belmonte, Jinchao Xu We shall report some new numerical experiments on unsteady motion of a falling sphere through a cylinder. The main motivation of our studies is to provide an initial attempt to identify a model responsible for a recent experimental result on a continual and irregular oscillation of a falling sphere in a worm-like micellar fluid, (Jayaraman and Belmonte (2003), Phys. Rev. E, 67). For our simulations, we select the Johnson-Segalman model,a non-monotonic shear stress-strain rate displayed by the model for the steady shear flow is suggested and possible to produce such an unusual behavior of sphere. In this talk, we briefly introduce our novel approach to simulate viscoelastic models and then report extensive numerical experiments from our falling sphere simulations. In particular, our reports shall be focused on the sensitivity of an oscillation of a sphere and also a negative wake to the slippage parameter that appears in the Gordon-Schowalter derivative. [Preview Abstract] |
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X32.00015: Variation, Recurrence and Correlation in Topologically Realistic System-Level Earthquake Simulations John Rundle, James Holliday, Paul Rundle, William Klein, Donald Turcotte Forecasting the onset and severity of extreme avalanche events in driven threshold systems, including neural networks, earthquakes, charge density waves, sandpiles and magnetic de-pinning transitions is complicated by the inability to directly observe many of the fundamental dynamical processes, together with the wide range of scales that characterize these systems. With respect to earthquakes, the economic damages from the most severe of these events amount to annualized economic costs of many billions of dollars. In systems such as these, we can only observe the space-time \textit{patterns} of extreme events, the largest earthquakes. Using these space-time patterns, and whatever is known about the dynamics, it often possible to construct numerical simulations that can be used to make \textit{predictions} about the future space-time evolution of the system and the possible occurrence of extreme events. The accuracy of these predictions and forecasts is limited by the proximity and similarity of the model trajectory through state space, to that of the actual system. In this talk we summarize current methods that are being developed based on space-time pattern recognition techniques, together with numerical simulation of the underlying dynamics. We also discuss how these techniques may be tested, together with the current results. [Preview Abstract] |
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X32.00016: Modeling of morphological evolution on Cu(111) surface: application of Self-Teaching KMC-MD method Oleg Trushin, Victor Naumov, Abdelkader Kara, Talat Rahman We present a novel integrated approach which combines Self-Teaching kinetic Monte-Carlo (STKMC) and molecular dynamics (MD), and its application in modeling morphological evolution on Cu(111) surface at homoepitaxial growth. MD is applied for modeling adatom-surface collision event, while STKMC is used for simulation of diffusion driven kinetics between deposition events. We use semi-empirical EAM potential for estimating energetics of different diffusion processes in STKMC and interatomic forces in MD simulation. STKMC represents standard KMC algorithm on lattice gas model with constantly accumulated database of atomic diffusion processes. This approach allows to include explicitly different single and many atomic processes and accurately take into account effect of local atomic surrounding. Adatoms are deposited with thermal energies, which corresponds to physical vapor deposition conditions. Using this method we are modeling morphological evolution on the surface during thin film growth in submonolayer regime and different postdeposition phenomena. [Preview Abstract] |
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