
Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design
(01 Jul  31 Aug 2009)
Jointly organized with Department of Mathematics in celebration of 80th Anniversary of Faculty of Science
~ Abstracts ~
Asymptotically correct finite difference schemes for highly oscillatory ODEs Anton Arnold, Vienna University of Technology, Austria
We are concerned with the numerical integration of ODEs of the form
$\epsilon^2 \psi_{xx} + a(x)\psi=0$ for given $a(x)\ge\alpha>0$ in the highly oscillatory regime $0<\epsilon\ll 1$ (appearing as a stationary Schr\"odinger equation, e.g.). In two steps we derive an accurate finite difference scheme that does not need to resolve each oscillation:
1) With a WKBansatz the dominant oscillations are "transformed out", yielding a much smoother ODE.
2) For the resulting oscillatory integrals we devise an asymptotic expansion both in $\eps$ and $h$.
In contrast to existing strategies, the presented method has (even for a large spatial step size $h$) the same weak limit (in the classical limit $\epsilon\to 0$) as the continuous solution. Moreover, it has an error bound of the order $O(\epsilon^2 h^2)$.
Ref: A. ARNOLD, N. BEN ABDALLAH and C. NEGULESCU: WKBbased schemes for the Schr\"odinger equation in the semiclassical limit, preprint 2009.
« Back... The Qtensor theory of liquid crystals John Ball, University of Oxford, UK
The lectures will survey what is known about the mathematics of the de Gennes Qtensor theory for describing nematic liquid crystals. This theory, despite its popularity with physicists, has been little studied by mathematicians and poses many interesting questions. In particular the lectures will describe the relation of the theory to other theories of liquid crystals, specifically those of OseenFrank and Onsager/MaierSaupe.
« Back... Interfaces, surface energy and solid phase transformations John Ball, University of Oxford, UK
Phase transformations in solids lead to interfaces between different variants of the product phase. In some materials these are atomistically sharp, while in others the interface thickness extends over a number of atomic spacings. The talk will discuss different models for describing such interfaces. This is joint work with Elaine Crooks (Swansea) and with Carlos MoraCorral (Bilbao).
« Back... Analysis and computation for the semiclassical limits of the nonlinear Schrodinger equations Weizhu Bao, National University of Singapore
In this talk, I will review recent results on analysis and efficient computation for the semiclassical limits of linear and nonlinear Schrodinger (NLS) equations. First, I will show our recent asymptotic and numerical results on the semiclassical limits of the ground and excited states of timeindependent NLS with a few typical external trapping potentials. Then I will review the formal semiclassical limit of the NLS by using different approaches including WKB method, Winger transform, Grenier's
generalized WKB analysis, etc. A timesplitting spectral (TSSP) method was introduced to efficiently compute the dynamics of the NLS in the semiclassical regimes. The numerical method is explicit, unconditionally stable, time reversible and time transverse invariant. Moreover, it conserves the position density in the discretized level and has the best spatial/temporal resolution for the NLS in the semiclassical regimes. Comparison between the solutions of the NLS and its quantum hydrodynamical limit are presented, especially when the quantum hydrodynamical equations have shocks and/or vacuum. Finally, the analysis and
computation results are extended for the NLS with an angular momentum rotation term and coupled nonlinear Schrodinger equations.
« Back... Stable solutions to the LawrenceDoniach equations in tilted magnetic fields Patricia Bauman, Purdue University, USA
We consider minimizers to the LawrenceDoniach energy for layered uperconductors with nonlinear Josephson coupling. When the exterior magnetic field is nearly parallel to the layers and the Josephson constant is sufficiently small, we show that the global minimizer has no vortices in the layers. We estimate the upper and lower critical magnetic fields in different directions, and identify the pattern of the order parameters in this case.
« Back... Analysis and computation for the ground states of twocomponent BoseEinstein condensates with an external driving field Yongyong Cai, National University of Singapore
In this talk, we prove existence and uniqueness results for the ground states of the coupled GrossPitaevskii equations for describing twocomponent BoseEinstein condensates with an external driving field and obtain the limiting behavior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomena of the ground sates in the problem.
« Back... A deterministic solver for a hybrid quantumclassical transport model in
NanoMOSFETs José A. Carrillo, University Autonoma Barcerona, Spain
We model a nanoMOSFET by a mesoscopic, timedependent, coupled quantumclassical system based on a subband decomposition and a simple scattering operator. We first compute the subband decomposition and electrostatic force field described by a SchrödingerPoisson coupled system solved by a NewtonRaphson iteration using the eigenvalue/eigenfunction decomposition. The transport in the classical direction for each subband modeled by semiclassical Boltzmanntype equations is solved by conservative semilagrangian characteristicbased methods. Numerical results are shown for both the thermodynamical equilibrium and timedependent simulations in typical nowadays nanoMOSFETs. This is a work in collaboration with N. BenAbdallah, M.J. Caceres and F. Vecil.
« Back... Fluidparticle interaction models: asymptotics, theory and numerics José A. Carrillo, University Autonoma Barcerona, Spain
We are interested in coupled microscopic/macroscopic models describing the
evolution of particles dispersed in a fluid. Fluidparticle interaction is
of primarily importance in sedimentation analysis of disperse suspensions
of particles in fluids, one of the issues being the separation of the solid
grains from the fluid by external forces: gravity settling processes or
centrifugal forces. On the other hand, aerosols and sprays can be also
modelled by fluidparticle type interactions in which bubbles of suspended
substances are seen as solid particles.
The system is modelled using a VlasovFokkerPlanck equation to describe
the microscopic motion of the particles coupled to the Euler equations for
a compressible fluid. We investigate dissipative quantities, equilibria
and their stability properties and the role of external forces. We also study
some asymptotic problems, their equilibria and stability and the
derivation of macroscopic twophase models. Numerical schemes capable of
dealing with the asymptotic limit situations are proposed. Numerical
simulations will be shown.
« Back... Quantum driftdiffusion models in semiconductor simulation Li Chen, Tsinghua University, China
As the dimensions of semiconductor device decrease, quantum effects have to be included in the modeling of the transport phenomena. A brief outline of the quantum fluid dynamic model in semiconductor simulation will be shown in the first part of this talk. Then a list of the mathematical results on one of these models quantum driftdiffusion model will be introduced, including the existence of global weak solution with different boundary conditions, long time behavior and semiclassical limit. The ideas ?entropy based methods used in getting those results will be listed in the end.
« Back... Molecular selfassembly on surfaces and surface nanotemplates Wei Chen, National University of Singapore
Creation of wellordered functional molecular arrays at the nanometer scale is one of the key issues in the development for future molecular or nanoelectronic devices, solidstate quantum computation, singleelectron devices, and biosensors. Molecular selfassembly on surfaces or surface nanotemplates via selective and directional covalent or noncovalent interactions offers a promising bottomup approach to fabricating molecular nanostructure arrays with desired functionalities over macroscopic areas.
Here, we demonstrate the formation of various well ordered C_{60} superstructures with tunable periodicity and symmetry using different molecular surface nanotemplates. It is found that that the formation of the tunable C_{60} molecular arrays arises from the delicate balance between the homointermolecular (vanderWaals forces), heterointermolecular (charge transfer) and moleculesubstrate interfacial interactions under different experimental conditions, which can be simply adjusted by choosing appropriate C_{60} and 6T, 6P or pentacene coverage and post annealing temperature. we also demonstrated a novel bottomup approach to fabricate selfassembled 2D binary molecular networks on graphite, whose structural stability is sustained through the formation of multiple intermolecular CF ... HC hydrogen bonds between the electronegative periphery F atoms of F_{16}CuPc and the electropositive periphery H atoms of 6P, pentacene or DIP. The supramolecular packing structures can be controlled by careful selection of molecular building blocks with appropriate geometry (size and shape) and molecular ratios. Our results suggest that selfassembling of molecular superstructures on surface nanotemplates represents a simple and effective method for the construction of highly ordered functional molecular nanostructure arrays, and offers a versatile route towards the fabrication of novel molecular interconnects and devices.
« Back... The secondorder multiscale simulation for the physics and mechanics behaviors of composites and their structures Junzhi Cui, Chinese Academy of Sciences, China
 Introduction  Background.
 Secondorder twoscale simulation for the physics and mechanics behaviors of the structure of composites with periodicity and quasiperiodicty.
 The statistically secondorder twoscale simulation for the physics and mechanics behaviors of the structure of composites with consistently and inconsistently random distribution.
 Some discussion on Multiscale simulations of composites and their structures.
« Back... Comparisons between the sineGordon equation and perturbed nonlinear Schrodinger equations for modeling light bullets Xuanchun Dong, National University of Singapore
Comparisons between the solution of the sineGordon (SG) equation and the solutions of perturbed nonlinear Schrodinger equations are studied numerically for the propagation of two space dimensional (2D) localized pulses in nonlinear dispersive optical media. We begin with the (2+1) sineGordon (SG) equation obtained as an asymptotic reduction in the two level dissipationless MaxwellBloch system, followed by the review on the perturbed nonlinear Schrodinger (NLS) equation in 2D for the SG pulse envelopes, which is globally wellposed and has all the relevant higher order terms to regularize the collapse of the standard critical NLS. The perturbed NLS is approximated by truncating the nonlinearity into finite higher order terms undergoing focusingdefocusing cycles.
Energy conservative and efficient semiimplicit Fourier pseudospectral discretizations for the SG and perturbed NLS are proposed. Numerical comparison results between the solutions of the SG and perturbed NLS as well as critical (cubic focusing) NLS are reported for the propa gation of light bullets. Based on our extensive numerical experiments, the solution of the perturbed NLS as well as its finite terms truncations are in qualitative and quantitative agreement with the solution of SG for the light bullets propagation even after the critical collapse of the cubic focusing NLS. In contrast, the standard critical NLS is in qualitative agreement with SG only before its collapse.
« Back... Diffuse interface modeling and simulation of some interface problems Qiang Du, Pennsylvania State University, USA
The diffuse interface (or phase field) method has been one of the popular approaches for the modeling and simulation of many interface problems in nature. In this series of lectures, we first present some of the basic ideas of the diffuse interface approach. Examples are shown to illustrate its effectiveness in practice. Next, we discuss the relevant mathematical theory, consider the sharp interface limit and make comparisons with other methods. We then focus on some recent works related to the application of the diffuse interface method to interface problems in materials science and biology, in particular, those problems involving elastic energy contributions. These specific applications are used to highlight the modeling and computational challenges. We also discuss a stochastic implicit interface method for modeling the effect of fluctuations in interfacial problems. Finally, we report some recent progress in the algorithmic development aspect. The lectures will be of introductory nature, with emphasis on the basic methodology, the important issues and some open problems.
« Back... Computational surface partial differential equations Charles Elliott, University of Warwick, UK
Evolutionary PDEs on stationary and moving surfaces appear in many applications such as the diffusion of surfactants on fluid interfaces, surface pattern formation on growing domains, segmentation on curved surfaces and phase separation on biomembranes and dissolving alloy surfaces.
In this talk I discuss three numerical approaches based on: (I) Surface Finite Elements and Triangulated Surfaces, (II)Level Set Method and Implicit Surface PDEs and (III) Phase Field Approaches and Diffuse Surfaces.
« Back... Predictive atomistic and coarsegrained modeling of epitaxial thin film growth Jim Evans, Iowa State University, USA
Atomistic modeling of homoepitaxial film growth on singleelement singlecrystal surfaces (A on A), when combined with kinetic Monte Carlo (KMC) simulation, has achieved remarkable predictive accuracy for some systems [1]. This applies not just for the description of initial submonolayer 2D island formation, but also for subsequent multilayer growth and kinetic roughening (including formation of 3D mounds, i.e., multilayer stacks of 2D islands). However, coarsegrained modeling alternatives are appealing from the perspective of algorithmic efficiency, and also to provide deeper insight into fundamental issues such as development 2D island distributions or 3D mound coarsening dynamics. We review the current state of this field [1]. Our recent efforts have begun to explore more complex deposition processes on binary alloy surfaces (e.g., A on BC, B+C on BC) [2] and on ternary quasicrystal surfaces (A on BCD) [3].
For the former, predictive atomistic modeling has been achieved, and for the latter coarsegrained stepdynamics modeling has provided significant insight.
Of particular interest here is heightselection of multilayer islands due to quantum size effects.
[1] J.W. Evans, P.A. Thiel, and M.C. Bartelt, Surf. Sci. Rep. 61 (2006) 1128.
[2] Han, Liu, Unal, Qin, Jing, Jenks, Thiel, Evans, Phys. Rev. Lett. 100
(2008) 116105.
[3] Unal, Fournee, Thiel, Evans, Phys. Rev. Lett. 102 (2009) 196103.
« Back... Coarsening of island distributions on surfaces: Ostwald vs Smoluchowski vs unconventional ripening pathways Jim Evans, Iowa State University, USA
Postdeposition evolution of distributions of 2D islands in pristine homoepitaxial systems provides an ideal testing ground for coarsening theories. Traditionally, Ostwald ripening (OR), i.e., dissolution of small islands and growth of larger ones, is expected to provide the dominant coarsening pathway.
Indeed, OR is often observed revealing behavior consistent with welldeveloped LSW theory. However, sometimes coarsening is dominated by Smoluchowski ripening (SR), i.e., diffusion and coalescence of islands. Here, typically detailed behavior deviates from predictions of classic rate equation predictions. We both elucidate the features controlling the dominant pathway and origin of the deviations from classic predictions [1]. Introducing even traceamounts of a chemical additive often greatly accelerates the coarsening process [1,2].
We provide two possible mechanisms, either additivecatalyzed coarsening for attachmentdetachment limited OR, or enhanced mass transport due to facile formation of a mobile metaladditive complex.
[1] Thiel, Shen, Liu, Evans, J. Phys. Chem. C 113 (2009) 5047 (Centennial Feature) [2] Shen, Liu, Thiel, Evans, J. Chem. Phys. 130 (2009) 094701
« Back... Material prediction based on first principles method Yuan Ping Feng, National University of Singapore
Materials design based on computational methods is playing a very important role in today?s materials science and engineering. Among various methods, the firstprinciples electronic structure method based on density functional theory is ideal for designing new materials because such methods do not require experimental inputs and prior knowledge on the materials. We have been using firstprinciples method to study properties of materials for future advanced technologies and to design new materials. Examples related to high dielectric constant oxides for applications in complementary metaloxidesemiconductor (CMOS) devices, magnetic semiconductors for spintronics applications, etc., will be discussed.
« Back... Sublinear scaling algorithms for the study of the electronic structure of material Carlos GarciaCervera, University of California, Santa Barbara, USA
I will discuss asymptoticbased algorithms for the study of the electronic structure of materials, in the context of density functional theory. I will illustrate the ideas using both the KohnSham and orbitalfree formulations.
This is joint work with Weinan E (Princeton University), and Jianfeng Lu (Princeton University).
« Back... A nonlocal vector calculus with application to nonlocal boundary value problems Max Gunzburger, Florida State University, USA
We develop a calculus for nonlocal operators that mimics Gauss' theorem and the Green's identities of classical vector calculus. The operators we treat do not involve derivatives. We then apply the nonlocal calculus to define variational formulations of nonlocal "boundary" value problems that mimic the Dirichlet and Neumann problems for secondorder scalar elliptic partial differential equations. For the nonlocal variational problems, we show how one can derive existence and uniqueness results and also how, under appropriate limits, they reduce to their classical analogs. Although we do not report on this in this talk, the results are easily extended to vector elliptic equations, and in particular, to the peridynamics model for materials.
This is joint work with Richard Lehoucq.
« Back... Toward quantitative analysis of nanoelectronics  state of the art and challenges Hong Guo, McGill University, Canada
Nanoelectronic devices operate by principles of quantum mechanics, their properties are closely influenced by the atomic and molecular structures of the device. It has been a challenge to calculate device characteristics including relevant microscopic details, especially when one wishes to predict these characteristics without relying on phenomenological parameters.
In this lecture, I will review the present status of nanoelectronic device theory, the existing theoretical and numerical difficulties, and some important problems of nanoelectronics. I will then discuss in detail a particularly useful progress achieved toward quantitative predictions of nonequilibrium and nonlinear charge/spin quantum transport in nanoelectronic devices from atomic point of view. The theoretical formalism is based on carrying out real space density functional theory (DFT) analysis within the Keldysh nonequilibrium Green's function (NEGF) framework [1,2]. The theoretical background as well as numerical implementation of the NEGFDFT formalism will be presented [1,2,3]. Quantitative comparisons to measured data will be presented. I will give many examples of calculating quantum transport in nanostructures starting from atomic arrangements of the device, including molecular wires, carbon nanostructures, magnetic tunnel junctions, disordered systems, and various spintronic systems. I will end the lecture by outlining a view on the existing challenges of nanoelectronics, and on developing tools powerful enough for nanoelectronics design automation.
I plan to cover the following technical issues in this 6hour lecture:
(1) Quantum transport theory within NEGF. After a brief technical discussion on how to derive transport formula using NEGF, I will discuss a symbolic derivation software we have developed recently using Mathematica, that automatically derives relevant NEGF and transport formula starting from the Hamiltonian.
(2) Computational method of NEGFDFT [1,2,3]. I will focus on important technical issues about how this formalism works and what are the important things to take care of in order to do a correct simulation. Other issues such as electronphonon scattering during current flow, strong correlation effects in tunnelling through oxides, will also be discussed.
(3) Computational method of NEGFDFTNVC [4]. I will discuss how to carry out nonequilibrium vertex correction (NVC) analysis of disorder scattering in nanoelectronic devices. Since any real system has some degree of disorder, configurational average of transport properties must be done. NVC allows one
to accomplish this very important task from first principles.
Acknowledgements. The work presented here were contributed by many students and postdocs over many years: Drs. Jian Wang, Jeremy Taylor, JoseLuis Mozos, Hatem Mehrez, Brian Larade, Gianni Taraschi, Qingrong Zheng, Wengang Lu, Eric Zhu, Lei Liu, Chaocheng Kaun, Pawel Pomorski, Yi Liu, Dan Robutsov, Nicolai Sergueev, Derek Waldron, Devrim Guclu, Vladimir Timochevski, and Chuncheng Wan. I'd like to also thank the following group members who contributed to the topics of this lecture: Dr. Yibin Hu, Dr. Wei Ji, Dr. Ferdows Zahid, Mr. Zimin Feng, Zhanyu Ning, Tao Ji, Manuel Smeu, Jesse Masson, Etienne Marcotte.
Some References:
[1] "Ab initio modelling of quantum transport properties of molecular electronic devices", Jeremy Taylor, Hong Guo, and Jian Wang, Phys. Rev. B 63, 245407 (2001).
[2] "Ab initio modelling of open systems: charge transfer, electron conduction, and molecular switching of a C60 device", Jeremy Taylor, Hong Guo and Jian Wang, Phys. Rev. B 63, R121104 (2001).
[3] "Nonlinear spincurrent and magnetoresistance of molecular tunnel junctions", Derek Waldron, Paul Haney, Brian Larade, Allan MacDonald and Hong Guo, Phys. Rev. Lett. 96, 166804 (2006).
[4] "Disorder scattering in magnetic tunnel junctions: theory of nonequilibrium vertex correction", Youqi Ke, Ke Xia and Hong Guo, Phys. Rev. Lett. 100, 166805 (2008).
« Back... Modeling nanoelectronics from atomic first principles Hong Guo, McGill University, Canada
In this talk, I will discuss an aspect of nanoelectronic device theory, namely modeling nanoelectronics from atomic first principles. Some important issues of quantum transport theory in the atomic limit will be reviewed. I will then report a recent theoretical development for treating atomistic disorder in nonlinear and nonequilibrium quantum transport modeling. The theory uses nonequilibrium vertex corrections to handle the configurational average of random disorder at the density matrix level. Using this technique, we have analyzed spin injection in magnetic tunnel junctions with interface roughness as well as with oxygen vacancies in the tunnel barrier. Disorder effect is found to significantly alter spin polarized tunneling. We will also present results concerning surface roughness scattering in Cu interconnects. Comparison with existing experimental data will be presented.
« Back... Tailored finite point method for high frequency waves in heterogeneous medium Zhongyi Huang, Tsinghua University, China
In this talk, we propose a tailoredfinitepoint method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, then we can get the approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constants, we can get the exact solution with only one point in each subdomain. Our finitepoint
method has uniformly convergent rate with respect to wave number $k$ in $L^2$norm.
« Back... Blowup criteria for the NavierStokes equations of multidimensional compressible fluids Song Jiang, Institute of Applied Physics and Computational Mathematics, China
We study an initial boundary value problem and the Cauchy problem for the multidimensional NavierStokes equations of compressible isentropic and nonisentropic flows. We will report some recent blowup criteria for the local strong solutions, including a criterion similar to the BealeKatoMajda criterion for ideal incompressible flows.
« Back... A generalization of the MacPherson  Srolovitz formula Duc Thinh Le, Pennsylvania State University, USA
The MacPhersonSrolovitz formula has been recently established as a generalization of the two dimensional von Neumann  Mullins relation for microstructure coarsening. In this talk we present an extension of the MacPhersonSrolovitz formula under more general junction conditions.
« Back... Some recent theoretical and numerical contributions to stochastic homogenization and related problem Claude Le Bris, École Nationale Des Ponts Et Chaussées, France
The talk will overview some recent contributions on several theoretical aspects and numerical approaches in stochastic homogenization. In particular, some variants of the theory of classical stochastic homogenization will be introduced. The relation between such homogenization problems and other multiscale problems in materials science will be emphasized. On the numerical front, some approaches will be presented, for acceleration of convergence in stochastic homogenization (representative volume element, variance reduction issues, etc) as well as for approximation of the stochastic problem when the random character is only a perturbation of a deterministic model. The talk is based upon a series of joint works with X. Blanc (CEA, Paris), PL. Lions (College de France, Paris), and F. Legoll, A. Anantharaman, R. Costaouec (ENPC, Paris).
« Back... POD and CVT based reducedorder modeling for partial differential equations Hyung Chun Lee, Ajou University, Korea
A discussion of reducedorder modeling for partial differential equations is given to provide a context for the construction and application of reducedorder bases. Review of the POD (proper orthogonal decomposition ) and CVT (centroidal Voronoi tessellation) approaches to reducedorder modeling are provided, including descriptions of POD and CVT reducedorder bases, their construction from snapshot sets, and their applications to the lowcost simulations of partial differential equations.
« Back... Microscopic origins of continuum balances and peridynamics Richard B. Lehoucq, Sandia National Labs, USA
Peridynamics (Silling 2000) is a continuum theory where the internal force density in the balance of linear momentum is given by an integral operator. This operator sums internal forces separated by a finite distance in contrast to a continuum theory where only contact forces are assumed. My presentation derives mass and momentum conservation laws for peridynamics using the principles of statistical mechanics. In particular, I show that the peridynamic force density integral operator is the phase space expected value of internal force density given by a general multibody interatomic potential. The derivations generalize the seminal work of IrvingKirkwood (1950), and build upon the elegant ideas due to Noll (1955) that generalized the former work. The approach presented avoids the standard limitation of a pairwise interatomic potential, and the peridynamic integral operator sidesteps the significant issues associated with determining a stress tensor given a multibody interatomic potential. However, a Cauchy (symmetric) stress tensor is derived so that the divergence of this stress tensor is equal to the peridynamic force density integral operator. This represents a significant generalization of previous definitions of microscopic stress to arbitrary multibody potentials. I also discuss how the integral operator can be replaced by a force density arising from the classical notion of contact forces. Hence, the path from Newton's second law to conservation of linear momentum for simple nonpolar materials traverses peridynamics. This is joint work with Mark Sears.
« Back... Coarsegraining molecular dynamics for crystalline solids Xiantao Li, Pennsylvania State University, USA
I will discuss a coarsegrained model of molecular dynamics in crystalline solids. Such system usually has an underlying lattice structure, and the empirical potentials are of quite simple forms. Thus it provides a nice setting in which coarsegraining (CG) methods can be considered. The goal of the CG method is to reduce the huge
number of atomic degrees of freedom, and arrive at an effective model in which only a small number of atoms are explicitly involved. I will discuss how the CG is done in both the static and dynamic settings, the connections to continuum elasticity models, and the application to fracture and dislocation dynamics.
« Back... The mathematical understanding of tauleaping algorithm Tiejun Li, Peking University, China
The tauleaping algorithm is proposed by D.T. Gillespie in 2001 for accelerating the simulation for chemical reaction systems. It is faster than the traditional stochastic simulation algorithm (SSA), which is an exact simulation algorithm. In this lecture, I will overview some recent mathematical results on tauleaping done by our group, which include the rigorous analysis, construction of the new algorithm, and the systematic analysis of the error.
« Back... Metallic glasses: It's all in the mix Yi Li, National University of Singapore
Materials such as glass or polystyrene are often called amorphous solids  literally ?without shape?  because their atoms are arranged randomly without the longrange repeating patterns seen in crystals. Scientists have also managed to make amorphous metal alloys known as metallic glasses, which promise great strength, elasticity and magnetic properties. But unlike the welldefined longrange order in the crystalline metals, the atomic arrangements in amorphous alloys remain mysterious at present and the details of how the atoms are packed in amorphous metals are generally far less understood than for the networkforming glasses. In this talk, I shall summarize the recent attempts made at the understanding of the atomic structure in metallic glasses and how one of our recent works gives new insight into this.
« Back... Heat/Phonon transport in nanostructures and Phononics Baowen Li, National University of Singapore
In the first part, I will focus on several fundamental issues such as whether heat conduction in nanostructures obeys the Fourier law, how heat pulse spreads in low dimensional nanostuctures, how to reduce thermal conductivity of nanowires and nanotubes. Both computational simulation and experimental results will be presented.
In the second part, I will discuss how to build different thermal devices such as thermal rectifier/diode, thermal transistor, thermal logic gate and thermal memory.
« Back... Introduction to molecular models Xiantao Li, Pennsylvania State University, USA
I will provide the following lectures
1. Introduction to molecular models
2. Statistical mechanics
3. Simulation technique
« Back... Surface diffusions on elastically stressed axisymmetric rods Xiao Fan Li, Illinois Institute of Technology, USA
Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and longtime behavior of such solid surfaces requires accurate simulations in both space and time.
Here we present a highorder boundary integral method for an elastically stressed solid with axisymmetry due to surface diffusions. Using the highorder boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in a finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a selfsimilar assumption. In the presence of elastic stress, we show that a finitetime, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.
« Back... Dynamical selftrapping of BoseEinstein condensates in shallow optical lattices Fong Yin Lim, Institute of High Performance Computing
We study the transport properties of a strongly repulsively interacting BEC through a shallow optical lattice of finite width. The study is carried out via numerically solving the GrossPitaevskii equation. Selftrapped states are observed for some sets of parameters, indicated by stopping in the expansion of BEC at certain lattice site.
Such selftrapped states can be explained analytically in terms of nonlinear Bloch waves, approximated by a truncated Bloch function. The results could help us in the design of atomtransporting wire in an atomic circuit, whose properties can be adjusted in a controllable way.
« Back... Topological vorticity and conserved geometric motion Fanghua Lin, Courant Institute, USA
After a quick review of some distinct feature of vortex dynamics in classical fluids, we shall describe a notion of topological vorticity that plays the similar important role as vorticity in the classical fluids. We can use the topological vorticity to study vortex dynamics in ferromagnets and BoseEinstein condensates for example. Then I shall expalin my recent joint work with JunCheng Wei on Kelvin motions of traveling vorticies solutions and some genral conserved geometric motion.
« Back... GinzburgLandau Equationssome recent developments and open problems Fanghua Lin, Courant Institute, USA
We shall first go over briefly some background and earlier work on the GinzburgLandau equations. Then we shall describe some recent work concerning generalized GinzburgLandau equations including multiple components GinzburgLandau equations and their applications.
« Back... Traction and outflow boundary conditions for the incompressible NavierStokes equations Jie Liu, National University of Singapore
We present numerical schemes for the incompressible NavierStokes equations (NSE) with open and traction boundary conditions. We use pressure Poisson equation (PPE) formulation and propose new boundary conditions for the pressure on the open or traction boundaries. After replacing the divergence free constraint by this pressure Poisson equation, we obtain an unconstrained NSE. For Stokes equation with open boundary condition on a simple domain, we prove unconditional stability of a first order semiimplicit scheme where the pressure is treated explicitly and hence is decoupled from the computation of velocity. Using either boundary condition, the schemes for the full NSE that treat both convection and pressure terms explicitly work well with various spatial discretizations including spectral collocation and $C^0$ finite elements. Moreover, when Reynolds number is of $O(1)$ and when the first order semiimplicit time stepping is used, time step size of $O(1)$ is allowed in benchmark computations for the full NSE. Besides standard stability and accuracy check, various numerical results including flow over a backward facing step, flow past a cylinder and flow in a bifurcated tube are reported. Numerically we have observed that using PPE formulation enables us to use the velocity/pressure pairs that do not satisfy the standard infsup compatibility condition. Our results extend that of H. Johnston and J.G. Liu (J. Comp. Phys. 199 (1) 2004, 221259) which deals with noslip boundary conditions only.
« Back... Some numerical analysis issues in material and fluids simulations JianGuo Liu, Duke University, USA
Many recently developed computation methods to overcome some challenges in multiscale material/fluids simulations such as removing stiffness in time stepping due to fast waves, controlling the numerical dissipation with respect to the large parameters in the underline system, effectively local upscaling, etc. Numerical Analysis for these methods are difficulty. In this talk, I will present some results along this direction for a class of asymptotic preserving schemes.
« Back... Existence of globally weak solutions to the flow of compressible liquid crystals system XianGao Liu, Fudan University, China
We study a simplified system for the compressible fluid of Nematic Liquid Crystals in a bounded domain in three Euclidean space and prove the global existence of the finite energy weak solutions.
« Back... Quantum simulation of materials at micron scales and beyond Gang Lu, California State University Northridge, USA
We present a multiscale modeling approach that can simulate multimillion atoms effectively via density functional theory. The method is based on the framework of the quasicontinuum (QC) approach with the densityfunctional theory (DFT) as its sole energetics formulation  there is no empirical input. The local QC part is formulated by the CauchyBorn hypothesis with DFT calculations for strain energy and stress. The nonlocal QC part is treated by a DFTbased embedding approach, which couples DFT nonlocal atoms to local region atoms. The methodQCDFTis applied to a nanoindentation study of an Al thin film, and the results are compared to a conventional QC approach. The results suggest that QCDFT represents a new direction for the quantum simulation of materials at length scales that are relevant to experiments. If time permits, an application of QCDFT to a novel magnetisminduced dislocation motion in NiAl alloys will be also presented.
References:
1. Q. Peng, X. Zhang, L. Hung, E.A. Carter and G. Lu, "Quantum simulation of materials at micron scales and beyond", Phys. Rev. B, 78, 054118 (2008).
2. X. Zhang, C.Y. Wang and G. Lu, "Electronic structure analysis of selfconsistent embedding theory for quantum mechanics/molecular mechanics simulations", Phys. Rev. B, 78, 235119 (2008).
3. X. Zhang and G. Lu, "Quantum mechanics/molecular mechanics methodology for metals based on orbitalfree density functional theory", Phys. Rev. B, 76, 245111 (2007).
4. G. Lu, E. Tadmor and E. Kaxiras, ?From electrons to finiteelements: a concurrent multiscale approach for metals?, Phys. Rev. B 73, 024108 (2006).
« Back... Applied partial differential equations: the Cambridge PDE group Peter Markowich, University of Cambridge, UK
We report on the work of the Cambridge based PDE group, covering a wide range of applications, from nonlinear Schrödinger equations to social science modeling
« Back... Gate controlled nonvolatile graphene ferroelectric memory and spin injection into graphene via MgO barriers Barbaros Oezyilmaz, National University of Singapore
The discovery of graphene in 2004 has triggered enormous experimental and theoretical efforts. As a gapless semiconductor, charge carriers in graphene can be tuned continuously from electrons to holes crossing the charge neutral Dirac point using an external electric field. Unlike conventional semiconductors, the doping process does not influence the mobility of charge carriers in graphene, which can exceed 10+5 cm+2/Vs1 at low temperature. Such dopingindependent mobility leads to the fielddependent conductance in graphene. Based on these two properties, many novel graphenebased device applications have been predicted. However, a paradigm shift in the microelectronics industry from Si to graphene also requires graphenebased memory applications. Despite graphene having intrinsically a high resistance state at the Dirac point and a low resistance state when heavily doped, reports on graphene for nonvolatile information storage is rarely seen. This is due to the difficulty in maintaining the resistance states in graphene without an external electric field.
I will show nonvolatile switching in graphene by using ferroelectric gating without having to break the lattice symmetry. We demonstrate basic writing and reading processes of a novel grapheneferroelectric memory device structure combining the field dependent conductance of graphene with the remnant electric field of ferroelectric thin films. A bistable state of high and low resistance value is realized by controlling the electrical doping level in graphene hysteretically, which is caused by a hysteretic switching of the polarization in the ferroelectric thinfilm. Our approach of ferroelectric gating also open up the possibility of studying graphene phenomena in the limit of high carrier concentration, which is not possible with dielectric gating.
I will also report on our resent results on spin transport in graphene observed in the nonlocal device geometry. Here we have used MBE grown MgO as a tunneling barrier.
« Back... Numerical simulation of coupled surface and grain boundary motion Zhenguo Pan, National University of Singapore
A coupled surface and grain boundary motion which arises in materials science is considered in a bicrystal in the context of the quarter loop geometry. Two types of normal curve velocities are involved: motion by mean curvature and motion by surface diffusion. Three curves meet at a single point with junction conditions applied. A formulation that describes the coupled normal motion of the curves and preserves arc length parametrization up to scaling is proposed. Numerical convergence and the numerical stability of the existing travelling waves will be shown.
« Back... Eigenvalue problem of magnetic Schrodinger operators Xingbin Pan, East China Normal University, China
Eigenvalue problems of magnetic Schrodinger operator have played important roles in the mathematical theory of superconductivity, liquid crystals and BoseEinstein condensates. In this talk we shall introduce basic estimates of the lowest eigenvale for large magnetic field, and give some applications of these estimates in the theory of nucleation of superconductivity and surface superconductivity, and in the theory of phase transition of liquid crystals from nematic phase to smectic phase.
« Back... Meissner states of 3dimensional superconductors Xingbin Pan, East China Normal University, China
Meissner state of bulk superconductors of type II loses its stability as the applied magnetic field increases to a critical field H_S. The Meissner states are described by the solutions of a partial differential system in 3dimensional space, which are called Meissner solutions. In this talk we shall show the existence of the Meissner solutions, and examine the convergence of the Meissner solutions to a solution of the limiting system as the GinzburgLandau parameter increases to infinity. Our results suggest that in order to determine the critical field H_S one needs to measure the maximum value of the tangential component of the induced magnetic field on the surface of the superconductor.
« Back... Smectic energies and existence results for lquid crystals Daniel Phillips, Purdue University, USA
We examine the problem of minimizing the ChenLubensky liquid crystal energy. This is a GinzburgLandau type energy where the smectic layering is described by a complex valued order parameter. In the case that the energy has a smectic C ground state we show that anchoring conditions on the smectic layering at the boundary are needed in order for minimizers to exist. We further give examples of strong and weak anchoring conditions that suffice.
This is joint work with Patricia Bauman and Jinhae Park.
« Back... Mathematical models for liquid crystals Daniel Phillips, Purdue University, USA
Liquid crystal materials can exist in a variety of phases that exhibit different levels of order. This order melts and defects appear if either their temperature is increased or if external stresses are applied. In this lecture we describe several mathematical models that are used to characterize and study these features.
« Back... A levelset method for selforganized pattern formation during heteroepitaxial growth Christian Ratsch, University of California, Los Angeles, USA
It is well know that strain leads to the formation and self organization of nanostructures and quantum dots during heteroepitaxial growth.
However, modeling these phenomena is a challenging task, because of the vastly different time and length scales involved, and the fact that elastic calculations are computationally expensive due to their long range. In this talk, we will discuss a model for heteroepitaxial growth that employs an island dynamics model with the levelset technique in combination with a fully selfconsistent elastic model. Adatoms are described in a meanfield approach, and we solve a diffusion equation for the adatom concentration. At every timestep in the simulation, we solve the elastic equations for the entire system. At every lattice site strain then changes the local bonding, and thus the potential energy surface for adatoms and the microscopic parameters of the simulation, such as adatom diffusion, and the rate of detachment from island edges.We will then present results for several growth phenomena: In the submonolayer regime, islands become smaller and more regular upon increasing strain, and the island size distribution narrows and sharpens. We will discuss how a spatially varying potential energy surface can be exploited for pattern formation.
Such spatial variations are for example a result of defects or other features that are buried under the substrate. Another example is the growth of stacked quantum dots, where islands selfalign on top of previously grown islands.
« Back... Massively parallel algorithms for the simulation of complex flows Ulrich Ruede, University ErlangenNuremberg, Germany
Large scale numerical simulation requires that we exploit parallelism on all levels. High performance computers will continue to be built as parallel systems with physically distributed memory, but each node will be have processors, each of which contains many cores. Additionally each core may rely on vectorization. Such systems can provide enormous compute power, but they may require a special programming and a new design of the algorithms.
The multigrid finite element solvers HHG developed at Erlangen have been run on up to tenthousand processor cores, solving systems with three hundred billion unknowns. As a second example, the talk will report on the Walberla software framework that is being developed for parallel computational fluid dynamics using on the Lattice Boltzmann method and which is being used to study multiphase flows in complex geometries and particulate flows with fully resolved fluidstructureinteraction.
« Back... Abinitio calculation of entropy and free energy in defected solids Salvy Russo, RMIT Univeristy, Australia
Calculating the properties of materials using Density Functional Theory (DFT) has been increasing popular over the last 1015 years. When predicting the thermodynamic stability of defects (including dopants) in solids using DFT, many studies have only considered the internal energy contribution to the free energy of defect formation.
In this talk we will consider how the various entropic contributions to the formation free energy of a defect can be calculated using DFT (or other levels of theory). These include the configurational, electronic and vibrational contributions to the total entropy of the defect. Various examples ranging from metallic nanoclusters to doped transition metal oxides will be discussed.
« Back... Ab initio methods for quantum transport in macromolecules Stefano Sanvito, Trinity College Dublin, Ireland
The nonequilibrium Green's function (NEGF) method for electron transport combined with density functional theory (DFT) is at present the workhorse of material specific transport calculations. Despite some difficulties connected to the meanfield nature of the semilocal approximations to DFT [1], NEGFDFT provides a powerful computational tool for research areas as diverse and magneto and molecular electronics, biological sensing, and in general nanoelectronics. Still challenges remain ahead in particular related to the ability of describing strong correlations, inelastic effects and in the make of algorithms scalable to large systems.
In recent years our group has developed the Smeagol code (www.smeagol.tcd.ie), at present probably the most versatile code for quantum transport available worldwide [2,3]. In this talk I will review the main capabilities of Smeagol and in particular I will tackle the problems arising when dealing with large devices. I will then discuss two examples.
First I will consider spintransport across a Mn12 molecule and demonstrate that orbital rehybridization determines entirely the features of the IV characteristics [4]. Interestingly the IV presents a number of negative differential conductances at various voltages which are the fingerprint of the magnetic state of the molecule. This opens up the possibility of an electrical readout of the molecular state.
Then I will move my attention to DNA. In particular I will discuss the transport properties of polymeric PolyC/PolyG strands connected to gold electrodes. The calculations will shed some light on the intrinsic nature of DNA transport and will tackle, with an effective theory, the effects due to the biological environment.
References
==========
[1] Selfinteraction errors in density functional calculations of electronic transport,
C. Toher, A. Filippetti, S. Sanvito, and Kieron Burke, Phys. Rev. Lett. 95 146402 (2005)
[2] Towards Molecular Spintronics, Alexandre Reily Rocha, Victor GarciaSuarez, Steve W. Bailey, Colin J. Lambert, Jaime Ferrer and Stefano Sanvito, Nature Materials 4, 335 (2005).
[3] Spin and Molecular Electronics in AtomicallyGenerated Orbital Landscapes, Alexandre Reily Rocha, Victor GarciaSuarez, Steve W. Bailey, Colin J. Lambert, Jaime Ferrer and Stefano Sanvito, Phys. Rev. B. 73, 085414 (2006).
[4] Magnetic state electrical readout of Mn12 molecules, C.D. Pemmaraju, I. Rungger and S. Sanvito, arXiv:0905.0281 (2009)
« Back... Phasefield models for multiphase complex fluids: modeling, numerical analysis and simulations Jie Shen, Purdue University, USA
I shall present an energetic variational phase field model for multiphase incompressible flows which leads to a set of coupled nonlinear system consisting a phase equation and the NavierStokes equations. We shall pay particular attention to situations with large density ratios as they lead to formidable challenges in both analysis and simulation.
I shall present efficient and accurate numerical schemes for solving this coupled nonlinear system, and show ample numerical results (air bubble rising in water, Newtonian bubble rising in a polymeric fluid, defect motion in a liquid crystal flow, etc.) which not only demonstrate the effectiveness of the numerical schemes, but also validate the flexibility and robustness of the phasefield model.
« Back... Efficient and accurate numerical schemes for the phasefield models for multiphase complex fluids Jie Shen, Purdue University, USA
I shall start with an introduction on an energetic variational phase field model for multiphase incompressible flows which leads to a set of coupled nonlinear system consisting a phase equation and the NavierStokes equations.
Then, I'll present efficient and accurate numerical schemes for solving this coupled nonlinear system. In particular, the following topics will be covered:
1. Splitting methods for unsteady incompressible NavierStokes equations
2. Fast spectralGalerkin methods for elliptic problems
3. Full discretization for the coupled phasefield model
4. Spectral moving meshing method for the coupled phasefield model
« Back... Grain growth, shape, and topology in all dimensions: beyond von NeumannMullins David Srolovitz, Princeton University, USA and Yeshiva University, USA
Cellular microstructures are ubiquitous in nature. They can be found in polycrystalline microstructures, foams, plant epidermis, ferroelectrics, complex fluids, and even in ice cream. In many situations, the cell/grain/bubble walls move to reduce their surface area (a surface tension effect), with a velocity proportional to the wall's mean curvature. As a result, the cells evolve and coarsen. Using this relation, and little else, von Neumann gave an exact formula for the growth rate of a cell in a 2d cellular structure, which is the basis of modern grain growth theory. Borrowing ideas from geometric probability, we present an exact solution for the same problem in 3d using the "mean width." We then describe why the mean width is the natural linear measure of grain size and topology and is useful across broad swaths of the sciences. Next, we extend this 50 yearold theory into all dimensions. Finally, we discuss using these ideas to efficiently simulate grain growth.
« Back... Multiparadigm simulations at the nanoscale: methodology and applications to functional nano materials Haibin Su, Nanyang Technological University
Multiparadigm methods to span the scales from quantum mechanics to practical issues of functional nanoassembly and nanofabrication are enabling first principles predictions to guide and complement the experimental developments by designing and optimizing computationally the materials compositions and structures to assemble nanoscale systems with the requisite properties. In this talk, we employ multiparadigm approaches to investigate functional nano materials with versatile character, including fullerene, carbon nanotube (CNT), graphene, and related hybrid structures, which have already created an enormous impact on next generation nano devices. The topics will cover the reaction dynamics of C60 dimerization and the more challenging complex tubular fullerene formation process in the peapod structures; the computational design of a new generation of peapod nanooscillators, the predicted magnetic state in NanoBuds; and optoelectronic properties of graphene nanoribbons.
« Back... Eventbyevent Monte Carlo simulations: Spatial resolution limits of MeV protons & keV electrons Chammika N B Udalagama, National University of Singapore
Progress in fabrication, experimentation and manipulation of structures at the micro/nanometer regimes constantly push the demands made of microscopy and lithography techniques. This has promoted the use of electrons and ions, with their smaller wavelengths, to improve on the diffraction limited visible photons and not so easily focused xray photons. But, to what dimensions can the use of electrons and ions be pursued? Which of Nature's characteristics limit their usefulness and spatial resolution? We attempt to gain insight into these fundamental issues via computational studies in the form of Monte Carlo simulations. Our software, DEEP (Deposition of Energy due to Electrons & Protons), unlike most other Monte Carlo particle penetration simulations software adopts an eventbyevent simulation formalism as opposed to that of continuous energy loss. This allows us to appreciate the richness of the energy loss process, particularly that of secondary electron or δray production. DEEP incorporates the EPDL97 crosssections together with the HansenKocbachStolterfoht (HKS) δray model for the relevant physics of ionmatter interactions. We will present recent results of the applications of DEEP to polymethylmethacrylate (PMMA) as the target along with results from recent experiments at CIBA, into high spatial resolution imaging of biological cells using MeV protons.
« Back... Some issues in the longtime simulation of complex systems Eric VandenEijnden, Courant Institute, USA
The dynamics of many systems of interest span many spatiotemporal scales, making their analysis by numerical simulations difficult. Indeed, while we are bound to simulate the dynamics at the smallest and fastest scales, we are often interested in the system's behavior in the largest and slowest scales. These are typically not accessible to brute force simulations, both because of the computational cost involved but also because these time scales are way beyond the time at which we lose pathwise accuracy with standard numerical integrators. These difficulties force us to change perspective and look at the systems from a probabilistic viewpoint. Indeed, besides being unreliable, long time numerical trajectories are also irreproducible due to sensitivity to initial conditions and/or small perturbations, and they are typically uninformative per se. By identifying the right statistical descriptors for the systems that characterize their behavior, like e.g. their invariant measure, the timecorrelation functions of suitable observable, or several statistical objects describing rare reactive, we can build algorithms that are tailormade to calculate these descriptors accurately and efficiently. In this talk this strategy will be elucidated and illustrated on examples arising from material sciences, atmospheric sciences and molecular dynamics.
« Back... Theory and modeling of reactive events Eric VandenEijnden, Courant Institute, USA
The dynamics of a wide range of systems involve reactive events, aka activated processes, such as conformation changes of macromolecules, nucleation events during firstorder phase transitions, chemical reactions, bistable behavior of genetic switches, or regime changes in climate. The occurrence of these events is related to the presence of dynamical bottlenecks of energetic and/or entropic origin which effectively partition the phasespace of the dynamical system into metastable basins. The system spends most of its time fluctuating within these longlived metastable states and only rarely makes transitions between them. The reactive events often determine the longtime evolution of the system one is primarily interested in. Unfortunately, computing up to the time scale at which these events occur represent an enormous challenge and so there is an urgent need for developing new numerical tools for such computations.
In the first lecture, I will explain why we may need to go beyond the standard framework of transition state theory (TST) to describe activated processes and reactive events, and I will present another framework, termed transition path theory (TPT), that permits to do that. Unlike TST, which gives mainly an expression for the rate of the reactive event, TPT describes more fully the statistical properties of the reactive trajectories (i.e. those trajectory by which the reactive event occurs), in particular in terms of their probability density function and their probability current.
In the second lecture, I will describe how TPT can be use to design and/or improve numerical methods for computing the pathways and rate of reactive events. I will focus in particular on the string method and milestoning.
« Back... Dynamic density functional theory and approximations to model crystalline materials Axel Voigt, Technische Universit, Dresden, Germany
The phase field crystal model is by now widely used in order to predict crystal nucleation and growth. We demonstrate using a finite element discretization the possibilities for various applications. For colloidal solidification with completely overdamped individual particle motion, we show that the phase field crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density functional theory. The different underlying approximations are discussed. We test the validity of the phase field crystal model against dynamical density functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a twodimensional colloidal suspension of parallel dipoles. As a second application we use the phase field crystal model to compute anisotropies of surface free energies of nanocrystals as a function of temperature. The approach allows to extract anisotropy functions with cusps. Furthermore we consider liquid phase epitaxy and analyse the transition from step flow growth to step bunching, facetting and formation of dislocations. As a last example we simulate the phase field crystal model on curved surfaces to model spherical crystallography. In particular we are interested in the formation of grain boundary scars on such surfaces.
Good agreement is only obtained by a drastic scaling of the free energies in the phase field crystal model in order to match the bulk freezing transition point.
« Back... Quantum thermal transport from classical molecular dynamics JianSheng Wang, National University of Singapore
Traditional molecular dynamics, since it is based on classical mechanics, produces only classical results. It is possible to simulate quantum thermal and electronic transport using a form of molecular dynamics subject to Langevin heat baths with correlated noises. The noise spectra and the memory kernel are derived by analyzing the effect of the leads of a junction system quantummechanically. It is shown that quantum ballistic transport can be reproduced for linear systems, and nonlinear effect can be understood as a quasiclassical approximation to the quantum problems. Results of thermal conductance for onedimensional lattice chain model, graphene nanoribbons, and nanotubes will be reported.
Refs. J.S. Wang, Phys. Rev. Lett. 99, 160601 (2007); J. T. Lü and J.S. Wang, J. Phys.: Condens. Matter, 21, 025503 (2009).
« Back... Phase field simulations of two phase fluid flow Xiao Ping Wang, Hong Kong University of Science and Technology, Hong Kong
In this talk, I will first describe a newly developed phase field model for two phase fluid flow based on Cahn Hilliard Navier Stokes equation with generalized Navier boundary condition. Then some numerical results on two phase flow on rough and patterned surfaces will be presented. Issues related to drop formation, dripping to jetting transition will also be discussed.
« Back... Boundary treatment, exact Hodge decomposition and the LBB condition for MAClike schemes on curvilinear domains WeiCheng Wang, National Tsinghua University, Taiwan
We propose a new finite difference scheme for NavierStokes equations in primitive formulation on curvilinear domains. With proper boundary treatment and interplay between covariant and contravariant components, the spatial discretization admits exact Hodge decomposition and energy identity. As a result, the pressure can be decoupled from the momentum equation with explicit time stepping. No artificial pressure boundary condition is needed. In addition, the spatial discretization is shown to satisfy the LadyzhenskayaBabuskaBrezzi (LBB) condition, leading to a rigorous error estimate of optimal order for the pressure. Numerical experiment demonstrates the robustness and efficiency of our scheme.
This is a joint work with YinLiang Huang and JianGuo Liu.
« Back... Dynamic transition theory and equilibrium phase transitions Shouhong Wang, Indiana University, USA
In this talk, I shall present a brief overview of the dynamic transition theory developed recently by Ma and myself, and its applications to equilibrium phase transitions. The main philosophy of the theory is to search for the full set of transition states, giving a complete characterization on stability and transition. The set of transition states physical "reality" is represented by a local attractor. Following this philosophy, the dynamic transition theory is developed to identify the transition states and to classify them both dynamically and physically.
The theory has a wide range of applications in both equilibrium and nonequilibrium phase transitions. The application of the theory to equilibrium phase transitions involves a combination of modeling, mathematical analysis and physical predictions. We adopt the general idea of the GinzburgLandau phenomenological approach, and introduce a unified timedependent GinzburgLandau model, based on the le Ch\^atlier principle. Applications to nonequilibrium transitions include typical problems in classical and geophysical fluid dynamics, in climate dynamics, and in chemical reactions. The modeling and the analysis of these problems, on the one hand, provide verifications of existing experimental and theoretical studies, and, on the other hand, lead to various new physical predictions.
To demonstrate the wide range of applications of the theory, I shall present two examples: one is the phase separation of binary systems modeled by the CahnHilliard equation, and the other is superfluidity of liquid helium3. In both cases, the study leads to some specific physical predictions, which are otherwise unknown from both the physical and mathematical points of view. For example, as a physical prediction, we derive the existence of a new superfluid phase C for liquid helium3.
« Back... An adaptive level set method for moving curves and its application to dislocation dynamics Hanquan Wang, Yunnan University of Finance and Economics, China
The original level set equations for motions of curves both in two dimensions and in three dimensions are solved on a uniform mesh, which does not have optimal efficiency in terms of calculations since the region near the curves is of most interest. Later improvement on calculation of level set equations includes narrowband based local level set techniques and treebased adaptive level set techniques. Both of them have their advantages and disadvantages.
In this talk, by taking consideration into their advantages, I present an adaptive level set method for motions of curves both in two dimensions and in three dimensions. The method first applies a simple algorithm to generate an adaptive grid which is composed by a fine mesh near the curve and a sparse mesh away from the curve; it next solve the level set equations on the adaptive grid with higherorder numerical methods such as thirdorder total variation diminishing (TVD) RungeKutta method in time and thirdorder weighted essentially nonoscillatory (WENO) scheme in space. I test this efficient and higherorder numerical method in several numerical examples and apply the method to study dislocation dynamics in material sciences.
This is a joint work with Professor Yang Xiang at Department of Mathematics of the HongKong University of Science and Technology.
« Back... Brillouin light scattering from nanostructures Zhikui Wang, National University of Singapore
Brillouin light scattering (BLS) is a nondestructive and noncontacting technique for investigating spin and acoustic dynamics, by detecting the inelastic scattered light by the spin waves (magnons) and elastic waves (phonons) in nanostructures. The observation of wellresolved Brillouin peaks arisen from eigenvibrations of nanospheres verified Lamb?s century old theory on eigenvibrations of elastic spheres. Quantization of bulk spin waves in nanowires and bandgap of spin waves in magnonic crystals (magnetic counterpart of semiconductors, photonic crystals or phononic crystals) were first observed using BLS. Experimental data obtained provide information such as quantization of spin and acoustic waves in nanostructures, as well as their magnetic and elastic properties. We found that the magnon frequency bandgaps could be tuned by applying an external magnetic field or by varying their structure dimensions. These findings are expected to stimulate further development of the theory and applications of magnonics.
« Back... Topics in surface and nanoscale science Andrew Wee, National University of Singapore
In this talk, I will present some recent work from our NUS surface science group in the areas of graphene and molecular electronics. Graphene research has been proceeding at a relentless pace since it was first isolated in 2004. It is the thinnest known material in the universe and the strongest ever measured. Graphene can sustain huge current densities, and displays record thermal conductivity and stiffness. Electron transport in graphene is described by a Diraclike equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. However, many materials challenges to producing large area high quality graphene still remain. I will discuss our work using in situ STM, synchrotron photoemission (PES) and density functional theory (DFT) calculations to investigate the structure and growth of epitaxial graphene on 6HSiC(0001).
In the field of organic and molecular electronics, the key issue is the understanding of moleculemetal and organicorganic interfaces. We used STM and synchrotron techniques to study selfassembled molecular arrays and organic heterojunctions. Some ongoing work and future perspectives will also be discussed.
« Back... Design of materials for sustainable manufacturing by computer modeling Ping Wu, Institute of High Performance Computing
Although Nobel Laureate Steven Chu (currently the 12th United States Secretary of Energy) already developed methods to cool and trap atoms with laser light in late last century, it is still a dream to use them to manufacture very small electronic components. Therefore, it is widely believed that we will hit the Moore's law limit in the years 20152020. Furthermore, we may soon face a manufacturing cost explosion based on Moore's second law, which is doubling in cost of chip fabrication plants every four years. New paradigms of sustainable technology are needed to get us around these limits. Computer modeling is capable of exploring these sustainable manufacturing solutions. In my presentation I shall use reallife case studies to outline the design of materials based on affordable computer modeling techniques.
« Back... A new version fast multipole method for evaluating the stress field of dislocation ensembles Yang Xiang, Hong Kong University of Science and Technology, Hong Kong
Dislocations are the primary carriers of plastic deformation in crystals. Dislocation dynamics simulation is becoming an important tool for the study of plastic behaviors of crystalline materials. A crucial part of dislocation dynamics simulation is the calculation of the stress field of dislocation ensembles due to the longrange interaction of dislocations. We apply a new version of the fast multipole method (FMM) to compute the stress field of dislocation ensembles, in which exponential expansions are introduced to diagonalize the multipoletolocal translations. Numerical experiments show that for a dislocation ensemble discretized into N dislocation segments, the new version of the FMM is asymptotically O(N) with an optimized prefactor, and very efficient for prescribed accuracy requirements.
« Back... Homogenization of noncoercive HamiltonJacobi equations Jack Xue Xin, University of California, Irvine, USA
Noncoercive HamiltonJacobi equations arise in modeling dynamical behavior of material interfaces in solids and fluids. Properties of homogenized Hamiltonians are compared for periodic and random media, nonlinearities and viscosity effect. Both Lagrangian and Eulerian approaches and examples will be discussed.
« Back... Binding and patterning of organic molecules on silicon surfaces Guo Qin Xu, National University of Singapore
Attaching functional organic layers to silicon surfaces is emerging as one of the promising approaches in the development of new semiconductorbased microelectronic devices and biosensors. It provides opportunities for incorporating molecular recognition, chirality, chemical/biological sensing, light emission/detection and lubrication for various technological needs. Recent systematic investigations on chemical reactions of organic molecules on silicon surfaces clearly demonstrated that both Si(100) and Si(111)7x7 can act as reagentlike substrates with a high reactivity for covalent binding of different classes of organic functionalities. Reaction mechanisms including [2+2]cycloaddition, [4+2]cycloaddition, dativebonding, dissociation and enelike reactions have been revealed and will be discussed, providing a moleculelevel understanding on reaction mechanisms, chemical and surfacesite selectivities at organic/silicon hybrid interfaces. In addition, new approaches for fabricating organic nanopatterns using selfassembled templates on silicon surfaces will be introduced, which can be useful in growing organic nanomaterials for developing nano or molecularscale devices.
« Back... On the different phases and dynamical models of liquid crystal Pingwen Zhang, Peking University, China
This talk provides a brief review of our basic understanding of liquid crystal phases from both macroscopic and microscopic points of view. From the macroscopic perspective, phases can be identified utilizing a series of thermodynamic properties based on classical thermodynamics; from the microscopic perspective, a phase needs to be defined on the basis of its structural symmetry and the types of order found in the phase. These two different perspectives can be reconciled by using statistical mechanics to bridge the length scale differences.
There are many different liquid crystalline phases that have been identified and characterized, the nematic phase possesses the lowest order with only long range molecular orientational order and short range positional and bond orientational order. The next class of liquid crystalline phases is the smectic phase, which possesses layered structures. In this talk, brief general descriptions are given for the thermodynamics and kinetics of phase transitions.
The EricksenLeslie, Tensor and DoiOnsager kinetic models will be introduced to study the phase and phase transition, the kinetichydrodynamic liquid crystalline model will be used to classify the pattern formation of microstructures and the dynamics of defects. The relation of liquid crystalline models, and their limited regions, will be pointed out.
« Back... Modelling the heteroepitaxial growth of novel surface nanostructures Yongwei Zhang, National University of Singapore and Institute of High Performance Computing
Surface roughening of a mismatched thin film leads to the formation of threedimensional islands, or quantum dots. This roughening is via surface diffusion driven by strain energy relaxation. This spontaneous roughening process was proposed to grow uniform and regular quantum dot arrays since uniform and regular quantum dot arrays with precisely controlled positions and sizes are desired for making the template for the next generation of nanoelectronic devices. However, numerical experimental results have shown that unguided selfassembled growth of quantum dots usually fails to realize perfectly ordered dot arrays. Hence how to reliably and reproducibly achieve ordered quantum dot arrays through surface prepatterning is an interesting topic.
In the present work, threedimensional finite element method was developed to investigate the selfassembly of heteroepitaxial quantum structures during StranskiKrastonov growth. In the model, various factors such as strain energy, surface energy, wetting effect, surface energy anisotropy and elastic anisotropy, and substrate surface prepatterning were taken into account, and the SiGe/Si material system was used as a model system. We consider quantum structures growing on both flat substrate surfaces without patterns or with patterns. Our computer simulations showed that various quantum dot surface patterns can be obtained by the guided selfassembled growth, including some novel surface structures such as quantumdot automata arrays, fortressenclosed quantumdot automata arrays, and ordered quantum dot arrays. Parametric studies have been performed to obtain the phase diagrams for obtaining various surface patterns. The present simulation work demonstrates that the coupling of surface prepatterns, surface energy anisotropy and elastic anisotropy strongly influences the surface roughening morphology, selfassembly and shape transition of epitaxial quantum dots, resulting in diverse evolution pathways.
« Back... Longtime asymptotic behaviour of a multiscale rodlike model of polymeric fluids Hui Zhang, Beijing Normal University, China
We investigate the longtime asymptotic behaviour of some multiscale rodlike models for polymeric fluids in various settings which include no flow, shear flow, general bounded domain with homogeneous and nonhomogeneous Dirichlet boundary conditions on the velocity. We use entropy approach to obtain the decay rates of dynamic states converging to the equilibrium in some norms by virtue of the CsiszarKullback inequality.
« Back... Introduction to dislocation dynamics Yongwei Zhang, National University of Singapore and Institute of High Performance Computing
Dislocations are an important class of defects in crystalline solids. Therefore, the subject of dislocations is essential for an understanding of many of the physical and mechanical properties of crystalline solids. We first show experimental observation of dislocations, and then discuss physical basis for dislocations and some elementary geometric properties of dislocations. We then discuss elastic properties and movement of dislocations. Under most dynamic conditions, dislocations move so slowly that the dynamic displacements are approximated quite accurately by these static solutions. However, when dislocation moving velocity is close to the speeds of sound, the dynamic effect may become important. We will discuss displacement and stress fields of the moving screw dislocations and the moving edge dislocations, dislocation acceleration and radiation, supersonic dislocations and dislocation mobility. It should be noted that many of the theories developed for specific experiments are still tentative. The theory of dislocations presented here is in quite a general approach.
« Back... The firstprinciples electronic structure calculations based on finite element discretizations Aihui Zhou, Chinese Academy of Sciences, China
In this presentation, we will give a brief introduction to firstprinciples elec
tronic structure calculations and talk about some recent fnite element compu
tations in quantum chemistry and materials science. This presentation is based
on the joint works with X. Dai, X. Gong, L. Shen, Z. Yang, and D. Zhang.
« Back...

