Multiscale particle dynamics in nanoimprint process

A multiscale particle method for coupling continuum and molecular models is described. In this method, the continuum model was assumed to be a lattice form and can be applied in non-characteristic areas or far-away regions from the large deformations to save computational time. Defining a series of critical energies for different lattice sizes is convenient for lattice refinement. In the thermal equilibrium case, the efficiency is around six times higher than that of a classical molecular dynamics (MD) simulation; in addition, great numerical precision is achieved. To test the connection at the molecular/continuum interface, a large-deformation case was studied in a nanoimprinting process. The results were compared with the MD simulation and it was found that the deviation could be reduced through a moderate adjustment of the critical energy in the lattices. This is good evidence that this method is a seamless treatment technology. PACS 02.70.Ns; 81.07.Lk; 81.16.Rf; 81.16.Nd; 62.25.-g     

Random-Cluster Analysis of a Class of Binary Lattice Gases

We introduce a class of binary lattice gases which can be viewed as a lattice analogue of the continuum Widom–Rowlinson model, and which also is related to the beach model of Burton and Steif. This new model is shown to exhibit phase transition for large particle intensities. Stochastic monotonicity results of varying strength are derived in various parts of the parameter space. The main tool is a random-cluster representation of the model, analogous to the Fortuin–Kasteleyn representation of the Potts model.     

Energy-based coupling of smooth particle hydrodynamics and molecular dynamics with thermal fluctuations

We propose a thermodynamically consistent and energy conserving coupling scheme between the atomistic and the continuum domain. The coupling scheme links the two domains using the DPDE (Dissipative Particle Dynamics at constant Energy) thermostat and is designed to handle strong temperature gradients across the atomistic/continuum domain interface. The fundamentally different definitions of temperature in the continuum and atomistic domain – internal energy and heat capacity versus particle velocity – are accounted for in a straightforward and conceptually intuitive way by the DPDE thermostat. We verify the here proposed scheme using a fluid, which is simultaneously represented as a continuum using Smooth Particle Hydrodynamics, and as an atomistically resolved liquid using Molecular Dynamics. In the case of equilibrium contact between both domains, we show that the correct microscopic equilibrium properties of the atomistic fluid are obtained. As an example of a strong non-equilibrium situation, we consider the propagation of a steady shock-wave from the continuum domain into the atomistic domain, and show that the coupling scheme conserves both energy and shock-wave dynamics.     

Statistical Geometry and Lattices

Statistical geometry furnishes the tool that allows the transfer of results from a lattice with finite lattice parameter to the continuum. Since lattice simulations are simpler than continuum ones, this suggests that larger scale simulations for the continuum might be more effectively carried out on a lattice with finite lattice parameter followed by the indicated transfer. We also show that a statistical geometry, peculiar to hard particles on a lattice, can be developed. Among other things, this opens the possibility that a scaled particle theory on a lattice might be derived.     

Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Super-Instantons, Perfect Actions, Finite-Size Scaling, and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the 2DO(N) models. The continuum limit is taken either in an infinitevolume or in a box whose size is a fixed fraction of the infinite-volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the socalled super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called “perfect actions”. It also shows that David’s recent claim that superinstanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.     

Towards the continuum coupling in nuclear lattice effective field theory I: A three-particle model

Weakly bound states often occur in nuclear physics. To precisely understand their properties, the coupling to the continuum should be worked out explicitly. As the first step, we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core. Our approach is consistent with the Lüscher formalism.     

Infrared Features of Unquenched Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has a maximum of α₀ ∼ 2 − 2.5 at around q = 0.5 GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind (KS) fermions). The Kugo-Ojima parameter c which saturated to about 0.8 in quenched simulations becomes consistent with 1 in the MILC configurations produced with the use of the Asqtad action, after averaging the dependence on polarization directions caused by the asymmetry of the lattice. The presence of the correction factor 1 + c ₁/q ² in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, c ₁ is confirmed of the order of a few GeV. The MILC configuration of a = 0.09 fm suggests also the presence of dimension-4 condensates with a sign opposite to the dimension-2 condensates. The gluon propagator, the ghost propagator, and the running coupling are compared with recent pQCD results including an anomalous dimension of fields up to the four-loop level.     

What is the Relativistic Volterra Lattice?

We develop a systematic procedure of finding integrable 6ldquo;relativistic” (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problem, which can be, in turn, interpreted as a new discrete time system. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then “relativistic”, the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the “relativistic” deformations were not known previously. Received: 1 April 1998 / Accepted: 21 July 1998     

A lattice test of strong coupling behaviour in QCD at finite temperature

We propose a set of lattice measurements which could test whether the deconfined, quark–gluon plasma, phase of QCD shows strong coupling aspects at temperatures a few times the critical temperature for deconfinement. The measurements refer to twist-two operators which are not protected by symmetries and which in a strong-coupling scenario would develop large, negative, anomalous dimensions, resulting in a strong suppression of the respective lattice expectation values in the continuum limit. Special emphasis is put on the twist-two operator with lowest spin (the spin-2 operator orthogonal to the energy–momentum tensor within the renormalization flow) and on the case of quenched QCD, where this operator is known for arbitrary values of the coupling: this is the quark energy–momentum tensor. The proposed lattice measurements could also test whether the plasma constituents are pointlike (as expected at weak coupling), or not.     

The lattice baryon spectrum in first order strong coupling approximation

Lattice baryon masses are calculated in first order strong coupling approximation with staggered fermions. Particular emphasis is given to the lattice quantum numbers and their relation to the continuum symmetry. Using non-local one-link fields, we found lattice baryon states which are new in first order strong coupling approximation.     

Simulating (electro)hydrodynamic effects in colloidal dispersions: Smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent (Phys. Rev. E 71, 036707 (2005)). An improved formulation called the “Smoothed Profile (SP) method” is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids.     

Inequalities for higher order Ising spins and for continuum fluids

The recently derived Fortuin, Kasteleyn and Ginibre (FKG) inequalities for lattice gasses are investigated for higher order Ising spin systems and multi-component lattice gasses. Conditions are given for the validity of the FKG inequalities for higher order spin systems with Hamiltonians of the form used recently as models for various physical systems, e.g.He ³–He ⁴ mixtures. We also investigate various inequalities for binary lattice gases and show how these can be carried over to continuum systems.Supported in part by U.S.A.F.O.S.R. # F 44620-71-C-0013.N.S.F. Graduate Trainee.     

Gauge symmetry as symmetry of matrix coordinates

We propose a new point of view on gauge theories, based on taking the action of symmetry transformations directly on the space coordinates. Via this approach the gauge fields are not introduced at the first step, and they can be interpreted as fluctuations around some classical solutions of the model. The new point of view is connected to the lattice formulation of gauge theories, and the parameter of the non-commutativity of the coordinates appears as the lattice spacing parameter. Through the statements concerning the continuum limit of lattice gauge theories, the suggestion arises that the non-commutative spaces are the natural ones to formulate gauge theories at strong coupling. Via this point of view, a close relation between the large-N limit of gauge theories and string theory can be made manifest. Received: 16 June 2000 / Published online: 8 September 2000     

Entropy and equilibrium state of free market models

Large adiabatic polarons in anisotropic crystals in the presence of constant magnetic field have been studied within the Holstein molecular crystal model in the continuum approximation. It was shown that magnetic field directed along the symmetry axis induces transverse confinement which may stabilize large polarons. They represent localized (soliton-like) nonlinear structure uniformly propagating along the symmetry axis and rotating around it in the same time. Such objects exist in 3D lattice provided that coupling constant and magnetic field do not exceed certain critical values. In contrast with pure 1D systems existence of large polarons is possible in a quite wider region of the values of coupling constant which may attain considerably higher values than in the pure 1D media. Furthermore, polaron effective mass, depending on the intensity of the applied magnetic field, may be considerably lighter than that of the the pure 1D polarons for the same values of coupling constant. This is the most significant difference with respect to pure 1D systems in the absence of magnetic field and may have substantial impact on polaron transport properties.     

Femtosecond optical investigation of electron–lattice interactions in an ensemble and a single metal nanoparticle

Electron–lattice energy exchange is investigated in an ensemble of silver nanoparticles of mean diameter 9 nm and in a single 30-nm particle using a femtosecond pump–probe technique. The dependences of the measured transient transmission change and of the electron energy loss kinetics on the excitation amplitude are compared to the results of numerical simulations of nonequilibrium electron relaxation and of the two-temperature model. The good agreement between the theoretical and experimental data indicates that, for the studied low particle density samples, hot-electron cooling is dominated by electron–lattice coupling in a nanoparticle both for weak and large electron heating with a minor influence of their surrounding environment (glass or polymer matrix). PACS 78.47.+p; 42.65.-k; 73.20.Mf     

Soliton patterns and breakup thresholds in hydrogen-bonded chains

The dynamics of protons in hydrogen-bonded quasi one-dimensional networks are studied using a diatomic lattice model of protons and heavy ions including a φ⁴ on-site substrate potential. It is shows that the model with linear and nonlinear coupling of the quartic type between lattice sites for the protons admits a richer dynamics that cannot be produced with linear couplings alone. Depending on two types of physical boundary conditions, namely of the drop or condensate type, and on conditions requiring the presence of linear and nonlinear dispersion terms, soliton patterns of compact support, whether with a peak, drop, bell, cusp, shock, kink, bubble or loop structure, are obtained within a continuum approximation. Phase trajectories as well as analytical studies provide information on the disintegration of soliton patterns upon reaching some critical values of the lattice parameters. The total energies of soliton patterns are computed exactly in the continuum limit. We also show that when anharmonic interactions of the phonon are taken into account, the width and energy of soliton patterns are in qualitative agreement with experimental data.     

TheO(3) non-linear σ-model on a 2 dimensional random lattice

TheO(3) σ-model on a 2-dimensional random lattice is studied numerically. The comparison of the continuum behaviors of the model on both random and regular lattices is carried out. It is shown that both lattices have the same continuum limit of the model, and the random lattice seems not to have the advantage of the wider scaling window compared to the same sized regular square lattice.     

Extended Scaling Relations for Planar Lattice Models

It is widely believed that the critical properties of several planar lattice systems, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective continuum fermionic theory obtained as a formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones predicted by Kadanoff (Phys Rev Lett 39:903–905, 1977) and by Luther and Peschel (Phys Rev B 12:3908–3917, 1975).