Discussions on the correspondence of dissipative particle dynamics and Langevin dynamics at small scales

We investigate the behavior of dissipative particle dynamics(DPD) within different scaling regimes by numerical simulations. The paper extends earlier analytical findings of Ripoll, M., Ernst, M. H., and Espa?nol, P.(Large scale and mesoscopic hydrodynamics for dissipative particle dynamics. Journal of Chemical Physics, 115(15),7271–7281(2001)) by evaluation of numerical data for the particle and collective scaling regimes and the four different subregimes. DPD simulations are performed for a range of dynamic overlapping parameters. Based on analyses of the current auto-correlation functions(CACFs), we demonstrate that within the particle regime at scales smaller than its force cut-off radius, DPD follows Langevin dynamics. For the collective regime,we show that the small-scale behavior of DPD differs from Langevin dynamics. For the wavenumber-dependent effective shear viscosity, universal scaling regimes are observed in the microscopic and mesoscopic wavenumber ranges over the considered range of dynamic overlapping parameters.     

A stochastic approach to capture crystal plasticity

A stochastic crystal plasticity model is proposed and applied within the rate-independent regime. As opposed to conventional deterministic algorithms wherein multiple slip systems are activated and redundant constraints may exist, the new Monte Carlo plasticity (MCP) paradigm is based on a stochastic chain of singly activated slip systems and thus avoids the possible ill-condition associated with multi-slip algorithms. The choice of the activated slip system is made at each Monte Carlo (MC) step based on the Metropolis algorithm. The MCP model is implemented within a Material Point Method (MPM) as a constitutive model to capture the elasto-plastic behavior of polycrystalline materials. A comparison with a commonly used singular value decomposition (SVD) algorithm indicates that MCP offers superior computational efficiency while maintaining comparable accuracy.     

An analytical approach to the dynamics of rotating shafts

An analytical procedure, based on the dynamic stiffness method, is proposed for the study of rotor dynamics problems. On the grounds of the governing differential equations of a continuous beam, the dynamic stiffness matrix of the rotating Timoshenko beam is derived, including the effects of translational and rotational inertia, gyroscopic moments and shear deformation of the shaft. Concentrated disks and isotropic, elastic bearings are taken into account in the element formulation. The results obtained by the proposed method are compared with both classical closed form solutions and finite element analyses taken from the literature.

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Sommario Nel presente lavoro viene esposto un procedimento analitico, basato sul metodo della rigidezza dinamica, per lo studio del comportamento dinamico dei rotori. In particolare, è ricavata la matrice di rigidezza dinamica della trave di Timoshenko rotante, che consente di tenere conto degli effetti dell'inerzia alla traslazione e alla rotazione, del momento giroscopico distribuito e della deformazione a taglio della trave. Nell'ambito della formulazione proposta, è possibile considerare, mediante inserimento diretto nella matrice di rigidezza dinamica, gli effetti dovuti alla presenza di dischi e di supporti elastici isotropi. Il metodo proposto è applicato alla determinazione delle velocità critiche di sistemi rotanti, con riferimento sia a casi semplici, per i quali è nota la soluzione analitica, sia al caso piu' complesso di un rotore già studiato in letteratura; per quest'ultimo esempio, in particolare, è presentato un confronto con i risultati delle analisi agli elementi finiti svolte da altri autori.

     

A sublinear-scaling approach to density-functional-theory analysis of crystal defects

We develop a sublinear-scaling method, referred to as MacroDFT, for the study of crystal defects using ab-initio Density Functional Theory (DFT). The sublinear scaling is achieved using a combination of the Linear Scaling Spectral Gauss Quadrature method (LSSGQ) and a Coarse-Graining approach (CG) based on the quasi-continuum method. LSSGQ reformulates DFT and evaluates the electron density without computing individual orbitals. This direct evaluation is possible by recourse to Gaussian quadrature over the spectrum of the linearized Hamiltonian operator. Furthermore, the nodes and weights of the quadrature can be computed independently for each point in the domain. This property is exploited in CG, where fields of interest are computed at selected nodes and interpolated elsewhere. In this paper, we present the MacroDFT method, its parallel implementation and an assessment of convergence and performance by means of test cases concerned with point defects in magnesium.     

A Padé approximant to the inverse Langevin function

Application of the methodology of Pade approximants to a Taylor expansion of the inverse Langevin function led to an accurate analytical expression. The approximation, retaining a finite extendibility of the Langevin spring, enables a convenient analysis of experimental data and analytical manipulations of material models.     

Dislocation dynamics: from microscopic models to macroscopic crystal plasticity

In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model with dislocation densities. We show how each model can be deduced from the previous one at a smaller scale.      

A new approach to studying the dynamics of a thin curved vortex

The paper studies the dynamics of a thin curved vortex in a potential flow of an ideal incompressible fluid. The flow is specified by a number of geometrical restrictions and does not satisfy the Biot–Savart law. The form of the derived equation of the vortex dynamics coincides with the form of the wellknown equation of local induction for selfinduced vortex motion. The parameters of the new equation are simultaneously flow parameters, and in this sense, they do not show uncertainty typical of classical equations. The coefficient of the new equation can take any specified values (not necessarily much greater than unity, as required according to the concept of local induction) and generally is a function of a natural filament parameter.     

An approach to the study of dynamics of work motivation using the diary method

This study is concerned with work motivation as a dynamic process. Twenty workers kept a motivation diary over a period of several weeks. Using a PDA they recorded their level of motivation, self-efficacy beliefs and perceived instrumentality with respect to the task being carried out. The time series obtained were analyzed using common procedures in the study of dynamic systems in order to determine whether motivation followed linear or nonlinear patterns. The results revealed highly nonlinear dynamics for the different variables studied. The implications of these findings are discussed and questions are raised regarding the basic assumptions underlying current theories and models of motivation, for example, the assumptions of linearity and stability.     

Elasticity,piezoelectricity and crystal lattice dynamics

A review of some recent developments in the area between the dynamical theory of crystal lattices, in the harmonic approximation, and the classical, linear theories of elasticity and piezoelectricity.

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Résumé Un examen de quelques évolutions récentes dans le champ entre la théorie dynamique des réseaux cristallins (upproximation harmonique) et les théories classiques, linéaires, de l'élasticité et de la piézoélectricité.

     

A dual-oscillator approach to complex-stiffness damping based on fourth-order dynamics

Nonlinear Dynamics - Direct modal analysis of second-order systems with damping is generally not possible unless the damping and stiffness matrices commute, thereby admitting simultaneous...     

A Lagrangian-based continuum homogenization approach applicable to molecular dynamics simulations

The continuum notions of effective mechanical quantities as well as the conditions that give meaningful deformation processes for homogenization problems with large deformations are reviewed. A continuum homogenization model is presented and recast as a Lagrangian-based approach for heterogeneous media that allows for an extension to discrete systems simulated via molecular dynamics (MD). A novel constitutive relation for the effective stress is derived so that the proposed Lagrangian-based approach can be used for the determination of the “stress–deformation” behavior of particle systems. The paper is concluded with a careful comparison between the proposed method and the Parrinello–Rahman approach to the determination of the “stress–deformation” behavior for MD systems. When compared with the Parrinello–Rahman method, the proposed approach clearly delineates under what conditions the Parrinello–Rahman scheme is valid.     

A discrete mechanics approach to dislocation dynamics in BCC crystals

A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treated within the theory as energy-minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory eliminates the need for regularization of the core singularity and inherently allows for dislocation reactions and complicated topological transitions. The quantization of slip to integer multiples of the Burgers’ vector leads to a large integer optimization problem. A novel approach to solving this NP-hard problem based on considerations of metastability is proposed. A numerical example that applies the method to study the emanation of dislocation loops from a point source of dilatation in a large BCC crystal is presented. The structure and energetics of BCC screw dislocation cores, as obtained via the present formulation, are also considered and shown to be in good agreement with available atomistic studies. The method thus provides a realistic avenue for mesoscale simulations of dislocation based crystal plasticity with fully atomistic resolution.     

Skin friction measurements on reflective surfaces using nematic liquid crystal

 A new liquid crystal technique for full surface skin friction measurements is introduced. With the new technique, the transmission of light through nematic liquid crystal viewed in reflection provides a quantitative measurement of the skin friction. The measurement technique is discussed with the aid of a model which describes the rotation dynamics of the liquid crystal molecules. Calibration experiments performed in a laminar flow duct demonstrate that the model captures the essential physics of the new technique. The measurement of skin friction downstream of a three dimensional roughness element in an incompressible laminar boundary layer is then presented as a demonstration of the utility of the technique. Received: 5 June 1998/Accepted: 13 November 1998     

Dynamic crystal plasticity: An Eulerian approach

In this paper an Eulerian rate-dependent single crystal model that accounts for high-strain rates, large strains and rotations is developed. The viscoplastic law as well as the evolution equations for the lattice are written in terms of vectorial and tensorial quantities associated with the current configuration. The viscoplastic law is obtained from Schmid law using an overstress approach. Such an expression for the viscoplastic law is motivated by the microdynamics of crystal defects. A general analysis of the plane-strain response of the proposed rigid-viscoplastic single crystal model is presented. It is shown that only one differential equation, involving the orientation of one composite in-plane slip system, is necessary to describe the lattice evolution. Several two-dimensional boundary value problems, such as equal-channel die extrusion and channel die compression are selected to illustrate the predictive capabilities of the model. The results show that even at relatively low strain rates the viscosity plays an important role in the development of localized deformation modes. At high crosshead velocity, the plastic properties and crystal anisotropy are less important while inertia effects are dominant. Finally, the grains interaction is investigated by analyzing the compression of a grains multicrystal.