Particle based models

Dispersion-Particle-Based Model. This is an improvement over the continuous-solid model and allows for dispersion. The results are... 

In particle-based models, the mean-field approximation also n ects short-ranged correlations in the polymeric fluid, e.g., the fluid-like packing of the particles or the correlations due to the selfavoidance of the polymers on short length scales. There is no small parameter which controls the magnitude of these correlation effects but they are incorporated into the coarse-grained parameters... 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

Like other multiscale methods, atomistic-continuum methods require an accurate treatment of the coupling between different domains. In addition to these difficulties, they pose serious challenges for performing extensive simulations. The physical processes described by continuum equations and particle-based models impose inherently distinct demands on the computer architerture. While continuum mechanics and hydrodynamics, typically dealing with regular meshes, are characterized by moderate computations with stractured communications, atomistic simulations are characterized by intense computations and intense interprocessor communications. As a result, large-scale simulations of this sort require a balanced computer architecture in terms of memory bandwidth and interconnea bandwidth. 

From Particle-Based Models for Computer Simulations to Self-Consistent Field Theory 201... 

From Field-Theoretic Hamiltonians to Particle-Based Models Soft-Core Models... 

Consider the otample that one wants to describe a small patch of the lamellar phase with cubic geometry (L = 5Reo). which is comprised of three lamellar sheets of a symmetric diblock copolymer with Tt = 10000 (cf Figure 5.5 for a similar system). In a particle-based model with hard-core repulsion, the segment density is limited by 1, where b = denotes the... 

In a self-assembling soft matter system, the composition also fluctuates little around the ideally ordered value however, the molecules are in a liquid state, that is, they diffuse and are not tethered to ideal positions. Therefore, there is no simple reference state of the particle-based model with a known free energy, and previous simulation techniques for calculating the absolute free energy of hard crystals do not straightforward carry over to self-assembling soft matter systems. 

Within a particle-based model, there is no well-defined reference state for the self-assembled structure. However, one can try to relate the seF-assembled structure to a disordered melt (or a different self-assembled morphology) via a reversible path and calculate the change of the free energy by thermodynamic integration. Typically, transitions between disordered and ordered morphologies or between different self-assembled structures are of first order. Thus, in an analogy to crystallization of hard condensed matter, there is no path in the space of physical intensive variables - for example, temperature, incompatibility, or composition - that reversibly cormects disordered and ordered structures. 

The main advantage of particle-based models over continuum treatments is their capability of being able to describe simultaneously membrane curvature and lipid chemistry, as well as their interplay how do specific lipids promote/prevent curvature stresses And how do lipids respond to curvature stresses, for example by partitioning between the inner and the outer monolayer of highly curved vesicles ... 

A large part of the computational literature is devoted to the mathematical identification of the mapping that we now use and also the the applicability of effective pair interactions. Technically, coarse-graining is a model reduction. Let /smaiKir p ) be a function describing an observable in the atomistic scale model. It depends on the position r and momenta p of the particles (in the case of a particle-based model). Similarly, /iaige( R > P ) is the same function in the nonatomistic model with positions R and momenta P. It is clear that / small =/large should be Valid, but for which ( R, P ) The equality... 

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