Microscopic configurations

This result is proportional to the number of configurational microscopic states, that is, the number of arrangements of N particles in... [Pg.80]

In the Maximum Entropy Method (MEM) which proceeds the maximization of the conditional probability P(fl p ) (6) yielding the most probable solution, the probability P(p) introducing the a priory knowledge is issued from so called ergodic situations in many applications for image restoration [1]. That means, that the a priori probabilities of all microscopic configurations p are all the same. It yields to the well known form of the functional 5(/2 ) [9] ... [Pg.115]

The dry gas seal is a variation of the mechanical contact seal. It differs in that it uses a microscopically thin layer of gas to separate and lubricate the faces. The seal is configured in a tandem or double-opposed seal arrangement. More complete details are covered in Chapter 5 under Dry Gas Seals. [Pg.117]

A key problem in the equilibrium statistical-physical description of condensed matter concerns the computation of macroscopic properties O acro like, for example, internal energy, pressure, or magnetization in terms of an ensemble average (O) of a suitably defined microscopic representation 0 r ) (see Sec. IVA 1 and VAl for relevant examples). To perform the ensemble average one has to realize that configurations = i, 5... [Pg.21]

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. [Pg.349]

To set up the kinetics, we introduce a function P(u, r, s t) which gives the probability that a given microscopic configuration... [Pg.474]

Molecular dynamics, in contrast to MC simulations, is a typical model in which hydrodynamic effects are incorporated in the behavior of polymer solutions and may be properly accounted for. In the so-called nonequilibrium molecular dynamics method [54], Newton s equations of a (classical) many-particle problem are iteratively solved whereby quantities of both macroscopic and microscopic interest are expressed in terms of the configurational quantities such as the space coordinates or velocities of all particles. In addition, shear flow may be imposed by the homogeneous shear flow algorithm of Evans [56]. [Pg.519]

Even though the basic idea of the Widom model is certainly very appealing, the fact that it ignores the possibihty that oil/water interfaces are not saturated with amphiphiles is a disadvantage in some respect. The influence of the amphiphiles on interfacial properties cannot be studied in principle in particular, the reduction of the interfacial tension cannot be calculated. In a sense, the Widom model is not only the first microscopic lattice model, but also the first random interface model configurations are described entirely by the conformations of their amphiphilic sheets. [Pg.657]

In the PPF, the first factor Pi describes the statistical average of non-correlated spin fiip events over entire lattice points, and the second factor P2 is the conventional thermal activation factor. Hence, the product of P and P2 corresponds to the Boltzmann factor in the free energy and gives the probability that on<= of the paths specified by a set of path variables occurs. The third factor P3 characterizes the PPM. One may see the similarity with the configurational entropy term of the CVM (see eq.(5)), which gives the multiplicity, i.e. the number of equivalent states. In a similar sense, P can be viewed as the number of equivalent paths, i.e. the degrees of freedom of the microscopic evolution from one state to another. As was pointed out in the Introduction section, mathematical representation of P3 depends on the mechanism of elementary kinetics. It is noted that eqs.(8)-(10) are valid only for a spin kinetics. [Pg.87]

More detailed theoretical approaches which have merit are the configurational entropy model of Gibbs et al. [65, 66] and dynamic bond percolation (DBP) theory [67], a microscopic model specifically adapted by Ratner and co-workers to describe long-range ion transport in polymer electrolytes. [Pg.508]

The rate equations determine the rate of change of the probability of a particular configuration, a, within an ensemble of growing crystals. They must include the rate constants for adding or subtracting units, which are assumed to obey microscopic reversibility. The net flux between configurations a and a which occur with probability P(a) and P(a ) respectively, and differ by one unit is ... [Pg.298]

All aspects of interferogram and experimental data acquisition and optical test rig control are provided by a computer program that also performs film thickness evaluation. It is believed that the film thickness resolution of the colorimetric interferometry measurement technique is about 1 nm. The lateral resolution of a microscope imaging system used is 1.2 /u,m. Figure 10 shows a perspective view of the measurement system configuration. This is an even conventional optical test rig equipped with a microscope imaging system and a control unit. [Pg.11]

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