Relaxation systems, model

An experimental and theoretical study of the degassing of an LDPE high-density foam is presented. Measurements of the mass, dimensions, and density as a function of storage time are reported. A geometrical model is described to represent the basic mass transport and volume relaxation processes in a cellular system. Model predictions were compared with experimental results. 12 refs. 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

The use of the compressibility term can be described as follows. The greater the stiffness a system model has, the more quickly the flow reacts to a change in pressure, and vice versa. For instance, if all fluids in the system are incompressible, and quasi-steady assumptions are used, then a step change to a valve should result in an instantaneous equilibrium of flows and pressures throughout the entire system. This makes for a stiff numerical solution, and is thus computationally intense. This pressure-flow solution technique allows for some compressibility to relax the problem. The equilibrium time of a quasi-steady model can be modified by changing this parameter, for instance this term could be set such that equilibrium occurs after 2 to 3 seconds for the entire model. However, quantitative results less than this timescale would then potentially not be captured accurately. As a final note, this technique can also incorporate flow elements that use the momentum equation (non-quasi-steady), but its strength is more suited by quasi-steady flow assumptions. 

The spectral density (see also Sections (7-5.2) and (8-2.5)) plays a prominent role in models of thermal relaxation that use harmonic oscillators description of the thermal environment and where the system-bath coupling is taken linear in the bath coordinates and/or momenta. We will see (an explicit example is given in Section 8.2.5) that /(co) characterizes the dynamics of the thermal environment as seen by the relaxing system, and consequently determines the relaxation behavior of the system itself. Two simple models for this function are often used ... 

Adolf et al [89] focused primarily on epoxy systems. They consider the key to the success of a constitutive model to be its choice of strain measure and the inclusion of free-energy-accelerated relaxations. The model only requires linear properties (i.e., properties that may be predictable by the methods developed in this book) for materials prior to their synthesis, since nonlinear behavior arises naturally from the formalism. Thermal properties and epoxy curing are also treated by their model. The authors have also attempted to treat failure by identifying a critical hydrostatic tension consistent with glassy failure. The model has been validated with a wide variety of types of material tests. The finite element simulations are performed in three dimensions. These authors have, thus far, done only a limited amount of preliminary work with heterophasic systems, but they report that the results were encouraging. 

Master equations have been used to describe relaxation and kinetics of clusters. The first approaches were extremely approximate, and served primarily as proof-of-principle. ° Master equations had been used to describe relaxation in models of proteins somewhat earlier and continue to be used in that context. " More elaborate master-equation descriptions of cluster behavior have now appeared. These have focused on how accurate the rate coefficients must be in order that the master equation s solutions reproduce the results of molecular dynamics simulations and then on what constitutes a robust statistical sample of a large master equation system, again based on both agreement with molecular dynamics simulations and on the results of a full master equation.These are only indications now of how master equations may be used in the future as a way to describe and even control the behavior of clusters and nanoscale systems of great complexity. ... 

Brochard and de Gennes [53] proposed a relaxation-controlled model for the dissolution of polymer droplets. When a droplet of polymer solution, of concentration Oo, is immersed in a solvent, two processes control the dissolution. The first step relates to the swelling of the polymer network by the solvent. This was assumed to be controlled by the cooperative diffusion coefficient, Dcoop- The second step corresponds to the viscous yield of the network and is controlled by the reptation time of the polymer, t,ep. The expression for the net solvent flux in such a system is given by... 

In summary we see that the use of the triple relaxation time model gives the same thermodynamic properties and essentially the same hydrodynamic properties as the exact hard-sphere system. It therefore follows that the corresponding kinetic equation (135) should give the proper limit for S k, to) at long wavelengths and low frequencies. The hydrodynamic behavior of S k, to) can be calculated using the macroscopic equations of fluid dynamics. All the essential features are summarized in the expression ... 

Dielectric experiments that involve studies of the relaxation function (r) are denoted as time-domain experiments, while those related to the complex permittivity function e (co) are considered dynamic experiments. The latter have the advantage of introducing an experimental timescale ( l/(o), which, when compared to the different intrinsic timescales of the system (the relaxation time x), provides useful information on the molecular level. In terms of the single-relaxation-time model of Debye (1921,1929), the complex permittivity for a dipolar mechanism can be written as follows ... 

A simple quantitative treatment of the solvent relaxation-induced Stokes shift is based on a model that assumes that the fluorophore is located in a cavity with radius a in a dipolar medium characterized by the bulk dielectric permittivity e and refractive index n (we should recall that the high-frequency limit of the dielectric permittivity e o equals the square of the refractive index n ). Classical treatment yields the Lippert equation [44] describing the difference, Av = va — vp, between the wavenumbers of the emission and absorption maxima of the fully relaxed system ... 

A dependence of relaxation times on free volume per molecule close to that described by equation 12 has been found by computer simulation of molecular motions in a polymer-solvent system modeled with a three-dimensional lattice, by Kran-buehl and Schardt. ... 

Functional description of the heart via models is important to study the heart s performance as a pump, to understand normal and disease conditions, and to serve as a building block in larger physiological system models [49]. Mechanical performance of the heart, more specifically the left ventricle, is typically characterized by estimates of ventricular elastance. The heart is an elastic bag that stiffens and relaxes with each heartbeat. Elastance is a measure of stiffness, classically defined as the differential relation between pressure and volume ... 

Model colloids have a number of properties that make them experimentally convenient and interesting systems to study. For instance, the timescale for stmctural relaxation of a colloidal fluid can be estimated as the time for a particle to diffuse a distance equal to its radius,... 

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