Hard order parameter

Ideological Background. Every macrosociety is regulated by ideas on and valuations of the aims of individual life and the means of achieving them, and therefore of the ensuing social, economic and political structures. The guiding principles are a set of collective macrovariables playing the role of a multidimensional order parameter in the society. A distinction between soft and hard order parameters can be made. 

Example B hep and fee Phases of Hard Spheres. We have already noted that the order parameter in ESPS need not be constructed out of the true energy functions of the two phases. The defining characteristic of an ESPS order parameter is that it measures the difference between the values of some chosen function of the common coordinate set u evaluated in the two phases, such that for some region (typically sufficiently small values ) of that quantity, an interphase switch can be successfully initiated. An ESPS order parameter merely provides a convenient thread that can be followed to the wormhole ends. 

In the case of hard spheres the energy function does not provide a usefully graded measure of how far we are from a wormhole The order parameter defined in Eq. (53) will generally be infinite because of hard-sphere overlap in the configurations created by the switch. But it is easy to find an alternative All... 

For simplicity we assume that the particles are magnetically hard.1 Then, the already developed formalism [Eqs. (4.90) and (4.293)] applies in full under two conditions e is identified with v and the internal relaxation time Tq is replaced by the external rotational diffusion (Debye) time x. In the modified equations, the orientation order parameter is given by (Pi)- Similarly to (4.294), we set... 

Formulas for the Leslie viscosities, in turn, were derived from the Smoluchowski equation for hard rods by Kuzuu and Doi (1983,1984 Semenov 1987), and are given in Eqs. (10-20) with ao = 0- These formulas require as inputs values of 2,54, k, and Dr, which are functions of polymer concentration C. Reasonably reliable analytic functions for these dependencies were obtained by Kuzuu and Doi using a perturbation expansion for large order parameter, yielding... 

The parameters C, D, E and F involve components of polarizability derivative tensors. Qjs is the displacive order parameter in the low-temperature phase and Qjq corresponds to which is present in the intermediate pseudo-phase. The damping constant T qjh) includes the effect of coupling between the hard mode and the reorientational relaxation of displaced lead atoms. 

Fig. 9. Two-parameter ordering phase diagram for a system of 500 identical hard spheres (Truskett et ai, 2000 Torquato et ai, 2000). Shown are the coordinates in structural order parameter space (r, ) for the equilibrium fluid (dot-dashed), the equilibrium FCC crystal (dashed), and a set of glasses (circles) produced with varying compression rates. Here, r is the translational order parameter from (26) and is the bond-orientational order parameter Q( from (25) normalized by its value in the perfect FCC crystal ( = Each circle...

The first step in quantitative description of pure polyamorphic fluid is a selection of the model that can qualitatively describe a possible multiplicity of critical points in wide range of temperatures and pressures. A great many of explanations of multicriticality in monocomponent fluids (perturbation theory models semiempirical models lattice models, two-state models, field theoretic models, two-order-parameter models, and parametric crossover model has been disseminated after the pioneering work by Hemmer and Stell Here we test more extensively the modified van der Waals equation of state (MVDW) proposed in work and refine this model by introducing instead of the classical van der Waals repulsive term a very accurate hard sphere equation of state over the entire stable and metastable regions... 

We return here to mean field theory with a scalar order parameter thick film geometry, assuming hard walls or surface against vacuum, respectively) at z = 0 and z = L. Starting again from eq. (14), we may disregard the x and y-coordinates [as in our treatment of the interfacial profile, eqs. (177)—(181)], but now we have to add a perturbation 2Fv(bare) to... 

Here we have omitted constant terms in the free energy and anticipated that a molecular field treatment of an Ising Hamiltonian that describes exactly the situation considered here, namely eq. (1), is consistent with eq. (220). The coefficient of the linear term in eq. (220) thus describes the action of a local field (i.e., the variable conjugate to the local order parameter) right at the hard walls (or free surfaces, respectively). If

order parameter of gas-liquid condensation, the field H can be interpreted as the binding potential of particles at the hard wall. 

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