Kinematics order parameters

The order parameter is essentially a kinematic measure, describing the state of order within a system without any intrinsic reference to what factors drove the system to the state of interest. For example, in thinking about the transition between the ordered and disordered states of an alloy, it is useful to define an order parameter that measures the occupation probabilities on different sublattices. Above the order-disorder temperature, the sublattice occupations are random, while below the critical temperature, there is an enhanced probability of finding a particular species on a particular sublattice. The conventional example of this thinking is that provided by brass which is a mixture of Cu and Zn atoms in equal concentrations on a bcc lattice. The structure can be interpreted as two interpenetrating simple cubic lattices where it is understood that at high temperatures we are as likely to find a Cu atom on one sublattice as the other. A useful choice for the order parameter, which we denote by r], is... 

An alternative approach to such kinematically extended continua is presented by Capriz et al. [9-11] and Svendsen [39, 40]. They introduce scalar-valued order parameters to describe the influence of the microstructure in analogy to the Ginzburg-Landau theory. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

In order to investigate the chemical and age properties of the thin and the thick disks separately we have performed the deconvolution of their velocity distributions. We show that about 25% of the sample has kinematics typical of the thick disk, adopting for its parameters V ag = — 51km s 1 and (<7u, v, w) = (63, 39, 39) km s-1. Stars having a probability higher than 80% to belong to the thin and thick disks were selected. Plots on Fig.l show nicely the... 

Abstract. In an effort to determine accurate stellar parameters and abundances for a large sample of nearby stars, we have performed the detailed analysis of 350 high-resolution spectra of FGK dwarfs and giants. This sample will be used to investigate behavior of chemical elements and kinematics in the thick and thin disks, in order to better constrain models of chemical and dynamical evolution of the Galaxy. 

The polarisation factor, C=D g. D j,. This is unity for polarisation, in which the electric field vector is perpendicular to the dispersion plane and cos(2 g) for polarisation in which the electric field vector lies in the dispersion plane. We may apply equation (4.20), which since h is real implies that Im(K o)=Im(K ), and, in order to express the solution simply, introduce the very important idea of deviation parameters, g and. These express the deviation of the incident and diffracted wavevectors from the kinematic assumption where k g = k ij =l/, and are defined as... 

The functional dependency, Eq. (1.62), is all that dimensional analysis can offer here. It cannot provide any information about the form of the function /. This can only be obtained experimentally. These experiments can however be carried out in a considerably simpler manner, since not the individual parameter but the numerical value of the process number Re has to be varied. This can be achieved by varying the stirrer speed n, the stirrer diameter d or the kinematic viscosity v. It is simplest to vary the kinematic viscosity, which can be varied over orders of magnitude in liquid mixtures of water and glycerine or molasses. In this way measurements were carried out to determine the power characteristic Ne(Re) of a blade stirrer of fixed geometry in a tank, see Fig. 1.36. 

In the literature, the constitutive equation for both the amorphous polymer and crystalline polymer has been well established. Therefore, we can direcdy use these relations to model the amorphous phase and crystalline phase of the SMPFs. We then need to consider the cychc texture change of both subphases because the mechanical behaviors of the individual microconstituents may vary when they are packed in a multiphase material system and a certain deviation in their mechanical responses may exist between the individual and their assembled configurations. Since this is a shape memory material, we also need to model the shape recovery behavior. After that, we can use the above micromechanics relation to assemble the macroscopic constitutive relation. In order to determine the parameters used in the constitutive model, we need to consider the kinematic relations under large deformation. Finally, we will discuss the numerical scheme to solve the coupled equations. 

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