Kawasaki dynamics

This only depends on the probability of the termini, the total adiabatic works, and the total weight of stochastic transitions. The first of these is for uncorrelated motion and is the one that occurs in Glauber or Kawasaki dynamics [75-78]. The last term is, of course, very sensitive to the specified trajectory and the degree to which it departs from the adiabatic motion. However, the stochastic transitions are the same on the forward and on the reverse trajectory, and the ratio of the probabilities of these is... 

Figure 5 Density relaxations in Monte Carlo simulations of the geometry shown in Fig. 4 with conditions same as in Fig. 3 /3fi = -5.5) (a) Grand canonical simulations. (6) Simulation with mass conservation. The solid line, dotted line, and the open circles are the Kawasaki dynamics, ideal diffusion, and the grand canonical result shown in (a) rescaled by td with ro = 2 gmcs. The inset shows the initiail diffusion-limited regime in the logarithmic scale.

The formulation of the path probability function entirely depends on the kinetics assumed in the study. The vacancy-mediated kinetics or the exchange kinetics(Kawasaki dynamics ) requires a large number of path variables which make numerical operations intractable. The spin flipping kinetics(Glauber dynamics ) generally does not conserve the species with time, however the conservation is assured at 1 1 stoichiometric composition without imposing any additional constraints. In this regard, the spin system... 

Monte-Carlo simulations of the equilibrium properties of the model are carried for a triangular lattice of 100 X 100 sites. The equilibrium is provided by a combination of Glauber (single-chain excitations) and Kawasaki dynamics (conserving the cholesterol content) [5]. Monte Carlo simulations allow for an accurate determination of thermal quantites like the isothermal compressibility ... 

KJ Stine, SA Rauseo, BG Moore, JA Wise, CM Knobler. Phys Rev A 41 6884-6892, 1990. CM Knobler, K Stine, BG Moore. In A Onuki, K Kawasaki, eds. Dynamics and Patterns in Complex Fluids (Springer Series in Physics, vol. 52). New York Springer-Verlag, 1990, pp 130-140. 

Li Y, Tanaka T (1990) In Onuki A, Kawasaki K (eds) Dynamics and Patterns in Complex Fluids, Springer-Verlag, Berlin, 52 44... 

Let us examine the critical dynamics near the bulk spinodal point in isotropic gels, where K + in = A(T — Ts) is very small, Ts being the so-called spinodal temperature [4,51,83-85]. Here, the linear theory indicates that the conventional diffusion constant D = (K + / )/ is proportional to T — Ts. Tanaka proposed that the density fluctuations should be collectively convected by the fluid velocity field as in near-critical binary mixtures and are governed by the renormalized diffusion constant (Kawasaki s formula) [84],... 

Onuki A (1988) In Tanaka F, Doi M, Ohta T (eds) Space-time organization in macromolecular fluids. Springer, Berlin Heidelberg New York, p 94 Onuki A (1989) In Kawasaki K, Suzuki M, Onuki A (eds) Formation, dynamics and statistics of patterns. World Scientific, Singapore,... 

Measurements of static light or neutron scattering and of the turbidity of liquid mixtures provide information on the osmotic compressibility x and the correlation length of the critical fluctuations and, thus, on the exponents y and v. Owing to the exponent equality y = v(2 — ti) a 2v, data about y and v are essentially equivalent. In the classical case, y = 2v holds exactly. Dynamic light scattering yields the time correlation function of the concentration fluctuations which decays as exp(—Dk t), where k is the wave vector and D is the diffusion coefficient. Kawasaki s theory [103] then allows us to extract the correlation length, and hence the exponent v. 

Thus oj(q = 0) vanishes as co q = 0) oc Xt % Yl" — % <2 n>> and eq. (201) hence implies the classical value Zd = 2 — ij. Although eq. (206) thus suggests a relationship between the dynamic exponent and static ones, this is not true if effects due to non-mean-field critical fluctuations are taken into account. In fact, for the kinetic Ising model (Kawasaki, 1972) extensive numerical calculations imply that z. 2.18 in d = 2 dimensions (Dammann and Reger, 1993 Stauffer, 1992 Landau et al., 1988) rather than Zc = 2 - r) = 1.75. Note also [this is already evident from eq. (206)] that not all fluctuations slow down as Tc is approached but only those associated with long wavelength order parameter variations. One can express this fact in terms of a dynamic scaling principle... 

Hashimoto, T., Takebe, T. and Fujioka, K., in Dynamics and Patterns in Complex Fluids", Onuki, A., and Kawasaki,... 

Kanaya, T., and Kaji, K., Dynamics in the glassy state and near glass transition temperature of amorphous polymers as smdied by neutron scattering, Adv. Polym. Sci., 154, 87-141 (2001). Kawasaki, K., Correlation-function approach to the transport coefficients near the critical point, Phys. Rev., 150, 291-306 (1966). 

Storage and loss moduli, G and G" and the dielectric loss, e" of a high-M PI99/PtBS348 miscible blend (Mpi = 9.9 x 10, Mpi g = 3.5 x 10 , w i = 50 wt%) measured at temperatures as indicated. The e" data are multiplied by a factor of 10. (Data taken, with permission, from Watanabe, H., Q. Chen, Y. Kawasaki, Y. Matsumiya, T. Inoue, and O. Urakawa, 2011. Entanglement dynamics in miscible polyisoprene/poly(p-ferf-butylstyrene) blends. Macromolecules 44 1570-1584.)... 

Watanabe, H., Q. Chen, Y. Kawasaki, Y. Matsumiya, T. Inoue, and O. Urakawa. 2011. Entanglement dynamics in miscible polyisoprene/poly(p-fcrf-butylstyrene) blends. Macromolecules 44 1570-1584. 

K. Kawasaki, M. Tokuyama, and T. Kawakatsu, (eds.) AIP Conf. Proc. 256, Slow Dynamics in Condensed Matter, Fukuoka, Japan, 1991 (AIP, New York, 1992). 

A problem arises when trying to write Eq. (90) in vector form in the space of dynamical variables. If n linear variables are needed to form a complete set, then there exist possible bilinear variables. Thus, V must be an nxn matrix, and AA is a vector in an n -dimensional space as it turns out, these considerations would complicate the manipulations we are about to perform. Kawasaki has given a very simple alternate way to treat the vectorial structure of Eq. (90). This is to extend the definition of the wave vector of. a variable to include an index, which specifies the identity of the variable itself. Thus, instead of AL, we now just write Ak, where k is understood to contain both the Fourier transform variable and the index i. Sums over k are similarly reinterpreted. Now, combinations of the linear variables can always be chosen such that the matrix io)k-k is diagonal in the space of dynamical variables. Henceforth, we shall always assume that such a choice has been made. Then Eq. (90) holds as a vector equation with the new interpretation of wave vector. 

T. Hashimoto, T. Takebe, K. Fujioka, in Dynamics and Patterns in Complex Fluids, ed. by A. Onuki, K. Kawasaki (Springer, New York, 1990b)... 

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