Takao Ohta

Kink dynamics in one-dimensional nonlinear systems

A certain class of nonlinear evolution equations of one space dimension which permits kink type solutions and includes one-dimensional time-dependent Ginzburg-Landau (TDGL) equations and certain nonlinear wave equations is studied in some strong coupling approximation where the problem can be reduced to the study of kink dynamics. A detailed study is presented for the case of TDGL equation with possible applications to the late stage kinetics of order-disorer phase transitions and spinodal decompositions. A special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics. A new conservation law for dissipative systems is found which corresponds to the momentum conservation law for wave equations.

Theory of Early Stage Spinodal Decomposition in Fluids near the Critical Point. II

In Figs. 3, 4, 5 and 6 the experimental points and the dashed lines of LBM have been taken from Ref. 1). Recently Professor Goldburg and Dr. Schwartz communicated to us that in Ref. 1) an error of factor 2 in time scale occurred in plotting the LBM results corresponding to 2-r=!LBM· This is also true in our work provided that L=L (or r=1), and the lines of LBM should be shifted to the left accordingly. On the other hand, if L~L as in our case, we have 2r-r=rLBM and the factor 2r is 1 r=1/2 as in our work. Then this error dissappears. In our work we have regarded the LBM results to be applicable to the model in which L=L (that is, the renormalization contribution to L comes from fluctuations with k>A=tr:) and long-range hydrodynamic interactions are absent. On the other hand, in drawing the LBM curve in Fig. 5 and the LBM curve with c=1/ v3 ( _,_) in Fig. 10 we have chosen r=L Thus, in order to be consistent with the above-mentioned interpretation of the LBM results, these curves ought to be moved appropriately to the right.

Kinetic Drumhead Model of Interface. I

A dynamical model is presented which describes the random motion of an interface of two coexisting phases. The Euclidean invariant stochastic equation of motion for the coordinate of the interface is derived systematically from the time-dependent Ginzburg-Landau model in the limit of infinitely deep potential well of the order parameter.

Kinetics of fluctuations for systems undergoing phase transitions - interfacial approach

Studies on kinetics of fluctuations in quenched fluid systems are reviewed on the basis of a new dynamical interfacial model. All the processes known to take place in critical fluid mixtures are identified for this model. We briefly discuss the Ostwald ripening and the interface stability with this model. An analogy with fully developed turbulence is noted and a possibility of intermittent states is indicated.

Scaling law in the ordering process of quenched thermodynamically unstable systems

Abstract The dynamics of phase separation in quenched thermodynamically unstable systems is studied. The scaling law exhibited in the late stage of the ordering process is investigated by the interface model. In the kinetics of the order-disorder transition the motion of random interfaces is shown to be responsible for the scaling law. The scaling form of the scattering function is obtained with particular attention to the fluctuating thermal noises. A droplet picture is used to discuss spinodal decomposition of off-critically quenched binary fluids. The sealing function is calculated explicitly in the region where the Brownian coagulation is most dominant for the phase separation. It is shown that the thermal noises are relevant to the scaling law in the ordering process driven by the Brownian coagulation whereas they are negligible in the kinetics of order-disorder transition.

Theory of semi-dilute polymer solutions. I. Static property in a good solvent

The authors study the static property of semi-dilute polymer solutions in a good solvent. Edwards transformation is employed to develop the conformation space renormalisation group theory in semi-dilute solutions. They are primarily concerned with the crossover behaviour from a dilute to semi-dilute regime. The first-order calculation on epsilon =(4-d) with d the dimensionality of space is performed for the asymptotic scaling functions of the radius of gyration, osmotic compressibility and the correlation length of the monomer density fluctuations.

The distribution function for internal distances in a self-avoiding polymer chain

Abstract The distribution function P of the vector r connecting two arbitrary fixed points on a self-avoiding chain is calculated to order ϵ = 4−d, d being the spatial dimensionality. This gives the cross-over behavior of P as a function of the length of the dangling ends.

Phase Hamiltonian in periodically modulated systems

We present a method to express a class of Ginzburg-Landau free energy functionals for systems exhibiting periodic modulation patterns in terms of the phase variables that describe smooth deformations of the patterns. Symmetry considerations for the resulting phase Hamiltonian lead to certain Cauchy-type relations among coefficients appearing in it. The theory is applied to lamellar, cylindrical and three-dimensionally periodic phases of diblock copolymer systems, and various elastic coefficients appearing in the phase Hamiltonian are explicitly calculated.

Domain growth in systems with multiple-degenerate ground states

We develop a statistical theory of growing domain structures in quenched systems with multiple-degenerate ground states where the order parameter is not conserved. Exact formulas are derived for the non-equilibrium structure functions for growing domains. As concrete examples the theory is applied to the p-state Johnson-Mehl model and the p-state cell model where the structure functions of the growing domains and the volume fraction of the metastable domain are calculated explicitly.

Polymer chain in good solvents under elongational flow

The properties of a single polymer chain under steady elongational flow are investigated by means of a renormalisation group method. Based on the Rouse Zimm model, the asymptotic scaling function of the end to end distribution is calculated by the epsilon =4-d expansion approximation with d being the spatial dimension of the system. The corrections due to the excluded volume effect and the hydrodynamic interaction are evaluated up to the order of epsilon . The effect of the flow on the scattering function is also described with a simple approximation.