International Journal of Modern Physics B

Liquid foams are concentrated dispersions of gas bubbles in a small amount of surfactant solution, which are perpetually out of equilibrium systems. The process of liquid draining through networks of Plateau borders in a fresh foam is so-called foam drainage, as a result of both gravitational and capillary forces, which has great effect on the stability of foams. From the view of foam physics and dynamics, this paper briefly introduces foam structure and major lifetime limiting factors of foam. The substantial progress on the theory of drainage, measuring techniques for liquid fractions, drainage in both one dimension and two dimensions, and drainage in microgravity circumstances are overviewed throughout. Remaining tasks are discussed and a multiscale methodology for foam drainage is proposed for future investigations.

The mixed-spin Ising model on a decorated square lattice with two different decorating spins of integer magnitudes S_B = 1 and S_C = 2 placed on horizontal and vertical bonds of the lattice, respectively, is examined within an exact analytical approach based on the generalized decoration–iteration mapping transformation. Besides the ground-state analysis, finite-temperature properties of the system are investigated in detail. The most interesting numerical result to emerge from our study relates to a striking critical behavior of the spontaneously ordered "quasi-1D" spin system. It was found that this quite remarkable spontaneous order arises when one sublattice of the decorating spins (either S_B or S_C) tends toward their "nonmagnetic" spin state S = 0, and the system becomes disordered only upon further single-ion anisotropy strengthening. In particular, the effect of single-ion anisotropy upon the temperature dependence of the total and sublattice magnetization is investigated.

We evaluate analytically and numerically the density of states (DOS) and the heat capacity in a spherical quantum dot formed by a spherical thin barrier. The control of the spherical barrier thickness or the potential barrier height is found to cause the dimensional transition from the three-dimensional (3D) behavior to the quasi-zero dimensional (Q0D) behavior in the DOS and the heat capacity. When the barrier is thick enough, the DOS shows the Q0D-like behavior but when the barrier is thin enough to allow electrons to tunnel through it, the temperature dependence of the heat capacity exhibits quite a distinct behavior depending on the electron density. Explicit numerical plots are given in the low density regime.

A boundary value problem associated with filtering governed by differential equations with time dependent coefficients and exhibiting a weak nonlinearity is solved. Namely, the boundary value problem is split into two independent boundary problems, i.e., that of Goursat for the concentration of a sorbate and that absorbed by a sorbent. Then each of the formulated problems is solved separately applying the Riemann transformation.

A new method for generating the multi-scroll chaotic attractors is introduced. It is demonstrated that the multi-scroll chaotic attractors can be generated using the saw-tooth function series and different number of scrolls can be designed easily by modifying the natural number n of the saw-tooth function. Various scroll attractors are illustrated not only by computer simulation, but also by the realization of an electronic circuit experiment on EWB.

By means of the multilinear variable separation approach, a general variable separation solution of the Boiti–Leon–Manna–Pempinelli equation is derived. Based on the general solution, some new types of localized structures — compacton and Jacobi periodic wave excitations are obtained by introducing appropriate lower-dimensional piecewise smooth functions and Jacobi elliptic functions.

A disordered alloy A_pB_1-p where both A and B represent magnetic atoms with respective spins S_A = 1/2 and S_B = 1 and whose magnetic interaction can be described by the Ising Hamiltonian is treated using the cluster-variational method. In this method, it is assumed that the system is built out of a "building block" which is embedded in an effective field. Taking the "building block" as a 4-atom cluster, the approximate free energy of the alloy is then obtained by treating the interactions between spins within the cluster of all possible configurations in an exact manner and the rest of the interaction by an effective variational field. The magnetization M and the transition temperature T_c are then calculated for different concentration and exchange parameters (J_AA, J_BB and J_AB). The magnetization M exhibits different kinds of ferrimagnetic behavior depending on the concentration and the relative strengths of the intra- and inter-sub-network exchange interactions. For antiferromagnetic J_AB, the sub-network magnetization saturates and is aligned antiferromagnetically at low temperature. The existence of the compensation temperature, T_cm, where the total magnetization reverses its direction, and depends sensitively on the relative values of J_AA/J_AB and J_BB/J_AB and p. For B (A)-rich alloy with small J_AB, the direction of the net magnetization remains unchanged up to T_c, and a maximum in M appears at intermediate T < T_c when J_BB ≫ J_AA(J_BB ≪ J_AA). When |J_AB| > J_AA, J_BB, T_c exhibits a maximum with p. The transition temperature is much less than the mean-field value in all cases. The magnetic susceptibility diverges as T tends to T_c and is Curie-Wiess like at T ≫ T_c. The meta-magnetic behavior has been found at high magnetic fields. Some of these results are in tune with the experimental observations in the amorphous rare-earth transition metal alloys.

We propose a new method for suppressing the timing jitters of soliton pulses by using periodic phase conjugations and optical spectral filters in a high bit-rate transmission system. It is proven that the tolerable transmission distance limited by timing jitters can be increased through modulating frequency shifts by optical phase conjugators and eliminating the interaction between dispersive waves and the central pulses by optical filters. Our results also show that the optical-phase-conjugated soliton with spectral filters is superior to the common soliton in suppressing polarization mode dispersion induced by random birefringence. The physical mechanisms of soliton timing jitters are analyzed.

This paper analyzes the synchronization control of new chaotic systems called Lorenz-like systems. Based on the Lyapunov stability theory, an adaptive controller and a parameter update rule are designed. It is proved that the controller and update rule not only achieve self-synchronization of Lorenz-like systems but can also make the Lorenz-like system asymptotically synchronized with the Rössler system, and further identify the uncertain system parameters. Numerical simulations have shown the effectiveness of the adaptive controller.

We report here results for collapses and revivals phenomenon for a collection of M two-level atoms contained in a volume having dimensions much smaller than the radiation wavelength and existing in the Dicke state |r,m〉. We use a perturbation approach and obtain in the lowest contributing order of perturbation second harmonic, besides the main Rabi frequency. The amplitude of the fundamental depends on m only, but the amplitude of the harmonic has dependence on r as well as m. If the atoms are in superradiant states, only the second harmonic is obtained. Revival time for the second harmonic is one half that for the fundamental. It is interesting to note that the number of atoms M does not matter in Rabi frequency, collapse times, revival times or in amplitudes, and only r and m matter. Values of r and m of atoms in a Dicke state can be determined, in principle, by observing Rabi oscillations and average atomic inversion.

A combination of small-cluster exact diagonalizations and a well-controlled approximative method is used to study the ground states of the Falicov–Kimball model extended by nonlocal Coulomb interaction (U_non). It is shown that the ground-state phase diagram as well as the picture of valence and metal–insulator transitions found for the conventional Falicov–Kimball model are strongly changed when the nonlocal Coulomb interaction is added. This is illustrated for three selected values of the on-site Coulomb interaction (U) that represent typical behaviors of the model for small, intermediate and strong interactions. A number of remarkable results are found: (i) the phase separation takes place for a wide range of U_non in all three interaction limits; (ii) in the weak and intermediate coupling limit, the model exhibits the nonlocal Coulomb interaction–induced insulator–metal transition; (iii) depending on the value of U_non, the model is able to describe both the continuous and the discontinuous changes of the f-electron occupation number; (iv) new types of inhomogeneous charge ordering (including various types of axial and diagonal stripes) are observed for nonzero U_non.

The unsteady flow in an annulus due to a velocity applied to one of the boundaries is addressed. The fluid considered is non-Newtonian, incompressible and electrically conducting. The strength of the applied magnetic field is time-dependent. Both analytical and numerical approaches are presented and compared. The nonlinear effects on the velocity profile are shown.