The diffusive relaxation of a colloidal fluid adsorbed in a porous medium depends on many factors, including the concentration and composition of the adsorbed colloidal fluid, the average structure of the porous matrix, and the nature of the colloid-colloid and colloid-substrate interactions. A simple manner to describe these effects is to model the porous medium as a set of spherical particles fixed in space at random positions with prescribed statistical structural properties. Within this model one may describe the relaxation of concentration fluctuations of the adsorbed fluid by simply setting to zero the short-time mobility of one species (the porous matrix) in a theory of the dynamics of equilibrium colloidal mixtures, or by extending such dynamic theory to explicitly consider the porous matrix as a random external field, as recently done in the framework of mode coupling theory [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)]. Here we consider the first approach and employ the self-consistent generalized Langevin equation (SCGLE) theory of the dynamics of equilibrium colloidal mixtures, to describe the dynamics of the mobile component. We focus on the short- and intermediate-time regimes, which we compare with Brownian dynamics simulations involving a binary mixture with screened Coulomb interactions for two models of the average static structure of the matrix: a porous matrix constructed by quenching configurations of an equilibrium mixture in which both species were first equilibrated together, and a preexisting matrix with prescribed average structure, in which we later add the mobile species. We conclude that in both cases, if the correct static structure factors are provided as input, the SCGLE theory correctly predicts the main features of the dynamics of the permeating fluid.

In 2003 Biskup et al. [Commun. Math. Phys. 242, 137 (2003)] gave a rigorous proof for the behavior of equilibrium droplets in the two-dimensional (2D) spin-1/2 Ising model (or, equivalently, a lattice gas of particles) on a finite square lattice of volume $V$ with a given excess $\delta M\equiv M-M_0$ of magnetization compared to the spontaneous magnetization $M_0=m_{0}V$. By identifying a dimensionless parameter $\Delta \left(\delta M\right)$ and a universal constant ${\Delta }_c$, they showed in the limit of large system sizes that for $\Delta <{\Delta }_c$ the excess is absorbed in the background (“evaporated” system), while for $\Delta >{\Delta }_c$ a droplet of the minority phase occurs (“condensed” system). By minimizing the free energy of the system, they derived an explicit formula for the fraction $\lambda \left(\Delta \right)$ of excess magnetization forming the droplet. To check the applicability of the asymptotic analytical results to much smaller, practically accessible, system sizes, we performed several Monte Carlo simulations of the 2D Ising model with nearest-neighbor couplings on a square lattice at fixed magnetization $M$. Thereby, we measured the largest minority droplet, corresponding to the condensed phase in the lattice-gas interpretation, at various system sizes $\left(L=40,80,\dots ,640\right)$. With analytical values for the spontaneous magnetization density $m_0$, the susceptibility $\chi$, and the Wulff interfacial free energy density ${\tau }_W$ for the infinite system, we were able to determine $\lambda$ numerically in very good agreement with the theoretical prediction. Furthermore, we did simulations for the spin-1/2 Ising model on a triangular lattice and with next-nearest-neighbor couplings on a square lattice. Again finding a very good agreement with the analytic formula, we demonstrate the universal aspects of the theory with respect to the underlying lattice and type of interaction. For the case of the next-nearest-neighbor model, where ${\tau }_W$ is unknown analytically, we present different methods to obtain it numerically by fitting to the distribution of the magnetization density $P\left(m\right)$.

A recently proposed numerical third-order thermodynamic perturbation theory (TPT) is extended to its fifth-order counterpart. Extensive performance evaluation based on several model potentials indicates that the fifth-order version is generally superior to both the third-order version and a well-known second-order macroscopic compressibility approximation TPT, and is at least comparable to an accurate self-consistent Ornstein-Zernike integral equation approximation (SCOZA) with regard to predictions of varying bulk thermodynamic properties. A bulk second-order direct correlation function (DCF) free of numerical solution of a bulk OZ integral equation, is proposed, which, in combination with the framework of classical density functional theory (DFT) and a thermodynamic consistency condition, extends the uniform fifth-order TPT to nonuniform case. Grand canonical ensemble Monte Carlo simulation is carried out to produce density profile of a core-softened fluid confined in a hard spherical cavity, the resultant density profile is employed to evaluate the performance of the present nonuniform fifth-order TPT and a recently proposed third +second-order perturbation DFT. It is found that the present nonuniform fifth-order TPT is generally more accurate than the third+second-order perturbation DFT. Additional advantages of the present nonuniform fifth-order TPT over the third +second-order perturbation DFT is discussed.

We calculated tracer diffusion in a sheared suspension of non-Brownian rigid spheres and propose a numerical method based on a boundary element method and Stokesian dynamics method. We present details of the numerical method and examine the accuracy of the method. The limitation of semidiluteness is due to the accuracy of the tracer velocity calculation. The results show that the diffusivity of fluid tracers is greater than that of suspended spheres in the semidilute regime. The diffusivity of the velocity gradient direction is about threefold greater than that in the vorticity direction. Simple scaling demonstrates that the diffusivity of fluid tracers increases with the square of the volume fraction of spheres in the semidilute regime, which is confirmed numerically.

A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. Following Carleson and Makarov [L. Carleson and N. Makarov, J. Anal. Math. 87, 103 (2002)], the evolution of the fingers is studied with use of the deterministic Loewner equation. The method is then extended to study the growth in a linear channel with reflecting sidewalls. One- and two-finger solutions are found and analyzed. It turns out that the presence of the walls has a significant influence on the shapes of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.

The adsorption geometry of various gases on top of a ${\text{C}}_{60}$ monolayer is investigated. The potential energy experienced by an adsorbate atom in the vicinity of a ${\text{C}}_{60}$ molecule consists of Lennard-Jones interactions integrated over the spherical surface of the molecule. The adsorption potential exhibits strongly attractive sites which lead to a commensurate phase. The next adsorption sites are assumed on the basis of the symmetries of the triangular ${\text{C}}_{60}$ array. The competition between different adsorption phases is solved by energy minimization. The onset pressure of each phase is computed and compared with experimental data for Kr on top of a ${\text{C}}_{60}$ monolayer.

The quasibound states of a particle in an inverted-Gaussian potential interacting with an intense laser field are studied using complex coordinate scaling and Floquet theory. The dynamics of the driven system is different depending on whether the driving field frequency is less than or greater than the ionization frequency. As the laser field strength is increased, a new quasibound state emerges as the result of a pitchfork bifurcation in the classical phase space. Changes in the time-averaged “dressed potential” appear related to this bifurcation and provide additional confirmation of the role of the bifurcation on the emergence of a new quasibound state. The Husimi plots of the quasibound state residues reveal strong support on the periodic orbits of the bifurcation at frequencies above the ionization frequency.

Small networks of chaotic units which are coupled by their time-delayed variables are investigated. In spite of the time delay, the units can synchronize isochronally, i.e., without time shift. Moreover, networks cannot only synchronize completely, but can also split into different synchronized sublattices. These synchronization patterns are stable attractors of the network dynamics. Different networks with their associated behaviors and synchronization patterns are presented. In particular, we investigate sublattice synchronization, symmetry breaking, spreading chaotic motifs, synchronization by restoring symmetry, and cooperative pairwise synchronization of a bipartite tree.

The response of a fluid to a stationary force in the presence of membranes has been studied. Two different geometries of membrane systems are considered: two parallel flat membranes and a nearly spherical vesicle. In the case of a force acting between two parallel membranes, an induced velocity both between and behind the membranes is found. Between the membranes, at large distances from the application point, the induced velocity decays with the distance as $1/r$, more slowly than between two solid walls where it decays as $1/r^2$, and similar to the decay in an unconfined liquid. Behind the membrane interface, the flow does not have a component normal to the membranes, and the normal component of the force does not affect the flow in this region. In the case of spherical symmetry, expressions for the flow both inside and outside the membrane vesicle are found in terms of spherical harmonics. We discuss the applications of our results to Brownian motion of particles in the system and the possibility of measuring the membrane internal viscosity.

We present analytical and numerical studies of the phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic transverse translation (wandering) of the low-amplitude breather between the chains and the one-chain-localization of the high-amplitude breather. These two modes of coupled nonlinear excitations, which involve a large number of anharmonic oscillators, can be mapped onto two solutions of a single pendulum equation, detached by a separatrix mode. We also show that these two regimes of coupled phase-coherent breathers are similar and are described by a similar pair of equations to the two regimes in the nonlinear tunneling dynamics of two weakly linked interacting (nonideal) Bose-Einstein condensates. On the basis of this profound analogy, we predict a tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around $\frac{\pi }{2}\mathrm{mod}\pi$. We also show that the magnitude of the static displacements of the coupled chains with nonlinear localized excitation, induced by the cubic term in the intrachain anharmonic potential, scales approximately as the total vibrational energy of the excitation, either a one- or two-chain one, and does not depend on the interchain coupling. This feature is also valid for a narrow stripe of several parallel-coupled nonlinear chains. We also study two-chain breathers which can be considered as bound states of discrete breathers, with different symmetry and center locations in the coupled chains, and bifurcation of the antiphase two-chain breather into the one-chain one. Bound states of two breathers with different commensurate frequencies are found in the two-chain system. Merging of two breathers with different frequencies into one breather in two coupled chains is observed. Wandering of the low-amplitude breather in a system of several, up to five, coupled nonlinear chains is studied, and the dependence of the wandering period on the number of chains is analytically estimated and compared with numerical results. The delocalizing transition of a one-dimensional (1D) breather in the 2D system of a large number of parallel-coupled nonlinear oscillator chains is described, in which the breather, initially excited in a given chain, abruptly spreads its vibrational energy in the whole 2D system upon decreasing the breather frequency or amplitude below the threshold one. The threshold breather frequency is above the cutoff phonon frequency in the 2D system, and the threshold breather amplitude scales as the square root of the interchain coupling constant. The delocalizing transition of the discrete vibrational breather in 2D and 3D systems of parallel-coupled nonlinear oscillator chains has an analogy with the delocalizing transition for Bose-Einstein condensates in 2D and 3D optical lattices.

Electromagnetic wave properties in the presence of a thin or thick coating on a cylinder are investigated. The theoretical treatment starts from the formulation of electromagnetic fields in all regions where the coating and the core are allowed to rotate. The angular velocities of the core and coating can be different and even antidirectional. The present general approach can be applied to a wide range of specific cases such as rotating and stationary and left-handed and right-handed core-coating combinations. In particular, the optical resonances due to the surface plolaritons and morphology-dependent resonances are examined. Because of the rotation, the resonances are found to shift, and the effects of velocity on such phenomena are investigated. The backscattering can thus be controlled to achieve suppression or enhancement by using proper metamaterial coatings. Physical insights as well as the numerical results are presented.

In this paper the formalism of the electromagnetic inverse source theory is used to investigate radiation enhancement due to antenna substrates. Particular attention is given to sources that are confined within a spherical volume and are embedded within two nested spheres of arbitrary materials. Emphasis is given to the special case when the two nested spheres are made up of materials with oppositely signed constitutive parameters. The analysis comprises forward, or radiation, characterization for a given configuration as well as inverse-theoretic characterization. The forward characterization is focused on the singular-value spectrum of the linear source-to-field mapping relevant to each configuration while the inverse-theoretic characterization is performed via the so-called “minimum-energy” sources capable of generating a prescribed exterior field. The derived formulation is based on constrained optimization and multipole theory. Importantly, it is non-antenna-specific. Thus, this formulation enables fair comparison of different substrate configurations by comparing optimal radiation in each configuration (i.e., the “best” in each one), as governed by a formally tractable source-energy cost function that is physically motivated by Ohmic loss control. The derived theory is accompanied by numerical results illustrating the effects on radiation enhancement of particular substrate designs.

Shear viscosities of supercritical nitrogen have been measured to 573 K and 7 GPa (70 kbars). Measurements were made in a diamond-anvil cell with a rolling-ball technique. Individual isotherms are well fitted by a modified Doolittle equation. The data demonstrate a close relation between viscosities and excess entropy; this relation is further explored for the systems argon, oxygen, carbon dioxide, sodium, cesium, and a Lennard-Jones fluid.

Two types of alternating morphology transitions have been observed in crystallization of $\mathrm{N}{\mathrm{H}}_4\mathrm{Cl}$ on agar plates. One is the alternating morphology transitions between dense branching morphology and sparse branching morphology, and the other is the alternating morphology transitions between dense branching morphology and zigzag branching morphology. The appearance of them is found to depend on the mass proportion of agar to $\mathrm{N}{\mathrm{H}}_4\mathrm{Cl}$ in the initial solution and the relative humidity. It is suggested that both the two alternating morphology transitions result from the oscillation of solute concentration in front of the growing interface caused by the competition of crystal growth and solute transfer at a moderate mass proportion. Which one of them occurs depends on the relative humidity, which controls the supersaturation.

The Ornstein-Zernike equation is applied to nematic colloids with up-down symmetry to determine how the electrostatic analogy and other phenomenological results appear in molecular theory. In contrast to phenomenological approaches, the molecular theory does not assume particular boundary conditions (anchoring) at colloidal surfaces. For our molecular parameters the resulting anchoring appears to be realistic, neither rigid nor infinitely weak. For this case, the effective force between a colloidal pair at large separation remains essentially constant over the entire region of nematic stability. We show that a simple van der Waals approximation gives a potential of mean force that in some important aspects is similar to the phenomenological results obtained in the limit of weak anchoring; at large separations the potential varies as ${\Sigma }^8$, where $\Sigma$ is the colloidal diameter. In contrast, the more sophisticated mean spherical approximation yields a ${\Sigma }^6$ dependence consistent with phenomenological calculations employing rigid boundary conditions. We show that taking proper account of the correlation (or magnetic coherence) length $\xi$ inherent in the nematic sample is essential in an analysis of the $\Sigma$ dependence. At infinite $\xi$ the leading $\Sigma$ dependence is ${\Sigma }^6$, but this shifts to ${\Sigma }^8$ when $\xi$ is finite. The correlation length also influences the orientational behavior of the effective interaction. The so-called quadrupole interaction that determines the long-range behavior at infinite $\xi$ transforms into a superposition of screened “multipoles” when $\xi$ is finite. The basic approach employed in this paper can be readily applied to a broad range of physically interesting systems. These include patterned and nonspherical colloids, colloids trapped at interfaces, and nematic fluids in confined geometries such as droplets.

We have studied the phase separation of a binary mixture of a polymer and a nematic liquid crystal at a dilute polymer concentration. Various types of regular self-assemblies of polymer droplets such as branched chains and zigzag chains have been observed in addition to the previously reported straight chains. The kinetic process of the self-assembly is dominated by the transformations of a topological defect accompanied by a droplet in addition to the simple growth of the droplet. The spontaneous transformation from a ring defect (Saturn-ring defect) to a point defect (dipole) is an essential process in forming a straight chain composed of droplets with the same size. We also find that the transformations are induced by a nearby droplet with a point defect. This leads to a wide size distribution of droplets in a chain cluster and results in a branched chain. The difference in the chaining mechanisms is discussed using an electrostatic analogy. We also clarify that the symmetry breaking in the assembly is governed by the direction in which the cell containing the binary mixture is rubbed.

We report an observation and mechanism of spontaneous periodic modulations of the nematic director close to the temperature $T_{NA}$ of a nematic-to-smectic-$\mathit{A}$ phase transition if the surface alignment slightly differs from a pure homeotropic one. Stripe domains appear in the nematic phase about one degree above $T_{NA}$ and persist into the Sm$\mathit{A}$ phase. The instability of the homogeneous state with respect to stripe domains is shown to be related to a very large bend constant which is much larger than the twist and splay elastic constants. The instability mechanism consists of reduction of the highly energetic bend deformation, induced by small surface director tilts, at the expense of a spontaneous periodic splay-twist modulation. Using smallness of the twist-to-bend and splay-to-bend elastic constant ratios, the critical condition of the instability and the modulation period are found analytically. Both the experimentally obtained and theoretically predicted domain period scales very closely to a square root of the cell thickness.

In cell culture, when cells are inoculated into fresh media, there can be a period of slow (or lag phase) growth followed by a transition to exponential growth. This period of slow growth is usually attributed to the cells’ adaptation to a new environment. However, we argue that, based on observations of shaken suspension culture of Dictyostelium discoideum, a model single-cell eukaryote, this transition is due to a density effect. Attempts to demonstrate the existence of implicit cell signaling via long-range diffusible messengers (i.e., soluble growth factors) through cell-medium separation and microfluidic flow perturbation experiments produced negative results. This, in turn, led to the development of a signaling model based on direct cell-to-cell contacts. Employing a scaling argument for the collision rate due to fluid shear, we reasonably estimate the crossover density for the transition into the exponential phase and fit the observed growth kinetics.