Using computer simulations, we studied the diffusion and structural relaxation in equilibrium smectic liquid-crystal bulk phases of parallel hard spherocylinders. These systems exhibit a non-Gaussian layer-to-layer diffusion due to the presence of periodic barriers and transient cages and show remarkable similarities with the behavior of out-of-equilibrium supercooled liquids. We detect a very slow interlayer relaxation dynamics over the whole density range of the stable smectic phase which spans a time interval of four time decades. The intrinsic nature of the layered structure yields a hopping-type diffusion which becomes more heterogeneous for higher packing fractions. In contrast, the in-layer dynamics is typical of a dense fluid with a relatively fast decay. Our results on the dynamic behavior agree well with that observed in systems of freely rotating hard rods but differ quantitatively as the height of the periodic barriers reduces to zero at the nematic-smectic transition for aligned rods, while it remains finite for freely rotating rods.

Monte Carlo simulation has been performed in a two-dimensional modified $XY$-model first proposed by Domany et al. [Phys. Rev. Lett. 52, 1535 (1984)] The cluster algorithm of Wolff has been used and multiple histogram reweighting is performed. The first-order scaling behavior of the quantities such as specific heat and free-energy barrier are found to be obeyed accurately. While the lowest-order correlation function was found to decay to zero at long distance just above the transition, the next-higher-order correlation function shows a nonzero plateau.

A reaction-Cattaneo equation with fluctuating relaxation time of the diffusive flux has been explored. It has been shown that depending on the strength of fluctuations, the dynamical system exhibits new oscillatory solutions as a result of Hopf and double Hopf bifurcations leading to spatiotemporal patterns. This analysis has been applied to two model nonlinear systems.

Due to various technological and medical demands, several methods for controlling the dynamical behavior of coupled oscillators have been developed. In the present study, we develop a method to control the individual phase relationship between coupled oscillators, in which multilinear feedback is used to modify the interaction between the oscillators. By carrying out a simulation, we show that the phase relationship can be well controlled by using the proposed method and the control is particularly robust when the target coupling function is selected properly.

The interference is considered of guided polariton modes in a two-port ring waveguide composed of dielectric nanospheres. The dependence of the guided polariton intensity on the relative orientation of the input and output channels is investigated. It is shown that, if the frequency of the external light source corresponds to one of the resonant modes of the waveguide ring segment, the guided polariton may be treated as two optical beams running along the ring segment in the opposite directions and interfering with each other. The multisphere Mie scattering formalism is used. The dipole approximation is shown to grasp the essence of physics. Our simple interpretation of the results is obtained in terms of scalar waves. The applications of the interference revealed in the manuscript are discussed as well.

Starting from microscopic molecular-dynamics (MD) simulations of constrained Lennard-Jones (LJ) clusters (with constant radius of gyration $R_g$), we construct two mesoscopic models [Langevin dynamics and dissipative particle dynamics (DPD)] by coarse graining the LJ clusters into single particles. Both static and dynamic properties of the coarse-grained models are investigated and compared with the MD results. The effective mean force field is computed as a function of the intercluster distance, and the corresponding potential scales linearly with the number of particles per cluster and the temperature. We verify that the mean force field can reproduce the equation of state of the atomistic systems within a wide density range but the radial distribution function only within the dilute and the semidilute regime. The friction force coefficients for both models are computed directly from the time-correlation function of the random force field of the microscopic system. For high density or a large cluster size the friction force is overestimated and the diffusivity underestimated due to the omission of many-body effects as a result of the assumed pairwise form of the coarse-grained force field. When the many-body effect is not as pronounced (e.g., smaller $R_g$ or semidilute system), the DPD model can reproduce the dynamic properties of the MD system.

A set of rectangular lattice Boltzmann methods for fluid flows is developed. It is shown that reformulating local equilibrium distribution functions can result in the rectangular lattice Boltzmann models without the aid of an interpolation for shallow water equations, Navier-Stokes equations, and axisymmetric flow equations. In addition, schemes for correct incorporation of force terms into the models are proposed for simulations of flows involving forces in practice. The methods completely retain the innate kinetic features and the simple procedure of the standard lattice Boltzmann method with an additional benefit of being suitable for rectangular lattices at little extra computational cost. The methodology is illustrated and validated through its application to different flow problems, demonstrating the potential power of the models.

We have developed a theoretical formulation for evaluating the nonadiabatic electron-transfer (ET) rate constant in condensed medium which takes into account both inelastic electron tunneling and nuclear quantum effects. The derived formula allows us to calculate the ET rate as a function of the free-energy gap between the ET donor and acceptor states using the information on the spectral density associated with environmental polarization fluctuation and the temporal correlation function of electronic tunneling matrix element. Model calculations have been performed illustratively.

Optical scattering spectra are recorded in situ on flowing colloidal polymeric nanocomposites which are sheared into photonic crystals at $150°\text{C}$ using a high-pressure quartz-cell multipass rheometer. Broadband spectroscopy of the resonant Bragg scattering peak allows the direct observation of crystal formation and melting of monodisperse core-shell particles. A range of flow conditions of this solventless, highly viscous melt reveals four distinct regimes of crystal growth and decay which match a simple rheological model. Extraction of crystal thickness, order and lattice spacing are validated by one-dimensional electromagnetic simulations.

By introducing a functional of the reduced density matrix, we generalize the definition of a quantum entropy which incorporates the indistinguishability principle of a system of identical particles. With the present definition, the principle of quantum maximum entropy permits us to solve the closure problem for a quantum hydrodynamic set of balance equations corresponding to an arbitrary number of moments in the framework of extended thermodynamics. The determination of the reduced Wigner function for equilibrium and nonequilibrium conditions is found to become possible only by assuming that the Lagrange multipliers can be expanded in powers of ${\hslash }^2$. Quantum contributions are expressed in powers of ${\hslash }^2$ while classical results are recovered in the limit $\hslash \to 0$.

We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or “space charge”) near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern layer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplification by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin-DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulas for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and superlimiting currents beyond the transition time, where the DL expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the superlimiting current beyond the diffusion-limiting current.

Langmuir monolayers provide an important system for the investigation of the intramolecular structure and intermolecular ordering of organic and bio-organic macromolecular amphiphiles at an interface between polar and nonpolar media, e.g., the liquid-gas interface. Specular x-ray and neutron reflectivity have contributed substantially to these investigations. However, these reflectivity techniques are generally limited by the absence of crucial phase information, the relatively small contribution of the amphiphile to the scattering-length density contrast across the interface, and the relatively limited range of momentum transfer available perpendicular to the interface. Although several procedures have been developed to provide model-independent solutions to the phase problem, there remains a limited ability to distinguish features of slightly differing contrast (i.e., the “sensitivity”) as well as their minimum allowable separation (i.e., the “spatial resolution”) along the length of the scattering-length density profile derived from the reflectivity data via solution to the phase problem. Here, we demonstrate how the well-known interferometric approach can be extended to the structural investigation of otherwise unperturbed Langmuir monolayers of these amphiphiles to provide a direct solution to the phase problem and importantly, substantially enhance both the sensitivity and the spatial resolution in the derived profiles.

We study the morphological evolution of strained islands in growing crystal films by use of a continuum description including wetting, elasticity, and deposition. We report different nonlinear regimes following the elastic instability and tuned by the flux. Increasing the flux, we first find an annealinglike dynamics, then a slower but nonconventional ripening followed by a steady regime, while the island density continuously increases. The islands develop spatial correlations and ordering with a narrow two-peaked distance distribution and ridgelike clusters of islands at high flux.

A theory of radiation absorption by dielectric mixtures is presented. The coarse-grained formulation is based on the wave-vector-dependent correlation functions of molecular dipoles of the host polar liquid and a density structure factor of the solutes. A nonlinear dependence of the dielectric absorption coefficient on the solute concentration is predicted and originates from the mutual polarization of the liquid surrounding the solutes by the collective field of the solute dipoles aligned along the radiation field. The theory is applied to terahertz absorption of hydrated saccharides and proteins. While the theory gives an excellent account of the observations for saccharides, without additional assumptions and fitting parameters, experimental absorption coefficient of protein solutions significantly exceeds theoretical calculations with dipole moment of the bare protein assigned to the solute and shows a peak against the protein concentration. A substantial polarization of protein’s hydration shell, resulting in a net dipole moment, is required to explain the disagreement between theory and experiment. When the correlation function of the total dipole moment of the protein with its hydration shell from numerical simulations is used in the analytical model, an absorption peak, qualitatively similar to that seen in experiment, is obtained. The existence and position of the peak are sensitive to the specifics of the protein-protein interactions. Numerical testing of the theory requires the combination of dielectric and small-angle scattering measurements. The calculations confirm that “elastic ferroelectric bag” of water shells observed in previous numerical simulations is required to explain terahertz dielectric measurements.

Periodic pillarlike microstructures can be created from initially flat polymer films via the electrohydrodynamic instabilities. Those patterns, however, are metastable. Our experimental observations show that the average pillar size increases slowly after linear growth. Major coarsening events then take place over times several orders of magnitude longer than the linear growth time. For all fill ratios, a logarithmic time dependence of the average pillar size can be identified, i.e., $⟨S⟩\propto \text{ln}t$. Thicker films, however, have faster coarsening rates than thinner films. Linear stability analysis of the pseudosteady states reveals two major coarsening mechanisms, collision and Ostwald ripening, which can also be identified from experimental images. We then reduce the original partial differential equation (PDE) into a pair of ODEs, which govern the interaction between pillars due to the above two coarsening mechanisms. From this, a logarithm scaling law is obtained for both low and high fill ratios and the coarsening rate is slower for lower fill ratios, consistent with experimental observations. We also find that arrays with more uniform sizes tend to start coarsening later, but they coarsen faster than more “disperse” arrays, which could be possibly utilized in experiments for controlling the onset and speed of coarsening. The logarithm scaling in the electrohydrodynamic coarsening phenomenon, which differs from coarsening in spinodal decomposition and dewetting of thin liquid films, is due to the significant nonlinear effect of Maxwell stresses and geometric confinement on the disjoining pressure at both top and bottom electrodes.

Equilibrium and motion of a contact line are viewed as analogs of phase equilibrium and motion of an interphase boundary. This point of view makes evident the tendency to minimization of the length of the contact line at equilibrium. The concept of line tension is, however, of limited applicability, in view of a qualitatively different relaxation response of the contact line, compared to a two-dimensional curve. Both the analogy and qualitative distinction extend to a nonequilibrium situation arising due to coupling with reversible substrate modification. Under these conditions, the contact line may suffer a variety of chemocapillary instabilities (fingering, traveling, and oscillatory), similar to those of dissipative structures in nonlinear nonequilibrium systems. The preference order of the various instabilities changes, however, significantly due to a different way the interfacial curvature is relaxed.

A wide family of methods is described for sampling in the canonical ensemble. The Bulgac-Kusnezov method is generalized to include a more complicated coupling structure and stochastic perturbations. It is shown that a controlled fluctuation of the potential surface or force field in a molecular model may be used as part of a sampling method (instead of the more standard friction or driving term). Numerical experiments demonstrate that the family includes methods that are effective for recovering canonical averages.

We evaluated the transport of polymeric particles internalized into living cancer cells. The mean-square displacement demonstrates superdiffusion with a scaling exponent of 1.25. Scaling exponents of a range of displacement moments are bilinear with moment order, exhibiting slopes of 0.6 and 0.8. Thus, we present experimental evidence of strong anomalous diffusion. Bilinearity indicates that particle motion is composed of subdiffusive regimes separated by active yet nonballistic flights. We discuss the results in terms of particle interactions with their microenvironment.

We report charge inversion within a nanoscopic biological protein ion channel in salts of multivalent ions. The presence of positive divalent and trivalent counterions reverses the cationic selectivity of the OmpF channel, a general diffusion porin located in the outer membrane of E. coli. We discuss the conditions under which charge inversion can be inferred from the change in sign of the measured quantity, the channel zero current potential. By comparing experimental results in protein channels whose charge has been modified after site-directed mutagenesis, the predictions of current theories of charge inversion are critically examined. It is emphasized that charge inversion does not necessarily increase with the bare surface charge density of the interface and that even this concept of surface charge density may become meaningless in some biological ion channels. Thus, any theory based on electrostatic correlations or chemical binding should explicitly take into account the particular structure of the charged interface.