Using a two-dimensional multiscale model based on the classical time-dependent density-functional theory for lattice systems we recently introduced, we numerically study the impact of elastic inhomogeneities on the growth of isolated inclusions in multiphase alloys. We demonstrate that the coupling between the overall interface structure (as determined by the shape of the inclusions) and the local, atomic-scale structure can be very large, and is able to significantly affect the behavior of inclusions during growth. Elasticity is shown to have a strong influence on the local energetics at interfaces, leading to shape modulations and kinetic faceting. Morphological and energetic changes induce oscillations in the chemical potential of the inclusions, opening the way to the stabilization of multi-inclusion microstructures, consistent with experiment. We demonstrate that the interface elastic misfit is a key parameter for controlling the strength of elastic effects.

Anisotropic diffusion of light was experimentally first observed in bulk nematic liquid crystals. The origin of anisotropy in such a system is due to the optical anisotropy of nematic liquid crystal and to anisotropic scattering of light from nematic orientational fluctuations. In polymer dispersed liquid crystals (PDLCs) anisotropic scatterers—i.e., nematic droplets—are embedded in an optically isotropic polymer. The anisotropy of diffusion of light in this system therefore depends only on the anisotropic scattering from a single nematic droplet and on the average orientation of the droplets in PDLCs. In the absence of an external field droplets in PDLCs are randomly oriented and diffusion of light is isotropic. In an external field the droplets are on average oriented in the direction of the external field and the diffusion of light becomes anisotropic. We calculated the diffusion tensor and expected anisotropy of the diffusion of light as a function of an external field, $kR$, and volume fraction using the theory developed for bulk nematic liquid crystals. Our calculations show that the anisotropy of diffusion tensor can have both the signs and that the magnitude of diffusion constants increase with increasing external field.

Seven model polydimethylsiloxane (PDMS) networks were obtained by hydrosilation of a difunctional vinyl-terminated PDMS prepolymer with a SiH-containing cross-linker. Viscoelastic experiments, completed by size exclusion chromatography and static light scattering experiments, were performed in order to study the influence of molecular parameters on the dynamic properties around the sol-gel threshold. The dynamic critical parameter $u$ was determined from experiments close to and above the sol-gel threshold. Our results show that the growth mechanism of PDMS clusters and the viscoelastic behavior are a function of the ratio $N∕N_e$, where $N$ and $N_e$ are, respectively, the numbers of Kuhn monomers between branch points and between entanglements. For $N∕N_e<1$, the growth mechanism of clusters is the critical percolation and $u=0.69$, and for $N∕N_e>1$, the growth mechanim of clusters is the diffusion-limited cluster aggregation and $u=0.76$.

The effect of an external applied lateral tension on the line tension between two domains of different thickness in a lipid bilayer membrane is calculated. The thick domain is treated as a liquid-ordered phase in order to model a raft in a biological membrane; the thin domain is considered a liquid-disordered phase to model the surrounding region. In our model, the monolayers elastically distort at the boundary to create a smooth rather than steplike boundary to avoid exposure of the hydrophobic interior of the thick raft to water. The energy of this distortion is described by the fundamental deformations of splay and tilt. This energy per unit length of boundary yields the line tension of the raft. Applying lateral tension alters the fundamental deformations such that line tension increases. This increase in line tension is larger when the spontaneous curvature of a raft is greater than that of the surround; if the spontaneous curvature of the raft is less than that of the surround, the increase of the line tension due to application of the lateral tension is more modest.

It is well known that for increasingly rarefied flow fields, predictions from continuum formulations, such as the Navier-Stokes equations, lose accuracy. The inclusion of higher-order terms, such as Burnett or high-order moment equations, could improve the predictive capabilities of such continuum formulations, but there has been only limited success. Here, we present a multiscale model. On the macroscopic level, the flow variables are updated based on the mass, momentum, and energy conservation through the fluxes. On the other hand, the fluxes are constructed on the microscopic level based on the gas-kinetic equation, which is valid in both continuum and near-continuum flow regimes. Based on this model, the nonequilibrium shock structure, Poiseuille flow, nonlinear heat conduction problems, and unsteady Rayleigh problem will be studied. In the near-continuum flow regime, the current gas-kinetic simulation is more efficient than microscopic methods, such as the direction Boltzmann solver and direct-simulation Monte Carlo method. In the continuum flow limit, the current formulation will go back to the gas-kinetic Navier-Stokes flow solver automatically.

Superdiffusion of two-dimensional (2D) liquids was studied using an equilibrium molecular dynamics simulation. At intermediate temperatures, the mean-squared displacement, probability distribution function (PDF), and velocity autocorrelation function (VACF) all indicate superdiffusion; the VACF has a long-time tail; and the PDF indicates no Lévy flights. These effects are predicted to occur in 2D dusty plasmas and other 2D liquids that can be modeled with a long-range repulsive potential.

We present a Hamiltonian formulation of coupled mode theory for scenarios in which the coupled modes are associated with different “parent structures,” such as two nearby waveguides. The relativistic nature of the photon leads to the complication that not any set of orthonormal modes can be used as a basis if the associated amplitudes are to satisfy canonical commutation relations. This difficulty is circumvented by the introduction of “dressed parent modes,” which are in fact seen to be the “coupled modes” of the system. While an exact solution of the linear problem within the restricted basis of interest formally must be found before these modes can be constructed, in practice they can be constructed directly from the modes of the parent structures. The approach can be applied to periodic parent structures, such as photonic crystal waveguiding structures, as well as to simpler waveguides. We illustrate the accuracy of the various approximations employed by studying two sample systems in detail. We derive the linear coupled mode equations, and show how the approach can be immediately generalized from the linear regime to treat problems in nonlinear quantum optics.

We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin-flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_{\chi }$ for the integrated response function, at variance with all the other exponents, is independent of temperature and of the presence of pinning. This universal character suggests a strict relation between $a_{\chi }$ and the topological properties of the networks, in analogy to what is observed on regular lattices.

Approximation formulas to predict values for bond percolation thresholds of periodic graphs make use of certain features of lattice graphs such as dimension and average degree. We show that a relationship exists between the average and second-moment of the degree of a graph and the average degree of its line graph. Using this relationship together with the well-known bond-to-site transformation between the bond percolation model on a graph and the site percolation model on its line graph, we create a new approximation formula that improves the accuracy of bond percolation threshold predictions.

Analytical models are developed for the translation and rotation of metallic rods in a uniform electric field. The limits of thin and thick electric double layers are considered. These models include the effect of stripes of different metals along the length of the particle. Modeling results are compared to experimental measurements for metallic rods. Experiments demonstrate the increased alignment of particles with increasing field strength and the increase in degree of alignment of thin versus thick electric double layers. The metal rods polarize in the applied field and align parallel to its direction due to torques on the polarized charge. The torque due to polarization has a second-order dependence on the electric field strength. The particles are also shown to have an additional alignment torque component due to nonuniform densities along their length. The orientation distributions of dilute suspensions of particles are also shown to agree well with results predicted by a rotational convective-diffusion equation.

An extensive study on the $(2+1)$-dimensional super-rough growth processes, described by a special class of linear growth equations, is undertaken. This special class of growth equations is of theoretical interests since they are exactly solvable and thus provide a window for understanding the intriguing anomalous scaling behaviors of super-rough interfaces. We first work out the exact solutions of the interfacial heights and the equal-time height difference correlation functions. Through our rigorous analysis, the detailed asymptotics of the correlation function in various time regimes are derived. Our obtained analytical results not only affirm the applicability of anomalous dynamic scaling ansatz but also offer a solid example for understanding a distinct universal feature of super-rough interfaces: the local roughness exponent is always equal to 1. Furthermore, we also perform some numerical simulations for illustration. Finally, we discuss what are the essential ingredients for constructing super-rough growth equations.

Velocity of propagation of electrical excitation in the heart is important for the understanding of complex arrhythmias such as ventricular fibrillation (VF). In this paper, we present a method to estimate the conduction velocity of electrical activation wavefronts that are defined to be a particular isovalue of any scalar field, such as electrical activation times, electrical phase, or indeed any other quantity that can be used to determine excitation wavefronts. This general method is based on tracking trajectories of material points that are assumed to be embedded within the wavefronts, whilst the direction of propagation is assumed to be perpendicular to the wavefront. We have derived an explicit expression for the conduction velocity in terms of the spatiotemporal gradients of the scalar field used to define wavefronts. Moreover, although it is often difficult to use activation times to compute conduction velocities during complex VF, we show that other scalar fields such as detrended voltage or electrical phase, which can faithfully represent the electrical activity during fibrillatory conduction, can be used to determine conduction velocities. We demonstrate the application of our method to determine conduction velocities from contact mapping recordings over the entire epicardial surface of the fibrillating pig heart.

We introduce Markov models for segmentation of symbolic sequences, extending a segmentation procedure based on the Jensen-Shannon divergence that has been introduced earlier. Higher-order Markov models are more sensitive to the details of local patterns and in application to genome analysis, this makes it possible to segment a sequence at positions that are biologically meaningful. We show the advantage of higher-order Markov-model-based segmentation procedures in detecting compositional inhomogeneity in chimeric DNA sequences constructed from genomes of diverse species, and in application to the E. coli K12 genome, boundaries of genomic islands, cryptic prophages, and horizontally acquired regions are accurately identified.

The size of particles that can be trapped in optical tweezers ranges from tens of nanometers to tens of micrometers. This size regime also includes large single molecules. Here we present experiments demonstrating that optical tweezers can be used to collect polyethylene oxide molecules suspended in water. The molecules that accumulate in the focal volume do not aggregate and therefore represent a region of increased molecule concentration, which can be controlled by the trapping potential. We also present a model that relates the change in concentration to the trapping potential. Since many protein molecules have molecular weights for which this method is applicable the effect may be useful in assisting nucleation of protein crystals.

We study the elasticity of cross-linked networks of thermally fluctuating stiff polymers. As compared to their purely mechanical counterparts, it is shown that these thermal networks have a qualitatively different elastic response. By accounting for the entropic origin of the single-polymer elasticity, the networks acquire a strong susceptibility to polydispersity and structural randomness that is completely absent in athermal models. In extensive numerical studies we systematically vary the architecture of the networks and identify a wealth of phenomena that clearly show the strong dependence of the emergent macroscopic moduli on the underlying mesoscopic network structure. In particular, we highlight the importance of the polymer length, which to a large extent controls the elastic response of the network, surprisingly, even in parameter regions where it does not enter the macroscopic moduli explicitly. Understanding these subtle effects is only possible by going beyond the conventional approach that considers the response of typical polymer segments only. Instead, we propose to describe the elasticity in terms of a typical polymer filament and the spatial distribution of cross-links along its backbone. We provide theoretical scaling arguments to relate the observed macroscopic elasticity to the physical mechanisms on the microscopic and mesoscopic scales.

We suggest a method for suppression of collective synchrony in an ensemble of all-to-all interacting units. The suppression is achieved by organizing an interaction between the ensemble and a passive oscillator. Technically, this can be easily implemented by a simple feedback scheme. The important feature of our approach is that the feedback signal vanishes as soon as the control is successful. The technique is illustrated by the simulation of a model of an isolated population of neurons. We discuss the possible application of the technique in neuroscience.

A growing number of experimental and theoretical works have been addressing various aspects of the viscous fingering formation in rotating Hele-Shaw cells. However, only a few of them consider the influence of Coriolis forces. The studies including Coriolis effects are mostly restricted to the high-viscosity-contrast limit and rely on either purely linear stability analyses or intensive numerical simulations. We approach the problem analytically and use a modified Darcy’s law including the exact form of the Coriolis effects to execute a mode-coupling analysis of the system. By imposing no restrictions on the viscosity contrast $A$ (dimensionless viscosity difference) we go beyond linear stages and examine the onset of nonlinearities. Our results indicate that when Coriolis effects are taken into account, an interesting interplay between the Reynolds number Re and $A$ arises. This leads to important changes in the stability and morphological features of the emerging interfacial patterns. We contrast our mode-coupling approach with previous theoretical models proposed in the literature.

Recent experiments demonstrate an efficient transformation of high intensity laser pulse into a relativistic electron beam with a very high current density exceeding ${10}^{12}\mathrm{A}{\mathrm{cm}}^{-2}$. The propagation of such a beam inside the target is possible if its current is neutralized. This phenomenon is not well understood, especially in dielectric targets. In this paper, we study the propagation of high current density electron beam in a plastic target using a particle-in-cell simulation code. The code includes both ionization of the plastic and collisions of newborn electrons. The numerical results are compared with a relatively simple analytical model and a reasonable agreement is found. The temporal evolution of the beam velocity distribution, the spatial density profile, and the propagation velocity of the ionization front are analyzed and their dependencies on the beam density and energy are discussed. The beam energy losses are mainly due to the target ionization induced by the self-generated electric field and the return current. For the highest beam density, a two-stream instability is observed to develop in the plasma behind the ionization front and it contributes to the beam energy losses.

A technique has been developed to derive the dynamic properties of an ensemble of particles in dusty plasmas by using fluorescent tracer particles. The tracers form an integral part of the entire dust system. The dynamic properties of the dust system is reconstructed from the motion of the tracer. This technique allows long-duration experiments and is applied to a two-dimensional Coulomb cluster where the flow field, intershell rotation, and stagnation points of the flow have been identified.

In the theoretical framework of the Floquet instability analysis we have investigated the onset instability of the one-dimensional pendulum array, a macroscopic expression of the Frenkel-Kontorova chain, subjected to vertical vibration after the continuum approximation. The Floquet instability calculation shows that the onset instability of the array always responds to the forcing frequency subharmonically. The theoretical predictions of the critical forcing conditions and onset instability waves have been validated by experiments. Good agreement between the theoretical calculations and experimental observations has been achieved for the onset instabilities with both long and short wavelengths.