In gyro-traveling-wave devices, several waves can be excited at different cyclotron harmonics simultaneously. This paper analyzes the interaction between three waves synchronous with gyrating electrons at different cyclotron harmonics in two relativistic gyro-amplifier configurations; viz., gyro-traveling-wave tubes and gyrotwystrons. Two types of nonlinear interactions are considered: (a) excitation of two waves at cyclotron harmonics by a wave excited at the fundamental resonance, and (b) excitation of a wave at the fundamental resonance and another wave at the third harmonic by a wave excited at the second cyclotron harmonic. The effect of the overlapping of electron cyclotron resonances on the performance of relativistic gyrodevices is investigated as well.

We present an investigation of the modulational instability of partially coherent signals in electrical transmission lines. Starting from the modified Ginzburg-Landau equations and the Wigner-Moyal representation, we derive a nonlinear dispersion relation for the modulational instability. It is found that the effect of signal broadbandness reduces the growth rate of the modulational instability.

We derive the multi-scaling of probability distributions of multi-particle configurations for the binary reaction-diffusion system $A+A\to \varnothing$ in $d⩽2$ and for the ternary system $3A\to \varnothing$ in $d=1$. For the binary reaction we find that the probability $P_t(N,\mathrm{\Delta }V)$ of finding $N$ particles in a fixed volume element $\mathrm{\Delta }V$ at time $t$ decays in the limit of large time as $(\ln t∕t{)}^N(\ln t{)}^{-N(N-1)∕2}$ for $d=2$ and $t^{-Nd∕2}{t}^{-N(N-1)\epsilon ∕4+\mathcal{O}\left({\epsilon }^2\right)}$ for $d<2$. Here $\epsilon =2-d$. For the ternary reaction in one dimension we find that $P_t(N,\mathrm{\Delta }V)\sim \left(\frac{\ln t}{t}{)}^{N∕2}\right(\ln t{)}^{-N(N-1)(N-2)∕6}$. The principal tool of our study is the dynamical renormalization group. We compare predictions of $\epsilon$ expansions for $P_t(N,\mathrm{\Delta }V)$ for a binary reaction in one dimension against the exact known results. We conclude that the $\epsilon$ corrections of order two and higher are absent in the previous answer for $P_t(N,\mathrm{\Delta }V)$ for $N=1,2,3,4$. Furthermore, we conjecture the absence of ${\epsilon }^2$ corrections for all values of $N$.

We present a coupled-dipole treatment of radiation dynamics in the weak-coupling regime in a finite three-dimensional photonic crystal structure. The structure is discretized in real space and the self-consistent local field is computed. We illustrate the computation of radiation dynamics by calculating the spontaneous emission rate for a source located in a defect cavity inside a slab photonic crystal structure. We compute the cavity spectral response, the near-field modal structure, and the far-field radiation pattern of the microcavity. We also discuss our results in light of the recent experimental near-field observations of the optical modes of a photonic crystal microcavity.

We study the propagation of incoherent accessible solitons in strongly nonlocal media with arbitrary response function. Based on the linear propagation equation and the mutual coherence function approach, we obtain an exact analytical solution of such incoherent accessible solitons. The solitons radius is related to the total power as well as the coherence characteristics of the incoherent beam. We find that there is not a threshold for incoherent solitons exist in strongly nonlocal media because the model is linear. Evolution behaviors of the solitons width and the coherence radius are also described when the solitons undergo linear harmonic oscillation.

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction. It has been also shown numerically that the well-known turnover feature can be restored from our model.

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size $t$. We compute the disorder average distributions of the local time, the inverse local time, the occupation time, and the inverse occupation time and show that in many cases disorder modifies the behavior drastically.

In this paper we present results of structural studies of compacting experimental systems of ductile grains in two and three dimensions. The high precision of our two-dimensional experiments enables a detailed study of the evolution of coordination numbers and local crystalline arrangements as a function of the packing fraction. The structure in both dimensions deviates considerably from that of hard disks and spheres, although geometrically, crystalline arrangements dominate on a local scale (in two dimensions). In three dimensions, the evolution of the coordination number is compared to experimental packings of hard and ductile grains from the literature. This comparison shows that the evolution of coordination number with packing fraction is not unique for ductile systems in general, but must depend on rheology and grain size.

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the patterns, as well as their gap distributions. The particles added to the cluster can follow either ballistic trajectories, with probability $P_{\mathrm{ba}}$, or random ones, with probability $P_{\mathrm{rw}}=1-P_{\mathrm{ba}}$. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of $P_{\mathrm{ba}}$ continuously increases from $d_f\approx 1.72$ (DLA dimensionality) for $P_{\mathrm{ba}}=0$ to $d_f\approx 2$ (BA dimensionality) for $P_{\mathrm{ba}}=1$. However, the lacunarity and the active zone width exhibit a distinct behavior: they are convex functions of $P_{\mathrm{ba}}$ with a maximum at $P_{\mathrm{ba}}\approx 1∕2$. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{\mathrm{ba}}$ and rapidly vanishes for $P_{\mathrm{ba}}>1∕2$, in agreement with recent results concerning the asymptotic scaling of DLA clusters.

We report here a self-organized electroless deposition of copper in an ultrathin layer of $\mathrm{Cu}\mathrm{S}{\mathrm{O}}_4$ electrolyte. Microscopically the branching rate of the copper deposits is significantly decreased, forming an array of smooth polycrystalline filaments. Compared with a conventional electrodeposition system, no macroscopic electric field is involved and the thickness of the electrolyte layer is greatly decreased. Therefore the electroless deposition takes place in a nearly ideal, two-dimensional diffusion-limited environment. We suggest that restriction of the thickness of the electrolyte film is responsible for the generation of smoother branches of the electrodeposits. Our data also show that even in a diffusion-limited scenario the aggregate morphology is not necessarily very ramified and fractal-like.

We have studied the phase sequence and physical properties of an asymmetric bent-core material with a chiral rigid cholesteryl moiety, and a flexible achiral alkyl side chain at the other end. The combination of the achiral bent core with the chiral cholesteryl unit results in properties different from those of both the usual calamitic and bent-core materials. We find that the presence of the bent core unit induces a wide-temperature-range optically isotropic (probably BPIII) mesophase between the isotropic and cholesteric (chiral nematic) phases. Below the cholesteric phase a ferroelectric smectic-$C^{*}$ structure occurs in which the bent-core units do not seem to form a polar close packing.

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.

We develop the theory of the $k$-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the $k$-core percolation is an unusual, hybrid phase transition with a jump emergence of the $k$-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the $k$-core, explain the meaning of the order parameter for the $k$-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called “corona” of the $k$-core plays a crucial role (corona is a subset of vertices in the $k$-core which have exactly $k$ neighbors in the $k$-core). It turns out that the $k$-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the $k$-core may result in the collapse of a vast region of the $k$-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the $k$-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.

Simulated mixing rates of the Rayleigh-Taylor instability for miscible fluids with physical mass diffusion are shown to agree with experiment; for immiscible fluids with physical values of surface tension the numerical data lie in the center of the range of experimental values. The simulations are based on an improved front tracking algorithm to control numerical surface tension and on improved physical modeling to allow physical values of mass diffusion or surface tension. Compressibility, after correction for variable density effects, has also been shown to have a strong influence on mixing rates. In summary, we find significant dependence of the mixing rates on scale breaking phenomena. We introduce tools to analyze the bubble merger process and confirm that bubble interactions, as in a bubble merger model, drive the mixing growth rate.

We studied a nematic liquid crystal (LC) cylinder under the action of an axial electric field ${\mathbf{E}}_0$. Elaborate modeling of the free energy leads to the conclusion that the configuration of the molecules is “escaped radial” for low $E_0$; a phase transition, however, occurs for a critical value $E_c$, the configuration becoming axial for $E_0>E_c$. From these results, the position-dependent dielectric tensor is determined and the photonic band (PB) structure is calculated for a photonic crystal of LC cylinders. It is shown that by varying $E_0$ a PB gap can be fully tuned from open to closed. Also, switching to a supercritical field can give rise to interesting polarization and directional effects in the propagation of light.

Stochastic acceleration, defined in terms of a stochastic equation of motion for the acceleration, is derived from a Hamiltonian model. A free particle is coupled bilinearly to a harmonic bath through the particle’s momentum and coordinate. Under appropriate conditions, momentum coupling induces velocity diffusion which is not destroyed by the spatial coupling. Spatial-momentum coupling may induce spatial subdiffusion. The thermodynamic equilibrium theory presented in this paper does not violate the second law of thermodynamics, although the average velocity squared of the particle may increase in time without bound.

We report on studies of dynamic self-assembled structures induced by a vertical alternating magnetic field in an ensemble of magnetic particles suspended on a liquid surface. We find the formation of nontrivially ordered dynamic snakelike objects in a certain range of field magnitudes and frequencies. In order to probe the properties of the “snakes,” we study their magnetic response to in-plane magnetic field applied at different angles with respect to its axis. The segments of the snake exhibit long-range antiferromagnetic ordering mediated by the surface waves, while each segment is composed of ferromagnetically aligned chains of microparticles. We propose a simple phenomenological model where the effect of surface waves is replaced by an effective exchange interaction to describe the observations. In the framework of the proposed model, the effective exchange constant corresponding to different regimes of magnetic driving was extracted from the experimental data.

Several aspects of the dynamics of a granular two-dimensional (2D) packing of disks slowly tilted until the system loses stability and an avalanche takes place are discussed. The evolution of the system, constructed with monodisperse disks placed on a thin cell, is studied by image analysis. As in the 3D case (packing of spheres), the system undergoes several rearrangements of different magnitude before the avalanche takes place. For thick systems, not only are small rearrangements detected but also displacements of large clusters of disks are observed in the bulk and on the free surface of the packing. In particular, characteristic angles and the avalanche mass were determined for samples of different heights. On thick systems, velocity fields of large rearrangements are presented and changes in the internal structure of the packing produced by these rearrangements are analyzed. It is found that the main effects of rearrangements is to increase the disorder of the system. Also, as the disorder of the system increases its stability threshold decreases.

The interaction and pair correlation function of weakly charged colloidal particles in quasi-one-dimensional colloid-polymer systems are determined by enhanced video microscopy and digital image analysis. The pair correlation function is found to depend not only on the polymer concentration, but also on the degree of confinement; in particular, it depends on whether the channel width is such that mutual passage of the colloid particles is possible or not. These findings are compared with exact results on short-range order in linear continuous systems.

We determine membrane capacitance, $C$ as a function of dc voltage for the human embryonic kidney (HEK) cell. $C$ was calculated from the admittance, $Y$, obtained during a voltage ramp when the HEK cell was held in whole-cell patch-clamp configuration. $Y$ was determined at frequencies of 390.625 and $781.25\mathrm{Hz}$ from the measured current, $i$ obtained with a dual-sinusoidal stimulus. We find that the fractional increase in the capacitance, $C$ is small $(<1\%)$ and grows with the square of the voltage, $\Psi$. $C$ can be described by: $C=C\left(0\right)(1+\alpha {(\Psi +{\psi }_s)}^2)$ [where $C\left(0\right)$: Capacitance at $0\text{volts}$, ${\psi }_s$: Difference in surface potential between cytoplasmic and extracellular leaflets and $\alpha$: Proportionality constant]. We find that $\alpha$ and ${\psi }_s$ are 0.120 $(\pm 0.01){\mathrm{V}}^{-2}$ and $-0.073$ $(\pm 0.017)\mathrm{V}$ in solutions that contain ion channel blockers and 0.108 $(\pm 0.29){\mathrm{V}}^{-2}$ and $-0.023$ $(\pm 0.009)\mathrm{V}$ when $10\mathrm{mM}$ sodium salicylate was added to the extracellular solution. This suggests that salicylate does not affect the rate at which $C$ grows with $\Psi$, but reduces the charge asymmetry of the membrane. We also observe an additional linear differential capacitance of about $(-46{\mathrm{fFV}}^{-1})$ in about 60% of the cells, this additional component acts simultaneously with the quadratic component and was not observed when salicylate was added to the solution. We suggest that the voltage dependent capacitance originates from electromechanical coupling either by electrostriction and/or Maxwell stress effects and estimate that a small electromechanical force $(\approx 1\mathrm{pN})$ acts at physiological potentials. These results are relevant to understand the electromechanical coupling in outer hair cells (OHCs) of the mammalian cochlea, where an asymmetric bell-shaped $C$ versus $\Psi$ relationship is observed upon application of a similar field. Prestin, a membrane protein expressed in OHCs is required to observe this function. When we compare the total charge contributions from HEK cell membrane ($7\times {10}^4$ electrons, $10\mathrm{pF}$ cell) with that determined for prestin transfected cells (up to $5\times {10}^6$ electrons) we conclude that the charge contributions from the collective motion of membrane proteins and lipids in the field is dwarfed relative to that when prestin is present. We suggest that the capacitance-voltage relationships should be similar to that observed for HEK cells for OHCs that do not express prestin in their membranes.