The near-resonant beat wave excitation of an electron plasma wave (EPW) can be employed for generating the trains of few-femtosecond electromagnetic (EM) pulses in rarefied plasmas. The EPW produces a comoving index grating that induces a laser phase modulation at the difference frequency. As a result, the cascade of sidebands red and blue shifted by integer multiples of the beat frequency is generated in the laser spectrum. The bandwidth of the phase-modulated laser is proportional to the product of the plasma length, laser wavelength, and amplitude of the electron density perturbation. When the beat frequency is lower than the electron plasma frequency, the redshifted spectral components are advanced in time with respect to the blueshifted ones near the center of each laser beat note. The group velocity dispersion of plasma compresses so chirped beat notes to a few-laser-cycle duration thus creating a train of sharp EM spikes with the beat periodicity. Depending on the plasma and laser parameters, chirping and compression can be implemented either concurrently in the same, or sequentially in different plasmas. Evolution of the laser beat wave and electron density perturbations is described in time and one spatial dimension in a weakly relativistic approximation. Using the compression effect, we demonstrate that the relativistic bistability regime of the EPW excitation [G. Shvets, Phys. Rev. Lett. 93, 195004 (2004)] can be achieved with the initially subthreshold beat wave pulse.

The quantum Monte Carlo (QMC) technique is an extremely powerful method to treat many-body systems. Usually the quantum Monte Carlo method has been applied in cases where the interaction potential has a simple analytic form, like the $1∕r$ Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a nontrivial problem. Obtaining the potential from any grid-based finite-difference method for every walker and every step is infeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo calculation within the overall quantum Monte Carlo scheme. We have developed a modified “walk on spheres” algorithm using Green’s function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated with variational, diffusion, and other Monte Carlo techniques. We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.

An elementary proof is shown on the necessary existence of negative coefficients in splitting methods of order $p⩾3$.

We assess the relative importance of spatial congestion and lowered temperature in the slowing dynamics of supercooled glycerol near the glass transition. We independently vary both volume $V$ and temperature $T$ by applying high pressure and monitor the dynamics by measuring the dielectric susceptibility. Our results demonstrate that both variables are control variables of comparable importance. However, a generalization of the concept of fragility of a glass-former shows that the dynamics are quantitatively more sensitive to fractional changes in $V$ than $T$. We identify a connection between the fragility and a recently proposed density-temperature scaling which indicates that this conclusion holds for other liquids and polymers.

We analyze theoretically and experimentally the influence of current noise on the longitudinal mode hopping dynamics of a bulk semiconductor laser. It is shown that the mean residence times on each mode have different sensitivity to external noise added to the bias current. In particular, an increase of the noise level enhances the residence time on the longitudinal mode that dominates at low current, evidencing the multiplicative nature of the stochastic process. A two-mode rate equation model for a semiconductor laser is able to reproduce the experimental findings. Under a suitable separation of the involved time scales, the model can be reduced to a one-dimensional bistable potential system with a multiplicative stochastic term related to the current noise strength. The reduced model clarifies the influence of the different noise sources on the hopping dynamics.

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

Monte Carlo computer simulations of a quasi two-dimensional (2D) dipolar fluid at low and intermediate densities indicate that the structure of the fluid is well described by an ideal mixture of self-assembling clusters. A detailed analysis of the topology of the clusters, of their internal energy and of their size (or mass) distributions is used to obtain approximations to their partition functions. Within the scope of these approximations, the results of this work suggest that the 2D dipolar fluid undergoes a phase transition from a dilute phase characterized by a number of disconnected clusters to a condensed phase characterized by a network or spanning (macroscopic) cluster that includes most of the particles in the system.

In a contact-density chain-growth study we investigate the solubility-temperature pseudophase diagram of a lattice polymer in a cavity with an attractive surface. In addition to the main phases of adsorbed and desorbed conformations we find numerous subphases of collapsed and expanded structures.

A theoretical description of the dynamics of DNA molecules and actin filaments in solution as measured experimentally by fluorescence correlation spectroscopy is provided and compared to recent experimental results. Particular attention is paid to the contribution of the intramolecular dynamics to the fluorescence correlation function. Using a semiflexible chain model, a theoretical expression is presented for the fluorescence correlation spectroscopy correlation function. The dependence of this function on various model parameters, such as chain length, persistence length, and fluorescence label density, is discussed. Our investigations show that the intramolecular dynamics provides a significant contribution or even dominates the correlation function as soon as the longest intramolecular relaxation time significantly exceeds the shortest experimentally accessible time. Correspondingly, the shape of the correlation function changes considerably. Approximate analytical expressions are provided, which are in qualitative agreement with the exact theoretical solutions as well as experimental results, for both DNA and actin filaments. Our approach is in agreement with the predictions of the Zimm model, in the limit of very flexible polymers, as well as the predictions of semiflexible polymer models with respect to the intramolecular dynamics in solution.

Epilepsy is a dynamic disease in which self-organization and emergent structures occur dynamically at multiple levels of neuronal integration. Therefore, the transient relationship within multichannel electroencephalograms (EEGs) is crucial for understanding epileptic processes. In this paper, we show that the global relationship within multichannel EEGs provides us with more useful information in classifying two different epilepsy types than pairwise relationships such as cross correlation. To demonstrate this, we determine the global network structure within channels of the scalp EEG based on the minimum spanning tree method. The topological dissimilarity of the network structures from different types of temporal lobe epilepsy is described in the form of the divergence rate and is computed for 11 patients with left (LTLE) and right temporal lobe epilepsy (RTLE). We find that patients with LTLE and RTLE exhibit different large scale network structures, which emerge at the epoch immediately before the seizure onset, not in the preceding epochs. Our results suggest that patients with the two different epilepsy types display distinct large scale dynamical networks with characteristic epileptic network structures.

Using analytical and numerical methods we demonstrate that the pulse propagation equations accounting for the quantum description of the Raman transition and for the optical Kerr nonlinearity have a multiparameter family of nontopological solitary wave solutions. We study properties of these solitons and report the transition from stable to unstable regimes of propagation. We also discuss the feasibility of observation of these structures in gas filled hollow-core photonic crystal fibers.

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod’s model for cultural dissemination.

We present experimental results on fast-electron energy deposition into solid targets in ultrahigh intensity laser-matter interaction. X-ray $K\alpha$ emission spectroscopy with absolute photon counting served to diagnose fast-electron propagation in multilayered targets. Target heating was measured from ionization-shifted $K\alpha$ emission. Data show a $200\mathrm{\mu }\mathrm{m}$ fast-electron range in solid Al. The relative intensities of spectrally shifted $\mathrm{Al}K\alpha$ lines imply a mean temperature of a few tens of eV up to a $100\mathrm{\mu }\mathrm{m}$ depth. Experimental results suggest refluxing of the electron beam at target rear side. They were compared with the predictions of both a collisional Monte Carlo and a collisional-electromagnetic, particle-fluid transport code. The validity of the code modeling of heating in such highly transient conditions is discussed.

Plane-wave representations are used to formulate the exact solutions to frequency-domain and time-domain sources illuminating a magnetodielectric slab with complex permittivity $ϵ\left(\omega \right)$ and permeability $\mu \left(\omega \right)$. In the special case of a line source at $z=0$ a distance $d<L$ in front of an $L$-wide lossless double-negative (DNG) slab with $\kappa \left({\omega }_0\right)=ϵ\left({\omega }_0\right)∕{ϵ}_0=\mu \left({\omega }_0\right)∕{\mu }_0=-1$, the single-frequency $\left({\omega }_0\right)$ solution exhibits not only “perfectly focused” fields for $z>2L$ but also divergent infinite fields in the region $2d<z<2L$. In contrast, the solution to the same lossless $\kappa \left({\omega }_0\right)=-1$ DNG slab illuminated by a sinusoidal wave that begins at some initial time $t=0$ (and thus has a nonzero bandwidth, unlike the single-frequency excitation that begins at $t=-\infty$) is proven to have imperfectly focused fields and convergent finite fields everywhere for all finite time $t$. The proof hinges on the variation of $\kappa \left(\omega \right)$ about $\omega ={\omega }_0$ having a lower bound imposed by causality and energy conservation. The minimum time found to produce a given resolution is proportional to the estimate obtained by G. Gómez-Santos, [Phys. Rev. Lett. 90, 077401 (2003)]. Only as $t\to \infty$ do the fields become perfectly focused in the region $z>2L$ and divergent in the region $2d<z<2L$. These theoretical results, which are confirmed by numerical examples, imply that divergent fields of the single-frequency solution are not caused by an inherent inconsistency in assuming an ideal lossless $\kappa \left({\omega }_0\right)=-1$ DNG material, but are the result of the continuous single-frequency wave (which contains infinite energy) building up infinite reactive fields during the infinite duration of time from $t=-\infty$ to the present time $t$ that the single-frequency excitation has been applied. An analogous situation occurs at the resonant frequencies of a lossless cavity. A single-frequency (zero-bandwidth) source inside the cavity produces infinite fields at a resonant frequency, whereas the same source turned on at time $t=0$ (so that it has a nonzero bandwidth) produces finite fields.

Multispecies interacting charged particles in a two-dimensional quadratic trap are studied. The ground-state configurations for different particle and species numbers are obtained by molecular dynamics simulation. It is found that particles with similar mass-to-charge ratio tend to populate a common shell, whose location depends on the particle mass-to-charge ratio, and that the greater the latter, the closer are the particles to the center of the trap. This scaling for the ground-state configuration is independent of the total particle and species numbers in the system.

The small-scale rheology of Carbopol ETD 2050, a polymer gel with a yield stress, is studied as a function of polymer concentration by measuring the diffusion of submicron-sized spherical fluorescent particles suspended in gel. Dynamic light scattering is used to determine the mean-squared displacement $⟨r^2\left(\tau \right)⟩$ of the particles as a function of lag time $\tau$. Fluorescence microscopy is used to track the particle trajectories directly, from which $⟨r^2\left(\tau \right)⟩$ and the van Hove correlation function are determined. From our results we calculate the microrheological viscous and elastic moduli of the material. The two techniques cover complementary ranges of $\tau$ and $⟨r^2\left(\tau \right)⟩$ and give results that agree well. The microrheological moduli are substantially smaller than the bulk values as determined by conventional shear rheometry. The bulk viscoelastic behavior is dominated by the elastic modulus, while at low enough concentrations and high enough frequencies the microrheological response is predominantly viscous. These results will be discussed in the context of the gel structure.

The influence of a random-anisotropy- (RA-) type disorder on the phase separation of the nematogen–non-nematogen mixture is studied. A combination of the phenomenological Landau–de Gennes and Flory-Huggins theories is used. We assume that the non-nematogen component (i.e., impurity) enforces the RA disorder to the enclosing thermotropic liquid-crystal (LC) phase. The Imry-Ma argument is used according to which the lower-temperature phase exhibits a domain-type pattern. The disorder strength is measured in terms of the dimensionless parameter $\Lambda$. We consider the case in which the LC molecules and impurities mix in the isotropic phase for $\Lambda =0$. The impurities enforce a finite degree of orientational ordering even in the high-temperature paranematic phase. In the low-temperature phase they give rise to a domain-type structure, resulting in the distorted nematic (speronematic) phase. We show that the onset of orientational ordering increases the phase separation tendency. The RA field, however, opposes this tendency. With increasing value of $\Lambda$ the difference between the paranematic and speronematic ordering decreases. Consequently the structure of the phase-separated pattern can be much more complex in comparison to the $\Lambda =0$ case.

Using transmission electron microscopy, analytical modeling, and detailed numerical simulations, the iridescence observed from the comb rows of the ctenophore Beroë cucumis was investigated. It is shown that the changing coloration which accompanies the beating of comb rows as the animal swims can be explained by the weakly-contrasted structure of the refractive index induced by the very coherent packing of locomotory cilia. The colors arising from the narrow band-gap reflection are shown to be highly saturated and, as a function of the incidence angle, cover a wide range of the visible and ultraviolet spectrum. The high transparency of the structure at the maximal bioluminescence wavelength is also explained.

Capillary networks are essential in vertebrates to supply tissues with nutrients. Experiments of in vitro capillary formation show that endothelial cells randomly spread on a gel matrix autonomously organize to form vascular networks with a characteristic length independent of the initial cell density. A mathematical model based on free cell migration and on cell cross-talk mediated by soluble chemical factors has been recently proposed and explains the main dynamical and geometrical properties of the networks. We extend this model introducing the action of repulsive factors and we show that their activity results in a larger degree of reorganization of cellular matter and in more robust control over the size of the growing vascular network.