We extend the insertion approach for calculating depletion potentials to the case of nonspherical solutes. We suggest to employ the recently developed curvature expansion of density profiles close to complexly shaped walls. The approximations introduced in the calculation by the use of the curvature expansion and of weight functions for nonspherical objects can be tested independently. As an application for our approach we calculate and discuss the depletion potential between two hard oblate ellipsoids in a solvent of hard spheres. For this system we calculate the entropic force and torque acting on the objects.

In our experiments, we investigate in situ the growth of three-dimensional xenon crystals into an undercooled pure melt. Experimental studies have been extended from undisturbed growth conditions to more realistic growth conditions. Methods to characterize the transient growth of sidebranches of dendrites have been developed. Two types of sidebranches have been identified: Sidebranches initiated by selective amplification of thermal noise (type $N$) and sidebranches induced by macroscopic perturbations (type $P$). Type $N$ sidebranches start to grow 3–7 tip radii behind the tip and are not correlated at the four fins. It has been verified that the sidebranch amplitude grows exponentially to $z^{2∕5}$ as predicted by Brener and Temkin [E. Brener and D. Temkin, Phys. Rev. E 51, 351 (1995)]. Type $P$ sidebranches are initiated by macroscopic perturbations. They start to grow at the tip and their amplitudes are significantly higher than the ones of type $N$ sidebranches. The growth of type $P$ sidebranches is symmetric at the four fins. The tip positions of type $P$ sidebranches separate from the tip shape of a dendrite at a distance of about $5R$ from the tip, while for type $N$ sidebranches this distance is about $10R$.

We have studied the hexatic-$B$–smectic-$A$ $\left(\mathrm{Hex}B\text{−}\mathrm{Sm}A\right)$ transition in $n$-hexyl-$4^{\prime }\text{−}n$-pentyloxybiphenyl-4-carboxylate (65OBC) by means of a high-resolution ac photopyroelectric (PPE) calorimetric technique. A procedure for the interpretation of the PPE data, which allows the detection of an internal heating source due to strain annealing and/or latent heat, has been applied. We have found that the strain present in the sample depends on the kinetics of formation of the smectic phase once the sample is cooled from the isotropic one. The strain field keeps memory of this kinetics and can be only partially annealed on decreasing the temperature or cycling it around the $\mathrm{Hex}\text{−}\mathrm{Sm}A$ transition. A reversible ordering-disordering process has been found at $T_c$ and has been explained in terms of the competition between the order parameter variation with temperature and the constraints imposed by the disorder. The results confirm that the transition has a weakly first-order character with a specific heat critical exponent that disagrees with the available theoretical predictions. Our data show the importance of the disorder in 65OBC and we tried to clarify what would be the consequence of this result in theoretical modeling devoted to solving the puzzle of the $\mathrm{Hex}B\text{−}\mathrm{Sm}A$ transition in this compound.

One of the major questions in complex network research is to identify the range of mechanisms by which a complex network can self organize into a scale-free state. In this paper we investigate the interplay between a fitness linking mechanism and both random and preferential attachment. In our models, each vertex is assigned a fitness $x$, drawn from a probability distribution $\rho \left(x\right)$. In Model A, at each time step a vertex is added and joined to an existing vertex, selected at random, with probability $p$ and an edge is introduced between vertices with fitnesses $x$ and $y$, with a rate $f(x,y)$, with probability $1-p$. Model B differs from Model A in that, with probability $p$, edges are added with preferential attachment rather than randomly. The analysis of Model A shows that, for every fixed fitness $x$, the network’s degree distribution decays exponentially. In Model B we recover instead a power-law degree distribution whose exponent depends only on $p$, and we show how this result can be generalized. The properties of a number of particular networks are examined.

We study the dynamics of two microfluidic droplets emitters placed in parallel. We observe complex dynamical behavior, including synchronization, quasiperiodicity, and chaos. This dynamics has a considerable impact on the properties of the resulting emulsions: chaotic and quasi-periodic regimes give rise to polydispersed emulsions with poorly controllable characteristics, whereas synchronized regimes generate well-controlled monodispersed emulsions. We derive a dynamical model that reproduces the trends observed in the experiment.

The interaction of electromagnetic radiation with free electrons in the presence of an active medium has some appealing outcomes. Among them is particle acceleration by stimulated emission of radiation (PASER). In its framework, energy stored in an active medium (microscopic cavities) is transferred directly to an $e$-beam passing through. We have developed a two-dimensional analytic model for the evaluation of the energy exchange occurring as a train of electron microbunches traverses a dilute resonant medium. Efficient interaction occurs at resonance—namely, when the frequency of the train matches the resonance frequency of the medium. It is shown that the energy exchange is $\gamma$ independent for relativistic energies and it drops dramatically with an increase of the beam’s radius. Based on this model, we have evaluated the relative change in the kinetic energy of a 0.1-nC $45\text{−}\mathrm{MeV}$ macrobunch traversing an excited ${\mathrm{CO}}_2$ gas mixture—the former being modulated at the ${\mathrm{CO}}_2$ laser wavelength. Good agreement is found between the theoretical predictions and the results of the PASER experiment performed recently at Brookhaven National Laboratory.

A general Hamiltonian suitable for perturbative analysis of rapidly accelerating beams is derived from first principles. With the proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, yet is able to take into account the rapid acceleration, rf focusing, magnetic focusing, and average space-charge forces in rf photoinjectors. From the linear Hamiltonian, the beam-envelope evolution is solved and analyzed, which better illuminates the invariant-envelope solution as well as the theory of emittance compensation. The third-order nonlinear Hamiltonian is derived and analyzed to some extent. To make the analysis systematic and self-contained, alternative derivations are given for the smoothed ponderomotive rf focusing and the transfer matrix of a rf cavity.

In this work we give an alternative method to calculate the transition probability densities (TPD) for the velocity space, phase space, and Smoluchowsky configuration space of a Brownian gas of charged particles in the presence of a constant magnetic field. Our proposal consists in transforming, by means of a rotation matrix, the Langevin equation of a charged particle in the velocity space into another velocity space where the behavior is quite similar to that of ordinary Brownian motion. A similar strategy is also applied to the phase-space. In consequence, in the transformed space both the Fokker-Planck and Fokker-Planck-Kramers equations are solved following Chandrasekhar’s methodology. Our results are compared with those obtained by Czopnik and Garbaczewski [Phys. Rev. E 63, 021105 (2001)].

Transitions in structural heterogeneity of colloidal depletion gels formed through short-range attractive interactions are correlated with their dynamical arrest. The system is a density and refractive index matched suspension of 0.20 volume fraction poly(methyl methacyrlate) colloids with the nonadsorbing depletant polystyrene added at a size ratio of depletant to colloid of 0.043. As the strength of the short-range attractive interaction is increased, clusters become increasingly structurally heterogeneous, as characterized by number-density fluctuations, and dynamically immobilized, as characterized by the single-particle mean-squared displacement. The number of free colloids in the suspension also progressively declines. As an immobile cluster to gel transition is traversed, structural heterogeneity abruptly decreases. Simultaneously, the mean single-particle dynamics saturates at a localization length on the order of the short-range attractive potential range. Both immobile cluster and gel regimes show dynamical heterogeneity. Non-Gaussian distributions of single particle displacements reveal enhanced populations of dynamical trajectories localized on two different length scales. Similar dependencies of number density fluctuations, free particle number, and dynamical length scales on the order of the range of short-range attraction suggests a collective structural origin of dynamic heterogeneity in colloidal gels.

Liquid-crystal phases with both solid and liquid characteristics are unique, since they exhibit chirality on both molecular and mesoscopic levels under special circumstances. We have studied binary composites formed by mixing of a chiral dimer (B-Ch), in which a bent core is covalently linked to a promesogenic cholesterol unit through a flexible spacer, and an achiral bent-core mesogen having two vicinal fluorine atoms (B-2F). The pure materials show smectic phases featuring ${\mathrm{C}}_2$ symmetry. The dimer B-Ch displays conventional chiral smectic C $\left({\mathrm{SmC}}^{*}\right)$ phase with a chirality—induced polarization $P_c\sim 30\mathrm{nC}∕{\mathrm{cm}}^2$, whereas B-2F possesses synclinic and anticlinic antiferroelectric “banana” smectic $\left(\mathrm{SmC}P\right)$ phase with a relatively high-polarization $\left(P_b\right)$ value of about $900\mathrm{nC}∕{\mathrm{cm}}^2$. Mixing these two materials we were able to measure $P_c$, and we have verified that the molecular chirality contributes to the polarization of banana phases only in synclinic configurations.

The depletion effect between two spherical colloidal particles in nonadsorbing polymer solutions is investigated using the self-consistent field theory. The density distributions of polymer segments, the depleted amount and depletion potential are calculated numerically in bispherical coordinates. The effects of chain length, bulk concentration, and solvency are also investigated. In the dilute regime the depleted amount and the depletion potential decrease as the two spherical particles approach to each other. The depth of interaction increases and the width of interaction varies slightly with increasing bulk concentrations. In the semidilute regime, with increasing bulk concentrations the width of interaction decreases and the depth of interaction increases. No distinct repulsive potential is observed in semidilute regime. However, at high concentration the depleted amount exhibits a barrier. The width and the depth of depletion potential increase with increasing the chain length and the solvency. The contact potential is proportional to the polymer concentration and almost independent on the solvency. In addition, the effect of depletion interaction on colloidal stability is analyzed.

The broadband conductive spectroscopy covering the range ${10}^{-2}\text{to}{10}^6\mathrm{Hz}$ has been employed to examine both the ionic and the segmental motions in polymer salt complexes (PSCs), consisting of polyethylene oxide (PEO), $\mathrm{Li}\mathrm{Cl}{\mathrm{O}}_4$, or $\mathrm{Li}\mathrm{C}{\mathrm{F}}_3\mathrm{S}{\mathrm{O}}_3$. The temperature dependence of dc conductivity has been analyzed using Vogel-Tamman-Fulcher (VTF) equation and the results suggest that the temperature dependence of the dc conductivity can be well described in terms of the free volume changes with temperature. The ac conductivity at low temperatures (below $223\mathrm{K}$) remains unchanged with the temperature, exhibiting nearly linear frequency dependence. This observation, not previously reported in polymers, indicates clearly that nearly constant loss (NCL) phenomenon, usually observed in glassy and ceramic ion conductors, is also operative in polymer electrolytes. Furthermore, a crossover from a NCL to cooperative ion hopping at higher temperatures in the frequency dependence of the conductivity has been observed. The analysis of the temperature dependence of both dc and ac conductivities demonstrates that there exists a direct correlation between the ionic conductivity and the segmental relaxation processes.

In this paper we describe how relativistic attosecond electron pulses could be produced in free space by ultrafast and ultraintense transverse magnetic (TM) laser beams. Numerical solutions of the time-dependent three-dimensional Maxwell-Lorentz equations reveal that electrons initially at rest at the waist of a multi-TW pulsed ${\mathrm{TM}}_{01}$ laser beam can be accelerated to multi-MeV energies. The use of a few-cycle laser beam and a compact initial electron cloud forces the particles to effectively interact with a single half-cycle of the laser field and form a pulse of attosecond duration.

The interaction between two parallel beams in one-dimensional discrete saturable systems has been investigated using lithium niobate nonlinear waveguide arrays. When the beams are separated by one channel and in phase it is possible to observe soliton fusion at low power levels. This result is confirmed numerically. By increasing the power, solitonlike propagation of weakly coupled beams occurs. When the beams are out-of-phase the most interesting numerically obtained result is the existence of oscillations which resemble the recently discovered Tamm oscillations.

We propose a simple equation for predicting self-diffusivity of fluids embedded in random matrices of identical, but dynamically frozen, particles (i.e., quenched-annealed systems). The only nontrivial input is the volume available to mobile particles, which also can be predicted for two common matrix types that reflect equilibrium and nonequilibrium fluid structures. The proposed equation can account for the large differences in mobility exhibited by quenched-annealed systems with indistinguishable static pair correlations, illustrating the key role that available volume plays in transport.

In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary Markov chain is linear in the number of steps. Three applications are discussed. A known result about entropy production is reproduced. A thermodynamic relation is derived for equilibrium systems with Metropolis dynamics. Finally, a link is made with recent results concerning a one-dimensional polymer model.

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species’ clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law’s exponent slightly differs from the individual-based model’s result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of $O\left(t^{-2∕3}\right)$.

The velocity distribution function of granular gases in the homogeneous cooling state as well as some heated granular gases decays for large velocities as $f\propto \exp (-\mathrm{const}\times v)$. That is, its high-energy tail is overpopulated as compared with the Maxwell distribution. At the present time, there is no theory to describe the influence of the tail on the kinetic characteristics of granular gases. We develop an approach to quantify the overpopulated tail and analyze its impact on granular gas properties, in particular on the cooling coefficient. We observe and explain anomalously slow relaxation of the velocity distribution function to its steady state.

We consider a liquid interface with different principal curvatures $\pm c$ and find that the mere presence of a spherical particle leads to a deformation field of quadrupolar symmetry; the corresponding “capillary quadrupole moment” is given by the ratio of the particle size and the curvature radius. The resulting pair interaction of nearby particles is anisotropic and favors the formation of aggregates of cubic symmetry. Since the single-particle trapping energy depends quadratically on curvature with a negative prefactor, a curvature gradient induces a lateral force that pushes the particles towards strongly curved regions of the interface. As an illustration we discuss the effects occuring on a catenoid.

We consider a coupled map lattice defined on a hypercube in $M$ dimensions, taken here as the information space, to model memory retrieval and information association by a neural network. We assume that both neuronal activity and spike timing may carry information. In this model the state of the network at a given time $t$ is completely determined by the intensity $y(\sigma ,t)$ with which the information pattern represented by the integer $\sigma$ is being expressed by the network. Logistic maps, coupled in the information space, are used to describe the evolution of the intensity function $y(\vec{\sigma },t)$ with the intent to model memory retrieval in neural systems. We calculate the phase diagram of the system regarding the model ability to work as an associative memory. We show that this model is capable of retrieving simultaneously a correlated set of memories, after a relatively long transient that may be associated to the retrieving of concatenated memorized patterns that lead to a final attractor.