We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static Euclidean space, starting from a simple class of infinite “shuffled lattice” initial conditions. These are obtained by applying independently to each particle on an infinite perfect lattice a small random displacement, and are characterized by a power spectrum (structure factor) of density fluctuations which is quadratic in the wave number $k$, at small $k$. For a specified form of the probability distribution function of the “shuffling” applied to each particle, and zero initial velocities, these initial configurations are characterized by a single relevant parameter: the variance ${\delta }^2$ of the “shuffling” normalized in units of the lattice spacing $\ell$. The clustering, which develops in time starting from scales around $\ell$, is qualitatively very similar to that seen in cosmological simulations, which begin from lattices with applied correlated displacements and incorporate an expanding spatial background. From very soon after the formation of the first nonlinear structures, a spatiotemporal scaling relation describes well the evolution of the two-point correlations. At larger times the dynamics of these correlations converges to what is termed “self-similar” evolution in cosmology, in which the time dependence in the scaling relation is specified entirely by that of the linearized fluid theory. Comparing simulations with different $\delta$, different resolution, but identical large scale fluctuations, we are able to identify and study features of the dynamics of the system in the transient phase leading to this behavior. In this phase, the discrete nature of the system explicitly plays an essential role.

We report on a detailed characterization of complex dielectric response of Na-DNA aqueous solutions by means of low-frequency dielectric spectroscopy $(40\mathrm{Hz}–110\mathrm{MHz})$. Results reveal two broad relaxation modes of strength $20<\Delta {\epsilon }_{\mathrm{LF}}<100$ and $5<\Delta {\epsilon }_{\mathrm{HF}}<20$, centered at $0.5\mathrm{kHz}<{\nu }_{\mathrm{LF}}<70\mathrm{kHz}$ and $0.1\mathrm{MHz}<{\nu }_{\mathrm{HF}}<15\mathrm{MHz}$. The characteristic length scale of the low-frequency (LF) process, $50<L_{\mathrm{LF}}<750\mathrm{nm}$, scales with DNA concentration as $c_{\mathrm{DNA}}^{-0.29\pm 0.04}$ and is independent of the ionic strength in the low added salt regime. Conversely, the measured length scale of the LF process does not vary with DNA concentration but depends on the ionic strength of the added salt as $I_s^{-1}$ in the high added salt regime. On the other hand, the characteristic length scale of the high-frequency (HF) process, $3<L_{\mathrm{HF}}<50\mathrm{nm}$, varies with DNA concentration as $c_{\mathrm{DNA}}^{-0.5}$ for intermediate and large DNA concentrations. At low DNA concentrations and in the low added salt limit the characteristic length scale of the HF process scales as $c_{\mathrm{DNA}}^{-0.33}$. We put these results in perspective regarding the integrity of the double stranded form of DNA at low salt conditions as well as regarding the role of different types of counterions in different regimes of dielectric dispersion. We argue that the free DNA counterions are primarily active in the HF relaxation, while the condensed counterions play a role only in the LF relaxation. We also suggest theoretical interpretations for all these length scales in the whole regime of DNA and salt concentrations and discuss their ramifications and limitations.

Translocation of a single stranded DNA (ssDNA) through an $\alpha$-hemolysin channel in a lipid membrane driven by applied transmembrane voltage $V$ was extensively studied recently. While the bare charge of the ssDNA piece inside the channel is approximately $12$ (in units of electron charge) measurements of different effective charges resulted in values between one and two. We explain these challenging observations by a large self-energy of a charge in the narrow water filled gap between ssDNA and channel walls, related to large difference between dielectric constants of water and lipid, and calculate effective charges of ssDNA. We start from the most fundamental stall charge $q_s$, which determines the force $F_s=q_{s}V∕L$ stalling DNA against the voltage $V$ ($L$ is the length of the channel). We show that the stall charge $q_s$ is proportional to the ion current blocked by DNA, which is small due to the self-energy barrier. Large voltage $V$ reduces the capture barrier which DNA molecule should overcome in order to enter the channel by $\mid q_c\mid V$, where $q_c$ is the effective capture charge. We expressed it through the stall charge $q_s$. We also relate the stall charge $q_s$ to two other effective charges measured for ssDNA with a hairpin in the back end: the charge $q_u$ responsible for reduction of the barrier for unzipping of the hairpin and the charge $q_e$ responsible for DNA escape in the direction of hairpin against the voltage. At small $V$ we explain reduction of the capture barrier with the salt concentration.

We derive an expression that represents the physical behavior of a polysaccharide molecule as it is stretched from the entropic region, through one or more ring conformational transformations, into the Hookean regime. The model adapts existing models in order to accommodate one or more force-induced conformational transformations of the glycan rings and is based on the concept of equilibrium between the clicked (longer conformers) and unclicked states. This equilibrium is determined by the Gibbs energy difference between these two states which is perturbed in favor of the clicked states by the force applied to the molecule. The derived expression is used to generate force-extension curves for model polymers and can illustrate the effect of the Gibbs energy for each transformation on the shape of these curves. It is also used to fit the force-extension curves of polysaccharides to obtain the Gibbs energy differences between the conformers. Good agreement was found between this model and experimental data on carboxymethylamylose, dextran, alginate, and pectin.

A modified Tomlinson equation with fractal potential is studied. The effective potential is numerically generated and its mesoscopic structure is gradually adjusted to different scales by a number of Fourier modes. It is shown that with the change of scale the intensity of velocity-dependent damping in an effective Langevin equation can be gradually substituted by an equivalent constant “dry friction.” For smooth macrosopic surfaces the effective equation completely reduces to the well known Coulomb law.

Diffusion of an asymmetric object is characterized by its translational and rotational diffusion coefficients. Until now, anisotropic diffusion studies have been based on ensemble averages. Here we present a theoretical basis for the analysis of the trajectories of a single particle with anisotropic diffusion coefficients. We discuss the relevance of this method for motion of biomolecules in the membrane of living cells.

The diffusion-controlled dissolution of a spherical particle consisting in two epitaxially stressed solid phases of a substitutional binary alloy in contact with an undersaturated solution is investigated. A linear stability analysis of the solid-liquid interface demonstrates that a morphological instability of the particle may occur due to the epitaxial stress generated by the spherical precipitate embedded in the solid matrix, the liquid pressure being neglected. The critical radius of the particle below which the interface is unstable is determined and the conditions for the roughness development are discussed.

In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a sphere. In both cases, we also discuss the case of two targets, including splitting probabilities and conditional mean first-passage times. In addition, we study the higher-order moments and the full distribution of the first-passage time. These results significantly extend our earlier contribution [Condamin et al., Phys. Rev. Lett. 95, 260601 (2005)].

We have developed an exactly solvable model that makes it possible to calculate the density profile of polymers filled inside a chemically nonuniform structure that consists of alternating layers that have different affinity for polymers. It is shown that the mean density of polymers in this layered structure is in excess relative to that in the uniform system that has the same average affinity for polymers. The average excess density of polymers in the layered structure is calculated as a function of their degree of polymerization, layer thickness, and affinities of the layers for polymers. The developed theoretical model is shown to have relevance to several experimentally important chemically nonuniform layered systems like microphase separated diblock copolymers and selective mixed brushes.

Vector potential formulation and parametric studies of electromagnetic scattering problems of a sphere characterized by the rotationally symmetric anisotropy are studied. Both $\overline{\mathit{ϵ}}$ and $\overline{\mathit{\mu }}$ tensors are considered herein, and four elementary parameters are utilized to specify the material properties in the structure. The field representations can be obtained in terms of two potentials, and both TE (TM) modes (with respect to $\widehat{\mathit{r}}$) inside (outside) the sphere can be derived and expressed in terms of a series of fractional-order (in a real or complex number) Ricatti-Bessel functions. The effects due to either electric anisotropy ratio $(A_e={ϵ}_t∕{ϵ}_r)$ or magnetic anisotropy ratio $(A_m={\mu }_t∕{\mu }_r)$ on the radar cross section (RCS) are considered, and the hybrid effects due to both $A_e$ and $A_m$ are also examined extensively. It is found that the material anisotropy affects significantly the scattering behaviors of three-dimensional dielectric objects. For absorbing spheres, however, the $A_e$ or $A_m$ no longer plays a significant role as in lossless dielectric spheres and the anisotropic dependence of RCS values is found to be predictable. The hybrid effects of $A_e$ and $A_m$ are considered for absorbing spheres as well, but it is found that the RCS can be greatly reduced by controlling the material parameters. Details of the theoretical treatment and numerical results are presented.

We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Lévy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Lévy white noise parameters. Depending on the value of the skewness $\beta$ of the Lévy noise, the escape can either become enhanced or suppressed: a negative asymmetry parameter $\beta$ typically yields a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index $\alpha$ that characterizes the jump length distribution of Lévy noise, exhibiting a marked discontinuity at $\alpha =1$. We find that the typical factor of 2 that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior versus time. Distinct non-exponential deviations occur, however, for low barrier heights.

On its opening day the London Millennium footbridge experienced unexpected large amplitude wobbling subsequent to the migration of pedestrians onto the bridge. Modeling the stepping of the pedestrians on the bridge as phase oscillators, we obtain a model for the combined dynamics of people and the bridge that is analytically tractable. It provides predictions for the phase dynamics of individual walkers and for the critical number of people for the onset of oscillations. Numerical simulations and analytical estimates reproduce the linear relation between pedestrian force and bridge velocity as observed in experiments. They allow prediction of the amplitude of bridge motion, the rate of relaxation to the synchronized state and the magnitude of the fluctuations due to a finite number of people.

We extend fluctuation theorems to a molecular refrigeration system that consists of Brownian particles in a heat bath under feedback control of their velocities. Such control can actively remove heat from the bath due to an entropy-pumping mechanism [Phys. Rev. Lett. 93, 120602 (2004)]. The presence of entropy pumping in an underdamped Brownian system modifies both the Jarzynski equality and the fluctuation theorems. We discover that the entropy pumping has a dual role of work and heat.

Within the Maxwell framework and using a transfer-matrix technique we have determined a general equation which governs the photonic band structure and the density of states of one-dimensional superlattices composed of two alternate layers characterized by different refractive indexes, which may take on positive as well as negative values. Besides the usual well-known results, we have found null-gap points for commensurate values of the optical path lengths of each layer. Furthermore, we have been able to characterize non-Bragg gaps that show up in frequency regions in which the average refractive index is null.

An improved scattering matrix method is developed to study a two-dimensional air-rigid sonic crystal with open resonant cavity, and the band structure and transmission properties are investigated. Numerical results show that both the band structure and the transmission coefficient are sensitive to the shape of the resonant cavity. The relationship between the resonant band gap and the shape of the resonant cavity is given. The high effective refractive index and the transmission ratio in the long wave range make such a system a good material for a sound lens.

Ultrafast magnetic resonance has been applied to measure the geometry of bubbles and slugs in a three-dimensional gas-solid two-phase flow. A bed of particles of diameter $0.5\mathrm{mm}$ were fluidized with gas velocities in the range of $0.08–0.26\mathrm{m}∕\mathrm{s}$. Bubbles were imaged in transverse as well as vertical planes with an acquisition time of down to $25\mathrm{ms}$ and a spatial resolution down to $1.7\mathrm{mm}$. Owing to the ultrafast character of these measurements, it is not only possible to evaluate correlations, e.g., for the bubble diameter, but also evaluate models of complex hydrodynamic phenomena, such as the splitting and coalescence of bubbles.

We present a computer simulation study on the crystalline phases of hard ellipsoids of revolution. For aspect ratios $⩾3$ the previously suggested stretched-fcc phase [Frenkel and Mulder, Mol. Phys. 55, 1171 (1985)] is replaced by a different crystalline phase. Its unit cell contains two ellipsoids with unequal orientations. The lattice is simple monoclinic. The angle of inclination of the lattice, $\beta$, is a very soft degree of freedom, while the two right angles are stiff. For one particular value of $\beta$, the close-packed version of this crystal is a specimen of the family of superdense packings recently reported [Donev et al., Phys. Rev. Lett. 92, 255506 (2004)]. These results are relevant for studies of nucleation and glassy dynamics of colloidal suspensions of ellipsoids.

Resonant activation and noise-enhanced stability were observed in an underdamped real physical system, i.e., Josephson tunnel junctions. With a weak sinusoidal driving force applied, the thermal activated escape from a potential well underwent resonancelike behaviors as a function of the driving frequency. The resonances also crucially depended on the initial condition of the system. Numerical simulations showed good agreement with the experimental results.

We propose a method for the global optimization of stochastic functions. During the course of the optimization, a probability distribution is built up for the location and the value of the global optimum. The concept of information entropy is used to make the optimization as efficient as possible. The entropy measures the information content of a probability distribution, and thus gives a criterion for decisions: From several possibilities we choose the one which yields the most information concerning location and value of the global maximum sought.

Recently Tao and Lan [Phys. Rev. E. 72, 041508 (2005)] experimentally reported that the rotation of a dielectric particle can reduce significantly the attracting interparticle force between the rotating dielectric particle and a stationary one in argon gas. We develop the Gu-Yu-Hui theory of relaxation [J. Chem. Phys. 116, 24 (2002)] to account for the Tao-Lan observations. Excellent agreement between the theoretical results and the Tao-Lan experimental data shows that the reduction in the attracting interparticle force is due to the effect of charge relaxation. We also show that the relaxation time of touching rotating particles can be accurately determined with the aid of the developed theory, for which, however, the well-known Maxwell-Wagner relaxation time is no longer valid.