We present a theoretical investigation of incoherent accessible white-light solitons in strongly nonlocal medium with noninstantaneous Kerr nonlinearity. This soliton has elliptic Gaussian intensity profile and anisotropic spatiotemporal coherence properties. For this soliton to exist, the spatial coherence distance should be larger for lower frequencies and shorter for higher frequencies. When the incident power differs from the critical value, we demonstrate the periodic harmonic oscillations of the accessible white-light solitons.

By means of singularity analysis, the integrability of a system of generalized coupled Hirota equations with parameter coefficients is tested. It is proven that the system passes the Painlevé test for integrability only in two distinct cases.

A procedure is proposed to construct highly accurate variational wave functions with large and very large numbers of basis functions. The procedure has a number of advantages in actual computations on parallel computer clusters. In particular, by using this procedure we have determined very accurate numerical values of the ground-state energies in the positronium ion ${\mathrm{Ps}}^{-}$ (or $e^{-}{e}^{+}{e}^{-}$) $(E=-0.262005070232980107770375\mathrm{a.u.})$ and hydrogen ion ${}^{\infty }\mathrm{H}^{-}$ $(E=-0.527751016544377196589759\mathrm{a.u.})$ The variational energies of the negative hydrogenlike ions (or ${\mathrm{H}}^{-}$-like ions) with the finite nuclear masses (${\mathrm{T}}^{-}$, ${\mathrm{D}}^{-}$, ${}^1\mathrm{H}^{-}$, and ${\mathrm{Mu}}^{-}$) are also presented. These energies are the best variational ground-state energies ever obtained for these ions.

The statistics of critical spin-spin correlation functions in Ising systems with nonfrustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to test for logarithmic corrections to pure power-law decay against distance. Fits of our data to conformal-invariance expressions, specific to logarithmic corrections to correlations on strips, give results with the correct sign, for the moments of order $n=0-4$ of the correlation-function distribution. We find an interval of disorder strength along which corrections to pure-system behavior can be decomposed into the product of a known $n$-dependent factor and an approximately $n$-independent one, in accordance with predictions. A phenomenological fitting procedure is proposed, which takes partial account of subdominant terms of correlation-function decay on strips. In the low-disorder limit, it gives results in fairly good agreement with theoretical predictions, provided that an additional assumption is made.

Using a straightforward theoretical approach, we show that an ensemble of dyes with a simple first-order photobleaching kinetics yields a power-law decaying emission intensity in a heterogeneous excitation field in bulk fluorescence experiments. Our theoretical considerations are experimentally confirmed for two distinct classes of small organic fluorophores represented by the classical laser dye rhodamine-6G on glass in air and the cyanine dye DiI(C18) in a thin polymethylmethacrylate film. Our results provide evidence that the time course of bleaching in a bulk sample in general does not allow derivation of the properties of survival times of individual quantum systems.

We investigate experimentally the formation and the transportation of a heap formed by granular materials in an inclined and vertically vibrated container. We observe how the transport velocity of heap up the container is related to the driving acceleration, the driving frequency, and the inclination of the container. An empirical law which governs the transport velocity of the heap is presented. An analogous experiment was performed with a heap-shaped Plexiglas block. We propose that the compressive force resulted from pressure gradient in ambient gas plays a crucial role in enhancing and maintaining a heap, and the ratchet effect causes the movement of the heap.

We report results of a systematic experimental study of interactions between charged polystyrene (PS) latex spheres at a water-air interface. Optical observations of stable bonded particle clusters and formation of circular chainlike structures at the interface demonstrate that the interaction potential is of dipole origin. Atomic force microscopy (AFM) is used to examine the distribution of charge groups on the colloidal surface. AFM phase images show patchy domains of size $\sim 100\mathrm{nm}$ on the particle surface, indicating that the surface charge distribution of the PS spheres is not uniform, as is commonly believed. Such patchy charges can introduce fluctuating in-plane dipoles, leading to an attraction at short interparticle separations. A theoretical analysis is given to explain the mechanism for attractions between like-charged particles at the interface.

Attempts to identify a species on the basis of its DNA sequence on purely statistical grounds have been formulated for more than a decade. The most prominent of such genome signatures relies on neighborhood correlations (i.e., dinucleotide frequencies) and, consequently, attributes species identification to mechanisms operating on the dinucleotide level (e.g., neighbor-dependent mutations). For the examples of Mus musculus and Rattus norvegicus we analyze short- and intermediate-range statistical correlations in DNA sequences. These correlation profiles are computed for all chromosomes of the two species. We find that with increasing range of correlations the capacity to distinguish between the species on the basis of this correlation profile is getting better and requires ever shorter sequence segments for obtaining a full species separation. This finding suggests that distinctive traits within the sequence are situated beyond the level of few nucleotides. The large-scale statistical patterning of DNA sequences on which such genome signatures are based is thus substantially determined by mobile elements (e.g., transposons and retrotransposons). The study and interspecies comparison of such correlation profiles can, therefore, reveal features of retrotransposition, segmental duplications, and other processes of genome evolution.

Atomistic simulations are used to test the equations of continuum contact mechanics in nanometer scale contacts. Nominally spherical tips, made by bending crystals or cutting crystalline or amorphous solids, are pressed into a flat, elastic substrate. The normal displacement, contact radius, stress distribution, friction, and lateral stiffness are examined as a function of load and adhesion. The atomic scale roughness present on any tip made of discrete atoms is shown to have profound effects on the results. Contact areas, local stresses, and the work of adhesion change by factors of 2 to 4, and the friction and lateral stiffness vary by orders of magnitude. The microscopic factors responsible for these changes are discussed. The results are also used to test methods for analyzing experimental data with continuum theory to determine information, such as contact area, that cannot be measured directly in nanometer scale contacts. Even when the data appear to be fit by continuum theory, extracted quantities can differ substantially from their true values.

An equality was recently proved relating energy dissipation to the difference of the response and velocity correlation functions for a class of Langevin equations. We generalize this for the physically important case of particles in a fluid, where bath fluctuations are nonlocal in time due to hydrodynamic modes. We also show that the inclusion of a mass term does not alter the result and provide a simple physical interpretation of the original equality.

We describe a method for investigating nonlinearity in irregular fluctuations (short-term variability) of time series even if the data exhibit long-term trends (periodicities). Such situations are theoretically incompatible with the assumption of previously proposed methods. The null hypothesis addressed by our algorithm is that irregular fluctuations are generated by a stationary linear system. The method is demonstrated for numerical data generated by known systems and applied to several actual time series.

The effects of radiation reaction on electron beam dynamics are studied in the context of plasma-based accelerators. Electrons accelerated in a plasma channel undergo transverse betatron oscillations due to strong focusing forces. These oscillations lead to emission by the electrons of synchrotron radiation, with a corresponding energy loss that affects the beam properties. An analytical model for the single particle orbits and beam moments including the classical radiation reaction force is derived and compared to the results of a particle transport code. Since the betatron amplitude depends on the initial transverse position of the electron, the resulting radiation can increase the relative energy spread of the beam to significant levels (e.g., several percent). This effect can be diminished by matching the beam into the channel, which could require micron sized beam radii for typical values of the beam emittance and plasma density.

The multiple scattering of coherent surface acoustic wave packets in a microstructure is studied using an ultrafast optical technique. By recording a set of acoustic transfer functions, we show that it is possible to implement time-reversal acoustics and refocus the wave packets up to the GHz range, two orders of magnitude higher than usual. Many applications in time-reversal acoustics are thus transposable to correspondingly smaller structures, opening the way to efficient nondestructive characterization and manipulation of multiple scattering on the microscale.

A rather simple random-walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site with respect to each other, and consist of infinite arrays of absorbing sites separated by two nonabsorbing sites. Exact explicit expressions for the long-time velocity and the effective diffusion coefficient are obtained and discussed. In particular, it is shown that the direction of the steady motion can be reversed by conveniently varying the values of either the mean residence times in the lattice states or the transition rates to the absorbing and nonabsorbing sites.

We give simple expressions for the mean of the max and min bounds of the critical-to-classical crossover functions, previously calculated [Bagnuls and Bervillier, Phys. Rev. E 65, 066132 (2002)] within the massive renormalization scheme of the ${\Phi }_d^4\left(n\right)$ model in three dimensions $(d=3)$ and scalar order parameter $(n=1)$ of the Ising-like universality class. The mean functions are determined relying on the properties of the theoretical functions in the two limiting three-dimensional (3D) Ising-like and mean-field-like descriptions close to the Wilson-Fisher fixed point and to the Gaussian fixed point, respectively. Such descriptions correspond to the preasymptotic domains near each fixed point where a Wegner expansion restricted to two terms (leading and first confluent terms) is valid. The Ising-like preasymptotic domain description includes the correlations between parameters due to the error-bar determination of the exponents and amplitude combinations very close to the Wilson-Fisher fixed point. Adding the equivalent description of the mean field preasymptotic domain close to the Gaussian fixed point leads to define each mean crossover function with three calculated parameters. Fixing a unique value of one parameter whatever the selected mean crossover function, we use this parameter as a relative sensor to estimate the dominant nature, either (Ising-like) critical, or (mean-field-like) classical, of the crossover behavior. Finally, we obtain an explicit criterion to measure the extension of the Ising-like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite, using a well-controlled number of system-dependent parameters (like in the subclass of one-component fluids).

The ionic contribution to the electrical current in an electrolytic cell submitted to an external voltage linearly increasing with the time is evaluated. The investigation is performed in the limit of small and large electric field, in which the density of ions depends on the actual electric field in the sample. In the analysis, it is assumed that the ionic separation induced by an external field can be described by a surface density of charge. We show that the ions are responsible for a peak in the current, followed by a delay in the application of the external voltage. From the analysis of the peak and its delay, it is possible to obtain information on the density of ions in thermodynamical equilibrium, and on the mobility of the ions in the considered liquid.

We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time dependence is specified by an external protocol. We give conditions on potential and protocol under which the fluctuations of the dissipative work satisfy an exact symmetry for all times. We also present counterexamples to that fluctuation theorem when our conditions are not satisfied. Finally, we consider the dissipated heat, which differs from the work by a temporal boundary term. We explain why there is a correction to the standard fluctuation theorem due to the unboundedness of that temporal boundary. However, the corrected fluctuation relation has again a general validity.

Simple theoretical interpretation has been made on the previously reported odd-even behavior of the emergence of ferroelectricity and antiferroelectricity in homologous series of bent-core mesogens with the same chiral end chains $(S,S)$; compounds with even and odd carbon numbers (including oxygen) exhibit ferroelectric and antiferroelectric $B2$ phases, respectively. The odd-even behavior was confirmed in newly synthesized racemic compounds with chiral end chains of $R$ and $S$ forms $(R,S)$ together with $(R,R)$ and $(S,S)$ forms. According to our theoretical interpretation, ferroelectricity should be more stable in $(R,S)$ compounds than in $(S,S)$ compounds. Actually, the transition temperature from the isotropic phase to the $\mathrm{Sm}\text{−}CP$ phase was higher and the temperature range of the $B2$ phase was broader in the $(R,S)$ compound than in the $(S,S)$ compound.