We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of the two-component nonlinear Schrödinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route, we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS, and RW solutions. We then consider the RW solution as the starting point and derive AB, MS, and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrödinger equation with a modified nonlinearity parameter. Through this two-way approach we establish a broader understanding of these rational solutions, which will be of interest in a variety of situations.

The pressure loads on two identical spherical bubbles impulsively introduced in an inviscid simple shear flow are calculated. The interaction force due to these pressure loads is employed to model the dynamics of air bubbles injected to a low-viscosity fluid sheared in a Couette device at the first shear flow instability where the bubbles are trapped inside the stable Taylor vortex. It was shown that the interaction between the bubbles in the primary shear flow drives them away from each other. The performed simulations revealed that in an inviscid flow the separation distances between equal size bubbles undergo complex periodic motion. The presence of low-viscosity results in a qualitative change of the interaction pattern: The bubbles either eventually assume an ordered string with equal separation distances between all neighbors or some of them collide. The first regime is qualitatively similar to the behavior of bubbles at low Reynolds number [Prakash et al., Phys. Rev. E 87, 043002 (2013)]. Furthermore, if the Reynolds number exceeds some critical value the temporal behavior of the separations becomes nonmonotonic and exhibits over- and undershooting of the equilibrium separations. The latter effects were observed in the experiments, but are not predicted by the low Reynolds number model of the process [Prakash et al., Phys. Rev. E 87, 043002 (2013)].

We investigate hexatic membranes embedded in Euclidean $D$-dimensional space using a reparametrization invariant formulation combined with exact renormalization group equations. An $\mathit{XY}$ model coupled to a fluid membrane, when integrated out, induces long-range interactions between curvatures described by a Polyakov term in the effective action. We evaluate the contributions of this term to the running surface tension, bending, and Gaussian rigidities in the approximation of vanishing disinclination (vortex) fugacity. We find a non-Gaussian fixed point where the membrane is crinkled and has a nontrivial fractal dimension.

It is well known experimentally that well-quenched amorphous solids exhibit a plastic instability in the form of a catastrophic shear localization at a well-defined value of the external strain. The instability may develop to a shear band that in some cases is followed by a fracture. It is also known that the values of the yield strain (and yield stress), as well as the direction of the shear band with respect to the principal stress axis, vary considerably with variations in the external loading conditions. In this paper we present a microscopic theory of these phenomena for two-dimensional athermal amorphous solids that are strained quasistatically. We present analytic formulas for the yield strains for different loading conditions, as well as for the angles of the shear bands. We explain that the external loading conditions determine the eigenvalues of the quadrupolar Eshelby inclusions which model the nonaffine displacement field. These inclusions model elementary plastic events and determine both the yield strain and the direction of the shear band. We show that the angles of the shear bands with respect to the principal stress axis are limited theoretically between ${30}^{\circ }$ and ${60}^{\circ }$. Available experimental data conform to this prediction.

Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence of noise [Mathis, Herz, and Stemmler, Phys. Rev. Lett. 109, 018103 (2012)]. Indeed, the cortex seems to use periodic, multiscale grid codes to represent position accurately. Here we show how such codes can be read out without taking the long-term limit; even on short time scales, the precision of such codes scales exponentially in the number $N$ of neurons. Does this finding also hold for neurons that are not firing in a statistically independent fashion? To assess the extent to which biological grid codes are subject to statistical dependences, we first analyze the noise correlations between pairs of grid code neurons in behaving rodents. We find that if the grids of two neurons align and have the same length scale, the noise correlations between the neurons can reach values as high as $0.8$. For increasing mismatches between the grids of the two neurons, the noise correlations fall rapidly. Incorporating such correlations into a population coding model reveals that the correlations lessen the resolution, but the exponential scaling of resolution with $N$ is unaffected.

Molecular motors are involved in key transport processes in the cell. Many of these motors can switch from an active to a nonactive state, either spontaneously or depending on their interaction with other molecules. When active, the motors move processively along the filaments, while when inactive they are stationary. We treat here the simple case of spontaneously switching motors, between the active and inactive states, along an open linear track. We use our recent analogy with vehicular traffic, where we go beyond the mean-field description. We map the phase diagram of this system, and find that it clearly breaks the symmetry between the different phases, as compared to the standard total asymmetric exclusion process. We make several predictions that may be testable using molecular motors in vitro and in living cells.

The community structure and the robustness are two important properties of networks for analyzing the functionality of complex systems. The community structure is crucial to understand the potential functionality of complex systems, while the robustness is indispensable to protect the functionality of complex systems from malicious attacks. When a network suffers from an unpredictable attack, its structural integrity would be damaged. Earlier studies focused on the integrity of the node structure or the edge structure when a network suffers from a single-level malicious attack on the nodes or the edges. In this study, we model the attack on the network as a two-level targeted one. Then, we propose a community robustness index to evaluate the integrality of the community structure when the network suffers from the modeled attack. The proposed index plays an important role in analyzing the ability of the real systems to resist unpredictable failures. Finally, based on the proposed community robustness index, a greedy algorithm is devised to mitigate the network attack. Experiments on three real network systems show that with minor changes in links the community robustness of networks can be greatly improved. The results also demonstrate that the community structures in the optimized networks remain practically unchanged compared with the original ones.

We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have derived the generalized master equations for this transport using continuous time random walks, characterized by jump and waiting time densities, as the underlying stochastic process. The forcing is incorporated through a vertex- and time-dependent bias in the jump densities governing the random walking particles. As a particular case, we consider particle forcing proportional to the concentration of particles on adjacent vertices, analogous to self-chemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pair-aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices. The steady states do not exhibit this pair aggregation if the transport is random on the vertices, i.e., without forcing. The manifestation of pair aggregation on a transport network may thus be a signature of self-chemotactic-like forcing.

This paper reports that an initially opaque plasma foil, irradiated by a laser pulse with intensity below the self-induced transparency (SIT) threshold, will become transparent, if a flux of energetic electrons is present. Based on this phenomenon, named flux-induced transparency (FIT), an approach to obtaining ultrasharp-front laser pulses is proposed. With the presence of an energetic-electron flux generated by a $p$-polarized laser irradiating an overdense plasma foil from the rear side, the propagation of an $s$-polarized laser irradiating the front surface of the foil can be manipulated. The transmitted $s$-polarized laser pulse has an ultrasharp front which rises by three orders of magnitude within a few laser cycles. The profile of the transmitted pulse is tunable by controlling the time at which the energetic-electron flux arrives at the front surface.

We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.

The scaling of local height fluctuations is studied numerically in lattice growth models of the class of the nonlinear stochastic equation of Villain-Lai-Das Sarma (VLDS) in substrate dimensions $d=1$ and 2. In $d=1$, the average local slopes of the conserved restricted solid-on-solid (CRSOS) models converge to a finite value in the long-time limit, with power-law corrections in time whose exponents are close to $0.1$. Other VLDS models in $d=1$, such as that of Das Sarma and Tamborenea, show a divergence of local slopes up to ${10}^6$ monolayers, typical of anomalous roughening, but a comparison of roughness distributions shows that they scale as the linear fourth-order growth equation in those time scales. Normal scaling is also obtained in a modified VLDS equation with instability suppression, in contrast to recent numerical works. In $d=2$, a CRSOS model and a model with lateral aggregation of diffusing particles show normal scaling of the local slopes, also with small correction exponents. These results consistently show that the VLDS class has normal dynamic scaling in $d=1$ and 2, in agreement with the theoretical predictions of Phys. Rev. Lett. 94, 166103 (2005), and they show that the apparently anomalous features observed in previous works are effects of large scaling correction terms or crossover effects.

Via event-driven molecular dynamics simulations and experiments, we study the packing-fraction and shear-rate dependence of single-particle fluctuations and dynamic correlations in hard-sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single-particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies [Chikkadi et al., Europhys. Lett. 100, 56001 (2012)], we further address the issue of anisotropy of the dynamic correlations.

For bosons carrying spin-one degree of freedom, we introduce an embedded Gaussian orthogonal ensemble of random matrices generated by random two-body interactions in the presence of a mean field that is spin ($S$) scalar [called BEGOE(1+2)-$S1$]. Embedding algebra for the ensemble, for $m$ bosons in $\Omega$ number of single-particle levels (each triply degenerate), is $\mathrm{U}\left(3\Omega \right)\supset \mathrm{G}\supset \mathrm{G}1\otimes \mathrm{SO}\left(3\right)$ with SO(3) generating the spin $S$. A method for constructing the ensemble for a given $(\Omega ,m,S)$ has been developed. Numerical calculations show that (i) the form of the fixed-($m$, $S$) density of states is close to a Gaussian; (ii) for a strong enough interaction, level fluctuations follow GOE; (iii) fluctuation in energy centroids is large; and (iv) spectral widths are nearly constant with respect to $S$ for $S<S_{\text{max}}/2$. Moreover, we identify two different pairing symmetry algebras in the space defined by $\text{BEGOE}(1+2)-S1$ and numerical results show that random interactions generate ground states with maximal value for the pair expectation value.

We derive and study a theoretical description for single-file diffusion, i.e., diffusion in a one-dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion for long times. The novelty of the present approach is that it allows for the derivation of correlations between a tagged particle and other particles of the system at a given distance with empty sites in between. The behavior of the correlation gives deeper insights into the processes involved. The numerical integration of differential equations are in good agreement with Monte Carlo simulations.

A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.

In this paper we obtain the phase diagram of a four-species predator-prey lattice model by using the proposed gradient method. We consider cyclic transitions between consecutive states, representing invasion or predation, and allowed the exchange between neighboring neutral pairs. By applying a gradient in the invasion rate parameter one can see, in the same simulation, the presence of two symmetric absorbing phases, composed by neutral pairs, and an active phase that includes all four species. In this sense, the study of a single-valued interface and its fluctuations give the critical point of the irreversible phase transition and the corresponding universality classes. Also, the consideration of a multivalued interface and its fluctuations bring the percolation threshold. We show that the model presents two lines of irreversible first-order phase transition between the two absorbing phases and the active phase. Depending on the value of the system parameters, these lines can converge into a triple point, which is the beginning of a first-order irreversible line between the two absorbing phases, or end in two critical points belonging to the directed percolation universality class. Standard simulations for some characteristic values of the parameters confirm the order of the transitions as determined by the gradient method. Besides, below the triple point the model presents two standard percolation lines in the active phase and above a first-order percolation transition as already found in other similar models.

The recently proposed fluctuation relation in unfolding forces [Phys. Rev. E 84, 060101(R) (2011)] is reexamined taking into account the explicit time dependence of the force distribution. The stretching of a tethered Rouse polymer is exactly solved and the ratio of the probabilities of positive to negative forces is shown to be an exponential in force. Extensive steered molecular dynamics simulations of unfolding of deca alanine peptide confirm the form of fluctuation relation proposed earlier, but with explicit correct time dependence of unfolding forces taken into account. From exact calculations and simulations, a linear dependence of the constant in the exponential of the fluctuation relation on average unfolding forces and inverse temperature is proposed.

We examine the solvent-mediated interaction between two neutral colloidal particles due to preferential adsorption in a near-critical binary mixture. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [J. Chem. Phys. 136, 114704 (2012)]. We calculate the free energy and the force between two colloidal particles as functions of the temperature $T$, the composition far from the colloidal particles $c_{\infty }$, and the colloid separation $\ell$. The interaction is much enhanced when the component favored by the colloid surfaces is poor in the reservoir. For such off-critical compositions, we find a surface of a first-order bridging transition $\ell ={\ell }_{\mathrm{cx}}(T,c_{\infty })$ in the $T$-$c_{\infty }$-$\ell$ space in a universal, scaled form, across which a discontinuous change occurs between separated and bridged states. This surface starts from the bulk coexistence surface (CX) and ends at a bridging critical line where $\ell$ is determined by $T$ as $\ell ={\ell }_c\left(T\right)$. On approaching the critical line, the discontinuity vanishes and the derivatives of the force with respect to $T$ and $\ell$ both diverge. Furthermore, bridged states continuously change into separated states if $c_{\infty }$ (or $T$) is varied from a value on CX to a value far from CX with $\ell$ kept smaller than ${\ell }_c\left(T\right)$.

The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro- and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable. We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh-Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths.

Positron annihilation lifetime spectroscopy (PALS) measurements were performed between 93 and 293 K in order to study the supercooled smectic-$E$ (Sm-$E$) phase of 4-$n$-butyl-4${}^{\prime }$-isothiocyanato-1,1${}^{\prime }$-biphenyl (4TCB), the ordered molecular crystal of 4TCB, and the phase transition between the Sm-$E$ phase and the ordered molecular crystal of 4TCB. The phase transition was well reflected in the abrupt increase of the ortho-positronium ($o$-Ps) lifetime and intensity. The value of the $o$-Ps lifetime in the Sm-$E$ liquid crystalline phase of 4TCB, i.e., 2.21 ns at room temperature, was explained by the formation of bubbles induced by Ps atoms, which are created due to a liquidlike state of the butyl chains of 4TCB molecules in the Sm-$E$ phase. The temperature dependence of the $o$-Ps intensity for the supercooled Sm-$E$ phase can be explained by thermal generation of sites where bubbles are formed; an activation energy equal to $0.30\pm 0.02$ eV was estimated. This value was compared with the activation energies of molecular motions. The $o$-Ps lifetime in the ordered molecular crystal was interpreted as originating from the annihilation of $o$-Ps confined in molecular vacancy-type imperfections in the crystal lattice. The value of the $o$-Ps pickoff annihilation between 1.8 and 1.9 ns is in accordance with the size of the molecular vacancy for the 4TCB crystal lattice. Its intensity is lower than 5$\%$. The isothermal crystallization of the 4TCB Sm-$E$ phase was observed by PALS. The low-dimensional crystal growth was concluded from the Avrami equation fitted to the time dependence of the $o$-Ps intensity, which resulted in an Avrami exponent equal to 1.73.