We respond to the comment of Zhu et al. [Phys. Rev. E 82, 038101 (2010)] and show that the results in question are not misleading.

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, $⟨x^n⟩\sim t^{\mu n}$, where $\mu <1$ is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrödinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasicontinuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.

We investigate the stability of a uniform flow of self-propelled particles in a two-dimensional optimal velocity model. As an initial condition, the particles are distributed uniformly in a narrow region of the space. This condition corresponds to a migration of organisms. It is found that the uniform flow is unstable and a meandering motion appears by numerical simulations. We also show the instability exists for any values of parameters by the linear analysis. It means that there is no stable uniform flow in this model.

An extensive analytical and numerical study on a class of growth processes with spatiotemporally correlated noise in arbitrary dimension is undertaken. In addition to the conventional investigation on the interface morphology and interfacial widths, we pay special attention to exploring the characteristics of the slope-slope correlation function $S\left(\mathbf{r},t\right)$ and the $\left[Q\right]$-th degree residual local interfacial width $w\left[Q\right]\left(l,t\right)$, whose importance has been somewhat overlooked in the literature. Based on the above analysis, we give a plausible theoretical explanation about the various experimental observations of kinetically and thermodynamically unstable surface growth. Furthermore, through explicit examples, we show that the statistical methods of calculating the exponents (including the dynamic exponent $z$, the global roughness exponent $\alpha$, and the local roughness exponent ${\alpha }_{\text{loc}}$), based on the scaling of $S\left(\mathbf{r},t\right)$ and $w\left[Q\right]\left(l,t\right)$, are very reliable and rarely influenced by the finite time and/or finite-size effects. Another important issue we focus on in this paper is related to numerical calculation. For the specific class of growth processes discussed in this paper, we develop a very efficient and accurate algorithm for numerical calculation of the dynamics of interface configuration, the structure factor, the various correlation functions, the interfacial width and its variants in arbitrary dimensions, even with very large system size and very late time. The proposed systematical algorithm can be easily generalized to other linear processes and some special nonlinear processes.

We present spectroscopic and optical studies of a non-layer-shrinkage ferroelectric liquid crystal DSiKN65. The orientational order parameters $S$, measured with respect to the smectic layer normal using IR spectroscopy on a sample aligned homeotropically, does not exhibit any significant variation between the smectic-$A^{\ast }$ and smectic-$C^{\ast }$ phases. In contrast the birefringence of a planar homogenous sample abruptly increases at the smectic-$A^{\ast }$ to smectic-$C^{\ast }$ transition. This suggests a general increase in the orientational order, which can be described by the orientational order parameters $S^{\prime }$ defined with respect to the director. Simultaneous increase of $S^{\prime }$ and the director tilt $\Theta$ may explain the low shrinkage of smectic layers, which is consistent with recent theoretical models describing the smectic-$A^{\ast }$ to smectic-$C^{\ast }$ transition for such materials.

Two nanosegregating siloxane-terminated mesogens with chiral $\left(S,S\right)$-2,3-epoxyoctyloxy side chains (E6, E11 )have been synthesized. These compounds form chiral $\text{Sm}{A}^{\ast }$ and $\text{Sm}{C}^{\ast }$ phases and show an untypical behavior of the spontaneous polarization which increases with decreasing temperature in a convex manner while the tilt angle saturates. We compare these results with results obtained for two similar mesogens with chiral $\left(R,R\right)$-2,3-difluorooctyloxy side chains (F6, F11), which both show a typical concave curvature with decreasing temperature. A theoretical explanation is given for the unexpected temperature dependency of the spontaneous polarization. The materials also exhibited first-order $\text{Sm}{C}^{\ast }\text{-Sm}{A}^{\ast }$ phase transitions and hence, very high values of the tilt angle. All substances show increased de Vries character in the range of 50%, which is substantially higher than 20% for the nonsiloxane analogs. Furthermore, for the latter materials, second-order phase transitions are common, while the siloxane materials exhibit first-order $\text{Sm}{A}^{\ast }\text{-Sm}{C}^{\ast }$ phase transitions. These results clearly suggest that the achievement of nanosegregation is a powerful tool to induce de Vries behavior and to promote first-order $\text{Sm}{A}^{\ast }\text{-Sm}{C}^{\ast }$ phase transitions.

We present a numerical study of forced polymer translocation by using two separate pore models. Both of them have been extensively used in previous forced translocation studies. We show that variations in the pore model affect the forced translocation characteristics significantly in the biologically relevant range of the pore force, i.e., the driving force. Details of the model are shown to change even the obtained scaling relations, which is a strong indication of strongly out-of-equilibrium dynamics in the computational studies which have not yet succeeded in addressing the characteristics of the forced translocation for biopolymers at realistic length scale.

We investigate the evolution of random positive linear maps with various type of disorder by analytic perturbation and direct simulation. Our theoretical result indicates that the statistics of a random linear map can be successfully described for long time by the mean-value vector state. The growth rate can be characterized by an effective Perron-Frobenius eigenvalue that strongly depends on the type of correlation between the elements of the projection matrix. We apply this approach to an age-structured population dynamics model. We show that the asymptotic mean-value vector state characterizes the population growth rate when the age-structured model has random vital parameters. In this case our approach reveals the nontrivial dependence of the effective growth rate with cross correlations. The problem was reduced to the calculation of the smallest positive root of a secular polynomial, which can be obtained by perturbations in terms of Green’s function diagrammatic technique built with noncommutative cumulants for arbitrary $n$-point correlations.

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher values of elasticity accompanies the establishment of mixing features. The peculiar dynamical behavior observed in the simulations is found to be related to the appearance of filamental propagating patterns, which develop even in the limit of very small inertial nonlinearities, thanks to the feedback of elastic forces on the flow.

Aspects of magnetoelectric birefringence phenomena are investigated in the context of electromagnetic wave propagation in isotropic nonlinear media in the eikonal approximation. It is shown that these phenomena can be produced as a unique effect in isotropic systems in the presence of external electric and magnetic fields, provided specific dielectric properties are present.

A design method of electromagnetic (EM) cloaks which can change the scattering pattern of the concealed object to that of a reduced perfect electric conducting (PEC) line or ring (two-dimensional case) is proposed in this paper. It is based on the radial transformation method. The boundary of the concealed space is crushed to an arbitrary line or a ring in the designs, and it is thus called the line-projecting or ring-projecting here. When the line or the ring is shrunk to a point, the EM cloak becomes the normally called invisibility cloak. While in the ring-projecting, none of the constitutive parameters of the EM cloaks is singular, so it may be easier to be realized compared with the singular one. Circular, elliptical and diamond cloaks are designed and simulated as examples. Furthermore, the proposed method is also valid in the design of cloaks with three-dimensional structure.

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson’s coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons’ ${\tau }_b$ is a considerably more robust measure of the degree-degree association.

Most liquid crystals show low sensitivity to magnetic field. However, in this paper we show that a small bias magnetic field not only breaks the symmetry of the ground state, but also plays a crucial role in facilitating the reorientation induced by a large test magnetic field. In particular, a small bias field may alter significantly the strength of the test field needed to observe a given reorientation of the liquid crystal. Moreover, the bias field interacts with other symmetry breaking features of the cell, e.g., pretilt, to change also the qualitative features of the equilibrium state.

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-binding model with a quasiperiodic potential. When the period of coin operators is incommensurate to the lattice spacing, we rigorously show that the limit distribution of the quantum walk is localized at the origin. We also numerically study the eigenvalues of the one-step time evolution operator and find the Hofstadter butterfly spectrum which indicates the fractal nature of this class of quantum walks.

In a recent work, active use of the vocal tract has been reported for singing oscines. The reconfiguration of the vocal tract during song serves to match its resonances to the syringeal fundamental frequency, demonstrating a precise coordination of the two main pieces of the avian vocal system for songbirds characterized by tonal songs. In this work we investigated the Great Kiskadee (Pitangus sulfuratus), a suboscine bird whose calls display a rich harmonic content. Using a recently developed mathematical model for the syrinx and a mobile vocal tract, we set up a computational model that provides a plausible reconstruction of the vocal tract movement using a few spectral features taken from the utterances. Moreover, synthetic calls were generated using the articulated vocal tract that accounts for all the acoustical features observed experimentally.

Complexity in the temporal organization of neural systems may be a reflection of the diversity of their neural constituents. These constituents, excitatory and inhibitory neurons, comprise a well-defined ratio in vivo and form the substrate for rhythmic oscillatory activity. To begin to elucidate the dynamical implications that underlie this balance, we construct neural circuits not ordinarily found in nature and study the resulting temporal patterns. We culture several networks of neurons composed of varying fractions of excitatory and inhibitory cells and use a multielectrode array to study their temporal dynamics as this balance is modulated. We use the electrode burst as the temporal imprimatur to signify the presence of network activity. Burst durations, interburst intervals, and the number of spikes participating within a burst are used to illustrate the vivid differences in the temporal organization between the various cultured networks. When the network consists largely of excitatory neurons, no network temporal structure is apparent. However, the addition of inhibitory neurons evokes a temporal order. Calculation of the temporal autocorrelation shows that when the number of inhibitory neurons is a major fraction of the network, a striking network pattern materializes when none was previously present.

We study the fluctuation-dissipation theorem for a Brownian particle driven into a nonequilibrium steady state experimentally. We validate two different theoretical variants of a generalized fluctuation-dissipation theorem. Furthermore, we demonstrate that the choice of observables crucially affects the accuracy of determining the nonequilibrium response from steady state nonequilibrium fluctuations.

We introduce a method to study random Boolean networks with asynchronous stochastic update. Each node in the state space network starts with equal occupation probability, which then evolves to a steady state. Attractors and the sizes of their basins are determined by the nodes left occupied at late times. As for synchronous update, the basin entropy grows with system size only for critical networks. We determine analytically the distribution for the number of attractors and basin sizes for networks with connectivity $K=1$. These differ from the case of synchronous update for all $K$.

The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete with selection processes that tend to reduce genetic variation. Here, we show that the Bose-Einstein distribution describe the multiple stationary states of a diploid population under this multiloci evolutionary dynamics. Moreover, the evolutionary process might undergo an interesting condensation phase transition in the universality class of a Bose-Einstein condensation when a finite fraction of pairs of linked loci is fixed into given allelic states. Below this phase transition the genetic variation within a species is significantly reduced and only maintained by the remaining polymorphic loci.