A classical two-dimensional (2D) model for an artificial atom is used to make a numerical “exact” study of elastic and nonelastic scattering. Interesting differences in the scattering angle distribution between this model and the well-known Rutherford scattering are found in the small energy and/or small impact parameter scattering regime. For scattering off a classical 2D hydrogen atom different phenomena such as ionization, exchange of particles, and inelastic scattering can occur. A scattering regime diagram is constructed as function of the impact parameter $\left(b\right)$ and the initial velocity $\left(v\right)$ of the incoming particle. In a small regime of the $(b,v)$ space the system exhibits chaos, which is studied in more detail. Analytic expressions for the scattering angle are given in the high impact parameter asymptotic limit.

We present an implementation of quantum annealing (QA) via lattice Green’s function Monte Carlo (GFMC), focusing on its application to the Ising spin glass in transverse field. In particular, we study whether or not such a method is more effective than the path-integral Monte Carlo- (PIMC) based QA, as well as classical simulated annealing (CA), previously tested on the same optimization problem. We identify the issue of importance sampling, i.e., the necessity of possessing reasonably good (variational) trial wave functions, as the key point of the algorithm. We performed GFMC-QA runs using such a Boltzmann-type trial wave function, finding results for the residual energies that are qualitatively similar to those of CA (but at a much larger computational cost), and definitely worse than PIMC-QA. We conclude that, at present, without a serious effort in constructing reliable importance sampling variational wave functions for a quantum glass, GFMC-QA is not a true competitor of PIMC-QA.

In this Comment, we point out that the ninth-order expressions for electromagnetic fields for a fundamental Gaussian beam given by Wang and Webb [Phys. Rev. E 72, 046501 (2005)] are incorrect. The correct expressions for the electromagnetic field components up to ninth order are given.

Using a multivariable series method, we calculated the eighth-order expression of the vector potential of a fundamental Gaussian beam, thereby correcting the mistake in our previous paper [Phys. Rev. E 72, 046501 (2005)].

To characterize the pairing specificity of RNA secondary structures as a function of temperature, we analyze the statistics of the pairing weights as follows: for each base $\left(i\right)$ of the sequence of length $N$, we consider the $(N-1)$ pairing weights $w_i\left(j\right)$ with the other bases $(j\ne i)$ of the sequence. We numerically compute the probability distributions $P_1\left(w\right)$ of the maximal weight $w_i^{\max }={\max }_j\left[w_i\left(j\right)\right]$, the probability distribution $\Pi \left(Y_2\right)$ of the parameter $Y_2\left(i\right)={\sum }_j{w}_i^2\left(j\right)$, as well as the average values of the moments $Y_k\left(i\right)={\sum }_j{w}_i^k\left(j\right)$. We find that there are two important temperatures $T_c<T_{\text{gap}}$. For $T>T_{\text{gap}}$, the distribution $P_1\left(w\right)$ vanishes at some value $w_0\left(T\right)<1$, and accordingly the moments $\overline{Y_k\left(i\right)}$ decay exponentially as ${\left[w_0\left(T\right)\right]}^k$ in $k$. For $T<T_{\text{gap}}$, the distributions $P_1\left(w\right)$ and $\Pi \left(Y_2\right)$ present the characteristic Derrida-Flyvbjerg singularities at $w=1∕n$ and $Y_2=1∕n$ for $n=1,2,\dots$. In particular, there exists a temperature-dependent exponent $\mu \left(T\right)$ that governs the singularities $P_1\left(w\right)\sim {(1-w)}^{\mu \left(T\right)-1}$ and $\Pi \left(Y_2\right)\sim {(1-Y_2)}^{\mu \left(T\right)-1}$ as well as the power-law decay of the moments $\overline{Y_k\left(i\right)}\sim 1∕k^{\mu \left(T\right)}$. The exponent $\mu \left(T\right)$ grows from the value $\mu (T=0)=0$ up to $\mu \left(T_{\text{gap}}\right)\sim 2$. The study of spatial properties indicates that the critical temperature $T_c$ where the large-scale roughness exponent changes from the low temperature value $\zeta \sim 0.67$ to the high temperature value $\zeta \sim 0.5$ corresponds to the exponent $\mu \left(T_c\right)=1$. For $T<T_c$, there exists frozen pairs of all sizes, whereas for $T_c<T<T_{\text{gap}}$, there exists frozen pairs, but only up to some characteristic length diverging as $\xi \left(T\right)\sim 1∕{(T_c-T)}^{\nu }$ with $\nu \simeq 2$. The similarities and differences with the weight statistics in Lévy sums and in Derrida’s random energy model are discussed.

Motivated by mapping from a stochastic system with spatially random rates, we consider disordered nonconserving free-fermion systems using a scaling procedure for the equations of motion. This approach demonstrates disorder-induced localization acting in competition with the asymmetric driving. We discuss the resulting implications for the original stochastic system.

The formation of a shock wave in one-dimensional granular gases is considered, for both the dry and the wet cases, and the results are compared with the analytical shock wave solution in a sticky gas. Numerical simulations show that the behavior of the shock wave in both cases tends asymptotically to the sticky limit. In the inelastic gas (dry case) there is a very close correspondence to the sticky gas, with one big cluster growing in the center of the shock wave, and a steplike stationary velocity profile. In the wet case, the shock wave has a nonzero width which is marked by two symmetric heavy clusters performing breathing oscillations with slowly increasing amplitude. All three models have the same asymptotic energy dissipation law, which is important in the context of the free cooling scenario. For the early stage of the shock formation and asymptotic oscillations we provide analytical results as well.

The singing by songbirds is a most convincing example in the animal kingdom of functional lateralization of the brain, a feature usually associated with human language. Lateralization is expressed as one or both of the bird’s sound sources being active during the vocalization. Normal songs require high coordination between the vocal organ and respiratory activity, which is bilaterally symmetric. Moreover, the physical and neural substrate used to produce the song lack obvious asymmetries. In this work we show that complex spatiotemporal patterns of motor activity controlling airflow through the sound sources can be explained in terms of spontaneous symmetry breaking bifurcations. This analysis also provides a framework from which to study the effects of imperfections in the system’ s symmetries. A physical model of the avian vocal organ is used to generate synthetic sounds, which allows us to predict acoustical signatures of the song and compare the predictions of the model with experimental data.

We use the wavelet transform modulus maxima method to investigate the multifractal properties of strand-asymmetry DNA walk profiles in the human genome. This study reveals the bifractal nature of these profiles, which involve two competing scale-invariant (up to repeat-masked distances $\lesssim 40\mathrm{kbp}$) components characterized by Hölder exponents $h_1=0.78$ and $h_2=1$, respectively. The former corresponds to the long-range-correlated homogeneous fluctuations previously observed in DNA walks generated with structural codings. The latter is associated with the presence of jumps in the original strand-asymmetry noisy signal $S$. We show that a majority of upward (downward) jumps colocate with gene transcription start (end) sites. Here 7228 human gene transcription start sites from the refGene database are found within $2\mathrm{kbp}$ from an upward jump of amplitude $\Delta S⩾0.1$ which suggests that about 36% of annotated human genes present significant transcription-induced strand asymmetry and very likely high expression rate.

We develop an athermal version of the shear-transformation-zone (STZ) theory of amorphous plasticity in materials where thermal activation of irreversible molecular rearrangements is negligible or nonexistent. In many respects, this theory has broader applicability and yet is simpler than its thermal predecessors. For example, it needs no special effort to assure consistency with the laws of thermodynamics, and the interpretation of yielding as an exchange of dynamic stability between jammed and flowing states is clearer than before. The athermal theory presented here incorporates an explicit distribution of STZ transition thresholds. Although this theory contains no conventional thermal fluctuations, the concept of an effective temperature is essential for understanding how the STZ density is related to the state of disorder of the system.

In the preceding paper, we developed an athermal shear-transformation-zone (STZ) theory of amorphous plasticity. Here we use this theory in an analysis of numerical simulations of plasticity in amorphous silicon by Demkowicz and Argon (DA). In addition to bulk mechanical properties, those authors observed internal features of their deforming system that challenge our theory in important ways. We propose a quasithermodynamic interpretation of their observations in which the effective disorder temperature, generated by mechanical deformation well below the glass temperature, governs the behavior of other state variables that fall in and out of equilibrium with it. Our analysis points to a limitation of either the step-strain procedure used by DA in their simulations, or the STZ theory in its ability to describe rapid transients in stress-strain curves, or perhaps to both. Once we allow for this limitation, we are able to bring our theoretical predictions into accurate agreement with the simulations.

In this paper we report that there are two different types of destruction of the phase synchronization (PS) regime of chaotic oscillators depending on the parameter mismatch as well as in the case of the classical synchronization of periodic oscillators. When the parameter mismatch of the interacting chaotic oscillators is small enough, the PS breaking takes place without the destruction of the phase coherence of chaotic attractors of oscillators. Alternatively, due to the large frequency detuning, the PS breaking is accomplished by loss of the phase coherence of the chaotic attractors.

We show the existence of steadily moving solitary pulses (SPs) in the complex Ginzburg-Landau equation, which includes the cubic-quintic nonlinearity and a conservative linear driving term, whose amplitude is a standing wave with wave number $k$ and frequency $\omega$, the motion of the SPs being possible at resonant velocities $\pm \omega ∕k$, which provide for locking to the drive. The model may be realized in terms of traveling-wave convection in a narrow channel with a standing wave excited in its bottom (or on the surface). An analytical approximation is developed, based on an effective equation of motion for the SP coordinate. Direct simulations demonstrate that the effective equation accurately predicts characteristics of the driven motion of pulses, such as a threshold value of the drive’s amplitude. Collisions between two solitons traveling in opposite directions are studied by means of direct simulations, which reveal that they restore their original shapes and velocity after the collision.

Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov’ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting solitary waves. These dynamical equations contain a single parameter, which accounts for the different forms of nonlinearity. When this parameter is zero, these dynamical equations are integrable, and the exact analytical solutions are derived. When this parameter is nonzero, the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively. Thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established. The origin of these fractal structures is also explored. It is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite-time singularities. Based on this observation, an analytical criterion for the existence and locations of fractal structures is obtained. Lastly, these analytical results are applied to the generalized nonlinear Schrödinger equations with various nonlinearities such as the saturable nonlinearity, and predictions on their weak interactions of solitary waves are made.

Nodal domains are studied both for real ${\psi }_R$ and imaginary part ${\psi }_I$ of the wave functions of an open microwave cavity and found to show the same behavior as wave functions in closed billiards. In addition we investigate the variation of the number of nodal domains and the signed area correlation by changing the global phase ${\phi }_g$ according to ${\psi }_R+i{\psi }_I=e^{i{\phi }_g}({\psi }_R^{\prime }+i{\psi }_I^{\prime })$. This variation can be qualitatively, and the correlation quantitatively explained in terms of the phase rigidity characterizing the openness of the billiard.

We present a dynamic van der Waals theory starting with entropy and energy functional with gradient contributions. The resultant hydrodynamic equations contain the stress arising from the density gradient. It provides a general scheme of two-phase hydrodynamics involving the gas-liquid transition in nonuniform temperature. Some complex hydrodynamic processes with evaporation and condensation are examined numerically. They are (i) adiabatically induced spinodal decomposition, (ii) piston effect with a bubble in liquid, (iii) temperature and velocity profiles around a droplet in heat flow, (iv) efficient latent heat transport at small liquid densities (the mechanism of heat pipes), (v) boiling in gravity with continuous bubble formation and rising, and (vi) spreading and evaporation of liquid on a heated boundary wall.

A compact physiologically based mean-field formulation of brain dynamics is proposed to model observed brain activity and electroencephalographic (EEG) signals. In contrast to existing formulations, which are more detailed and complicated, our model is described by a single second-order delay differential equation that encapsulates salient aspects of the physiology. The model captures essential features of activity mediated by fast corticocortical connections and delayed feedbacks via extracortical pathways and external stimuli. In the linear regime, these features can be simply expressed by three coefficients derived from the properties of these physiological pathways and explicit nonlinear approximations are also derived. This compact model successfully reproduces the main features of experimental EEG’s and the predictions of previous models, including resonance peaks in EEG spectra and nonlinear dynamics. As an illustration, key features of the dynamics of epileptic seizures are shown to be reproduced by the model. Due to its compact form, the model will facilitate insight into nonlinear brain dynamics via standard nonlinear techniques and will guide analysis and investigation of more complex models. It is thus a useful tool for analyzing complex brain activity, especially when it exhibits low-dimensional dynamics.

We study the excitable Greenberg-Hastings cellular automaton model on scale-free networks. We obtain analytical expressions for no external stimulus the uncoupled case. It is found that the curves, the average activity $F$ versus the external stimulus rate $r$, can be fitted by a Hill function, but not exactly, there exists a relation $F\sim r^{\alpha }$ for the low-stimulus response, where the Stevens-Hill exponent $\alpha$ ranges from $\alpha =1$ in the subcritical regime to $\alpha =0.5$ at criticality. At the critical point, the range is maximal, but not divergent. We also calculate the average activity $F^k\left(r\right)$ and the dynamic range ${\Delta }^k\left(p\right)$ for nodes with given connectivity $k$. It is interesting that nodes with larger connectivity have larger optimal range, which could be applied in biological experiments to reveal the network topology.

In this article we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a node, having randomly assigned coordinates in a $1\times 1$ square, is added and connected to a previously existing node $i$, which minimizes the quantity $r_i^2∕k_i^{\alpha }$, where $r_i$ is the geographical distance, $k_i$ the degree, and $\alpha$ a free parameter. The degree distribution obeys a power-law form when $\alpha =1$, and an exponential form when $\alpha =0$. When $\alpha$ is in the interval (0, 1), the network exhibits a stretched exponential distribution. We prove that the average topological distance increases in a logarithmic scale of the network size, indicating the existence of the small-world property. Furthermore, we obtain the geographical edge length distribution, the total geographical length of all edges, and the average geographical distance of the whole network. Interestingly, we found that the total edge length will sharply increase when $\alpha$ exceeds the critical value ${\alpha }_c=1$, and the average geographical distance has an upper bound independent of the network size. All the results are obtained analytically with some reasonable approximations, which are well verified by simulations.

We report anomalous oscillatory features in the spectra of cross-polarized backscattered light from inhomogeneous dielectric microparticles. Numerical experiments based on the finite-difference-time-domain method demonstrate that cross-polarized backscattered spectra exhibit oscillation frequencies with two a priori surprising features. First, the oscillation frequencies decrease as the correlation length $\left(L_c\right)$ of the particle’s refractive index increases. Second, high-frequency oscillations exist even for $L_c$ much smaller than the optical wavelength. These findings are exactly opposite to what is observed in co-polarized backscattering spectra, and are not expected from conventional optical scattering theory. We explain this anomalous behavior by examining the path-length distributions of the backscattered photons in the cross polarization.