We demonstrate that period-doubled discrete breathers appear from the anticontinuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between subharmonic solutions of the driven Morse oscillator. Subharmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits subharmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.

We show that the hydrodynamic description can be applied to modeling the ionic response in dense plasmas for a wide range of length scales that are experimentally accessible. Using numerical simulations for the Yukawa model, we find that the maximum wave number $k_{\max }$ at which the hydrodynamic description applies is independent of the coupling strength, given by $k_{\max }{\lambda }_s\simeq 0.43$, where ${\lambda }_s$ is the ionic screening length. Our results show that the hydrodynamic description can be used for interpreting x-ray scattering data from fourth generation light sources and high power lasers. In addition, our investigation sheds new light on how the domain of validity of the hydrodynamic description depends on both the microscopic properties and the thermodynamic state of fluids in general.

Most existing works on transportation dynamics focus on networks of a fixed structure, but networks whose nodes are mobile have become widespread, such as cell-phone networks. We introduce a model to explore the basic physics of transportation on mobile networks. Of particular interest is the dependence of the throughput on the speed of agent movement and the communication range. Our computations reveal a hierarchical dependence for the former, while an algebraic power law is found between the throughput and the communication range with the exponent determined by the speed. We develop a physical theory based on the Fokker-Planck equation to explain these phenomena. Our findings provide insights into complex transportation dynamics arising commonly in natural and engineering systems.

In this study, the fluctuation-dissipation theory is invoked to shed light on input-output interindustrial relations at a macroscopic level by its application to indices of industrial production (IIP) data for Japan. Statistical noise arising from finiteness of the time series data is carefully removed by making use of the random matrix theory in an eigenvalue analysis of the correlation matrix; as a result, two dominant eigenmodes are detected. Our previous study successfully used these two modes to demonstrate the existence of intrinsic business cycles. Here a correlation matrix constructed from the two modes describes genuine interindustrial correlations in a statistically meaningful way. Furthermore, it enables us to quantitatively discuss the relationship between shipments of final demand goods and production of intermediate goods in a linear response framework. We also investigate distinctive external stimuli for the Japanese economy exerted by the current global economic crisis. These stimuli are derived from residuals of moving-average fluctuations of the IIP remaining after subtracting the long-period components arising from inherent business cycles. The observation reveals that the fluctuation-dissipation theory is applicable to an economic system that is supposed to be far from physical equilibrium.

The standard kicked top involves a periodically kicked angular momentum. By considering this angular momentum as a collection of entangled spins, we compute the bipartite entanglement dynamics as a function of the dynamics of the classical counterpart. Our numerical results indicate that the entanglement of the quantum top depends on the specific details of the dynamics of the classical top rather than depending universally on the global properties of the classical regime. These results are grounded on linking the entanglement rate to averages involving the classical angular momentum, thereby explaining why regular dynamics can entangle as efficiently as the classically chaotic regime. The findings are in line with previous results obtained with a two-particle top model, and we show here that the standard kicked top can be obtained as a limiting case of the two-particle top.

We report that the subthreshold emission spectra of vertical-cavity surface-emitting lasers (VCSELs) can be analogously used to manifest the quantum-billiard energy spectra. The Fourier-transformed distributions of the subthreshold emission spectra are demonstrated to display various peak structures that are in good agreement with the results of the quantum-billiard model. We also verify that the statistical analyses of the nearest-neighbor eigenvalue spacing distributions obey a Poisson distribution for an equilateral-triangular device and a Wigner distribution for a stadium-shaped device.

Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in cases in which the Damköhler number is large. This effect is found to saturate the front speed to values comparable with the speed of the turbulent motions. By comparing with direct numerical simulations, it is found that the effective correlation time is much shorter than for nonreacting flows. The nonlinearity of the reaction term is found to make the front speed slightly faster.

Knowledge of protein folding pathways and inherent structures is of utmost importance for our understanding of biological function, including the rational design of drugs and future treatments against protein misfolds. Computational approaches have now reached the stage where they can assess folding properties and provide data that is complementary to or even inaccessible by experimental imaging techniques. Minimal models of proteins, which make possible the simulation of protein folding dynamics by (systematic) coarse graining, have provided understanding in terms of descriptors for folding, folding kinetics, and folded states. Here we focus on the efficiency of equilibration on the coarse-grained level. In particular, we applied a new regularized stochastic quasi-Newton (S-QN) method, developed for accelerated configurational space sampling while maintaining thermodynamic consistency, to analyze the folding pathway and inherent structures of a selected protein, where regularization was introduced to improve stability. The adaptive compound mobility matrix $B$ in S-QN, determined by a factorized secant update, gives rise to an automated scaling of all modes in the protein, in particular an acceleration of protein domain dynamics or principal modes and a slowing down of fast modes or “soft” bond constraints, similar to lincs/shake algorithms, when compared to conventional Langevin dynamics. We used and analyzed a two-step strategy. Owing to the enhanced sampling properties of S-QN and increased barrier crossing at high temperatures (in reduced units), a hierarchy of inherent protein structures is first efficiently determined by applying S-QN for a single initial structure and $T=1>T_{\theta }$, where $T_{\theta }$ is the collapse temperature. Second, S-QN simulations for several initial structures at very low temperature ($T=0.01<T_F$, where $T_F$ is the folding temperature), when the protein is known to fold but conventional Langevin dynamics experiences critical slowing down, were applied to determine the protein domain dynamics (collective modes) toward folded states, including the native state. This general treatment is efficient and directly applicable to other coarse-grained proteins.

We solve the monomer-dimer problem on a nonbipartite lattice, a simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the nonbipartite nature of the lattice, the well-known method of solving single-monomer problems with a Temperley bijection cannot be used. In this paper, we derive the solution by mapping the problem onto one of closed-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value $c=-2$.

We study the translocation of stiff polymers through a nanopore, driven by the chemical-potential gradient exerted by binding proteins (chaperones) on the trans side of the pore. Bound chaperones prevent backsliding through the pore and, therefore, partially rectify the polymer passage. We show that the sequence of chain monomers with different binding affinity for the chaperones significantly affects the translocation dynamics. In particular, we investigate the effect of the nearest-neighbor adjacency probability of the two monomer types. Depending on the magnitude of the involved binding energies, the translocation speed may either increase or decrease with the adjacency probability. We determine the mean first passage time and show that, by tuning the effective binding energy, the motion changes continuously from purely diffusive to ballistic translocation.

Here we study how large-scale variability of oceanic plankton is affected by mesoscale turbulence in a spatially heterogeneous environment. We consider a phytoplankton-zooplankton (PZ) ecosystem model, with different types of zooplankton grazing functions, coupled to a turbulent flow described by the two-dimensional Navier-Stokes equations, representing large-scale horizontal transport in the ocean. We characterize the system using a dimensionless parameter, $\gamma =T_B/T_F$, which is the ratio of the ecosystem biological time scale $T_B$ and the flow time scale $T_F$. Through numerical simulations, we examine how the PZ system depends on the time-scale ratio $\gamma$ and find that the variance of both species changes significantly, with maximum phytoplankton variability at intermediate mixing rates. Through an analysis of the linearized population dynamics, we find an analytical solution based on the forced harmonic oscillator, which explains the behavior of the ecosystem, where there is resonance between the advection and the ecosystem predator-prey dynamics when the forcing time scales match the ecosystem time scales. We also examine the dependence of the power spectra on $\gamma$ and find that the resonance behavior leads to different spectral slopes for phytoplankton and zooplankton, in agreement with observations.

The properties of ferrogels in homogeneous magnetic fields are studied using a simple microscopic model and Monte Carlo simulations. The main phenomena of interest concern the anisotropy and enhancement of the elastic moduli that result from applying uniform magnetic fields before and after the magnetic grains are locked in to the polymer-gel matrix by cross-linking reactions. The positional organization of the magnetic grains is influenced by the application of a magnetic field during gel formation, leading to a pronounced anisotropy in the mechanical response of the ferrogel to an applied magnetic field. In particular, the elastic moduli can be enhanced to different degrees depending on the mutual orientation of the fields during and after ferrogel formation. The model represents ferrogels by ensembles of dipolar spheres dispersed in elastic matrices. Experimental trends are shown to be reflected accurately in the simulations of the microscopic model. In addition, the simulations yield microscopic insights on the organization of the magnetic grains. Finally, simple relationships between the elastic moduli and the magnetization are proposed. If supplemented by the magnetization curve, these relationships yield the dependencies of the elastic moduli on the applied magnetic field, which are often measured directly in experiments.

Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction dynamics between individual components is mediated by a global variable making the mean-field description exact. Using the example of financial markets, we show that asset price can be such a global variable with the critical role of coordinating the actions of agents who are otherwise independent. The resulting model accurately reproduces empirical properties such as the universal scaling of the price fluctuation and volume distributions, long-range correlations in volatility, and multiscaling.

A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.

This paper studies the propagation of solitons in the nonlinear $\mathit{LC}$ transmission line (NLCTL) with capacitor impurity. Based on Kirchhoff’s laws, the numerical simulation shows that the amplitude of the soliton will be increased or decreased when it is close to the positive or negative impurity. Then, it will be split into reflected and transmitted waves by both the positive and negative impurities. Furthermore, their final amplitude and propagating speeds are almost independent of the impurity polarity. The observations near the impurity can be understood in the physical picture of the linear uncoupled energy absorption. By these results, we find that the impurity-soliton interactions (ISIs) in NLCTLs for both inductance and capacitance impurities, which have been seen to be different before, actually can be unified. They also indicate that the ISIs in NLCTLs essentially can be integrated with those in many other soliton systems, such as the Frenkel-Kontorova model and hydrodynamics. Moreover, the impurity-induced influence on the NLCTL solitons can also be well interpreted in the framework of the nonlinear Schrödinger model with an impurity term derived from the discrete voltage propagation equations by means of the perturbation method.

In several biologically relevant situations, cell locomotion occurs in polymeric fluids with Weissenberg number larger than 1. Here we present results of three-dimensional numerical simulations for the steady locomotion of a self-propelled body in a model polymeric (Giesekus) fluid at low Reynolds number. Locomotion is driven by steady tangential deformation at the surface of the body (the so-called squirming motion). In the case of a spherical squirmer, we show that the swimming velocity is systematically less than that in a Newtonian fluid, with a minimum occurring for Weissenberg numbers of order 1. The rate of work done by the swimmer always goes up compared to that occurring in the Newtonian solvent alone but is always lower than the power necessary to swim in a Newtonian fluid with the same viscosity. The swimming efficiency, defined as the ratio between the rate of work necessary to pull the body at the swimming speed in the same fluid and the rate of work done by swimming, is found to always be increased in a polymeric fluid. Further analysis reveals that polymeric stresses break the Newtonian front-back symmetry in the flow profile around the body. In particular, a strong negative elastic wake is present behind the swimmer, which correlates with strong polymer stretching, and its intensity increases with Weissenberg number and viscosity contrasts. The velocity induced by the squirmer is found to decay in space faster than in a Newtonian flow, with a strong dependence on the polymer relaxation time and viscosity. Our computational results are also extended to prolate spheroidal swimmers and smaller polymer stretching are obtained for slender shapes compared to bluff swimmers. The swimmer with an aspect ratio of two is found to be the most hydrodynamically efficient.

We generalize earlier calculations of the RA (immediate reversals allowed) and RF (immediate reversals forbidden) model with multiple monomers per site, including a parameter in the model, so that both cases studied before are particular cases of the model considered here. Also, we calculate the bulk free energy of the model using Gujrati’s prescription, which leads to corrections in the localization of coexistence lines and qualitative changes in the phase diagram of the model. Thus, this calculation provides an example in which the use of the method of iterating recursion relations starting with natural initial conditions to locate coexistence loci is not trustworthy and may lead to qualitatively different results. A continuous collapse transition appears in all cases as a tricritical point.

Nonlinear dynamics of magnetic field lines generated by simple electric current elements are investigated. In general, the magnetic field lines show behavior similar to that of the Hamiltonian systems; in fact, they can be generally transformed into Hamiltonian systems with 1.5 degrees of freedom, obey the Kolmogorov-Arnold-Moser (KAM) theorem, and generate chaotic trajectories. In the case where unperturbed systems are described by two action (slow) and one angle (fast) variables, however, it is found that the periodic orbits of the unperturbed systems vanish for arbitrarily small symmetry-breaking perturbations (a breakdown of the KAM theorem) and drifting or periodic trajectories appear. The mechanism of this phenomenon is investigated analytically by weak nonlinear stability analysis. It is also shown numerically that scattering processes of the perturbed system exhibit typical features of chaotic dynamical systems.

The grain in the plasma gets charged until the net plasma flux to the grain surface vanishes. In the absence of any analytical formula, this ambipolar condition is utilized to compute the grain charge indirectly. The present work proposes an approximate analytical expression for the grain charge that is exact in the asymptotic limit and in which the relative error between analytical and numerically computed solutions is less than $3\%$. Using this formula, we show that, much like the plasma sheath, the Bohm criterion is satisfied near the dust surface.

The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite $\hslash$, we identify a strong dependence of the current on the structure of the chaotic region. Moreover, we have determined the robustness of the current against thermal fluctuations in the very weak coupling regime. In the case of strong forcing, the current is determined by the shape of a chaotic attractor. In both cases the temperature quickly stabilizes the ratchet, but in the latter it also destroys the asymmetry responsible for the current generation. Finally, applications to isomerization reactions are discussed.