In this paper, we show that there is a family of well-known integrable systems whose spectral fluctuations decay as $1/f^4$, and thus do not follow the $1/f^2$ law recently conjectured for integrable systems. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.

The dynamic response of prestressed semiflexible biopolymers is characterized by the propagation and relaxation of tension, which arises due to the near inextensibility of a stiff backbone. It is coupled to the dynamics of contour length stored in thermal undulations but also to the local relaxation of elongational strain. We present a systematic theory of tension dynamics for stiff yet extensible wormlike chains. Our results show that even moderate prestress gives rise to distinct Rouse-like extensibility signatures in the high-frequency viscoelastic response.

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a complete graph, a cycle graph, and a path graph. An accurate approximation for the cover time distribution, with computational complexity of $O\left(2n\right)$, is also presented. The approximation is numerically tested only for graphs with $n\le 1000$ nodes.

We present a unified description of heat flow in two-terminal hybrid quantum systems. Using simple models, we analytically study nonlinear aspects of heat transfer between various reservoirs—metals, solids, and spin baths—mediated by the excitation and the relaxation of a central (subsystem) mode. We demonstrate rich nonlinear current-temperature characteristics, originating from either the molecular anharmonicity or the reservoir (complex) energy spectra. In particular, we establish sufficient conditions for thermal rectification in two-terminal junctions. We identify two classes of rectifiers. In type-$A$ rectifiers the energy-dependent density of states of the reservoirs are dissimilar. In type-$B$ rectifiers the baths are identical, but include particles whose statistics differ from that of the subsystem, to which they asymmetrically couple. Nonlinear heat flow and specifically thermal rectification are thus ubiquitous effects that could be observed in a variety of systems—phononic, electronic, and photonic.

Recently we proposed a method to solve the perturbed Boltzmann equation modeled by the Bhatnagar-Gross-Krook operator [Phys. Rev. E 74, 041204 (2006)]. In this work we use this method to derive linear transport equations in the whole collisionality range. A comparison of the closure relations derived up to the third order in the Knudsen number (super-Burnett) yields the same results as the Chapman-Enskog expansion. The contribution of the projection operators to the transport is investigated. It is pointed out that their contributions are not negligible in the super-Burnett equations and very significant in the collisionless range. The test of stability of the super-Burnett equations is also performed. It is shown that the stability problem can be related to the positivity of the generalized transport coefficients. Using the Padé approximants, nonlocal transport coefficients are proposed which present the desirable stability properties.

Transport properties of a multiscale carbonate rock are predicted from pore scale models, reconstructed using a continuum geometrical modeling technique. The method combines crystallite information from two-dimensional high-resolution images with sedimentary correlations from a three-dimensional low-resolution microcomputed tomography ($\mu$-CT) image to produce a rock sample with calibrated porosity, structural correlation, and transport properties at arbitrary resolutions. Synthetic $\mu$-CT images of the reconstructed model match well with experimental $\mu$-CT images at different resolutions, making it possible to predict physical transport parameters at higher resolutions.

We have investigated experimentally the influence of a magnetic interaction between the grains on the compaction dynamics of a granular pile submitted to a series of taps. The granular material used to perform this study is a mixture of metallic and glass grains. The packing is immersed in homogeneous external magnetic field. The magnetic field induces an interaction between the metallic grains that constitutes the tunable cohesion. The compaction characteristic time and the asymptotic packing fraction have been measured as a function of the Bond number which is the ratio between the cohesive magnetic force and the grain weight. These measurements have been performed for different fractions of metallic beads in the pile. When the pile is only made of metallic grains, the characteristic compaction time increases as the square root of the Bond number. While the asymptotic packing fraction decreases as the inverse of the Bond number. For mixtures, when the fraction of magnetized grains in the pile is increased, the characteristic time increases while the asymptotic packing fraction decreases. A simple mesoscopic model based on the formation of granular chains along the magnetic field direction is proposed to explain the observed macroscopic properties of the packings.

The existence of gas-liquid coexistence in dipolar fluids with no other contribution to attractive interaction than dipole-dipole interaction is a basic and open question in the theory of fluids. Recent Monte Carlo work by Camp and co-workers indicates that a fluid of charged hard dumbbells does exhibit gas-liquid (g-l) coexistence. This system has the potential to answer the above fundamental question because the charge-to-charge separation, $d$, on the dumbbells may be reduced to, at least in principle, yield the dipolar fluid limit. Using the molecular-dynamics technique we present simulation results for the g-l critical point of charged soft dumbbells at fixed dipole moment as function of $d$. We do find a g-l critical point at finite temperature even at the smallest $d$ value $\left({10}^{-4}\right)$. Reversible aggregation appears to play less a role than in related model systems as $d$ becomes small. Consequently attempts to interpret the simulation results using either an extension of Flory’s lattice theory for polymer systems, which includes reversible assembly of monomers into chains, or the defect model for reversible networks proposed by Tlusty and Safran are not successful. The overall best qualitative interpretation of the critical parameters is obtained by considering the dumbbells as dipoles immersed in a continuum dielectric.

In the soft-mode turbulence (SMT) in electroconvection of homeotropic nematic systems, which is a kind of spatiotemporal chaos induced by nonlinear interaction between two two-dimensional (2D) $XY$ fields, the Nambu-Goldstone modes, and the convective modes, a curious line structure called blackline has been discovered. We measured the density of the blackline as a function of control parameters, ac voltage, and frequency. By detailed observations and analysis, it is clarified that the blackline is a structure of the nematic director in the $x\text{−}y$ plane and includes a sequence of point defects. We discussed similarity with the density of the blackline and that of the point defect in the conventional 2D $XY$ model. The occurrence of this type of defects is only due to the symmetry in the SMT and independent of the properties of fluctuations.

Recent experiments in hippocampal neurons have demonstrated the existence of compartments with elevated levels of second messenger molecules such as cyclic AMP. This compartmentalization is believed to be necessary to ensure downstream signaling specificity. Here we use analytical and numerical techniques to investigate the diffusion of a second messenger in the soma and in the dendrite of a neuron. We obtain analytical solutions for the diffusion field and examine the limit in which the width of the dendrite is much smaller than the radius of the soma. We find that the concentration profile depends both on the degradation rate and the width of the dendrite and that compartmentalization can be indeed be achieved for small width to soma radius ratio.

Morphogen profiles play a vital role in biology by specifying position in embryonic development. However, the factors that influence the shape of a morphogen profile remain poorly understood. Since morphogens should provide precise positional information, one significant factor is the robustness of the profile to noise. We compare three experimentally relevant classes of morphogen profiles (linear, exponential, and algebraic) to see which is most precise when subject to both external embryo-to-embryo fluctuations and internal fluctuations due to intrinsically random processes such as diffusion. We find that both the kinetic parameters and the overall gradient shape (e.g., exponential versus algebraic) can be optimized to generate maximally precise positional information.

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schrödinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory.

The influence of weak uniaxial small-scale anisotropy on the stability of the scaling regime and on the anomalous scaling of the single-time structure functions of a passive scalar advected by the velocity field governed by the stochastic Navier-Stokes equation is investigated by the field theoretic renormalization group and operator-product expansion within one-loop approximation of a perturbation theory. The explicit analytical expressions for coordinates of the corresponding fixed point of the renormalization-group equations as functions of anisotropy parameters are found, the stability of the three-dimensional Kolmogorov-like scaling regime is demonstrated, and the dependence of the borderline dimension $d_c∊\left(2,3\right]$ between stable and unstable scaling regimes is found as a function of the anisotropy parameters. The dependence of the turbulent Prandtl number on the anisotropy parameters is also briefly discussed. The influence of weak small-scale anisotropy on the anomalous scaling of the structure functions of a passive scalar field is studied by the operator-product expansion and their explicit dependence on the anisotropy parameters is present. It is shown that the anomalous dimensions of the structure functions, which are the same (universal) for the Kraichnan model, for the model with finite time correlations of the velocity field, and for the model with the advection by the velocity field driven by the stochastic Navier-Stokes equation in the isotropic case, can be distinguished by the assumption of the presence of the small-scale anisotropy in the systems even within one-loop approximation. The corresponding comparison of the anisotropic anomalous dimensions for the present model with that obtained within the Kraichnan rapid-change model is done.

Two phase microfluidic systems creating size-controlled microdroplets have recently emerged as powerful tools to achieve liquid compartmentalization for high throughput chemical and biological assays. Emulsion electrocoalescence is a destabilization process that can be used in droplet-based platforms for water phase separation to enable lab-on-a-chip applications in biotechnology, including particle or cell recovery. In this paper, we report upon a series of phenomena associated with electrocoalescence of water microdroplet-in-oil populations in microfluidics. In our experiments, we formed microdroplets whose size and dispersion in the channel were varied according to the ratio of the flow rates of the two phases. Different types of electrocoalescence between droplets were obtained. For low applied voltages, drops merged in pairs over the electrode region; for higher values of the applied voltage, a cascade of droplet coalescence was produced against the flow direction, for a range of droplet sizes, lateral distributions of droplets in the channel and localized electric fields.

The site percolation threshold for the random Voronoi network is determined numerically, with the result $p_c=0.71410\pm 0.00002$, using Monte Carlo simulation on periodic systems of up to $40000$ sites. The result is very close to the recent theoretical estimate $p_c\approx 0.7151$ of Neher et al. For the bond threshold on the Voronoi network, we find $p_c=0.666931\pm 0.000005$ implying that, for its dual, the Delaunay triangulation $p_c=0.333069\pm 0.000005$. These results rule out the conjecture by Hsu and Huang that the bond thresholds are 2/3 and 1/3, respectively, but support the conjecture of Wierman that, for fully triangulated lattices other than the regular triangular lattice, the bond threshold is less than $2\text{sin}\pi /18\approx 0.3473$.

We study the interplay between structural and conductivity (composite) disorder and the collective electrical response in random network models. Translating the problem of time-dependent electrical response (resonance and transient relaxation) in binary random composite networks to the framework of generalized eigenvalues, we study and analyze the scaling behavior of the density of resonances in these structures. We found that by controlling the density of shortcuts (topological randomness) and/or the composite ratio of the binary links (conductivity disorder), one can effectively shape resonance landscapes or suppress or enhance long transient delays in the corresponding random impedance networks.

We study spectral behavior of sparsely connected random networks under the random matrix framework. Subnetworks without any connection among them form a network having perfect community structure. As connections among the subnetworks are introduced, the spacing distribution shows a transition from the Poisson statistics to the Gaussian orthogonal ensemble statistics of random matrix theory. The eigenvalue density distribution shows a transition to the Wigner’s semicircular behavior for a completely deformed network. The range for which spectral rigidity, measured by the Dyson-Mehta ${\Delta }_3$ statistics, follows the Gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure. The spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure, whereas the density distribution and the ${\Delta }_3$ statistics remain identical to the undeformed network. On the other hand the ${\Delta }_3$ statistics is useful for the larger deformation strengths. Finally, we analyze the spectrum of a protein-protein interaction network for Helicobacter, and compare the spectral behavior with those of the model networks.

Pizza tossing and certain forms of standing-wave ultrasonic motors (SWUMs) share a similar process for converting reciprocating input into continuous rotary motion. We show that the key features of this motion conversion process such as collision, separation and friction coupling are captured by the dynamics of a disk bouncing on a vibrating platform. The model shows that the linear or helical hand motions commonly used by pizza chefs and dough-toss performers for single tosses maximize energy efficiency and the dough’s airborne rotational speed; on the other hand, the semielliptical hand motions used for multiple tosses make it easier to maintain dough rotation at the maximum speed. The system’s bifurcation diagram and basins of attraction also provide a physical basis for understanding the peculiar behavior of SWUMs and provide a means to design them. The model is able to explain the apparently chaotic oscillations that occur in SWUMs and predict the observed trends in steady-state speed and stall torque as preload is increased.