The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillment of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T_c^{\ast }$, whereas the fraction of unbound base pairs grows continuously around and above $T_c^{\ast }$. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus $T$. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuously versus $T$ while the specific heat displays a remarkable peak at $T_c^{\ast }$. The location of the peak versus $T$ varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second-order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.

Networks of the biopolymer actin, cross-linked by the compliant protein filamin, form soft gels. They can, however, withstand large shear stresses due to their pronounced nonlinear elastic behavior. The nonlinear elasticity can be controlled by varying the number of cross-links per actin filament. We propose and test a model of rigid filaments decorated by multiple flexible linkers that is in quantitative agreement with experiment. This allows us to estimate loads on individual cross-links, which we find to be less than 10 pN.

Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected $d$-dimensional network exhibit robust scale-invariance properties, independently of the particular cost function considered, as long as it is convex. We find that, in the limit of large currents, the distribution decays as a power law with an exponent equal to $\left(2d-1\right)/\left(d-1\right)$. The current distribution can be exactly calculated in $d=2$ for all values of the current. Numerical simulations further suggest that the scaling properties remain unchanged for both random injections and by randomizing the convex cost functions.

In this paper we focus on the influence of passive elements on the collective dynamics of oscillatory ensembles. Two major effects considered are (i) the influence of passive elements on the synchronization properties of ensembles of coupled nonidentical oscillators and (ii) the influence of passive elements on the wave dynamics of such systems. For the first effect, it is demonstrated that the introduction of passive elements may lead to both an increase or decrease in the global synchronization threshold. For the second effect, it is also demonstrated that the steady state of the passive element is a key parameter which defines how this passive element affects the wave dynamics of the oscillatory ensemble. It was shown that for different values of this parameter, one can observe increase or decrease in wave propagation velocity and increase or decrease in synchronization frequency in oscillatory ensembles with the growth of influence of passive elements. The results are obtained for the models of cardiac cells dynamics as well as for the Bonhoeffer–Van der Pol model and are compared with data of real biological experiments.

We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.

Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be split into two parts: pseudocontinuous and strongly unstable. The pseudocontinuous part of the spectrum mediates destabilization of periodic solutions.

A Lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken Galilean invariance, the asymptotic form of the probability distribution function of negative velocity differences. The origin of Burgers intermittency is found to rely on the dynamical coupling between shocks, identified to instantons, and noncoherent background fluctuations, which—then—cannot be discarded in a consistent statistical description of the flow.

In the context of dissipation element analysis of scalar fields in turbulence [L. Wang and N. Peters, J. Fluid Mech. 608, 113 (2008)], the elongation of elements by the velocity difference at the minimum and maximum points was found to increase linearly with the length of an element. This paper attempts to provide a theoretical basis for this finding by analyzing two-point properties along the gradient trajectories, of which dissipation elements consist. An equation of the two-point correlation function for the product of the scalar gradient along the same trajectory can be obtained. Similar to the idea of deriving Kolmogorov’s 4/5 law, there exist a scaling in the inertial range for the velocity difference, however, not same as Kolmogorov’s 1/3 scaling. Specifically, by conditioning on gradient trajectories we obtain a linear relation between the velocity difference and the arclength between two points on the same trajectory. Results from direct numerical simulation (DNS) show satisfactory agreement with the theoretical prediction. This result and the derivation thereof may generally be helpful for broad stream of similar statistical and scaling studies of turbulent flows.

The time history of subsequent tunneled wave packets can represent a more meaningful way to describe signal evolutions and to determine the group delay than the detection of a demodulated monopulse envelope. In the present experimental research, the delay of transmitted tunneled packets was found to be shorter than that measurable in vacuum, in good agreement with the phase time and Esposito’s equation and independent of the barrier length. The wave packets did not show narrowing and “reshaping,” so these phenomena did not appear to be the reason of the short delay experienced. The latter was not found to be proportional to the amplitude of the incident signal.

When noise is present in a scattering system, particles tend to escape faster from the scattering region as compared with the noiseless case. For chaotic scattering, noise can render particle-decay exponential, and the decay rate typically increases with the noise intensity. We uncover a scaling law between the exponential decay rate and the noise intensity. The finding is substantiated by a heuristic argument and numerical results from both discrete-time and continuous-time models.

Using the quasiexact density-matrix renormalization-group method and ground-state analysis we study interface delocalization transitions in wide two-dimensional Ising strips subject to long-ranged boundary fields with opposite signs at the two surfaces. Based on this approach, our explicit calculations demonstrate that critical wetting transitions do exist for semi-infinite two-dimensional systems even if the corresponding effective interface potentials decay asymptotically for large $\ell$ as slow as ${\ell }^{-\delta }$ with $\delta <2$, where $\ell$ is the distance of the mean interface position from the one-dimensional surface. This supersedes opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)] and by Privman and Švrakić [Phys. Rev. B 37, 5974 (1988)] obtained within effective interface models. The corresponding wetting phase diagram is determined, including the cases $\delta =2$ and $\delta =49$ with the latter mimicking short-ranged surface fields. Our analysis highlights the limits of reliability of effective interface models.

The excess adsorption $\Gamma$ in two-dimensional Ising strips $\left(\infty \times L\right)$, subject to identical boundary fields at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1{j}^{-p}$, is studied for various values of $p$ and along various thermodynamic paths below the bulk critical point by means of the density-matrix renormalization-group method. The crossover behavior between the complete-wetting and critical-adsorption regimes, occurring in semi-infinite systems, is strongly influenced by confinement effects. Along isotherms $T=\text{const}$ the asymptotic power-law dependences on the external bulk field, which characterize these two regimes, are pre-empted by capillary condensation. Along the pseudo-first-order phase-coexistence line of the strips, which varies with temperature, we find a broad crossover regime in which both the thickness of the wetting film and $\Gamma$ increase as functions of the reduced temperature $\tau$ but do not follow any power law. Above the wetting temperature the order-parameter profiles are not slablike but exhibit wide interfacial variations and pronounced tails.

Using Brownian dynamics computer simulations we show that binary mixtures of colloids driven in opposite directions by an oscillating external field exhibit axial segregation in sheets perpendicular to the drive direction. The segregation effect is stable only in a finite window of oscillation frequencies and driving strengths and is taken over by lane formation in the direction of the driving field if the driving force is increased or the oscillation frequency is decreased. In the crossover regime, bands tilted relative to the drive direction are observed. Possible experiments to verify the axial segregation are discussed.

In this work we extend recent study of the properties of the dense packing of “superdisks,” by Y. Jiao et al. [Phys. Rev. Lett. 100, 245504 (2008)] to the jammed state formed by these objects in random sequential adsorption. The superdisks are two-dimensional shapes bound by the curves of the form ${\left|x\right|}^{2p}+{\left|y\right|}^{2p}=1$, with $p>0$. We use Monte Carlo simulations and theoretical arguments to establish that $p=1/2$ is a special point at which the jamming density, ${\rho }_J\left(p\right)$, has a discontinuous derivative as a function of $p$. The existence of this point can be also argued for by a phenomenological excluded-area argument.

We extend the early time ordering theory of Cahn, Hilliard, and Cook (CHC) so that our generalized theory applies to solid-to-solid transitions. Our theory involves spatial-symmetry breaking (the initial phase contains a symmetry not present in the final phase). The predictions of our generalization differ from those of the CHC theory in two important ways: exponential growth does not begin immediately following the quench and the objects that grow exponentially are not necessarily Fourier modes. Our theory is consistent with simulation results for the long-range antiferromagnetic Ising model.

The extension of a particle (translational deviation) in an isotropic harmonic potential well is linearly proportional and parallel to the applied force. In an anisotropic trapping potential, the extension is instead related to the applied force by a compliance tensor. Using the focal spot of a high numerical aperture zone plate to create an elliptical potential and microfluidics to apply a calibrated force, we measure the two-dimensional extension of a trapped spherical particle. As a function of the orientation of the elliptical potential, the extension sweeps out a circular trajectory, exhibiting extensions both parallel (coflow) and perpendicular (cross flow) to the direction of the flow. The results fit well to a compliance tensor model.

We study the effect of the length scales $\alpha$ and $\beta$ in the Navier–Stokes-$\alpha \beta$ equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier–Stokes-$\alpha$ and Navier–Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for $\beta <\alpha$. The vorticity structures predicted by the Navier–Stokes-$\alpha \beta$ equations also improve as $\beta$ decreases away from $\alpha$. However, optimal choices for $\alpha$ and $\beta$ depend not only on the problem of interest but also on the grid resolution.

In this paper, a lattice Boltzmann model for simulating temperature-sensitive ferrofluids is presented. The lattice Boltzmann equation for modeling the magnetic field is formulated using a scalar magnetic potential. Introducing a time derivative into the original elliptic equation for the scalar potential leads to an advection-diffusion equation, with an effective velocity determined by the temperature gradient. The time derivative is multiplied by an adjustable preconditioning parameter to ensure that the lattice Boltzmann solution remain close to a solution of the original elliptic equation for the scalar potential. To test the present lattice Boltzmann model, numerical simulations for the thermomagnetic nature convection of the ferrofluids in a cubic cavity are carried out. Good agreement between the obtained results and experimental data shows that the present lattice Boltzmann model is promising for studying temperature-sensitive ferrofluid flows.

We consider the effective motion along a cylinder of a particle that freely diffuses in the bulk and intermittently binds to the cylinder. From an exact approach we derive the different regimes of the effective motion along the cylinder characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, interestingly, a saturation regime characteristic for the cylindrical geometry. This saturation in a finite system is not terminal but eventually turns over to normal diffusion along the cylinder. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.

Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and $XY$ universality classes. Several surface universality classes of the confining surfaces are considered, some of which are relevant for recent experiments. An approach introduced previously [O. Vasilyev et al., EPL 80, 60009 (2007)], based inter alia on an integration scheme of free-energy differences, is utilized to compute the universal scaling functions of the critical Casimir forces in the critical range of temperatures above and below the bulk critical temperature. The resulting predictions are compared with corresponding experimental data for wetting films of fluids and with available theoretical results.