Self-propelled particles move along circles rather than along a straight line when their driving force does not coincide with their propagation direction. Examples include confined bacteria and spermatozoa, catalytically driven nanorods, active, anisotropic colloidal particles and vibrated granulates. Using a non-Hamiltonian rate theory and computer simulations, we study the motion of a Brownian “circle swimmer” in a confining channel. A sliding mode close to the wall leads to a huge acceleration as compared to the bulk motion, which can further be enhanced by an optimal effective torque-to-force ratio.

Long-range interactions (LRIs) slow down the excitation trapping in quantum transport on a one-dimensional chain with traps at both ends when compared to the case with only nearest-neighbor interactions. This is in contrast to the corresponding classical case, in which LRIs lead to faster excitation trapping. The reason for the slowing down is to be found in subtle changes—due to LRIs—in the spectrum of the Hamiltonian. Pertubation theory allows an analytical analysis of this fact.

For a two-level quantum mechanical system, we derive microscopically the exact expression for the fluctuation of microscopic work in a multistep nonequilibrium process, and we rigorously prove that in an isothermal process, the fluctuation is vanishingly small and the most probabilistic work is just equal to the difference of the free energy. Our study demonstrates that the convergence of the microscopic work in the isothermal process is due to the nature of the isothermal process rather than the usual thermodynamic limit condition. Our investigation justifies the validity of a “minimum work principle” formulation of the second law even for a small system far from the thermodynamic limit.

The Casimir force and free energy at low temperatures have been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is made. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the analytic results.

We study the breakdown of a random fiber bundle model (RFBM) with $n$ discontinuities in the threshold distribution using the global load sharing scheme. In other words, $n+1$ different classes of fibers identified on the basis of their threshold strengths are mixed such that the strengths of the fibers in the $i\text{th}$ class are uniformly distributed between the values ${\sigma }_{2i-2}$ and ${\sigma }_{2i-1}$, where $1⩽i⩽n+1$. Moreover, there is a gap in the threshold distribution between $i\text{th}$ and $(i+1)\text{−}\text{th}$ class. We show that although the critical stress depends on the parameter values of the system, the critical exponents are identical to that obtained in the recursive dynamics of a RFBM with a uniform distribution and global load sharing. The avalanche size distribution, on the other hand, shows a nonuniversal, non-power-law behavior for smaller values of avalanche sizes which becomes prominent only when a critical distribution is approached. We establish that the behavior of the avalanche size distribution for an arbitrary $n$ is qualitatively similar to a RFBM with a single discontinuity in the threshold distribution $(n=1)$, especially when the density and the range of threshold values of fibers belonging to strongest $(n+1)\text{−}\text{th}$ class is kept identical in all the cases.

The mathematics of time-dependent nonlinear response theory frequently leads to results which although formally exact, are not amenable to experimental application or even to use in computer simulations. Here we give a rigorous derivation of a tractable expression for the thermostatted nonlinear response of classical many body systems to time-dependent dissipative fields. The theory also allows for the concurrent parametric transformation of the system Hamiltonian. Our analysis shows once again the intimate relationship between nonequilibrium free-energy relations such as the Jarzynski equality and nonlinear response theory. We make a few remarks concerning the maximum entropy production approximation.

A well-defined two-dimensional single barchan dune under the force of a shearing water flow is investigated experimentally. From an initially prepared triangular heap a rapid relaxation to a steady-state solution is observed with constant mass, shape, and velocity. This attractor exhibits all characteristic features of barchan dunes found in nature, namely a gently inclined windward side, crest, brink, and steep lee face. The relaxation time towards the steady state increases with mass. For small dunes we find significant deviations from a fixed height-length aspect ratio. As predicted by recent theoretical models, the migration velocity scales reciprocal to the length of the dune.

$\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$-based ferrogels were prepared with both isotropic and anisotropic orientation of the magnetic anisotropy axis of the magnetic particles. In contrast to the superparamagnetic properties of the ferrofluid, the ferrogels exhibit hysteresis, indicating that (i) a significant fraction of magnetic particles has volumes beyond the critical value that allows Néelian relaxation, and (ii) a mechanical interaction between the particles and the polymer network exists, which prevents the particles from Brownian relaxation. The contribution of such particles was investigated by field cooling field warming and zero field cooling field warming measurements as well as temperature-dependent magnetization measurements. By application of an external field during gel polymerization, a magnetic texture was induced as confirmed by the angular dependence of $m_R∕m_S$ and $H_C$. The net-magnetic torque, exerted on the magnetic particles in an anisotropic ferrogel in combination with the soft elastic properties of the gel matrix enables the application as torsional soft actuator as demonstrated.

A wide-range memory effect in deformed helix ferroelectric liquid crystals (DHFLCs) has been investigated by electro-optical and textural methods. A comparative study has been performed on strongly and weakly anchored surfaces of DHFLC cells. The saturation voltage has been compared in both types of cells by studying the variation of tilt angle and spontaneous polarization with applied voltage. The long-lasting memory effect has been observed in untreated (weakly anchored) cells. It has been proposed that perfect memory in DHFLC cells without any surface treatment is due to the possibility of the absence of depolarization and ionic charges over the surfaces of the cells.

On cooling through the isotropic-to-nematic phase transition in a cell whose substrates induce a large pretilt angle ${\theta }_0$ from the vertical direction, but with no preferential azimuthal orientation, tilt domains appear. The boundary walls between reverse tilt domains are found to be bendlike and twistlike when ${\theta }_0(T=T_{NI})$ is sufficiently large just below the isotropic-nematic phase transition temperature $T_{NI}$—i.e., for a nearly planar orientation. Here the director becomes planar approximately midway through the wall, and we refer to this type of wall as “polar horizontal,” which is topologically stable. However, if ${\theta }_0(T=T_{NI})$ is sufficiently small just below $T_{NI}$—i.e., closer to vertical orientation—a splay like and twistlike domain wall obtains, where the director is vertically oriented approximately midway through the wall; we refer to this type of wall as “polar vertical,” whose stability depends on the anchoring. On cooling through the nematic phase, the pretilt angle ${\theta }_0$ decreases, with the director aligning closer to the vertical orientation. Nevertheless, the structures of both types of domain walls remain unchanged on variation of ${\theta }_0$ with temperature owing to topological constraints and also are unchanged after the application and removal of a large electric field. We examine the structure of domain walls for the liquid crystal ZLI-4330 (Merck) as a function of pretilt angle ${\theta }_0(T=T_{NI})$ and calculate a critical value ${\theta }_0^c(T=T_{NI})$ of the pretilt angle just below $T_{NI}$ for which the predominance of domain walls crosses over from polar horizontal to polar vertical.

Viruses have traditionally been studied as pathogens, but in recent years they have been adapted for applications ranging from drug delivery and gene therapy to nanotechnology, photonics, and electronics. Although the structures of many viruses are known, most of their biophysical properties remain largely unexplored. Using Brillouin light scattering, we analyzed the mechanical rigidity, intervirion coupling, and vibrational eigenmodes of Wiseana iridovirus (WIV). We identified phonon modes propagating through the viral assemblies as well as the localized vibrational eigenmode of individual viruses. The measurements indicate a Young’s modulus of $\sim 7\mathrm{GPa}$ for single virus particles and their assemblies, surprisingly high for “soft” materials. Mechanical modeling confirms that the DNA core dominates the WIV rigidity. The results also indicate a peculiar mechanical coupling during self-assembly of WIV particles.

We demonstrate experimentally control of a chaotic system on time scales much shorter than in any previous study. Combining a multisection laser with an external Fabry-Perot etalon, the chaotic output transforms into a regular intensity self-pulsation with a frequency in the $10\text{−}\mathrm{GHz}$ range. The control is noninvasive as the feedback from the etalon is minimum when the target state is reached. The optical phase is identified as a crucial control parameter. Numerical simulations agree well with the experimental data and uncover global control properties.

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen et al., Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

In complex network research clique percolation, introduced by Palla, Derényi, and Vicsek [Nature (London) 435, 814 (2005)], is a deterministic community detection method which allows for overlapping communities and is purely based on local topological properties of a network. Here we present a sequential clique percolation algorithm (SCP) to do fast community detection in weighted and unweighted networks, for cliques of a chosen size. This method is based on sequentially inserting the constituent links to the network and simultaneously keeping track of the emerging community structure. Unlike existing algorithms, the SCP method allows for detecting $k$-clique communities at multiple weight thresholds in a single run, and can simultaneously produce a dendrogram representation of hierarchical community structure. In sparse weighted networks, the SCP algorithm can also be used for implementing the weighted clique percolation method recently introduced by Farkas et al. [New J. Phys. 9, 180 (2007)]. The computational time of the SCP algorithm scales linearly with the number of $k$-cliques in the network. As an example, the method is applied to a product association network, revealing its nested community structure.

A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In fact, the density function of residence times near stagnation points obeys an inverse-square law, due to a mechanism similar to type-I intermittency. However, unlike intermittent chaos, in which the alternation between long stagnant phases and rapid moving phases occurs in a random manner, here the alternation occurs in a quasiperiodic manner. In particular, in the case of a gradient with the golden ratio, the renewal of the largest residence time occurs at positions corresponding to the Fibonacci sequence. Finally, the asymptotic long-time behavior, in the form of a nested logarithm, is theoretically derived. Compared with the Pomeau-Manneville intermittency, a significant difference in the relaxation property of the long-time average of the dynamical variable is found.

Analytical expressions for the collision frequency for momentum transfer and the friction force experienced by a Maxwellian ion population drifting with respect to the uniform neutral atom background are derived. The calculations make use of different models for the collision cross section for momentum transfer accounting for the relative speed $v_r$ between the colliding particles. These results are compared with the currently used semi-empirical equations for the friction force and collision frequency in the fluid equations for weakly ionized plasmas. The kinetic model calculations are in agreement for suprathermal ion flows while they present discrepancies of orders of magnitude for subthermal ion drift speeds $u_d$. However, for the collision cross section ${\sigma }_m\sim 1∕v_r$, the magnitude of the friction force results proportional to $u_d$ and the collision frequency becomes constant regardless of the magnitude of the ion drift speed in both cases. These results are relevant for ion populations drifting in a plasma which could be approximated by shifted Maxwellian distributions, as in collisional plasma sheaths or plasma double layers.

The bifurcation ratio for the equiprobable binary tree model is formulated. We obtain the exact expression of the $k\text{th}$ moment of the second-order streams. We also obtain a recursive equation between $r\text{th}$ and $(r+1)\text{th}$ order streams. Horton’s law is confirmed numerically by calculating this recursive equation and asymptotic properties of the bifurcation ratio are discussed.

Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter $\Delta$ the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. $NPT$ Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with $\Delta >0$ are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich et al., Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter $\Delta >0$ is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter ${\sigma }_c$ of the Schulz distribution, and three-phase equilibria can occur for large values of ${\sigma }_c$.

To better understand the subsurface velocity field and flowing layer structure, we have performed a detailed numerical study using the discrete element method for the flow of monodisperse particles in half-full three-dimensional (3D) and quasi-2D rotating tumblers. Consistent with prior measurements at the surface, a region of high speed flow with axial components of velocity occurs near each endwall in long tumblers. This region can be eliminated by computationally omitting the friction at the endwalls, confirming that a mass balance argument based on the slowing of particles immediately adjacent to the frictional endwalls explains this phenomenon. The high speed region with the associated axial flow near frictional endwalls persists through the depth of the flowing layer, though the regions of high velocity shift in position and the velocity is lower compared to the surface. The axial flow near the endwalls is localized and independent with the length of the tumbler for tumblers longer than one tumbler diameter, but these regions interact for shorter tumblers. In quasi-2D tumblers, the high speed regions near the endwalls merge resulting in a higher velocity than occurs in a long tumbler, but with a flowing layer that is not as deep. Velocity fluctuations are altered near the endwalls. Particle velocity fluctuations are greatest just below the surface and diminish through the depth of the flowing layer.

The segmentation of vertebrate embryos, a process known as somitogenesis, depends on a complex genetic network that generates highly dynamic gene expression in an oscillatory manner. A recent proposal for the mechanism underlying these oscillations involves negative-feedback regulation at transcriptional translational levels, also known as the “delay model” [J. Lewis Curr. Biol. 13, 1398 (2003)]. In addition, in the zebrafish a longitudinal positional information signal in the form of an Fgf8 gradient constitutes a determination front that could be used to transform these coupled intracellular temporal oscillations into the observed spatial periodicity of somites. Here we consider an extension of the delay model by taking into account the interaction of the oscillation clock with the determination front. Comparison is made with the known properties of somite formation in the zebrafish embryo. We also show that the model can mimic the anomalies formed when progression of the determination wave front is perturbed and make an experimental prediction that can be used to test the model.