We analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time-periodic forces. We focus on the stochastic resonance and phase frequency synchronization of the collective variable, defined as the arithmetic mean of the variable characterizing each element of the array. For single-unit systems, stochastic resonance can be understood with the powerful tools of linear response theory. Proper noise-induced phase frequency synchronization for a single-unit system in this linear response regime does not exist. For coupled arrays, our numerical simulations indicate an enhancement of the stochastic resonance effects leading to gains larger than unity as well as genuine phase frequency synchronization. The nonmonotonicity of the response with the strength of the coupling strength is investigated. Comparison with simplifying schemes proposed in the literature to describe the random response of the collective variable is carried out.

The distribution of spatial domain structures originated during one- and three-dimensional Poisson-Voronoi transformations are computed analytically extending the recently obtained results for the two-dimensional case. The presented method gives a full description of the developed microstructure and is valid for tessellations of any dimensionality. The temporal and spatial dependences of the domain structure are completely discriminated and separated, showing the existence of geometric configurations independent of time. A single computation of the probability distribution of these geometric configurations allows us to calculate the total free-boundary and size probability distributions at any desired time. The obtained results show full agreement with stochastic simulations and reproduce completely the previously existing partial results. A discussion about the potential applications of the method to the calculation of other geometrical properties and the characteristics of the final static structure leading to a Gamma distribution of sizes is also presented.

We study a moving-boundary model of nonconserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin-film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and attachment processes. A small-slope approximation allows us to derive effective interface evolution equations (IEEs) in which parameters are related to those of the full moving-boundary problem. In particular, the form of the linear dispersion relation of the IEE changes drastically for slow or for instantaneous attachment kinetics. In the former case the IEE takes the form of the well-known (noisy) Kuramoto-Sivashinsky equation, showing a morphological instability at short times that evolves into kinetic roughening of the Kardar-Parisi-Zhang (KPZ) class. In the instantaneous kinetics limit, the IEE combines the Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity, and we provide a numerical study of the ensuing dynamics. In all cases, the long preasymptotic transients can account for the experimental difficulties in observing KPZ scaling. We also compare our results with relevant data from experiments and discrete models.

If the constituent particles of fluid phases interact via long-ranged van der Waals forces, the effective Hamiltonian for interfaces between such fluid phases contains—in lateral Fourier space—nonanalytic terms $\sim q^4\ln q$. Similar nonanalytic terms characterize the effective Hamiltonian for two interacting interfaces which can emerge between the three possible coexisting fluid phases in binary liquid mixtures. This is in contrast with the structure of the phenomenological Helfrich Hamiltonian for membranes, which does not contain such nonanalytic terms. We show that under favorable conditions for the bulk densities characterizing a binary liquid mixture and for the long-ranged interparticle interactions, the corresponding effective Hamiltonian for a model fluid membrane does not exhibit such nonanalytic contributions. We discuss the properties of the resulting effective Hamiltonian, with a particular emphasis on the influence of the long range of the interactions on the coefficient of the bending rigidity.

Adhesion of membranes and filaments on periodic rippled surfaces is studied by means of a one-dimensional model. The adhesion behavior is found to depend crucially on the shape of the ripples. Fakir-carpet and sinusoidal patterns are studied in detail. Infinite staircases of periodic ground states are found, with a periodicity diverging at a transition line. Moreover, the boundaries of the regions of existence of metastable states form a complex sequence on the fakir-carpet surface. This is inferred to lead to an unbinding transition by progressive stages when fluctuations are negligible. The occurrence of adhesion transitions for graphene, carbon nanotubes, and lipidic membranes is discussed quantitatively.

We compute the surface-induced morphology and the free-energy pathways as a cylindrical liquid crystalline filament with preferred homeotropic (orthogonal) interface orientation passes through a sequence of growing sinusoidal perturbations and breaks up into droplets. Liquid crystalline morphology is determined using a simulated annealing algorithm [R. K. Goyal and M. M. Denn, Phys. Rev. E, 75, 021704 (2007)] to minimize the Oseen-Frank free energy. A first-order morphological transition with a finite energy barrier is required when the perturbation amplitude exceeds a critical value, and it is possible that progress towards breakup will be kinetically trapped in a varicose cylindrical shape. This result may be related to the apparent kinetic trapping of dispersed nematic $4^{\prime }$-octyl-4-biphenylcarbonitrile in a gel state reported by Inn and Denn [J. Rheol., 49, 887 (2005)].

We study static and dynamic correlation functions of segmental charge density fluctuation on a rodlike polymer in ionic solutions. The polymer is described by an effective Hamiltonian which incorporates the Coulomb interaction between fluctuating charges screened by ionic fluid environment. We analytically calculate the correlation functions and discuss how charge distribution and dynamics are affected by counterion valency and concentration in electrolyte. We find that the charge correlation exhibits an underdamped oscillation with a wavelength comparable to the counterion size and with the amplitude increasing with the counterion valency. The dynamic correlation of charge density is shown to decay with a characteristic time varying with the counterion valency and concentration. The multivalency gives rise to faster decay of the correlation than that given by one dimensional diffusion.

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this system, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.

We consider circular ensembles with nonuniform weight functions. We investigate the universality of short-range and long-range level fluctuations, which are important in the study of quantum chaotic systems. We analyze a set of hierarchic relations among the correlation functions to obtain the level density for a wide class of potentials and to demonstrate universality of correlation functions in the case of weak periodic potentials (where the term potential refers to the logarithm of the weight function). Analytic study of circular unitary ensemble is done with the help of orthogonal polynomials on the unit circle. For circular orthogonal and symplectic ensembles, we introduce skew-orthogonal polynomials on the unit circle. We consider the asymptotic forms of the polynomials for the three types of ensembles with weak potentials to give a proof of the universality. The analytic results are verified by Monte Carlo simulations of the ensembles with different weight functions. We also discuss the implications of these results in the context of conductance fluctuations in mesoscopic systems and show that the universality breaks down for strong potentials.

We demonstrate that a dynamical system can be switched from a stable steady state to a previously unknown unstable (saddle) steady state using proportional feedback coupling to an auxiliary unstable system. The simplest one-dimensional nonlinear model is treated analytically, the more complicated two-dimensional pendulum is considered numerically, while the damped Duffing-Holmes oscillator is investigated analytically, numerically, and experimentally. Experiments have been performed using a simplified version of the electronic Young-Silva circuit imitating the dynamical behavior of the Duffing-Holmes system. The physical mechanism behind the switching effect is discussed.

Capillary jetting of a fluid dispersed into another immiscible phase is usually limited by a critical capillary number, a function of the Reynolds number and the fluid property ratios. Critical conditions are set when the minimum spreading velocity of small perturbations $v_{-}^{*}$ along the jet (marginal stability velocity) is zero. Here we identify and describe parametric regions of high technological relevance, where $v_{-}^{*}>0$ and the jet flow is always supercritical independently of the dispersed liquid flow rate; within these relatively broad regions, the jet does not undergo the usual dripping-jetting transition, so that either the jet can be made arbitrarily thin (yielding droplets of any imaginably small size), or the issuing flow rate can be made arbitrarily small. In this work, we provide illustrative analytical studies of asymptotic cases for both negligible and dominant inertia forces. In this latter case, requiring a nonzero jet surface velocity, axisymmetric perturbation waves “surf” downstream for all given wave numbers, while the liquid bulk can remain static. In the former case (implying small Reynolds flow) we found that the jet profile small slope is limited by a critical value; different published experiments support our predictions.

A model is developed which explains the collective plasma phenomena associated with the extended Franck-Hertz experiment described in an earlier paper by Nicoletopoulos [Eur. J. Phys. 23, 533 (2002)]. The particular focus is on the formation of the free steady-state monotonic double layer. The approach used is a Bernstein-Greene-Kruskal theory in which one postulates the space potential and a suitable multicomponent electron distribution and uses Poisson’s equation to solve for a physically meaningful ion distribution. A key feature is that the input space potential is chosen with a spatial scale much larger than the electron Debye length, with a restricting condition derivable from the prescribed form of volume production of positive ions. The model provides good quantitative agreement with the experimental results for mercury vapor, and can provide sufficient and necessary conditions for double layer formation in other atomic gases in similar experimental arrangements.

In the semidiscrete limit and in suitably scaled coordinates, the voltage of a system of coupled nonlinear dispersive transmission lines is described by a nonlinear Schrödinger equation. This equation is used to study the transverse stability of solitary waves of the system. Exact results for the growth rate and the corresponding perturbation function of linear transverse perturbations are obtained in terms of the network’s and soliton’s parameters.

The phase diagram of $\alpha$-cyclodextrin/water/4-methylpyridine solutions, a system undergoing inverse melting, has been studied by differential scanning calorimetry, rheological methods, and x-ray diffraction. Two different fluid phases separated by a solid region have been observed in the high $\alpha$-cyclodextrin concentration range $(c⩾150\mathrm{mg}∕\mathrm{ml})$. Decreasing $c$, the temperature interval where the solid phase exists decreases and eventually disappears, and a first-order phase transition is observed between the two different fluid phases.

The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin-coherent-state formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finite-size effects are also analyzed, leading in particular to logarithmic corrections near the singularities occurring in the spectrum. Finally, we also compute expectation values of the spin operators in a semiclassical analysis in order to illustrate some subtle effects occurring in one region of the parameter space.

We devise a message passing algorithm for probabilistic inference in composite systems, consisting of a large number of variables, that exhibit weak random interactions among all variables and strong interactions with a small subset of randomly chosen variables; the relative strength of the two interactions is controlled by a free parameter. We examine the performance of the algorithm numerically on a number of systems of this type for varying mixing parameter values.

We analyze the dynamics of paramagnetic particles on a paramagnetic substrate under a rotational magnetic field. When the paramagnetic particles are subjected to a rotational magnetic field, the rotational plane of which is perpendicular to the substrate surface, the particles form chain clusters caused by the dipole-dipole interaction between the particles and these clusters display a tumbling motion under certain conditions. In this case, the angular momentum of the clusters is converted to a translational one through the force of friction acting between the particles and substrate and, as a result, the clusters move along the surface of the substrate. We analyze the conditions under which the tumbling motion occurs and the dependence of the translational velocity of a cluster on the control parameters by the Stokesian dynamics method. Based on the dynamics of magnetic particles, we propose a method of manipulating nano- and microparticles using a rotational magnetic field. We demonstrate the manipulation of magnetic and nonmagnetic particles, a carbon nanotube, and a biological cell.

Smectic-$A$ elastomers combine the positional long-range order of mesogenic molecules in one dimension with the rubber elasticity of a polymer network. While the influence of uniaxial mechanical fields on the phase structure has been investigated intensively during recent years, the impact of shear forces on the orientation of mesogens remains unclear. We present x-ray experiments under shear strain, showing an induced macroscopic tilt depending on the applied shear angle and geometry of the setup.

Stenull and Lubensky [Phys. Rev. E 76, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a smectic-$A$ elastomer subjected to a simple shear will develop smectic-$C$-like tilt of the director. Recently, Kramer and Finkelmann [e-print arXiv:0708.2024; Phys. Rev. E 78, 021704 (2008)], performed shear experiments on smectic-$A$ elastomers using two different shear geometries. One of the experiments, which implements simple shear, produces clear evidence for the development of smectic-$C$-like tilt. Here, we generalize a model for smectic elastomers introduced by Adams and Warner [Phys. Rev. E 71, 021708 (2005)] and use it to study the magnitude of $\mathrm{Sm}C$-like tilt under shear for the two geometries investigated by Kramer and Finkelmann. Using reasonable estimates of model parameters, we estimate the tilt angle for both geometries, and we compare our estimates to the experimental results. The other shear geometry is problematic since it introduces additional in-plane compressions in a sheetlike sample, thus inducing instabilities that we discuss.

The male Troides magellanus—a birdwing butterfly that lives in a restricted area of the Philippines—concentrates on its hindwings at least two distinct optical processes that contribute to its exceptional visual attraction. The first is the very bright uniform yellow coloration caused by a pigment which generates yellow-green fluorescence, and the other is a blue-green iridescence which results from light diffraction at grazing emergence under a specific illumination. Detailed optical measurements reveal that these optical effects are correlated, the fluorescence being enhanced by illuminations conditions that favor the occurrence of the iridescence. These effects are analyzed, with the conclusion that both of them depend on the same optical device: a one-dimensional microribs grating which appear on the sides of the ridges that run along the yellow scales.