Aggregation processes generally lead to broad distributions of sizes involving exponential tails. Here, experiments on the capillary-driven coalescence of regularly spaced flexible structures yields a self-similar distribution of sizes with no tail. At a given step, the physical process imposes a maximal size for the aggregates, which appears as the relevant scale for the distribution. A simple toy model involving the aggregation of nearest neighbors exhibits the same statistics. A mean-field theory accounting for a maximal size is in agreement with both experiments and numerics. This approach is extended to iterative fragmentation processes where the largest object is broken at each step.

Closed-loop or feedback control ratchets use information about the state of the system to operate with the aim of maximizing the performance of the system. In this paper we investigate the effects of a time delay in the feedback for a protocol that performs an instantaneous maximization of the center-of-mass velocity. For the one and the few particle cases the flux decreases with increasing delay, as an effect of the decorrelation of the present state of the system with the information that the controller uses, but the delayed closed-loop protocol succeeds to perform better than its open-loop counterpart provided the delays are smaller than the characteristic times of the Brownian ratchet. For the many particle case, we also show that for small delays the center-of-mass velocity decreases for increasing delays. However, for large delays we find the surprising result that the presence of the delay can improve the performance of the nondelayed feedback ratchet and the flux can attain the maximum value obtained with the optimal periodic protocol. This phenomenon is the result of the emergence of a dynamical regime where the presence of the delayed feedback stabilizes one quasiperiodic solution or several (multistability), which resemble the solutions obtained in the so-called threshold protocol. Our analytical and numerical results point towards the feasibility of an experimental implementation of a feedback controlled ratchet that performs equal or better than its optimal open-loop version.

By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martín-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.

A thermoreversible (physical) gel of a nematic liquid crystal in its planar configuration is investigated. The transition temperatures of the gel are thermally and rheologically determined. The temperature for the nematic-isotropic transition is higher than that for the gel-sol transition, allowing the network to grow in the oriented nematic phase. The electrical Fréedericksz transition of the gel is investigated by using both an optical and an electrical detection method. The transition can be adjusted within a large voltage range by selecting the temperature of the sample. This behavior is determined by the thermal properties of the thermoreversible gel network.

The dielectric anisotropy of liquid crystals causes director reorientation in an applied electric field and is thus at the heart of electro-optic applications of these materials. The components of the dielectric tensor are frequency dependent. Until recently, this frequency dependence was not accounted for in a description of director dynamics in an electric field. We theoretically derive the reorienting dielectric torque acting on the director, taking into account the entire frequency spectrum of the dielectric tensor. The model allows one to include the effects of multiple relaxations in both parallel and perpendicular components of the dielectric tensor, thus generalizing a recent model [Y. Yin et al., Phys. Rev. Lett. 95, 087801 (2005)] limited by the single-relaxation approach. The model predicts the “dielectric memory effect” (DME)—i.e., dependence of the dielectric torque on both the “present” and “past” values of the electric field and the director. The model describes the experimentally observed director reorientation in the case when the rise time of the applied voltage is smaller than the dielectric relaxation time. In typical materials such as pentylcyanobiphenyl (5CB), in which the dielectric anisotropy is positive at low frequencies, the DME slows down the director reorientation in a sharply rising electric field, as the sharp front is perceived as a high-frequency excitation for which the dielectric anisotropy is small or even of a negative sign. In materials that are dielectrically negative, the DME speeds up the response when a sharp pulse is applied.

We examine the role of electrostatic interactions in the assembly of empty spherical viral capsids. The charges on the protein subunits that make the viral capsid mutually interact and are expected to yield electrostatic repulsion acting against the assembly of capsids. Thus, attractive protein-protein interactions of nonelectrostatic origin must act to enable the capsid formation. We investigate whether the interplay of repulsive electrostatic and attractive interactions between the protein subunits can result in the formation of spherical viral capsids of a preferred radius. For this to be the case, we find that the attractive interactions must depend on the angle between the neighboring protein subunits (i.e., on the mean curvature of the viral capsid) so that a particular angle(s) is (are) preferred energywise. Our results for the electrostatic contributions to energetics of viral capsids nicely correlate with recent experimental determinations of the energetics of protein-protein contacts in the hepatitis B virus [P. Ceres A. Zlotnick, Biochemistry 41, 11525 (2002)].

The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.

The spatial energy distributions of beams of protons accelerated by ultrahigh intensity $(>{10}^{19}\mathrm{W}∕{\mathrm{cm}}^2)$ picosecond laser pulse interactions with thin foil targets are investigated. Using separate, low intensity $(<{10}^{13}\mathrm{W}∕{\mathrm{cm}}^2)$ nanosecond laser pulses, focused onto the front surface of the target foil prior to the arrival of the high intensity pulse, it is demonstrated that the proton beam profile can be actively manipulated. In particular, results obtained with an annular intensity distribution at the focus of the low intensity beam are presented, showing smooth proton beams with a sharp circular boundary at all energies, which represents a significant improvement in the beam quality compared to irradiation with the picosecond beam alone.

We study magnetic effects induced by rigidly rotating plates enclosing a cylindrical magnetohydrodynamic (MHD) Taylor-Couette flow at the finite aspect ratio $H∕D=10$. The fluid confined between the cylinders is assumed to be liquid metal characterized by small magnetic Prandtl number, the cylinders are perfectly conducting, an axial magnetic field is imposed with Hartmann number $\text{Ha}\approx 10$, and the rotation rates correspond to Reynolds numbers of order ${10}^2–{10}^3$. We show that the end plates introduce, besides the well-known Ekman circulation, similar magnetic effects which arise for infinite, rotating plates, horizontally unbounded by any walls. In particular, there exists the Hartmann current, which penetrates the fluid, turns in the radial direction, and together with the applied magnetic field gives rise to a force. Consequently, the flow can be compared with a Taylor-Dean flow driven by an azimuthal pressure gradient. We analyze the stability of such flows and show that the currents induced by the plates can give rise to instability for the considered parameters. When designing a MHD Taylor-Couette experiment, special care must be taken concerning the vertical magnetic boundaries so that they do not significantly alter the rotational profile.

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.

We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in $\mathcal{D}$ dimensions. The results in $\mathcal{D}=1$ are those of the thermodynamic Bethe ansatz for the nonlinear Schrödinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for $\mathcal{D}⪢1$ and, in the limit $\mathcal{D}\to \infty$, a phase transition occurs at $T>0$. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite $\mathcal{D}$.

We show that the correlation between the frequency of subthreshold pacemaker activity and the response of an excitable array is resonantly dependent on the intensity of additive spatiotemporal noise. Thereby, the effect of the underlying network, defining the interactions among excitable units, largely depends on the coupling strength. Only for intermediate coupling strengths is the small world property able to enhance the stochastic resonance, whereas for smaller and larger couplings the impact of the transition from diffusive to random networks is less profound. Thus, the optimal interplay between a localized source of weak rhythmic activity and the response of the whole array demands a delicate balance between the strength of excitation transfer and the effectiveness of the network structure to support it.

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.

The Green-function formalism for the electromagnetic field in a magnetoelectric (ME) medium is constructed as a generalization of conventional Casimir theory. Zero temperature is assumed. It is shown how the formalism predicts electromagnetic momentum to be extracted from the vacuum field, just analogous to how energy is extracted in the Casimir case. The possibility of extracting momentum from vacuum was discussed recently by Feigel [Phys. Rev. Lett. 92, 020404 (2004)]. In contrast to Feigel’s approach, we assume that the ME coupling occurs naturally, rather than being produced by external strong fields. We also find the same effect qualitatively via another route by considering one single electromagnetic mode.

We study finite-size effects on the dynamics of a one-dimensional zero-range process which shows a phase transition from a low-density disordered phase to a high-density condensed phase. The current fluctuations in the steady state show striking differences in the two phases. In the disordered phase, the variance of the integrated current shows damped oscillations in time due to the motion of fluctuations around the ring as a dissipating kinematic wave. In the condensed phase, this wave cannot propagate through the condensate, and the dynamics is dominated by the long-time relocation of the condensate from site to site.

The master asymptotic behavior of the usual parachor correlations, expressing surface tension $\sigma$ as a power law of the density difference ${\rho }_L-{\rho }_V$ between coexisting liquid and vapor, is analyzed for a series of pure compounds close to their liquid-vapor critical point, using only four critical parameters ${\left({\beta }_c\right)}^{-1}$, ${\alpha }_c$, $Z_c$, and $Y_c$, for each fluid. This is accomplished by the scale dilatation method of the fluid variables where, in addition to the energy unit ${\left({\beta }_c\right)}^{-1}$ and the length unit ${\alpha }_c$, the dimensionless numbers $Z_c$ and $Y_c$ are the characteristic scale factors of the ordering field along the critical isotherm and of the temperature field along the critical isochore, respectively. The scale dilatation method is then formally analogous to the basic system-dependent formulation of the renormalization theory. Accounting for the hyperscaling law $\frac{\delta -1}{\delta +1}=\frac{\eta -2}{2d}$, we show that the Ising-like asymptotic value ${\pi }_a$ of the parachor exponent is unequivocally linked to the critical exponents $\eta$ or $\delta$ by $\frac{{\pi }_a}{d-1}=\frac{2}{d-(2-\eta )}=\frac{\delta +1}{d}$ (here $d=3$ is the space dimension). Such mixed hyperscaling laws combine either the exponent $\eta$ or the exponent $\delta$, which characterizes bulk critical properties of $d$ dimension along the critical isotherm or exactly at the critical point, with the parachor exponent ${\pi }_a$ which characterizes interfacial properties of $d-1$ dimension in the nonhomogeneous domain. Then we show that the asymptotic (symmetric) power law ${\left({\alpha }_c\right)}^{d-1}{\beta }_c\sigma =D_{\rho }^{\sigma }{\left(\frac{{\rho }_L-{\rho }_V}{2{\rho }_c}\right)}^{{\pi }_a}$ is the two-dimensional critical equation of state of the liquid-gas interface between the two-phase system at constant total (critical) density ${\rho }_c$. This power law complements the asymptotic (antisymmetric) form $({\mu }_{\rho }-{\mu }_{\rho ,c})\frac{{\rho }_c}{p_c}=\pm D_{\rho }^c{\mid \frac{\rho -{\rho }_c}{{\rho }_c}\mid }^{\delta }$ of the three-dimensional critical equation of state for a fluid of density $\rho \ne {\rho }_c$ and pressure $p\ne p_c$, maintained at constant (critical) temperature $T=T_c$ [${\mu }_{\rho }\left({\mu }_{\rho ,c}\right)$ is the specific (critical) chemical potential; $p_c$ is the critical pressure; and $T_c$ is the critical temperature]. We demonstrate the existence of the related universal amplitude combination $D_{\rho }^c{\left(D_{\rho }^{\sigma }\right)}^{d∕(1-d)}=R_{D\sigma }=\text{universal}$ constant, constructed with the amplitudes $D_{\rho }^{\sigma }$ and $D_{\rho }^c$, separating then the respective contributions of each scale factor $Y_c$ and $Z_c$, characteristic of each thermodynamic path, i.e., the critical isochore and the critical isotherm (or the critical point), respectively. The main consequences of these theoretical estimations are discussed in light of engineering applications and process simulations where parachor correlations constitute one of the most practical methods for estimating surface tension from density and capillary rise measurements.

We consider a class of bistable periodically perturbed ordinary differential equations of importance in mathematical physics and derive an asymptotic criterion for the existence of a tricritical point (TCP). Surprisingly, in the adiabatic limit the criterion is local and very simple. It also allows one to calculate the location of a TCP in parameter space, which we illustrate with three examples.

In this paper we investigate some statistical mechanical properties of systems consisting of two hard disks in a circular cavity and two hard spheres in a cylindrical pore. Both systems conserve not only the total energy but the total angular momentum, and this conservation affects thermodynamic quantities such as the temperature and pressure of these systems. We show the dependence of the thermodynamic quantities of these systems on conserved quantities with a statistical mechanical treatment and molecular dynamics simulations.

We present a theory for the lifetime $T(N,f)$ of a ligand-receptor cluster with $N$ bonds under constant external force $F=fN$, where $f$ is force per bond. We show that there exists a critical force per bond $f_c$ such that at large $N$ when $f>f_c$ the lifetime $T(N,f)$ is independent of cluster size $N$; when $f<f_c$ the lifetime scales as $\ln \left[T(N,f)\right]\sim N$ due to a free energy barrier with height $\sim N$ along the dissociation path; when $f=f_c$, the lifetime scales as $T(N,f)\sim N^{1∕3}$ due to strong fluctuation of a number of closed bonds. Our study shows that adhesion clusters with more bonds are more stable at small $f$ but respond to external force as fast as smaller adhesion clusters at large $f$.

We consider the influence of global feedback control which acts on an oscillatory system governed by a subcritical Ginzburg-Landau equation. Exact solutions corresponding to solitary-wave solutions are obtained. A generalized variational approach is applied for the simplification of the whole problem and its reduction to a finite-dimensional dynamical model. The finite-dimensional evolution model is used for studying the indirect interaction between solitary waves caused by the global control. The stability analysis is held in the framework of the finite-dimensional model. The boundaries of monotonic and oscillatory instabilities are obtained. The basic types of dynamics provided by the finite-dimensional model are described and compared with the results of a direct numerical simulation of the original equation.