The stability of a simple dynamical system subject to multiplicative one-side pulse noise with hidden periodicity is investigated both analytically and numerically. The stability analysis is based on the exact result for the characteristic functional of the renewal pulse process. The influence of the memory effects on the stability condition is analyzed for two cases: (i) the dead-time-distorted Poissonian process, and (ii) the renewal process with Pareto distribution. We show that, for fixed noise intensity, the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity.

A self-consistent rate-equation (RE) approach to irreversible island growth and nucleation is presented which takes into account cluster mobility. As a first application, we consider the irreversible growth of compact islands on a two-dimensional surface in the presence of monomer deposition (with rate $F$) and monomer diffusion (with rate $D_1$) while the mobility of an island of size $s$ is assumed to satisfy $D_s=D_1{s}^{-\mu }$ where $\mu >0$. Results are obtained for the dependence of the island-density and island-size distribution (ISD) on the parameters $D_1/F$, $\mu$, and coverage $\theta$. For all values of $\mu$, we find excellent agreement between our self-consistent RE results and simulation results for the island and monomer densities, up to and even somewhat beyond the coverage corresponding to the peak island density. We also find good agreement between our self-consistent RE and simulation results for the portion of the ISD corresponding to island sizes less than the average island-size $S$. However, for larger island sizes the effects of correlations become important and as a result the agreement is not as good. Using our self-consistent RE approach we also demonstrate that the discrepancies between simulations and recent mean-field predictions for the exponent $\tau \left(\mu \right)$ describing the power-law size dependence of the ISD for $\mu <1$ can be explained almost entirely by geometric effects. Our results are also compared with those obtained using a simpler mean-field Smoluchowski approach. In general, we find that, except for the case $\mu =1/2$ (for which the island and monomer densities are reasonably well predicted), such an approach leads to results which are in poor agreement with the simulations.

We study the dependence of the critical size of the nucleus on the density of impurity by carrying out a Monte Carlo simulation. We assume that the impurities are fixed on a crystal surface, and neglect restoration of bonds between an impurity atom and an adsorbed atom. We initially prepare one cluster in the system and investigate the change of the cluster size. When the cluster size is the critical value, the frequency of increasing the cluster size is equal to that of decreasing the size. With increasing the impurity density, the critical nucleus becomes large. When the impurity density is sufficiently high, regardless of the initial cluster size, the cluster vanishes after a long time interval, namely, the critical cluster size is diverged.

The changes in the x-ray diffraction diagram induced by an electric field have been studied in four bent-core liquid crystals. Two of the compounds present columnar B${}_1$ phases and the other two show dark conglomerate (DC) structures. In the B${}_1$ materials the electric field gives rise to switchable phases whose diffraction pattern is that of the smectic C polar (SmCP) phase. In the DC structures the positions of the Bragg reflections remain essentially unaltered, but in one of the compounds the peaks become narrower under field, indicating that the correlation length of the smectic order increases. A slight enhancement of the smectic spacing is found in the DC phases upon field application.

We investigate the cholesteric-nematic transition induced by an external bulk field in a sample of finite thickness $\ell$. The analysis is performed by considering a tilted magnetic field with respect to the easy direction imposed by rigid boundary conditions inducing planar orientation. In the case of parallel orientation between the magnetic field and of the easy direction, in the limit of $\ell \to \infty$ we reobtain the results of de Gennes where the effective pitch of the cholesteric is a continuous function of the magnetic field diverging at the critical field related to the cholesteric-nematic transition. For finite $\ell$ we obtain a cascade of transitions, where the bulk expels a half-pitch at a time to avoid divergences in the elastic energy, in a similar manner as solids expel defects in the presence of strong deformation. In the case of oblique orientation between the magnetic field and the easy direction, only the completely untwisted state depends on the tilt angle. Therefore, only the cholesteric-nematic transition depends on the tilt angle while all the other magnetic transition values are unchanged.

We consider a three-state model comprising tumor cells, effector cells, and tumor-detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress tumor cell growth completely. Whereas the deterministic model does not reveal a stable tumor-free state, the auto-correlated noise combined with cross-correlation functions can either lead to tumor-dormant states, tumor progression, as well as to an elimination of tumor cells. The auto-correlation function exhibits a finite correlation time $\tau$, while the cross-correlation functions shows a white-noise behavior. The evolution of each of the three kinds of cells leads to a multiplicative noise coupling. The model is investigated by means of a multivariate Fokker-Planck equation for small $\tau$. The different behavior of the system is, above all, determined by the variation of the correlation time and the strength of the cross-correlation between tumor and tumor-detecting cells. The theoretical model is based on a biological background discussed in detail, and the results are tested using realistic parameters from experimental observations.

In this Brief Report, we calculate the electric-double-layer (EDL) electrostatic potential in a system of several layers of immiscible electrolytes. Verwey-Niessen theory predicts that at the interface between two immiscible electrolytes back-to-back EDLs are formed. The present analysis extends this idea to the case where the immiscible liquids are contained inside a domain with given electrostatic potentials at its boundaries, where the thickness of the individual liquid layer can be comparable to the EDL thickness. Such a system gives rise to a situation where the overall EDL electrostatic potential in the system is dictated by the competitive influences of the boundary-induced effects and the effects induced by the jump in the ion-solvent interaction potential at the liquid-liquid interfaces. Invoking Debye-Hückel linearization, we derive an analytical result for the EDL electrostatic potential for two immiscible electrolyte layers, and extend it for a general system of $N$ such immiscible electrolyte layers. We demonstrate that, depending upon the nature of the interfacial ion-solvent interaction potential jump, the overall EDL potential may manifest a strong influence of the boundary conditions or may invert the influence of the boundary conditions. Effects such as a variation of the ratio of the permittivity or the thickness of the liquids also dictate the overall potential profiles.

In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed at a given value. Within this scheme of finite-size scaling, we exploit the statistical covariance between the observables in a Monte Carlo simulation in order to reduce the statistical errors of the quantities involved in the computation of the critical exponents. This method is general and does not require additional computational time. This approach is demonstrated in the Ising model in two and three dimensions, where large gain factors in CPU time are obtained.

Complex systems consisting of vector or matrix oscillators can synchronize to a common state characterized by a frequency matrix with distinct eigenvalues, leading to multiple frequencies of synchronization. In quantum networked systems the synchronized state is a linear combination of states corresponding to different energy levels. Suitable symmetry-breaking network interactions, however, allow only one or more such frequencies to appear. A specific example in three dimensions, where all trajectories lie on the 2-sphere, is a model of interacting spin-1 quantum angular momentum states, where synchronization to a nontrivial frequency occurs despite the presence of zero-frequency modes of oscillation.

In this work we study the properties of a relativistic mixture of two nonreacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity. In particular, we address the nature of the density, or pressure gradient term that arises in the solution of the linearized Boltzmann equation in this context. Such an effect, also present for the single component problem, has, so far, not been analyzed from the point of view of the Onsager resciprocity relations. To address this matter, we propose two alternatives for the Onsagerian matrix which comply with the corresponding reciprocity relations. The implications of both representations are briefly analyzed.

Near the liquid-vapor critical point in pure fluids, material and thermal properties vary considerably with temperature. In a series of microgravity experiments, sulfur hexafluoride (SF${}_6$) was heated ∼1 K above its critical temperature, then quenched below the critical temperature in order to form gas and liquid domains. We found a power law exponent of 0.389 ± 0.010 for the growth of the wetting layer thickness during the intermediate stage of phase separation. Full and microscopic view images of the sample cell unit were analyzed to determine the changes in the size distribution of liquid droplets inside the gas phase over time. We found that the distribution of diameters for liquid droplets always contains a fraction of very small droplets, presumably due to a continuous nucleation process. At the same time, the size distribution flattens over time and rapidly includes large-size droplets, presumably generated through a coalescence mechanism. By following both a large gas bubble over two hours of video recordings, we found periodic and synchronous motion of the gas bubble along both the $x$ and $y$ directions. By following a large liquid droplet embedded into the large gas bubble, we found periodic, out of phase motions, which we related to Marangoni convection. The experimentally measured velocity of the liquid droplet is in good agreement with the theoretical predicted velocity of ∼0.386 μm/s obtained from Young's thermocapillary effect.

Magnetophoresis—the motion of magnetic particles under applied magnetic gradient—is a process of great interest in novel applications of magnetic nanoparticles and colloids. In general, there are two main different types of magnetophoresis processes: cooperative magnetophoresis (a fast process enhanced by particle-particle interactions) and noncooperative magnetophoresis (driven by the motion of individual particles in magnetic fields). In the case of noncooperative magnetophoresis, we have obtained a simple analytical solution which allows the prediction of the magnetophoresis kinetics from particle characterization data (size and magnetization). Our comparison with new experimental results shows good quantitative agreement. In addition, we show the existence of a universal curve onto which all experimental results should collapse after proper rescaling. The range of applicability of the analytical solution is discussed in light of the predictions of a magnetic aggregation model [Soft Matter 7, 2336 (2011)].

We present experimental measurements of dynamical heterogeneities in a dense system of microgel spheres, sheared at different rates and at different packing fractions in a microfluidic channel, and visualized with high-speed digital video microscopy. A four-point dynamic susceptibility is deduced from video correlations, and is found to exhibit a peak that grows in height and shifts to longer times as the jamming transition is approached from two different directions. In particular, the time for particle-size root-mean square relative displacements is found to scale as ${\tau }^{*}\sim {\left(\dot{\gamma }\Delta {\phi }^4\right)}^{-1}$, where $\dot{\gamma }$ is the strain rate and $\Delta \phi =|\phi -{\phi }_c|$ is the distance from the random close-packing volume fraction. The typical number of particles in a dynamical heterogeneity is deduced from the susceptibility peak height and found to scale as $n^{*}\sim {\left(\dot{\gamma }\Delta {\phi }^4\right)}^{-0.3}$. Exponent uncertainties are less than ten percent. We emphasize that the same power-law behavior is found at packing fractions above and below ${\phi }_c$. Thus our results considerably extend a previous observation of $n^{*}\sim {\dot{\gamma }}^{-0.3}$ for granular heap flow at fixed packing below ${\phi }_c$. Furthermore, the implied result $n^{*}\sim {\left({\tau }^{*}\right)}^{0.3}$ compares well with the expectation from mode-coupling theory and with prior observations for driven granular systems.

We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluid-fluid and fluid-wall long-range forces. We first reexamine the wetting properties of the model in the zero-curvature limit, i.e., for a planar wall, using an effective interfacial Hamiltonian approach in the framework of the well known sharp-kink approximation (SKA). We obtain very good agreement with a mean-field density functional theory (DFT), fully justifying the use of SKA in this limit. We then turn our attention to substrates of finite curvature and appropriately modify the so-called soft-interface approximation (SIA) originally formulated by Napiórkowski and Dietrich [Phys. Rev. B34, 6469 (1986)] for critical wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the SKA functional form for the film growth. However, it turns out that the agreement between SKA and our DFT is only qualitative. We then show that the quantitative discrepancy between the two is due to the overestimation of the liquid-gas surface tension within SKA. On the other hand, by relaxing the assumption of a sharp interface, with, e.g., a simple “smoothing” of the density profile there, markedly improves the predictive capability of the theory, making it quantitative and showing that the liquid-gas surface tension plays a crucial role when describing wetting on a curved substrate. In addition, we show that in contrast to SKA, SIA predicts the expected mean-field critical exponent of the liquid-gas surface tension.

Two identical autonomous dynamical systems coupled in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. Recently, AS was shown to occur in systems of simplified neuron models, requiring the coupling of the neuronal membrane potential with its delayed value. However, this coupling has no obvious biological correlate. Here we propose a canonical neuronal microcircuit with standard chemical synapses, where the delayed inhibition is provided by an interneuron. In this biologically plausible scenario, a smooth transition from delayed synchronization (DS) to AS typically occurs when the inhibitory synaptic conductance is increased. The phenomenon is shown to be robust when model parameters are varied within a physiological range. Since the DS-AS transition amounts to an inversion in the timing of the pre- and post-synaptic spikes, our results could have a bearing on spike-timing-dependent plasticity models.

We investigated the folding transition between an elongated coil state and a compact state on a single polymer chain confined in a small space with different stiffness with the aid of Monte Carlo simulation. In a flexible polymer, the folding transition is retarded in a confined space. In contrast, the transition is promoted for a semiflexible chain, in which the discontinuity of the volume change occupied by a single chain is diminished by confinement. This unique confinement effect is interpreted in terms of conformational entropy and self-avoiding repulsive interaction.

The multibody dynamics of a system of chemical swarm robots in a porous environment is investigated. The chemical swarm robots are modeled as Brownian particles capable of delivering an encapsulated chemical payload toward a given target location and releasing it in response to an external stimulus. The presence of chemical signals (chemo-attractant) in the system plays a crucial role in coordinating the collective movement of the particles via chemotaxis. For a number of applications, such as distributed chemical processing and targeted drug delivery, the understanding of factors that govern the collective behavior of the particles, especially their ability to localize a given target, is of immense importance. A hybrid modeling methodology based on the combination of the Brownian dynamics method and diffusion problem coupled through the chemotaxis phenomena is used to analyze the impact of a varying signaling threshold and the strength of chemotaxis on the ability of the chemical robots to fulfill their target localization mission. The results demonstrate that the selected performance criteria (the localization half time and the success rate) can be improved when an appropriate signaling process is chosen. Furthermore, for an optimum target localization strategy, the topological complexity of the porous environment needs to be reflected.

A dynamical model is presented for chiral change in DNA molecules. The model is an extension of the conventional elastic model, which incorporates the structure of base pairs and uses a spinor representation for the DNA configuration together with a gauge principle. Motivated by a recent experiment reporting chiral transitions between right-handed B-DNA and left-handed Z-DNA [Lee et al., Proc. Natl. Acad. Sci. (USA) 107, 4985 (2010)], we analyze the free energy for the particular case of linear DNA with an externally applied torque. The model shows that there exists, at low temperature, a rapid structural change depending on the torque exerted on the DNA, which causes switching in B and Z domain sizes. This can explain the frequent switches of DNA extension observed in experiments.

The stationary points (SPs) of a potential-energy landscape play a crucial role in understanding many of the physical or chemical properties of a given system. However, unless they are found analytically, no efficient method is available to obtain all the SPs of a given potential. We present a method, called the numerical polynomial-homotopy-continuation method, which numerically finds all the SPs, and is embarrassingly parallelizable. The method requires the nonlinearity of the potential to be polynomial-like, which is the case for almost all of the potentials arising in physical and chemical systems. We also certify the numerically obtained SPs so that they are independent of the numerical tolerance used during the computation. It is then straightforward to separate out the local and global minima. As a first application, we take the XY model with power-law interaction, which is shown to have a polynomial-like nonlinearity, and we apply the method.

We study the traffic dynamics in complex networks where each link is assigned a limited and identical bandwidth. Although the first-in–first-out (FIFO) queuing rule is widely applied in the routing protocol of information packets, here we argue that if we drop this rule, the overall throughput of the network can be remarkably enhanced. We propose some efficient routing strategies that do not strictly obey the FIFO rule. Compared to the routine shortest-path strategy, throughput for both Barabási-Albert (BA) networks and the Internet can be improved by a factor of more than five. We calculate the theoretical limitation of the throughput. In BA networks, our proposed strategy can achieve 88% of the theoretical optimum, yet for the Internet, it is about 12%, implying that we still have a huge space to further improve the routing strategy for the Internet. Finally, we discuss possibly promising ways to design more efficient routing strategies for the Internet.