We have considered a Brownian particle confined in a two-dimensional bilobal enclosure where the state of the particle represents a bit of information having binary value 0 (left lobe) or 1 (right lobe). A time linear force is applied on the particle, driving it selectively to a particular lobe, and thus erasing one bit of information. We explore the statistics of heat and work associated with memory erasure to realize the Landauer limit in the entropic domain. Our results suggest that the mean value of work done associated with the complete erasure procedure satisfies the Landauer bound even when the memory is purely entropic in nature.

Mean-field theory tells us that the classical critical exponent of susceptibility is twice that of magnetization. However, linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances, in the low-energy phase. We clarify that this strange exponent is due to the existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by $N$-body simulations for the equilibrium states and a family of quasistationary states.

In this paper, we show how the numerical theory introduced by the authors [Carbone and Putignano, J. Mech. Phys. Solids 61, 1822 (2013)] can be effectively employed to study the contact between viscoelastic rough solids. The huge numerical complexity is successfully faced up by employing the adaptive nonuniform mesh developed by the authors in Putignano et al. [J. Mech. Phys. Solids 60, 973 (2012)]. Results mark the importance of accounting for viscoelastic effects to correctly simulate the sliding rough contact. In detail, attention is, first, paid to evaluate the viscoelastic dissipation, i.e., the viscoelastic friction. Fixed the sliding speed and the normal load, friction is completely determined. Furthermore, since the methodology employed in the work allows to study contact between real materials, a comparison between experimental outcomes and numerical prediction in terms of viscoelastic friction is shown. The good agreement seems to validate—at least partially—the presented methodology. Finally, it is shown that viscoelasticity entails not only the dissipative effects previously outlined, but is also strictly related to the anisotropy of the contact solution. Indeed, a marked anisotropy is present in the contact region, which results stretched in the direction perpendicular to the sliding speed. In the paper, the anisotropy of the deformed surface and of the contact area is investigated and quantified.

The number of stem cells in a colonic crypt is often very small, which leads to large intrinsic fluctuations in the cell population. Based on the model of cell population dynamics with linear feedback in a colonic crypt, we present a stochastic dynamics of the cell population [including stem cells (SCs), transit amplifying cells (TACs), and fully differentiated cells (FDCs)]. The Fano factor, covariance, and susceptibility formulas of the cell population around the steady state are derived by using the Langevin theory. In the range of physiologically reasonable parameter values, it is found that the stationary populations of TACs and FDCs exhibit an approximately threshold behavior as a function of the net growth rate of TACs, and the reproductions of TACs and FDCs can be classified into three regimens: controlled, crossover, and uncontrolled. With the increasing of the net growth rate of TACs, there is a maximum of the relative intrinsic fluctuations (i.e., the Fano factors) of TACs and FDCs in the crossover region. For a fixed differentiation rate and the net growth rate of SCs, the covariance of fluctuations between SCs and TACs has a maximum in the crossover region. However, the susceptibilities of both TACs and FDCs to the net growth rate of TACs have a minimum in the crossover region.

Clustering, or transitivity, a behavior observed in real-world networks, affects network structure and function. This property has been studied extensively, but most of this research has been limited to clustering in single networks. The effect of clustering on the robustness of coupled networks, on the other hand, has received much less attention. Only the case of a pair of fully coupled networks with clustering has recently received study. Here we generalize the study of clustering of a fully coupled pair of networks and apply it to a partially interdependent network of networks with clustering within the network components. We show, both analytically and numerically, how clustering within networks affects the percolation properties of interdependent networks, including the percolation threshold, the size of the giant component, and the critical coupling point at which the first-order phase transition changes to a second-order phase transition as the coupling between the networks is reduced. We study two types of clustering, one proposed by Newman [Phys. Rev. Lett. 103, 058701 (2009)] in which the average degree is kept constant while the clustering is changed, and the other by Hackett et al. [Phys. Rev. E 83, 056107 (2011)] in which the degree distribution is kept constant. The first type of clustering is studied both analytically and numerically, and the second is studied numerically.

We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent $\sim 0.5$ as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.

An analytical model for energy absorption during the interaction of an ultrashort, ultraintense laser with an overdense plasma is proposed. Both the compression effect of the electron density profile and the oscillation of the electron plasma surface are self-consistently included, which exhibit significant influences on the laser energy absorption. Based on our model, the general scaling law of the compression effect depending on laser strength and initial density is derived, and the temporal variation of the laser absorption due to the boundary oscillating effect is presented. It is found that due to the oscillation of the electron plasma surface, the laser absorption rate will vibrate periodically at $\omega$ or 2$\omega$ frequency for the $p$-polarized and $s$-polarized laser, respectively. The effect of plasma collision on the laser absorption has also been investigated, which shows a considerable rise in absorption with increasing electron-ion collision frequency for both polarizations.

Shock ignition concept is a promising approach to inertial confinement fusion that may allow obtaining high fusion energy gains with the existing laser technology. However, the spike driving laser intensities in the range of 1–10 PW/cm${}^2$ produces the energetic electrons that may have a significant effect on the target performance. The hybrid numerical simulations including a radiation hydrodynamic code coupled to a rapid Fokker-Planck module are used to asses the role of hot electrons in the shock generation and the target preheat in the time scale of 100 ps and spatial scale of 100 $\mu$m. It is shown that depending on the electron energy distribution and the target density profile the hot electrons can either increase the shock amplitude or preheat the imploding shell. In particular, the exponential electron energy spectrum corresponding to the temperature of 30 keV in the present HiPER target design preheats the deuterium-tritium shell and jeopardizes its compression. Ways of improving the target performance are suggested.

The study of the low temperature phase of spin glass models by means of Monte Carlo simulations is a challenging task, because of the very slow dynamics and the severe finite-size effects they show. By exploiting at the best the capabilities of standard modern CPUs (especially the streaming single instruction, multiple data extensions), we have been able to simulate the four-dimensional Edwards-Anderson model with Gaussian couplings up to sizes $L=70$ and for times long enough to accurately measure the asymptotic behavior. By quenching systems of different sizes to the critical temperature and to temperatures in the whole low temperature phase, we have been able to identify the regime where finite-size effects are negligible: $\xi \left(t\right)\lesssim L/7$. Our estimates for the dynamical exponent ($z\simeq 1/T$) and for the replicon exponent ($\alpha \simeq 1.0$ and $T$ independent), that controls the decay of the spatial correlation in the zero overlap sector, are consistent with the replica symmetry breaking theory, but the latter differs from the theoretically conjectured value.

Adversarial satisfiability (AdSAT) is a generalization of the satisfiability (SAT) problem in which two players try to make a Boolean formula true (resp. false) by controlling their respective sets of variables. AdSAT belongs to a higher complexity class in the polynomial hierarchy than SAT, and therefore the nature of the critical region and the transition are not easily parallel to those of SAT and worthy of independent study. AdSAT also provides an upper bound for the transition threshold of the quantum satisfiability problem (QSAT). We present a complete algorithm for AdSAT, show that 2-AdSAT is in $\mathbf{P}$, and then study two stochastic algorithms (simulated annealing and its improved variant) and compare their performances in detail for 3-AdSAT. Varying the density of clauses $\alpha$ we claim that there is a sharp SAT-UNSAT transition at a critical value whose upper bound is ${\alpha }_c\lesssim 1.5$, suggesting a much stricter upper bound for the QSAT transition than those previously found.

We present a treatable generalization of the Sherrington-Kirkpatrick (SK) model which introduces correlations in the elements of the coupling matrix through multiplicative disorder on the single variables and investigate the consequences on the phase diagram. We define a generalized $q_{EA}$ parameter and test the structural stability of the SK results in this correlated case evaluating the de Almeida–Thouless line of the model. As a main result we demonstrate the increase of temperature chaos effects due to heterogeneities.

The Soret coefficient ($S_T$) of positively charged magnetic colloids was measured as a function of the nanoparticles’ diameter. The $Z$-scan technique and the generalization of the thermal lens model proved to be a reliable technique to measure $S_T$. We show that $S_T$ is negative and increases with the particle's diameter, being best described by a functional dependence of the type $S_T\propto d_0$. Potentiometric and conductometric experiments show that the particle's surface charge decreases as the temperature increases, changing the electrostatic interaction between the nanoparticles. The temperature gradient imposed in the ferrofluid by the Gaussian laser beam leads to the formation of the particle's concentration gradient. The origin of this phenomenon is discussed in terms of the decrease of the particle's surface charge in the hottest region of the sample and the thermoelectric field due to the inhomogeneous distribution of hydrogenous ions present in the colloidal suspension.

Inspired by recent experiments on hierarchically structured adhesives, we analyze here the effect of spatial variation in surface topography and shear modulus of an elastomeric adhesive on its ability to adhere strongly to a flexible contactor. The undulation of surface and modulus both were assumed to be periodic with periodicity, which is either identical or different for the two parameters; for identical periodicity, the phase lag between the respective undulations is also systematically varied. Calculations show that during continuous lifting of the flexible contactor from complete initial contact, the interfacial crack between the two adherents does not propagate continuously but intermittently, with crack arrest and initiation at the vicinity of minimum thickness and modulus of the layer; the torque required to initiate an arrested crack increases significantly over that required to propagate it on a smooth adhesive surface. The adhesion strength estimated from the corresponding force vs displacement plot is calculated to be higher than that achieved on a smooth and featureless adhesive surface. For in-phase variation in topography and shear modulus of the layer, the adhesive strength is found to be higher than for nonzero phase lag between the two parameters. The adhesion strength is found to diminish also for nonidentical periodicity between modulus and surface undulation. We have derived a scaling law for relating adhesion strength to several of these parameters.

We show that both the extraordinarily large nonlinear response and the light-induced permanent reorientation in liquid crystals doped by the azo dye methyl red originates from the same phenomenon of modification of the charge density on the irradiated surface. The demonstration is done by applying ac voltage to the samples, showing that in this case no permanent anchoring is possible. The measurements confirm the role of photoisomerization that gives a transient contribution to the actual reorientation process only in the high dose regime. This result allows us to draw a picture for light-induced effects that might be applied to a large class of compounds.

This article presents a physical theory for the aggregation of ionomer molecules in aqueous solution. To study this phenomenon, we consider a system of charged rigid rods with uniform surface charge immersed in water. The free-energy functional derived for this system consists of hydrophobic and direct electrostatic contributions as well as entropic terms. Energy minimization gives the stable aggregation number as a function of surface charge density, surface tension, geometric parameters, and density of rods in solution. We provide configuration diagrams of the system, which display the impact of the hydrophobic and electrostatic interaction strengths on the stabilization of finite-size bundles.

The self-assembly of biomolecules, such as peptides and proteins, into filaments is conventionally understood as a nucleated polymerization reaction. However, detailed analysis of experimental observation has revealed recently that nucleation pathways generate growth-competent nuclei via a cascade of metastable intermediate species, which are omitted in conventional models of filamentous growth based on classical nucleation theory. Here we take an analytical approach to generalizing the classical theory of nucleated polymerization to include the formation of these prenucleation clusters, providing a quantitative general classification of the behavior exhibited by these nucleation-conversion-polymerization reactions. A phase diagram is constructed, and analytical predictions are derived for key experimental observables. Using this approach, we delineate the characteristic time scales that determine the nature of biopolymer growth phenomena.

We present a stochastic formalism for signal transduction processes in a bacterial two-component system. Using elementary mass action kinetics, the proposed model takes care of signal transduction in terms of a phosphotransfer mechanism between the cognate partners of a two-component system, viz., the sensor kinase and the response regulator. Based on the difference in functionality of the sensor kinase, the noisy phosphotransfer mechanism has been studied for monofunctional and bifunctional two-component systems using the formalism of the linear noise approximation. Steady-state analysis of both models quantifies different physically realizable quantities, e.g., the variance, the Fano factor (variance/mean), and mutual information. The resultant data reveal that both systems reliably transfer information of extracellular environment under low external stimulus and in a high-kinase-and-phosphatase regime. We extend our analysis further by studying the role of the two-component system in downstream gene regulation.

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies $L$ sites and attempts movements over a distance of $d$ lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity) to parametrized finite networks, and show that a variety of biological and social networks are hyperbolic. This hyperbolicity property has strong implications on the higher-order connectivity and other topological properties of these networks. Specifically, we derive and prove bounds on the distance among shortest or approximately shortest paths in hyperbolic networks. We describe two implications of these bounds to crosstalk in biological networks, and to the existence of central, influential neighborhoods in both biological and social networks.

We study the conditions of amplitude death in a network of delay-coupled limit cycle oscillators by including time-varying delay in the coupling and self-feedback. By generalizing the master stability function formalism to include variable-delay connections with high-frequency delay modulations (i.e., the distributed-delay limit), we analyze the regimes of amplitude death in a ring network of Stuart-Landau oscillators and demonstrate the superiority of the proposed method with respect to the constant delay case. The possibility of stabilizing the steady state is restricted by the odd-number property of the local node dynamics independently of the network topology and the coupling parameters.