We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We show that, in this case of broken symmetry, the corrections to scaling contain information on the Goldstone modes. We present a comprehensive Lee-Yang analysis, including the density of zeros, and confirm recent numerical estimates for critical exponents.

We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady state of a chain with $N$ sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle $\theta$. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady-state currents scale as $1/N^2$ for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to $2\theta /N$.

The drag force on an object, or “intruder,” in a granular material arises from interparticle friction, as well as the cyclic creation and buckling of force chains within the material. In contrast to fluids, for which drag forces are well understood, there is no straightforward relationship between speed and mean drag force in granular materials. We investigate spherical intruder particles of varying radii moving at low speeds through granular beds. The system can be parametrized using the dimensionless Froude number $\text{Fr}=2v/\sqrt{gR}$, for intruders of radius $R$ moving at a speed $v$. For frictional systems, we find the drag force obeys a linear relationship with $\text{Fr}$ for low Froude numbers above $\text{Fr}>1$. For $\text{Fr}<1$ we observe a deviation from this linear trend. This transition can be explained by considering the characteristic inertial and gravitational granular time scales of the system. We show that a suitably normalized measure of dissipated power obeys a linear relationship with the imposed intruder velocity, independent of the intruder dimensions. This is found to hold even for particles with no friction, identifying a relationship between the imposed motion of the intruder and the resistance of the granular material to purely geometric rearrangements.

Many fascinating phenomena such as large-scale collective flows, enhanced fluid mixing, and pattern formation have been observed in so-called active fluids, which are composed of particles that can absorb energy and dissipate it into the fluid medium. For active particles immersed in liquids, fluid-mediated viscous stresses can play an important role on the emergence of collective behavior. Here, we experimentally investigate their role in the dynamics of self-assembling magnetically driven colloidal particles which can rapidly form organized hexagonal structures. We find that viscous stresses reduce hexagonal ordering, generate smaller clusters, and significantly decrease the rate of cluster formation, all while holding the system at constant number density. Furthermore, we show that time and length scales of cluster formation depend on the Mason number (Mn), or ratio of viscous to magnetic forces, scaling as $t\propto \text{Mn}$ and $L\propto {\text{Mn}}^{-1/2}$. Our results suggest that viscous stresses hinder collective behavior in a self-assembling colloidal system.

We perform large-scale simulations of a two-dimensional lattice model for amorphous plasticity with random local yield stresses and long-range quadrupolar elastic interactions. We show that as the external stress increases towards the yielding phase transition, the scaling behavior of the avalanches crosses over from mean-field theory to a different universality class. This behavior is associated with strain localization, which significantly depends on the short-range properties of the interaction kernel.

In chiral smectic-$A$ (Sm-$A$) liquid crystals, an applied electric field induces a tilt of the optic axis from the layer normal. When these materials are of the de Vries type, the electroclinic tilt susceptibility is unusually large, with the field-induced director reorientation accompanied by a substantial increase in optical birefringence with essentially no change in the smectic layer spacing. In order to account for the observed electro-optic behavior, we assume that the molecular orientation distribution in the Sm-$A$ has two degrees of freedom: azimuthal orientation and tilt of the molecular long axis from the layer normal, with the tilt confined to a narrow range of angles. We present a generalized Langevin-Debye model of the response of this orientational distribution to applied field that gives a field-induced optic axis tilt, birefringence, and polarization dependence that agrees well with experimental measurements and reproduces the double-peaked polarization current response characteristic of a first-order Sm-$A^{*}$–Sm-$C^{*}$ transition. Additionally, we find that the measured field-induced polarization and the Langevin-Debye model predictions can be quantitatively described as pre-transitional behavior near the tricritical point of a recently published generalized 3D $XY$ model of interacting hard rods confined to reorient on a cone in the presence of an applied field.

Structures of the mesophases of five members of the 4-$n$-alkyl-4′-cyanobiphenyl homologous series (4-$n$-butyl-4′-cyanobiphenyl to 4-$n$-octyl-4′-cyanobiphenyl) doped with milled BaTiO${}_3$ nanoparticles were investigated by x-ray scattering. Clear solutions of each of the 4-$n$-alkyl-4′-cyanobiphenyls were first prepared in $n$-heptane and then doped with an $n$-heptane/nanoparticle dispersion, which led to gelation. The nanogels were found to be one-dimensional, multilayered, smectic nanostructures in each case. Surprisingly, a characteristic layer spacing of 4.5 nm was observed in all five homologues. Synchrotron x-ray scattering study of the multilayer structures of doped 4-$n$-pentyl-4′-cyanobiphenyl and 4-$n$-octyl-4′-cyanobiphenyl revealed nine orders of the primary Bragg reflection which were used to calculate the electron density profiles of the multilayers by Fourier analysis. The multilayers were found to consist of molecular bilayers wherein the mesogens were arranged in a head-to-head assembly of the polar head groups. The alkyl tails of the mesogenic molecules were freely movable and the tail-to-tail assembly was stabilized by heptane. The dissolved nanoparticles clearly induced a new self-assembled nanostructure in which the rigid aromatic part, and not the overall length, of the molecules defined the layer spacing.

Vesicles, closed membranes made of a bilayer of phospholipids, are considered as a biomimetic system for the mechanics of red blood cells. The understanding of their dynamics under flow and their rheology is expected to help the understanding of the behavior of blood flow. We conduct numerical simulations of a suspension of vesicles in two dimensions at a finite concentration in a shear flow imposed by countertranslating rigid bounding walls by using an appropriate Green's function. We study the dynamics of vesicles, their spatial configurations, and their rheology, namely, the effective viscosity ${\eta }_{\mathrm{eff}}$. A key parameter is the viscosity contrast $\lambda$ (the ratio between the viscosity of the encapsulated fluid over that of the suspending fluid). For small enough $\lambda$, vesicles are known to exhibit tank treading (TT), while at higher $\lambda$ they exhibit tumbling (TB). We find that ${\eta }_{\mathrm{eff}}$ decreases in the TT regime, passes a minimum at a critical $\lambda ={\lambda }_c$, and increases in the TB regime. This result confirms previous theoretical and numerical works performed in the extremely dilute regime, pointing to the robustness of the picture even in the presence of hydrodynamic interactions. Our results agree also with very recent numerical simulations performed in three dimensions both in the dilute and more concentrated regime. This points to the fact that dimensionality does not alter the qualitative features of ${\eta }_{\mathrm{eff}}$. However, they disagree with recent simulations in two dimensions. We provide arguments about the possible sources of this disagreement.

Microtubules consist of 13 protofilaments arranged in the form of a cylinder. The protofilaments are composed of longitudinally attached tubulin dimers that can exist in either a less curved state [GTP-bound tubulin (T)] or a more curved state [GDP-bound tubulin (D)]. Hydrolysis of T into D leaves the straight and laterally attached protofilaments of the microtubule in a mechanically stressed state, thus leading to their unzipping. The elastic energy in the unzipping protofilaments can be harnessed by a force transducer such as the Dam1-kinetochore ring complex in order to exert pulling force on chromosomes during cell division. In the present paper we develop a simple continuum model to obtain this pulling force as a function of the mechanical properties of protofilaments and the size of the Dam1-kinetochore ring. We also extend this model to investigate the role played by the T subunits found at the plus end of the microtubule (the T cap) on the mechanical stability of microtubules.

Protein flexibility is an intrinsic property and plays a fundamental role in protein functions. Computational analysis of protein flexibility is crucial to protein function prediction, macromolecular flexible docking, and rational drug design. Most current approaches for protein flexibility analysis are based on Hamiltonian mechanics. We introduce a stochastic model to study protein flexibility. The essential idea is to analyze the free induction decay of a perturbed protein structural probability, which satisfies the master equation. The transition probability matrix is constructed by using probability density estimators including monotonically decreasing radial basis functions. We show that the proposed stochastic model gives rise to some of the best predictions of Debye-Waller factors or B factors for three sets of protein data introduced in the literature.

We propose a new cellular dynamics scheme for the spontaneous cAMP oscillations in Dictyostelium discoideum. Our scheme seamlessly integrates both receptor dynamics and G-protein dynamics into our previously developed cellular dynamics scheme. Extensive computer simulation studies based on our new cellular dynamics scheme were conducted in mutant cells to evaluate the molecular network. The validity of our proposed molecular network as well as the controversial PKA-dependent negative feedback mechanism was supported by our simulation studies. Spontaneous cAMP oscillations were not observed in a single mutant cell. However, multicellular states of various mutant cells consistently initiated spontaneous cAMP oscillations. Therefore, cell-to-cell coordination via the cAMP receptor is essential for the robust initiation of spontaneous cAMP oscillations.

Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung et al., J. Math. Biol. 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about $80\%$ of the recordings of ABP together with ICP and the partial oxygen pressure (${\text{TiPO}}_2$) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.

We consider a modification of the adaptive contact process that, interpreted in the context of opinion dynamics, breaks the symmetry of the coevolutionary voter model by assigning to each node type a different strategy to promote consensus: Orthodox opinion holders spread their opinion via social pressure and rewire their connections following a segregationist strategy; heterodox opinion holders adopt a proselytic strategy, converting their neighbors through personal interactions, and relax to the orthodox opinion according to its representation in the population. We give a full description of the phase diagram of this asymmetric model, using the standard pair approximation equations and assessing their performance by comparison with stochastic simulations. We find that although global consensus is favored with regard to the symmetric case, the asymmetric model also features an active phase. We study the stochastic properties of the corresponding metastable state in finite-size networks, discussing the applicability of the analytic approximations developed for the coevolutionary voter model. We find that, in contrast to the symmetric case, the final consensus state is predetermined by the system's parameters and independent of initial conditions for sufficiently large system sizes. We also find that rewiring always favors consensus, both by significantly reducing convergence times and by changing their scaling with system size.

In order to investigate collective effects of interactions between pedestrians and attractions, this study extends the social force model. Such interactions lead pedestrians to form stable clusters around attractions, or even to rush into attractions if the interaction becomes stronger. It is also found that for high pedestrian density and intermediate interaction strength, some pedestrians rush into attractions while others move to neighboring attractions. These collective patterns of pedestrian movements or phases and transitions between them are systematically presented in a phase diagram. The results suggest that safe and efficient use of pedestrian areas can be achieved by moderating the pedestrian density and the strength of attractive interaction, for example, in order to avoid situations involving extreme desire for limited resources.

Experiments are presented to describe the effect of capacitive coupling of two electrochemical oscillators during Ni dissolution in sulfuric acid solution. Equivalent circuit analysis shows that the coupling between the oscillators occurs through the difference between the differentials of the electrode potentials. The differential nature of the coupling introduces strong negative nonisochronicity (i.e., phase shear, strong dependence of the period on the amplitude) in the coupling mechanism with smooth oscillators (under conditions just above a Hopf bifurcation point). Because of the negative nonisochronicity, asymmetrically coupled oscillators exhibit anomalous phase synchronization in the form of frequency difference enhancement. At strong coupling bistability is observed between in-phase and antiphase synchronized states. With relaxation oscillators, in contrast to the resistive coupling where antiphase synchronization can occur, the typical system response with weak coupling is out-of-phase synchronization. When the capacitance is applied on the individual resistors attached to the electrodes the oscillators exhibit weak positive nonisochronicity; this is in contrast with the strong negative nonisochronicity obtained with cross coupling. The proposed coupling configurations reveal the importance of the nonisochronicity level of oscillations for the experimentally observed synchronization patterns and also provide efficient ways of tuning the nonisochronicity level of the oscillations. This latter feature can be exploited to design synchronization features with a combination of resistive (difference) and capacitive (differential) coupling.

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

We investigate the dynamic mechanisms of generation of amplitude and phase resonance in a phenomenological electrochemical cell model in response to sinusoidal inputs. We describe how the attributes of the impedance and phase profiles change as the participating physicochemical parameters vary within a range corresponding to the existence of stable nodes and foci in the corresponding autonomous system, thus extending previous work that considered systems close to limit cycle regimes. The method we use permits us to understand how changes in these parameters generate amplifications of the cell's response at the resonant frequency band and captures some important nonlinear effects.

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

In this paper, we consider a radial displacement of a viscous fluid by another one of much lower viscosity through a three-dimensional uniform porous medium. It is well known that when a less viscous fluid is pumped at a constant injection rate, very complex interfacial patterns are formed. The control and eventual suppression of these instabilities are relevant to a large number of areas in science and technology. Here, we use a variational approach to search for an analytical form of an optimal flow rate so that the interface between two almost neutrally buoyant fluids grows, but the emergence of interfacial disturbances is minimized. We find a closed analytical solution for the ideal flow rate which surprisingly does not depend on either the properties of the fluids or the permeability of the porous medium.

In turbulent suspensions, collision rates determine how rapidly particles coalesce or react with each other. To determine the collision rate, many numerical studies rely on the ghost collision approximation (GCA), which simply records how often pairs of point particles come within a threshold distance. In many applications, the suspended particles stick (or in the case of liquid droplets, coalesce) upon collision, and it is the frequency of first contact which is of interest. If a pair of “ghost” particles undergoes multiple collisions, the GCA may overestimate the true collision rate. Here, using fully resolved direct numerical simulations of turbulent flows at moderate Reynolds number (${\mathrm{Re}}_{\lambda }=130$), we investigate the prevalence and properties of multiple collisions. We find the probability $P\left(N_c\right)$ for a given pair of ghost particles to collide $N_c$ times to be of the form $P\left(N_c\right)=\beta {\alpha }^{N_c}$ for $N_c>1$, where $\alpha$ and $\beta$ are coefficients which depend upon the particle inertia. We also investigate the statistics of the times that ghost particles remain in contact. We show that the probability density function of the contact time is different for the first collision. The difference is explained by the effect of caustics in the phase space of the suspended particles. We demonstrate that, as a result of multiple collisions, the GCA leads to a small, but systematic overestimate of the collision rate, which is of the order of $\sim 15\%$ when the particle inertia is small, and slowly decreases when inertia increases.