We study glass behavior in a mixture of elliptic and circular particles in two dimensions at low temperatures using an orientation-dependent Lennard-Jones potential. The ellipses have a mild aspect ratio ($\sim$$1.2)$ and tend to align at low temperatures, while the circular particles play the role of impurities disturbing the ellipse orientations at a concentration of $20\%$. These impurities have a size smaller than that of the ellipses and attract them in the homeotropic alignment. As a result, the coordination number around each impurity is mostly 5 or 4 in glassy states. We realize double glass, where both the orientations and the positions are disordered but still hold mesoscopic order. We find a strong heterogeneity in the flip motions of the ellipses, which sensitively depends on the impurity clustering. In our model, a small fraction of the ellipses still undergo flip motions relatively rapidly even at low temperatures. In contrast, the nonflip rotations (with angle changes not close to $\pm \pi$) are mainly caused by the cooperative configuration changes involving many particles. Then, there arises a long-time heterogeneity in the nonflip rotations closely correlated with the dynamic heterogeneity in displacements.

We study the irreversible growth of magnetic thin films under the influence of spatially periodic fields by means of extensive Monte Carlo simulations. We find first-order pseudo-phase-transitions that separate a dynamically disordered phase from a dynamically ordered phase. By analogy with time-dependent oscillating fields applied to Ising-type models, we qualitatively associate this dynamic transition with the localization-delocalization transition of spatial hysteresis loops. Depending on the relative width of the magnetic film $L$ compared to the wavelength of the external field $\lambda$, different transition regimes are observed. For small systems ($L<\lambda$), the transition is associated with the standard stochastic resonance regime, while for large systems ($L>\lambda$), the transition is driven by anomalous stochastic resonance. The origin of the latter is identified as due to the emergence of an additional relevant length scale, namely, the roughness of the spin domain switching interface. The distinction between different stochastic resonance regimes is discussed at length both qualitatively by means of snapshot configurations and quantitatively via residence-length and order-parameter probability distributions.

We report interesting self-assembly structures of nematic liquid-crystal colloid (NLCC) networks, which are arrested during cooling from the isotropic temperature to room temperature. The NLCC is composed of sterically stabilized colloidal particles and a nematic liquid crystal (NLC) with nematic-isotropic transition temperature ($T_{NI}$) that is much higher than those of previously studied 4-Cyano-4'-pentylbiphenyl and N-(4-Methoxybenzylidene)-4-butylaniline. We find that the structure of NLCCs depends on $T_{NI}$, cooling rates, and boundary conditions, varying from cellular network to hierarchical fern structures in different length scales. Our time-lapse study shows that the transition from the cellular network to the fern structure directly corresponds to the transition from a spinodal demixing to a nucleation-and-growth mechanism.

We model the mechanics of associating trivalent dendrimer network glasses with a focus on their energy dissipation properties. Various combinations of sticky bond (SB) strength and kinetics are employed. The toughness (work to fracture) of these systems displays a surprising deformation-protocol dependence; different association parameters optimize different properties. In particular, “strong, slow” SBs optimize strength, while “weak, fast” SBs optimize ductility via self-healing during deformation. We relate these observations to breaking, reformation, and partner switching of SBs during deformation. These studies point the way to creating associating-polymer network glasses with tailorable mechanical properties.

We investigate inverse stochastic resonance (ISR), a recently reported phenomenon in which the spiking activity of a Hodgkin-Huxley model neuron subject to external noise exhibits a pronounced minimum as the noise intensity increases. We clarify the mechanism that underlies ISR and show that its most surprising features are a consequence of the dynamical structure of the model. Furthermore, we show that the ISR effect depends strongly on the procedures used to measure it. Our results are important for the experimentalist who seeks to observe the ISR phenomenon.

We analyze zero-lag and cluster synchrony of delay-coupled nonsmooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with nonidentical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.

We investigate the critical properties of Ising models on a regularized Apollonian network (RAN), here defined as a kind of Apollonian network in which the connectivity asymmetry associated with its corners is removed. Different choices for the coupling constants between nearest neighbors are considered and two different order parameters are used to detect the critical behavior. While ordinary ferromagnetic and antiferromagnetic models on a RAN do not undergo a phase transition, some antiferrimagnetic models show an interesting infinite-order transition. All results are obtained by an exact analytical approach based on iterative partial tracing of the Boltzmann factor as an intermediate step for the calculation of the partition function and the order parameters.

Characterizing the influence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states. This transition cannot be explained only through the analysis of the spectral density of the connectivity matrix. We provide a low-dimensional approximation that shows the role of both the structure and disorder in the dynamics.

Thermosensitive fluorescent nanoparticles seeded in deionized water combined with confocal microscopy enables thermal mapping over three dimensions of the liquid phase flowing through a microchannel interrupted by a microdiaphragm. This experiment reveals the presence of a strong thermal gradient up to $\sim$10${}^5$ K$/$m only when hydrodynamic cavitation is present. Here hydrodynamic cavitation is the consequence of high shear rates downstream in the diaphragm. This temperature gradient is located in vortical structures associated with eddies in the shear layers. We attribute such overheating to the dissipation involved by the cavitating flow regime. Accordingly, we demonstrate that the microsizes of the device enhance the intensity of the thermal gap.

The appearance of vortex filaments, the power-law dependence of velocity and vorticity correlations and their multiscaling behavior are derived from the Navier-Stokes equation. This is possible due to interpretation of the Navier-Stokes equation as an equation with multiplicative noise and remarkable properties of random matrix products.

In a recent paper [Phys. Rev. E 86, 011134 (2012)], Mobilia introduces cooperation facilitators in the standard prisoner's dilemma game. He claims that natural selection favors the replacement of defection by cooperation in the weak-selection case if and only if their frequency satisfies a certain inequality. We show that this is not true, and we point out an error in the author's proof which follows from the improper handling of the large-population limit. In addition, we prove a stronger result that cooperation is favored for any selection strength if and only if the average payoff of cooperation is bigger than the average payoff of defection (which is a weaker condition than the author's inequality). We also show that, if we include self-interaction, then the presence of a fixed number of facilitators causes a rescaling of the payoff matrix, and for their certain frequency, cooperation becomes a dominant strategy, and the prisoner's dilemma simply disappears.

The fixation properties of a simple prisoner's dilemma game in the presence of “cooperation facilitators” have recently been investigated in finite and well-mixed populations for various dynamics [Mobilia, Phys. Rev. E 86, 011134 (2012)]. In a Comment, Miękisz claims that, for cooperation to be favored by selection in the standard prisoner's dilemma games with facilitators, it suffices that $f_{\mathsf{C}}>f_{\mathsf{D}}$ (where $f_{\mathsf{C}/\mathsf{D}}$ are the respective fitnesses of cooperators and defectors). In this Reply, we show that, in generic prisoner's dilemma games with $\ell$ cooperation facilitators, it is generally not sufficient that a single cooperator has a higher fitness than defectors to ensure that selection favors cooperation. In fact, it is also necessary that selection promotes the replacement of defection by cooperation in a population of size $N$, which requires that the fixation probability of a single cooperator exceeds ${(N-\ell )}^{-1}$. This replacement condition is independent of $f_{\mathsf{C}}>f_{\mathsf{D}}$ and, when the payoff for mutual defection is negative, it is shown to be more stringent than the invasion condition. Our results, illustrated by a series of examples, considerably generalize those reported in the paper [Phys. Rev. E 86, 011134 (2012)] and in the aforementioned Comment whose claims are demonstrated to be relevant only for a special subclass of prisoner's dilemma games.

Kinetics of irreversible bimolecular chemical reactions $A+A\to 0$ and $A+B\to 0$ on directed scale-free networks with the in-degree distribution $P_{\mathrm{in}}\left(k\right)\sim k^{-{\gamma }_{\mathrm{in}}}$ and the out-degree distribution $P_{\mathrm{out}}\left(\ell \right)\sim {\ell }^{-{\gamma }_{\mathrm{out}}}$ are investigated. Since the correlation between $k$ and $\ell$ of each node generally exists in directed networks, we control the correlation $\langle k\ell \rangle$ with the probability $r\in [0,1]$ by two different algorithms for the construction of the directed networks, i.e., the so-called $k$ and $\ell$ algorithms. For $r=1$, the $k$ algorithm gives $\langle k\ell \rangle =\langle k^2\rangle$, whereas the $\ell$ algorithm gives $\langle k\ell \rangle =\langle {\ell }^2\rangle$. For $r=0$, $\langle k\ell \rangle =\langle k\rangle \langle \ell \rangle$ for both algorithms. The kinetics of both reactions are analyzed using heterogeneous mean-field (HMF) theory and Monte Carlo simulations. The density of particles ($\rho$) algebraically decays in time $t$ as $\rho \left(t\right)\sim t^{-\alpha }$. The kinetics of both reactions are determined by the same rate equation, $d\rho /dt=a{\rho }^2+b{\rho }^{\theta -1}$, apart from coefficients. The exponent $\theta$ is determined by the algorithm: $\theta ={\gamma }_{\mathrm{in}}$ for the $k$ algorithm ($r\ge 0$) and $\theta ={\gamma }_{\min }$ for the $\ell$ algorithm ($r>0$), where ${\gamma }_{\min }$ is the smaller exponent between ${\gamma }_{\mathrm{in}}$ and ${\gamma }_{\mathrm{out}}$. For $\theta >3$, one observes the ordinary mean-field kinetics, $\rho \sim 1/t$ ($\alpha =1$). In contrast, for $\theta <3$, $\rho \left(t\right)$ anomalously decays with $\alpha =1/(\theta -2)$. The HMF predictions are confirmed by the simulations on quenched directed networks.

The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a Gaussian white noise magnetic field. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

We develop the scattering formalism to calculate the interaction between colloidal particles trapped at a fluid interface. Since, in addition to the interface, the colloids may also fluctuate in this system, we implement the fluctuation of the boundaries into the scattering formalism and investigate how the interaction between colloids is modified by their fluctuations. This general method can be applied to any number of colloids with various geometries at an interface. We apply the formalism derived in this work to a system of spherical colloids at the interface between two fluid phases. For two spherical colloids, this method very effectively reproduces the previous known results. For three particles we find analytical expressions for the large separation asymptotic energies and numerically calculate the Casimir interaction at all separations. Our results show an interesting three-body effect for fixed and fluctuating colloids. While the three-body effect strengthens the attractive interaction between fluctuating colloids, it diminishes the attractive force between colloids fixed at an interface.

We study the behavior of colloidal magnetic fluids at low density for various dipolar interaction strengths by performing extensive Langevin dynamics simulations with model parameters that mimic cobalt-based ferrofluids used in experiments. Our study mainly focuses on the structural and dynamical properties of dipolar fluids and the influence of structural changes on their dynamics. Drastic changes from chainlike to networklike structures in the absence of an external magnetic field are observed. This crossover plays an important role in the slowing down of dynamics that is reflected in various dynamical properties including the tracer diffusion and the viscosity and also in the structural relaxation.

We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean-field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allows us to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.

Formation of localized propagating patterns is a fascinating self-organizing phenomenon that happens in a wide range of spatially extended, excitable systems in which individual elements have resting, activated, and refractory states. Here we study a type of stochastic three-state excitable network model that has been recently developed; this model is able to generate a rich range of pattern dynamics, including localized wandering patterns and localized propagating patterns with crescent shapes and long-range propagation. The collective dynamics of these localized patterns have anomalous subdiffusive dynamics before symmetry breaking and anomalous superdiffusive dynamics after that, showing long-range spatiotemporal coherence in the system. In this study, the stability of the localized wandering patterns is analyzed by treating an individual localized pattern as a subpopulation to develop its average response function. This stability analysis indicates that when the average refractory period is greater than a certain value, there are too many elements in the refractory state after being activated to allow the subpopulation to support a self-sustained pattern; this is consistent with symmetry breaking identified by using an order parameter. Furthermore, in a broad parameter space, the simple network model is able to generate a range of interactions between different localized propagating patterns including repulsive collisions and partial and full annihilations, and interactions between localized propagating patterns and the refractory wake behind others; in this study, these interaction dynamics are systematically quantified based on their relative propagation directions and the resultant angles between them before and after their collisions. These results suggest that the model potentially provides a modeling framework to understand the formation of localized propagating patterns in a broad class of systems with excitable properties.

We consider three distinct and well-studied problems concerning network structure: community detection by modularity maximization, community detection by statistical inference, and normalized-cut graph partitioning. Each of these problems can be tackled using spectral algorithms that make use of the eigenvectors of matrix representations of the network. We show that with certain choices of the free parameters appearing in these spectral algorithms the algorithms for all three problems are, in fact, identical, and hence that, at least within the spectral approximations used here, there is no difference between the modularity- and inference-based community detection methods, or between either and graph partitioning.

We study the dynamics of a class of nonautonomous systems with pulsed nonlinearity that consist of a periodic sequence of linear and nonlinear autonomous systems, each one acting alone in a different time or space interval. We focus on the investigation of control capabilities of such systems in terms of altering their fundamental dynamical properties by appropriate parameter selections. For the case of single oscillators, the stability of the zero solution as well as the phase space topology is shown to drastically depend on parameters such as the frequency of the linear oscillations and the durations of the linear and nonlinear intervals. In cases of chain of coupled oscillators with pulsed onsite nonlinearity, it is shown that appropriate parameter selections can stabilize an otherwise unstable zero background allowing for the existence of dynamically robust localized excitations, whose evolution properties can now be explicitly determined and controlled.