We present a linear stability analysis of the incoherent state in a system of globally coupled identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.

We consider the onset of Boussinesq convection in a horizontal layer of electrically conducting fluid rotating about a vertical axis with an imposed vertical magnetic field. Rigid electrically insulating horizontal boundaries are assumed. Our goal is to identify the region of parameter values, for which rolls emerge at the onset of convection. The following conditions are necessary for convective fluid motion to set in as stable rolls: instability of the trivial steady state is monotonic; the rolls bifurcate supercritically; they are stable to perturbations of the form of rolls rotated by any angle (without an imposed magnetic field this is called the Küppers-Lortz instability). For each of the three conditions we derive equations for respective boundaries in the parameter space and determine the boundaries numerically.

Nonlinear, spatially periodic, long-wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general nonlinear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson’s equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the nonlinear time evolution of any (periodic) initial electron number density profile $n_e\left(x,t=0\right)$ can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength $\lambda ⪢{\lambda }_{\text{min}}\left(n_0,T_e\right)$, where $n_0=\text{const}$ and $T_e$ are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density $n_e\left(x_{\text{min}},t=0\right)$ must be larger than half its equilibrium value, $n_0/2$. Otherwise, the corresponding maximum $n_e\left(x_{\text{max}},t={\tau }_p/2\right)$, obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on $n_e\left(x,t=0\right)$ as one decreases $\lambda$, due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.

This paper proposes an improved lattice Boltzmann scheme for incompressible axisymmetric flows. The scheme has the following features. First, it is still within the framework of the standard lattice Boltzmann method using the single-particle density distribution function and consistent with the philosophy of the lattice Boltzmann method. Second, the source term of the scheme is simple and contains no velocity gradient terms. Owing to this feature, the scheme is easy to implement. In addition, the singularity problem at the axis can be appropriately handled without affecting an important advantage of the lattice Boltzmann method: the easy treatment of boundary conditions. The scheme is tested by simulating Hagen-Poiseuille flow, three-dimensional Womersley flow, Wheeler benchmark problem in crystal growth, and lid-driven rotational flow in cylindrical cavities. It is found that the numerical results agree well with the analytical solutions and/or the results reported in previous studies.

In this paper we present Green function technique applied to calculations of spin-spin correlations in systems governed by Ising Hamiltonian. This offers approximate yet reasonably accurate analytical results, as an alternative approach to direct computer simulation. Local spin operators are represented in terms of particle operators for fermions. Chain of Green functions for local magnetization on given site involves nearest neighbors and it is decoupled at the next-nearest-neighbors level. Therefore, still accounts at the lowest level for magnetic correlations between nearest neighbors. This technique was applied to binary alloy $A_x{B}_{1-x}$ with given atomic short range order. Calculations for stoichiometric $x=1/2$ composition show how temperature dependence of magnetization and spin-spin correlations are modified when atomic order parameter changes. We scanned this parameter from the case of ordered binary alloy, via random alloy, to clusterlike structure. In model calculations we (a) confirm characteristic $\lambda$-like shape of the magnetic specific heat near Curie temperature and (b) recover essential results of exact, two-dimensional Ising model. This supports our claim of usefulness of such analytical approach, which is easy and flexible to describe different geometries (clusters, thin films) and conditions imposed on spins located on specific atoms (spins partly pinned on the surface atoms).

In this paper, we study a macroscopic system of electrically interacting metallic beads organized as a sequence along an annulus. A random mechanical shaking mimics the thermal excitation. We exhibit non-Fickian diffusion (single-file diffusion) at large time. We measure the mobility of the particles and compare it to theoretical expectations. We show that our system cannot be accurately described by theories assuming only hard-sphere interactions. Its behavior is qualitatively described by a theory extended to more realistic potentials [M. Kollmann, Phys. Rev. Lett. 90, 180602 (2003)]. A correct quantitative agreement is shown and we interpret the discrepancies by the violation of the assumption of overdamped dynamics, which is a key point in the theory. We recast previous results on colloids with known interaction potentials and compare them quantitatively to the theory. Focusing on the transition between ordinary and single-file diffusions, we exhibit a dimensionless crossover time that is of order 1 both for colloids and our system, although the time and length scales differ by several orders of magnitude.

Applying the method of reflections, we derive the flow pattern around a confined colloidal particle with quasislip conditions at its surface, in powers of the ratio $a/h$ of particle radius and wall distance. The lowest order corresponds to a single reflection at the confining wall. Significant corrections occur at higher order: the linear term in $a/h$ modifies the amplitudes of the well-known one-reflection approximation, whereas new features arise in quadratic order. Our results agree with recent experiments where thermo-osmosis drives hydrodynamic attractive forces in confined colloids.

Within the continuum theory we study the magnetic segregation effects in ferronematics, i.e., suspensions of monodomain magnetic particles in nematic liquid crystals. Orientational and concentrational distributions in a ferronematic layer are obtained as functions of a magnetic field strength for different values of material parameters. Tricritical behavior of the Fréedericksz transition in ferronematics induced by magnetic field is revealed. It is found out that this transition can be either first- or second-order transition depending on the segregation degree. We derive the analytical expression for the tricritical segregation parameter, determining the phase-transition character change. The dependence of birefringence on the external magnetic field and the segregation parameter is studied.

Based on a mesoscopic theory we investigate the nonequilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress ${\sigma }_{xy}$ (rather than the usual shear rate, $\dot{\gamma }$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dot{\gamma }$, which then becomes time dependent. Shearing the system from an isotropic state, the stress-controlled flow properties turn out to be essentially identical to those at fixed $\dot{\gamma }$. Pronounced differences occur when the equilibrium state is nematic. Here, shearing at controlled $\dot{\gamma }$ yields several nonequilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the ${\sigma }_{xy}\text{−}\dot{\gamma }$ plane turns out to be tunable by the delay time entering our control scheme for ${\sigma }_{xy}$. Moreover, a sudden change in the control method can stabilize the chaotic states appearing at fixed $\dot{\gamma }$.

Experiments have shown that mechanical stress can regulate many cellular processes. However, in most cases, the exact regulatory mechanisms are still not well understood. One approach in improving our understanding of such mechanically induced regulation is the quantitative study of cell deformation under an externally applied stress. In this paper, an axisymmetric finite-element model is developed and used to study the deformation of single, suspended fibroblasts in an optical stretcher in which a stretching force is applied onto the surface of the cell. A feature of our physical model is a viscoelastic material equation whose parameters vary spatially to mimic the experimentally observed spatial heterogeneity of cellular material properties. Our model suggests that cell size is a more important factor in determining the maximal strain of the optically stretched fibroblasts compared to the thickness of the actin cortical region. This result could explain the higher deformability observed experimentally for malignant fibroblasts in the optical stretcher. Our model also shows that maximal stress propagates into the nuclear region for malignant fibroblasts whereas for normal fibroblasts, it does not. We discuss how this may impact the transduction of cancer signaling pathways.

Control of defect-mediated turbulence or spiral turbulence has been a subject of pattern dynamics study in the last two decades. As a result, many control strategies has been proposed in theory and tested in computer simulation. Here we propose a self-regulation system that can spontaneously eliminate topological defects in the reaction-diffusion system that suffers from the Doppler instability. The core of the self-regulation scheme is a feedback introduction of local inhomogeneities around spiral tips. We used modified FitzHugh-Nagumo model in computer simulations and light-sensitive Belousov-Zhabotinsky reaction in experiments to test the functionality of the proposed system. We found that if the inhomogeneities were induced on the spiral tips once they were identified, the spiral can be exterminated thus the spiral turbulence can be controlled. Compared with the studies on anatomic obstacles in heart, this self-regulation model may provide a possible mechanism for spontaneous termination of cardiac fibrillation.

Miscible displacement of a slice of a pollutant solution by a carrier solution in homogeneous porous media is examined. The carrier solution reacts with the slice solution to generate a chemical product, and as a result of differences in viscosities of the three species, a hydrodynamic instability known as viscous fingering is observed. The dynamics of the instability and the rate of consumption as well as spread of the pollutant are examined through numerical simulations. The study shows that the rate of consumption of the pollutant is the highest when the chemical product is the most or the least viscous solution in the system. It was also found that displacements in which the pollutant viscosity is the smallest or the largest of all three species lead to the widest spread of the pollutant in the porous media. In addition, the most complex finger structures are observed when the carrier solution has the smallest or largest viscosity in the flow. Furthermore, a mechanism of channeling whereby the carrier is able to break through the slice, therefore bypassing the pollutant, is found in cases where the chemical product is more viscous than the carrier solution. The dynamics of the displacement are analyzed and physical interpretations of their development are presented.

An effective photon mass and equivalent photon charge are calculated for plasmas with finite temperature, by using a second covariant quantization of the electromagnetic field, which is based on a nonlinear magnetofluid unification field formalism. Relativistic effects are considered both in the fluid bulk motion and in the thermal motion. The effective relativistic photon mass is found for transverse and longitudinal photons, while the equivalent relativistic photon charge is obtained for purely transverse photons. Both quantum quantities are the relativistic generalization, at finite temperature, of previous results [Mendonça et al., Phys. Rev. E 62, 2989 (2000)]. The dependence with temperature is studied in both cases.

Two rotational integration algorithms for rigid-body dynamics are proposed in velocity-Verlet formulation. The first method uses quaternion dynamics and was derived from the original rotational leap-frog method by Svanberg [Mol. Phys. 92, 1085 (1997)]; it produces time consistent positions and momenta. The second method is also formulated in terms of quaternions but it is not quaternion specific and can be easily adapted for any other orientational representation. Both the methods are tested extensively and compared to existing rotational integrators. The proposed integrators demonstrated performance at least at the level of previously reported rotational algorithms. The choice of simulation parameters is also discussed.

We have investigated the critical behavior of a three-dimensional random-bond Ising model for a series of the disorder strength by a finite-time scaling combining with Monte Carlo renormalization-group method in the presence of a linearly varying temperature. The method enables us to estimate a lot of critical exponents of both static and dynamic nature independently as well as the critical temperatures. The static exponents obtained agree well with most existing results, verify both the hyperscaling and the Rushbrooke scaling laws and their combined scaling law, which in turn validate their asymptotic nature, and corroborate the universality of the relevant random fixed point with respect to the forms of disorder. The dynamic critical exponent $z$ is estimated to 2.114(51), which is compatible with those obtained from experiments and renormalization-group analyses. The exponents at low and high disorder strengths do not satisfy all scaling laws and are argued to be crossover exponents that reflect crossover from the random fixed point to the pure and the percolation fixed point. They also indicate that the exponents that were previously suggested to be a distinct universality class for strong disorder strength in the literature may be just crossover. Our results demonstrate the effectiveness of the finite-time scaling method.

A unifying mathematical theory of nonequilibrium thermodynamics of stochastic systems in terms of master equations is presented. As generalizations of isothermal entropy and free energy, two functions of state play central roles: the Gibbs entropy $S$ and the relative entropy $F$, which are related via the stationary distribution of the stochastic dynamics. $S$ satisfies the fundamental entropy balance equation $dS/dt=e_p-h_d/T$ with entropy production rate $e_p\ge 0$ and heat dissipation rate $h_d$, while $dF/dt=-f_d\le 0$. For closed systems that satisfy detailed balance: $T{e}_p\left(t\right)=f_d\left(t\right)$. For open systems, one has $T{e}_p\left(t\right)=f_d\left(t\right)+Q_{hk}\left(t\right)$, where the housekeeping heat, $Q_{hk}\ge 0$, was first introduced in the phenomenological nonequilibrium steady-state thermodynamics put forward by Oono and Paniconi. $Q_{hk}$ represents the irreversible work done by the surrounding to the system that is kept away from reaching equilibrium. Hence, entropy production $e_p$ consists of free energy dissipation associated with spontaneous relaxation (i.e., self-organization), $f_d$, and active energy pumping that sustains the open system $Q_{hk}$. The amount of excess heat involved in the relaxation $Q_{ex}=h_d-Q_{hk}=f_d-T\left(dS/dt\right)$. Two kinds of irreversibility, and the meaning of the arrow of time, emerge. Quasistationary processes, adiabaticity, and maximum principle for entropy are also generalized to nonequilibrium settings.

We report here a unique in-plane self-templating electrochemical growth of arrays of copper nanopearl chains from an ultrathin layer of ${\text{CuSO}}_4$ electrolyte. Scanning electron microscopy indicates that the electrodeposit filaments form equally spaced bundles, which consist of long, straight, pearl-chain-like copper filaments with corrugated periodic structure. The bundle separation can be tuned by changing the applied electric current in electrodeposition. Experiments show that the periodic morphology on the nanopearl chain corresponds to the periodic distribution of copper and cuprous oxide. The mechanism for the bundle formation is discussed.

We measured the polarization- and angle-resolved optical scattering and reflection spectra of the quasiordered nanostructures in the bird feather barbs. In addition to the primary peak that originates from single scattering, we observed a secondary peak which exhibits depolarization and distinct angular dispersion. We explained the secondary peak in terms of double scattering, i.e., light is scattered successively twice by the structure. The two sequential single-scattering events are considered uncorrelated. Using the Fourier power spectra of the nanostructures obtained from the small-angle x-ray scattering experiment, we calculated the double scattering of light in various directions. The double-scattering spectrum is broader than the single-scattering spectrum, and it splits into two subpeaks at larger scattering angle. The good agreement between the simulation results and the experimental data confirms that double scattering of light makes a significant contribution to the structural color.

Despite the many works on contagion phenomena in both well-mixed systems and heterogeneous networks, there is still a lack of understanding of the intermediate regime where social group structures evolve on a similar time scale to individual-level transmission. We address this question by considering the process of transmission through a model population comprising social groups which follow simple dynamical rules for growth and breakup. Despite the simplicity of our model, the profiles produced bear a striking resemblance to a wide variety of real-world examples—in particular, empirical data that we have obtained for social (i.e., YouTube), financial (i.e., currency markets), and biological (i.e., colds in schools) systems. The observation of multiple resurgent peaks and abnormal decay times is qualitatively reproduced within the model simply by varying the time scales for group coalescence and fragmentation. We provide an approximate analytic treatment of the system and highlight a novel transition which arises as a result of the social group dynamics.

Up to now, the effects of having heterogeneous networks of contacts have been studied mostly for diseases which are not persistent in time, i.e., for diseases where the infectious period can be considered very small compared to the lifetime of an individual. Moreover, all these previous results have been obtained for closed populations, where the number of individuals does not change during the whole duration of the epidemics. Here, we go one step further and analyze, both analytically and numerically, a radically different kind of diseases: those that are persistent and can last for an individual’s lifetime. To be more specific, we particularize to the case of tuberculosis’ (TB) infection dynamics, where the infection remains latent for a period of time before showing up and spreading to other individuals. We introduce an epidemiological model for TB-like persistent infections taking into account the heterogeneity inherent to the population structure. This sort of dynamics introduces new analytical and numerical challenges that we are able to sort out. Our results show that also for persistent diseases the epidemic threshold depends on the ratio of the first two moments of the degree distribution so that it goes to zero in a class of scale-free networks when the system approaches the thermodynamic limit.