We demonstrate that waves in distinct layers of a neuronal network can become phase locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to derive an effective equation for the position of the wave in each layer, yielding a stochastic differential equation with multiplicative noise. Stability of the synchronous state is characterized by a Lyapunov exponent, which we can compute analytically from the reduced system. Our results extend previous work on limit-cycle oscillators, showing common noise can synchronize waves in a broad class of models.

We propose a self-consistent dynamo mechanism for the generation of large-scale magnetic fields in natural objects. Recent computational studies have described the formation of large-scale vortices in rotating turbulent convection. Here we demonstrate that for magnetic Reynolds numbers below the threshold for small-scale dynamo action, such turbulent flows can sustain large-scale magnetic fields, i.e., fields with a significant component on the scale of the system.

We investigate the irreversible growth of $(2+1)$-dimensional magnetic thin films. The spin variable can adopt three states $\left(s_i=\pm 1,0\right)$, and the system is in contact with a thermal bath of temperature $T$. The deposition process depends on the change of the configuration energy, which, by analogy to the Blume-Capel Hamiltonian in equilibrium systems, depends on Ising-like couplings between neighboring spins $\left(J\right)$ and has a crystal field $\left(D\right)$ term that controls the density of nonmagnetic impurities $\left(s_i=0\right)$. Once deposited, particles are not allowed to flip, diffuse, or detach. By means of extensive Monte Carlo simulations, we obtain the phase diagram in the crystal field vs temperature parameter space. We show clear evidence of the existence of a tricritical point located at $D_t/J=1.145\left(10\right)$ and $k_B{T}_t/J=0.425\left(10\right)$, which separates a first-order transition curve at lower temperatures from a critical second-order transition curve at higher temperatures, in analogy with the previously studied equilibrium Blume-Capel model. Furthermore, we show that, along the second-order transition curve, the critical behavior of the irreversible growth model can be described by means of the critical exponents of the two-dimensional Ising model under equilibrium conditions. Therefore, our findings provide a link between well-known theoretical equilibrium models and nonequilibrium growth processes that are of great interest for many experimental applications, as well as a paradigmatic topic of study in current statistical physics.

Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase separation becomes suppressed by moderate activity, consistent with recent experiments and simulations, and suggests a mechanism for reentrant cluster formation at high activity.

A wide spectrum of real-life systems ranging from neurons to botnets display spontaneous recovery ability. Using the generating function formalism applied to static uncorrelated random networks with arbitrary degree distributions, the microscopic mechanism underlying the depreciation-recovery process is characterized and the effect of varying self-healing capability on network robustness is revealed. It is found that the self-healing capability of nodes has a profound impact on the phase transition in the emergence of percolating clusters, and that salient difference exists in upholding network integrity under random failures and intentional attacks. The results provide a theoretical framework for quantitatively understanding the self-healing phenomenon in varied complex systems.

The spontaneous formation of heterogeneous patterns is a hallmark of many nonlinear systems, from biological tissue to evolutionary population dynamics. The standard model for pattern formation in general, and for Turing patterns in chemical reaction-diffusion systems in particular, are deterministic nonlinear partial differential equations where an unstable homogeneous solution gives way to a stable heterogeneous pattern. However, these models fail to fully explain the experimental observation of turbulent patterns with spatio-temporal disorder in chemical systems. Here we introduce a pattern-fluid model as a general concept where turbulence is interpreted as a weakly interacting ensemble obtained by random superposition of stationary solutions to the underlying reaction-diffusion system. The transition from turbulent to stationary patterns is then interpreted as a condensation phenomenon, where the nonlinearity forces one single mode to dominate the ensemble. This model leads to better reproduction of the experimental concentration profiles for the “stationary phases” and reproduces the turbulent chemical patterns observed by Q. Ouyang and H. L. Swinney [Chaos 1, 411 (1991)].

We generalize a simple Monte Carlo (MC) model for dilute gases to consider the transport behavior of positrons and electrons in Percus-Yevick model liquids under highly nonequilibrium conditions, accounting rigorously for coherent scattering processes. The procedure extends an existing technique [Wojcik and Tachiya, Chem. Phys. Lett. 363, 381 (2002)], using the static structure factor to account for the altered anisotropy of coherent scattering in structured material. We identify the effects of the approximation used in the original method, and we develop a modified method that does not require that approximation. We also present an enhanced MC technique that has been designed to improve the accuracy and flexibility of simulations in spatially varying electric fields. All of the results are found to be in excellent agreement with an independent multiterm Boltzmann equation solution, providing benchmarks for future transport models in liquids and structured systems.

The Goldstein-Kac telegraph process describes the one-dimensional motion of particles with constant speed undergoing random changes in direction. Despite its resemblance to numerous real-world phenomena, the singular nature of the resultant spatial distribution of each particle precludes the possibility of any a posteriori empirical validation of this random-walk model from data. Here we show that by simply allowing for random speeds, the ballistic terms are regularized and that the diffusion component can be well-approximated via the unscented transform. The result is a computationally efficient yet robust evaluation of the full particle path probabilities and, hence, the parameter likelihoods of this generalized telegraph process. We demonstrate how a population diffusing under such a model can lead to non-Gaussian asymptotic spatial distributions, thereby mimicking the behavior of an ensemble of Lévy walkers.

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyze carefully. In particular, we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.

Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014)]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the correlation functions. It is also demonstrated for a schematic model that the TMCT does not lead to the MCT scenarios either for transition-line crossings or for the appearance of higher-order glass-transition singularities.

We demonstrate the application of principal-component analysis (PCA) to the analysis of particle motion data in the form of a time series of images. PCA has the ability to resolve and isolate spatiotemporal patterns in the data. Using simulated data, we show that this translates into the ability to separate individual frequency components of the particle motion. We also show that PCA can be used to extract the fluid viscosity from images of particles undergoing Brownian motion. PCA thus provides an efficient alternative to more traditional particle-tracking methods for the analysis of microrheological data.

We report x-ray photon correlation spectroscopy experiments on the dynamics of the glass-former polypropylene glycol covering a temperature range from room temperature to the glass transition at $T_g=205$ K using silica tracer particles. Three temperature regimes are identified: At high temperatures, Brownian motion of the tracer particles is observed. Near $T_g$, the dynamics is hyperdiffusive and ballistic. Around $1.12T_g$, we observe an intermediate regime. Here the stretching exponent of the Kohlrausch-Williams-Watts function becomes $q$ dependent. By analyzing higher-order correlations in the scattering data, we find that dynamical heterogeneities dramatically increase in this intermediate-temperature regime. This leads to two effects: increasing heterogeneous dynamics and correlated motion at temperatures close to and below $1.12T_g$.

Linking our knowledge of organisms to our knowledge of ecological communities and ecosystems is a key challenge for ecology. Individual size distributions (ISDs) link the size of individual organisms to the structure of ecological communities, so that studying ISDs might provide insight into how organism functioning affects ecosystems. Similarly shaped ISDs among ecosystems, coupled with allometric links between organism size and resource use, suggest the possibility of emergent resource-use patterns in ecological communities. We drew on thermodynamics to develop a maximization principle that predicted both organism and community energy use. These predictions highlighted the importance of density-dependent metabolic rates and were able to explain nonlinear relationships between community energy use and community biomass. We analyzed data on fish community energy use and biomass and found evidence of nonlinear scaling, which was predicted by the thermodynamic principle developed here and is not explained by other theories of ISDs. Detailed measurements of organism energy use will clarify the role of density dependence in driving metabolic rates and will further test our derived thermodynamic principle. Importantly, our study highlights the potential for fundamental links between ecology and thermodynamics.

We investigate the propensities for amino acids to form a specific secondary structure when they are paired with other amino acids. Our investigations use molecular dynamics (MD) computer simulations, and we compare the results to those from the Protein Data Bank (PDB). Proper comparison requires weighting of the MD results in a manner consistent with the relative frequency of appearance in the PDB of each possible pair of amino acids. We find that the propensity for an amino acid to assume a secondary structure varies dramatically depending on the amino acid that is before or after it in the primary sequence. This cooperative effect means that when selecting amino acids to facilitate the formation of a secondary structure in peptide engineering experiments, the adjacent amino acids must be considered.

We present a Landau-type theory for the nonlinear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the nonlinear elastic behavior of these materials to fiber alignment induced by strain. We suggest an application to contact guidance of cell motility in tissue. We compare our theory to simulation of a disordered lattice model for biopolymers. We treat homogeneous deformations such as simple shear, hydrostatic expansion, and simple extension, and obtain good agreement between theory and simulation. We also consider a localized perturbation which is a simple model for a contracting cell in a medium.

A reduced description of exact coherent structures in the transition regime of plane parallel shear flows is developed, based on the Reynolds number scaling of streamwise-averaged (mean) and streamwise-varying (fluctuation) velocities observed in numerical simulations. The resulting system is characterized by an effective unit Reynolds number mean equation coupled to linear equations for the fluctuations, regularized by formally higher-order diffusion. Stationary coherent states are computed by solving the resulting equations simultaneously using a robust numerical algorithm developed for this purpose. The algorithm determines self-consistently the amplitude of the fluctuations for which the associated mean flow is just such that the fluctuations neither grow nor decay. The procedure is used to compute exact coherent states of a flow introduced by Drazin and Reid [Hydrodynamic Stability (Cambridge University Press, Cambridge, UK, 1981)] and studied by Waleffe [Phys. Fluids 9, 883 (1997)]: a linearly stable, plane parallel shear flow confined between stationary stress-free walls and driven by a sinusoidal body force. Numerical continuation of the lower-branch states to lower Reynolds numbers reveals the presence of a saddle node; the saddle node allows access to upper-branch states that are, like the lower-branch states, self-consistently described by the reduced equations. Both lower- and upper-branch states are characterized in detail.

Here proper orthogonal decomposition (POD) modal decomposition are performed for flow past a circular cylinder at supercritical Reynolds numbers by projecting this onto instability modes. The important task of modeling a cylinder wake by Stuart-Landau (SL) and the Stuart-Landau-Eckhaus (SLE) equation for instability modes is discussed, with the latter shown to be more consistent with multimodal pictures of POD and instability modes. The difficult task of finding the coefficients of the SLE equation is reported by taking a least squares approach for the reduced order model (ROM). The important aspect of the ROM is the choice of initial condition for the developed SLE equations, as these are stiff ordinary differential equations which are very sensitive to the choice of initial conditions. An accurate representation of enstrophy-based POD also reveals the presence of modes which occur in isolation (in comparison to modes that come in pairs) and the traditional approach of treating instability modes by SL or SLE equations does not work directly, which also reveals higher frequency variations. Quantifying effects of this mode by time-averaged Navier-Stokes equation (NSE) fail to show the variation of the phase of these isolated time-varying modes and this is captured here using direct numerical simulation (DNS) data by a multitime scale approach. A reconstructed 3-mode ROM solution and the disturbance vorticity from DNS match globally in the flow. The agreement between 3-mode SLE reconstruction and DNS also proves the consistency of the proposed method and helps explain the physical nature of the ensuing Hopf bifurcation following an instability.

We address the implications of finite ionic size and solvent polarization on the response of the electric double layer (EDL) at two cation-selective electrodes in nonequilibrium conditions. The current between the electrodes is driven by a steady-state dc bias in conjunction with a probing high-frequency ac voltage. We report that the finite ionic size (steric) effect is prominent at high voltages near the electrodes where the ion densities are high, while the solvent polarization dramatically alters impedance characteristics for thick EDLs owing to the alteration of solvent permittivity in regions with a high electric field. Depending on the magnitude of the dc bias, our results show that the steric effects and solvent polarization lead to dramatic alterations in the net impedance for moderately thick electric double layers as compared to an extremely thin one. We also highlight that the solvent polarization suppresses the anomalous growth of dc current (anomalous rectification effect) for applied high-frequency ac voltages.

Slowly compressed microcrystals deform via intermittent slip events, observed as displacement jumps or stress drops. Experiments often use one of two loading modes: an increasing applied stress (stress driven, soft), or a constant strain rate (strain driven, hard). In this work we experimentally test the influence of the deformation loading conditions on the scaling behavior of slip events. It is found that these common deformation modes strongly affect time series properties, but not the scaling behavior of the slip statistics when analyzed with a mean-field model. With increasing plastic strain, the slip events are found to be smaller and more frequent when strain driven, and the slip-size distributions obtained for both drives collapse onto the same scaling function with the same exponents. The experimental results agree with the predictions of the used mean-field model, linking the slip behavior under different loading modes.