The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions.

Alternans response, comprising a sequence of alternating long and short action potential durations in heart tissue, seen during rapid periodic pacing can lead to conduction block resulting in potentially fatal cardiac failure. A method of pacing with feedback control is proposed to reduce the alternans and therefore the probability of subsequent cardiac failure. The reduction is achieved by feedback control using small perturbations of constant magnitude to the original, alternans-generating pacing period $T$, viz., using sequences of two alternating periods of $T+\Delta T$ and $T-\Delta T$, with $\Delta T\ll T$. Such a control scheme for alternans suppression is demonstrated experimentally in isolated whole heart experiments. This alternans suppression scheme is further confirmed and investigated in detail by simulations of ion-channel-based cardiac models both for a single cell and in one-dimensional spatially extended systems. The mechanism of the success of our method can be understood in terms of dynamics in phase space, viz., as the state of activity of the cell being confined within a narrow volume of phase space for the duration of control, resulting in extremely diminished variation in successive action potential durations. Our method is much more robust to noise than previous alternans reduction techniques based on fixed point stabilization and should thus be more efficient in terms of experimental implementation, which has implications for clinical treatment for arrhythmia.

Two models of opinion dynamics are entangled in order to build a more realistic model of inflexibility. The first one is the Galam unifying frame (GUF), which incorporates rational and inflexible agents, and the other one is the Continuous Opinions and Discrete Actions model. While initially in GUF, inflexibility is a fixed given feature of an agent, it is now the result of an accumulation for a given agent who makes the same choice through repeated updates. Inflexibility thus emerges as an internal property of agents becoming a continuous function of the strength of its opinion. Therefore, an agent can be more or less inflexible and can shift from inflexibility along one choice to inflexibility along the opposite choice. These individual dynamics of the building up and falling off of agent inflexibility are driven by the successive local updates of the associated individual opinions. New results are obtained and discussed in terms of predicting outcomes of public debates.

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter.

A transient analysis to quantify droplet deformation under DC electric fields is presented. The full Taylor-Melcher leaky dielectric model is employed where the charge relaxation time is considered to be finite. The droplet is assumed to be spheroidal in shape for all times. The main result is an ODE governing the evolution of the droplet aspect ratio. The model is validated by extensively comparing predicted deformation with both previous theoretical and numerical studies, and with experimental data. Furthermore, the effects of parameters and stresses on deformation characteristics are systematically analyzed taking advantage of the explicit formulas on their contributions. The theoretical framework can be extended to study similar problems, e.g., vesicle electrodeformation and relaxation.

We study the forces and torques experienced by pill-shaped Janus particles of different aspect ratios where half of the surface obeys the no-slip boundary condition and the other half obeys the Navier slip condition of varying slip lengths. Using a recently developed boundary integral formulation whereby the traditional singular behavior of this approach is removed analytically, we quantify the strength of the forces and torques experienced by such particles in a uniform flow field in the Stokes regime. Depending on the aspect ratio and the slip length, the force transverse to the flow direction can change sign. This is a novel property unique to the Janus nature of the particles.

Using the field theoretic renormalization group technique, the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl number in the kinematic magnetohydrodynamic turbulence is investigated in the two-loop approximation. It is shown that the presence of helicity decreases the value of the turbulent magnetic Prandtl number and, at the same time, the two-loop helical contribution to the turbulent magnetic Prandtl number is at most $4.2\%$ (in the case with the maximal helicity) of its nonhelical value. These results demonstrate, on one hand, the potential importance of the presence of asymmetries in processes in turbulent environments and, on the other hand, the rather strong stability of the properties of diffusion processes of the magnetic field in the conductive turbulent environment with the spatial parity violation in comparison to the corresponding systems without the spatial parity violation. In addition, obtained results are compared to the corresponding results found for the two-loop turbulent Prandtl number in the model of passively advected scalar field. It is shown that the turbulent Prandtl number and the turbulent magnetic Prandtl number, which are the same in fully symmetric isotropic turbulent systems, are essentially different when one considers the spatial parity violation. It means that the properties of the diffusion processes in the turbulent systems with a given symmetry breaking can considerably depend on the internal tensor structure of advected quantities.

Supersolitons are a recent addition to the literature on large-amplitude solitary waves in multispecies plasmas. They are distinguished from the usual solitons by their associated electric field profiles which are inherently distinct from traditional bipolar structures. In this paper, dust-ion-acoustic modes in a dusty plasma with stationary negative dust, cold fluid protons, and nonthermal electrons are investigated through a Sagdeev pseudopotential approach to see where supersolitons fit between ranges of ordinary solitons and double layers, as supersolitons always have finite amplitudes. They therefore cannot be described by reductive perturbation treatments, which rely on a weak amplitude assumption. A systematic methodology and discussion is given to distinguish the existence domains in solitary wave speed and amplitude for the different solitons, supersolitons and double layers, in terms of compositional parameters for the plasma model under consideration.

An important aspect in numerical simulations of particle-laden turbulent flows is the interpolation of the flow field needed for the computation of the Lagrangian trajectories. The accuracy of the interpolation method has direct consequences for the acceleration spectrum of the fluid particles and is therefore also important for the correct evaluation of the hydrodynamic forces for almost neutrally buoyant particles, common in many environmental applications. In order to systematically choose the optimal tradeoff between interpolation accuracy and computational cost we focus on comparing errors: the interpolation error is compared with the discretization error of the flow field. In this way one can prevent unnecessary computations and still retain the accuracy of the turbulent flow simulation. From the analysis a practical method is proposed that enables direct estimation of the interpolation and discretization error from the energy spectrum. The theory is validated by means of direct numerical simulations (DNS) of homogeneous, isotropic turbulence using a spectral code, where the trajectories of fluid tracers are computed using several interpolation methods. We show that $B$-spline interpolation has the best accuracy given the computational cost. Finally, the optimal interpolation order for the different methods is shown as a function of the resolution of the DNS simulation.

We present a finite-time detailed fluctuation theorem of the form $\tilde{P}\left(\Delta S_{\mathrm{env}}\right)=e^{\Delta S_{\mathrm{env}}}\tilde{P}(-\Delta S_{\mathrm{env}})$ for an appropriately weighted probability density $\tilde{P}\left(\Delta S_{\mathrm{env}}\right)$ of the external entropy production in the environment $\Delta S_{\mathrm{env}}$. The fluctuation theorem is valid for nonequilibrium systems with constant rates starting with an arbitrary initial probability distribution. We discuss the implication of this relation for the case of a temperature quench in classical equilibrium systems. The fluctuation theorem is tested numerically for a Markov jump process with six states and for a surface growth model.

The translocation of a polymer through a pore in a membrane separating fluids of different viscosities is studied via several computational approaches. Starting with the polymer halfway, we find that as a viscosity difference across the pore is introduced, translocation will predominately occur towards one side of the membrane. These results suggest an intrinsic pumping mechanism for translocation across cell walls which could arise whenever the fluid across the membrane is inhomogeneous. Somewhat surprisingly, the sign of the preferred direction of translocation is found to be strongly dependent on the simulation algorithm: for Langevin dynamics (LD) simulations, a bias towards the low viscosity side is found while for Brownian dynamics (BD), a bias towards the high viscosity is found. Examining the translocation dynamics in detail across a wide range of viscosity gradients and developing a simple force model to estimate the magnitude of the bias, the LD results are demonstrated to be more physically realistic. The LD results are also compared to those generated from a simple, one-dimensional random walk model of translocation to investigate the role of the internal degrees of freedom of the polymer and the entropic barrier. To conclude, the scaling of the results across different polymer lengths demonstrates the saturation of the directional preference with polymer length and the nontrivial location of the maximum in the exponent corresponding to the scaling of the translocation time with polymer length.

Extracting statistical structures (including textures or contrasts) from a natural stimulus is a central challenge in both biological and engineering contexts. This study interprets the process of statistical recognition in terms of hyperparameter estimations and free-energy minimization procedures with an empirical Bayesian approach. This mathematical interpretation resulted in a framework for relating physiological insights in animal sensory systems to the functional properties of recognizing stimulus statistics. We applied the present theoretical framework to two typical models of natural images that are encoded by a population of simulated retinal neurons, and demonstrated that the resulting cognitive performances could be quantified with the Fisher information measure. The current enterprise yielded predictions about the properties of human texture perception, suggesting that the perceptual resolution of image statistics depends on visual field angles, internal noise, and neuronal information processing pathways, such as the magnocellular, parvocellular, and koniocellular systems. Furthermore, the two conceptually similar natural-image models were found to yield qualitatively different predictions, striking a note of warning against confusing the two models when describing a natural image.

We developed a statistical method for detecting discontinuous phase changes (phase shifts) in fluctuating alpha rhythms in the human brain from electroencephalogram (EEG) data obtained in a single trial. This method uses the state space models and the line process technique, which is a Bayesian method for detecting discontinuity in an image. By applying this method to simulated data, we were able to detect the phase and amplitude shifts in a single simulated trial. Further, we demonstrated that this method can detect phase shifts caused by a visual stimulus in the alpha rhythm from experimental EEG data even in a single trial. The results for the experimental data showed that the timings of the phase shifts in the early latency period were similar between many of the trials, and that those in the late latency period were different between the trials. The conventional averaging method can only detect phase shifts that occur at similar timings between many of the trials, and therefore, the phase shifts that occur at differing timings cannot be detected using the conventional method. Consequently, our obtained results indicate the practicality of our method. Thus, we believe that our method will contribute to studies examining the phase dynamics of nonlinear alpha rhythm oscillators.

Weak generalized synchrony in a drive-response system occurs when the response dynamics is a unique but nondifferentiable function of the drive, in a manner that is similar to the formation of strange nonchaotic attractors in quasiperiodically driven dynamical systems. We consider a chaotically driven monotone map and examine the geometry of the limit set formed in the regime of weak generalized synchronization. The fractal dimension of the set of zeros is studied both analytically and numerically. We further examine the stable and unstable sets formed and measure the regularity of the coupling function. The stability index as well as the dimension spectrum of the equilibrium measure can be computed analytically.

We report on the first investigation of the triple-layer coupling pattern formation in a dielectric barrier discharge system. The pattern basically consists of one discharge subpattern ignited in the gas gap and two surface-charge subpatterns deposited on the dielectric surfaces. The coupling of the three subpatterns (layers) is presented by analyzing the time-resolved discharge sequence of a white-eye hexagonal super lattice pattern (WEHSP). A triple-layer coupling reaction-diffusion regime is also established to conduct simulations and the simulated WEHSP agrees well with the experiment. This paper will provide a deeper understanding for the layer coupling mechanism in pattern formation.

The NMR propagator technique allows the measurements of the variance ${\sigma }^2=\langle {(\xi -\langle \xi \rangle )}^2\rangle$ of the displacements as a function of time $t$ when flowing in a porous media. The time dependence of σ is a very sensitive test of Gaussian behavior compared to the analysis of the shape of the propagators. Superdispersion occurs when ${\sigma }^2\propto t^{\alpha }$ with the exponent α larger than 1. In a homogeneous 30-μm grain pack and 10 < Pe < 35, we observed weak superdispersion in saturated conditions (α = 1.17) and gradually strong superdispersion as the water saturation decreases (up to α = 1.5) during steady-state oil-water two-phase flow. In saturated conditions, the corresponding longitudinal propagators and breakthrough curves are Gaussian or nearly Gaussian, whereas in two-phase conditions, the longitudinal propagators are nonsymmetric and the breakthrough curves show a tail at long times.

We analyze via theoretical approaches and molecular dynamics simulations the collective mode structure of strongly coupled two-dimensional binary Yukawa systems, for selected density, mass, and charge ratios, both in the liquid and crystalline solid phases. Theoretically, the liquid phase is described through the quasilocalized charge approximation (QLCA) approach, while in the crystalline phase we study the centered honeycomb and the staggered rectangular crystal structures through the standard harmonic phonon approximation. We identify “longitudinal” and “transverse” acoustic and optic modes and find that the longitudinal acoustic mode evolves from its weakly coupled counterpart in a discontinuous nonperturbative fashion. The low-frequency acoustic excitations are governed by the oscillation frequency of the average atom, while the high-frequency optic excitation frequencies are related to the Einstein frequencies of the systems.

Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called $\alpha$ effect when the turbulence is helical and if the domain is large enough for the $\alpha$ effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos.

We have calculated the equations of state, the viscosity and self-diffusion coefficients, and electronic transport coefficients of beryllium in the warm dense regime for densities from 4.0 to 6.0 g/cm${}^3$ and temperatures from 1.0 to 10.0 eV by using quantum molecular dynamics simulations. The principal Hugoniot curve is in agreement with underground nuclear explosive and high-power laser experimental results up to $\sim$20 Mbar. The calculated viscosity and self-diffusion coefficients are compared with the one-component plasma model, using effective charges given by the average-atom model. The Stokes-Einstein relationship, which connects viscosity and self-diffusion coefficients, is found to hold fairly well in the strong coupling regime. The Lorenz number, which is the ratio between thermal and electrical conductivities, is computed via Kubo-Greenwood formula and compared to the well-known Wiedemann-Franz law in the warm dense region.

We present a theory for the dynamical ion structure factor (DISF) and ion stopping power in an unmagnetized collisional quantum plasma with degenerate electron fluids and nondegenerate strongly correlated ion fluids. Our theory is based on the fluctuation dissipation theorem and the quantum plasma dielectric constant that is deduced from a linearized viscoelastic quantum hydrodynamical (LVQHD) model. The latter incorporates the essential physics of quantum forces, which are associated with the quantum statistical pressure, electron-exchange, and electron-correlation effects, the quantum electron recoil effect caused by the dispersion of overlapping electron wave functions that control the dynamics of degenerate electron fluids, and the viscoelastic properties of strongly correlated ion fluids. Both degenerate electrons and nondegenerate strongly correlated ions are coupled with each other via the space charge electric force. Thus, our LVQHD theory is valid for a collisional quantum plasma at atomic scales with a wide range of the ion coupling parameter, the plasma composition, and plasma number densities that are relevant for compressed plasmas in laboratories (inertial confinement fusion schemes) and in astrophysical environments (e.g., warm dense matter and the cores of white dwarf stars). It is found that quantum electron effects and viscoelastic properties of strongly correlated ions significantly affect the features of the DISF and the ion stopping power (ISP). Unlike previous theories, which have studied ion correlations in terms of the ion coupling parameter, by neglecting the essential physics of collective effects that are competing among each other, we have here developed a method to evaluate the dependence of the plasma static and dynamical features in terms of individual parameters, like the Wigner-Seitz radius, the ion atomic number, and the ion temperature. It is found that due to the complex nature of charge screening in quantum plasmas, the ion coupling parameter alone cannot be a good measure for determining ion correlation effects in a collisional quantum plasma, and such a characteristic of a dense quantum plasma should be evaluated against each of the plasma parameters involved. The present investigation thus provides testable predictions for the DISF and ISP and is henceforth applicable to a wide range of compressed plasma categories ranging from laboratory to astrophysical warm dense matter.