Solitonlike propagating modes have been proposed for excitable tissue, but have never been measured in cardiac tissue. In this study, we simulate an experimental protocol to elicit these propagating unstable wavelets (PUWs) in a detailed three-dimensional ventricular wedge preparation. PUWs appear as fixed-shape wavelets that propagate only in the direction of cardiac fibers, with conduction velocity approximately $40\%$ slower than normal action potential excitation. We investigate their properties, demonstrating that PUWs are not true solitons. The range of stimuli for which PUWs were elicited was very narrow (several orders of magnitude lower than the stimulus strength itself), but increased with reduced sodium conductance and reduced coupling in nonlongitudinal directions. We show that the phenomenon does not depend on the particular membrane representation used or the shape of the stimulating electrode.

Synaptic depression affects not only the mean responses of neurons but also the correlation of response variability in neural populations. Although previous studies have constructed a theory of correlation in a spiking neuron model by using the mean-field theory framework, synaptic depression has not been taken into consideration. We expanded the previous theoretical framework in this study to spiking neuron models with short-term synaptic depression. On the basis of this theory we analytically calculated neural correlations in a ring attractor network with Mexican-hat-type connectivity, which was used as a model of the primary visual cortex. The results revealed that synaptic depression reduces neural correlation, which could be beneficial for sensory coding. Furthermore, our study opens the way for theoretical studies on the effect of interaction change on the linear response function in large stochastic networks.

Resonant excitation of terahertz (THz) radiation based on beating of two spatial-Gaussian lasers having different frequencies and wave numbers but the same electric field amplitudes is proposed in a spatially periodic density plasma in the presence of a static magnetic field applied perpendicular to the direction of propagation of the lasers. In this process, the ponderomotive force is developed with its components parallel and perpendicular to the direction of propagation of the lasers. This leads to a nonlinear oscillatory current that resonantly excites the THz radiation with the frequency of the order of the upper hybrid frequency. The contribution of magnetic field, laser beamwidth, and amplitude and periodicity of the density ripples is discussed for the efficient THz radiation generation. With the optimization of these parameters, the efficiency on the order of 10${}^{-3}$ or larger can be achieved in the present scheme.

The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data. In this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy. More specifically, by exploitation of the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance or activation phenomenon, while near the plasma frequency a geometric resonance appears. Furthermore, detection performance in the geometric resonance region is maximized at the prescribed value of the bias current. The naive sample mean detector is outperformed, in terms of error probability, by the optimal likelihood ratio test. The latter exhibits only geometric resonance, showing monotonically increasing performance as the bias current approaches the junction critical current. In this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed, and a relationship with the error probability is found. Detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal. As a prototypical example we study the phase estimation problem of a sinusoidal current, which is accomplished by using the filter bank approach. Finally we show that for a physically feasible detector the performances are found to be very close to the Cramer-Rao theoretical bound. Applications might be found, for example, in some astronomical detection problems (where the all-sky gravitational and/or radio wave search for pulsars requires the analysis of nearly sinusoidal long-lived waveforms at very low signal-to-noise ratio) or to analyze weak signals in the subterahertz range (where the traditional electronics counterpart is difficult to implement).

We examine a lattice model of tumor growth where the survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the supply is correlated with the distribution of tumor cells, which as we suggest might mimic the angiogenic growth, the extinction shows different critical behavior. Such a correlation affects also the morphology of the growing tumors and drastically raises tumor-survival probability.

There are certain classes of resistors, capacitors, and inductors that, when subject to a periodic input of appropriate frequency, develop hysteresis loops in their characteristic response. Here we show that the hysteresis of such memory elements can also be induced by white noise of appropriate intensity even at very low frequencies of the external driving field. We illustrate this phenomenon using a physical model of memory resistor realized by ${\mathrm{TiO}}_2$ thin films sandwiched between metallic electrodes and discuss under which conditions this effect can be observed experimentally. We also discuss its implications on existing memory systems described in the literature and the role of colored noise.

The existing solution for the Langevin equation of an anisotropic fluid allowed the evaluation of the position-dependent perpendicular and parallel diffusion coefficients, using molecular dynamics data. However, the time scale of the Langevin dynamics and molecular dynamics are different and an ansatz for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the backward Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin dynamics, scales with the corresponding molecular dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from molecular dynamics.

Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability $p$ of CD, the surface tension $\nu$ and the nonlinear coefficient $\lambda$ of the associated equations have linear dependence on $p$ due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with $p$ according to the divergence of local height differences when $p\to 0$. The superposition of those scaling factors gives $\nu \sim p^2$ for random deposition with surface relaxation (RDSR) as the CD, and $\nu \sim p$, $\lambda \sim p^{3/2}$ for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability $p$ for the latter, is also constructed. It shows linear $p$ dependence of $\lambda$, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some $p$-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients.

We study the dynamic structure factor $S(k,t)$ of proteins at large wave numbers $k$, $k{R}_g\gg 1$, where $R_g$ is the gyration radius. At this regime measurements are sensitive to internal dynamics, and we focus on vibrational dynamics of folded proteins. Exploiting the analogy between proteins and fractals, we perform a general analytic calculation of the displacement two-point correlation functions, $\langle {[{\vec{u}}_i\left(t\right)-{\vec{u}}_j\left(0\right)]}^2\rangle$. We confront the derived expressions with numerical evaluations that are based on protein data bank (PDB) structures and the Gaussian network model (GNM) for a few proteins and for the Sierpinski gasket as a controlled check. We use these calculations to evaluate $S(k,t)$ with arrested rotational and translational degrees of freedom, and show that the decay of $S(k,t)$ is dominated by the spatially averaged mean-square displacement of an amino acid. The latter has been previously shown to evolve subdiffusively in time, $\langle {[{\vec{u}}_i\left(t\right)-{\vec{u}}_i\left(0\right)]}^2\rangle \sim t^{\nu }$, where $\nu$ is the anomalous diffusion exponent that depends on the spectral dimension $d_s$ and fractal dimension $d_f$. As a result, for wave numbers obeying $k^2\langle {\vec{u}}^2\rangle \gtrsim 1$, $S(k,t)$ effectively decays as a stretched exponential $S(k,t)\simeq S\left(k\right)e^{-{\left({\Gamma }_{k}t\right)}^{\beta }}$ with $\beta \simeq \nu$, where the relaxation rate is ${\Gamma }_k\sim {(k_{B}T/m{\omega }_o^2)}^{1/\beta }{k}^{2/\beta }$, $T$ is the temperature, and $m{\omega }_o^2$ the GNM effective spring constant describing the interaction between neighboring amino acids. The static structure factor is dominated by the fractal character of the native fold, $S\left(k\right)\sim k^{-d_f}$, with negligible to marginal influence of vibrations. The analytical expressions are first confronted with numerically based calculations on the Sierpinski gasket, and very good agreement is found between simulations and theory. We then perform PDB-GNM-based numerical calculations for a few proteins, and an effective stretched exponential decay of the dynamic structure factor is found, albeit their relatively small size. However, when rotational and translational diffusion are added, we find that their contribution is never negligible due to finite size effects. While we can still attribute an effective stretching exponent $\beta$ to the relaxation profile, this exponent is significantly larger than the anomalous diffusion exponent $\nu$. We compare our theory with recent neutron spin-echo studies of myoglobin and hemoglobin and conclude that experiments in which the rotational and translational degrees of freedom are arrested, e.g., by anchoring the proteins to a surface, will improve the detection of internal vibrational dynamics.

Three-dimensional photonic-crystal grains were found in the scales of the longhorn beetle Prosopocera lactator (Cerambycidae). The local geometric structure can be described as a face-centered-cubic array of spheres, connected by short rods, reminiscent of the “ball-and-stick” models used by solid-state chemists to visualize atomic structures. Based on scanning electron microscopy, x-ray nanotomography, optical measurements, photonic band-structure calculations, and computer simulations of the reflectance, the desaturated greenish coloration is shown to arise from the observed photonic polycrystalline structure. X-ray nanotomography is revealed as a very promising tool for photonic-crystal morphology studies.

Fading is the time-dependent variation in transmitted signal strength through a complex medium due to interference or temporally evolving multipath scattering. In this paper we use random matrix theory (RMT) to establish a first-principles model for fading, including both universal and nonuniversal effects. This model provides a more general understanding of the most common statistical models (Rayleigh fading and Rice fading) and provides a detailed physical basis for their parameters. We also report experimental tests on two ray-chaotic microwave cavities. The results show that our RMT model agrees with the Rayleigh and Rice models in the high-loss regime, but there are strong deviations in low-loss systems where the RMT approach describes the data well.

Nelkin scaling, the scaling of moments of velocity gradients in terms of the Reynolds number, is an alternative way of obtaining inertial-range information. It is shown numerically and theoretically for the Burgers equation that this procedure works already for Reynolds numbers of the order of 100 (or even lower when combined with a suitable extended self-similarity technique). At moderate Reynolds numbers, for the accurate determination of scaling exponents, it is crucial to use higher than double precision. Similar issues are likely to arise for three-dimensional Navier–Stokes simulations.

In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function, which can be set to induce a stationary swarm, a rotating swarm with uniform translation, and a rotating swarm with a stationary center of mass. An analysis of the mean field equations shows that without a spring potential the motion of the center of mass is determined explicitly by a multivalued function. For a nonzero spring potential the swarm converges to a vortex formation about a stationary center of mass, except at discrete bifurcation points where the center of mass will periodically trace an ellipse. The analytical results defining the behavior of the center of mass are shown to correspond with the numerical swarm simulations.

We study solution-space structure and solution-finding algorithms of a representative hard random constraint satisfaction problem with growing domains known as Model RB. Using rigorous methods, we show that solutions are grouped into disconnected clusters before the theoretical satisfiability phase transition point. Using the cavity method, it is shown that the entropy density obtained by belief propagation (BP) on random Model RB instances, which corresponds well to the analytical results, vanishes as the control parameter (constraint tightness) approaches the satisfiability threshold. From an algorithmic point of view, we find that reinforced BP, which performs much better than all existing algorithms, allows us to find solutions efficiently for instances in the regime that is very close to the satisfiability transition. These results also can shed light on the effectiveness of BP reinforcement on problems with a large number of states.

In this work we study the behavior of classical two-person, two-strategies evolutionary games on a class of weighted networks derived from Barabási-Albert and random scale-free unweighted graphs. Using customary imitative dynamics, our numerical simulation results show that the presence of link weights that are correlated in a particular manner with the degree of the link end points leads to unprecedented levels of cooperation in the whole games' phase space, well above those found for the corresponding unweighted complex networks. We provide intuitive explanations for this favorable behavior by transforming the weighted networks into unweighted ones with particular topological properties. The resulting structures help us to understand why cooperation can thrive and also give ideas as to how such supercooperative networks might be built.

In this paper we develop an analytical framework to study the effect of nonlinearity on irreversible energy transfer in a system of two weakly coupled oscillators with time-dependent parameters, with special attention to an analogy between classical energy transfer and nonadiabatic quantum tunneling. For preciseness, we suppose that a linear oscillator with constant parameters is excited by an initial impulse but a coupled quasilinear oscillator with slowly varying parameters is initially at rest. It is shown that the equations of the slow passage through resonance in this system are identical to quasilinear equations of nonadiabatic Landau-Zener tunneling. Due to revealed equivalence, a recently found analogy between irreversible energy transfer in a classical linear system and conventional linear Landau-Zener tunneling can be extended to quasilinear systems. An explicit analytical solution of the quasilinear problem is found with the help of an iteration procedure, wherein the linear solution is chosen as an initial approximation. Correctness of the constructed approximations is confirmed by numerical simulations. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics of coupled oscillators, suggest an approximate procedure for solving the quasilinear Landau-Zener equations with arbitrary initial conditions over a finite time interval.

A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piecewise linear model which exhibits various patterns of synchronization. Analytical solutions are obtained for this class of dynamical systems. Depending only on the number of particles, the synchronization occurs into states in which nearest neighbors oscillate in in-phase, antiphase, or phase-locked (time-shifted) trajectories.

Deformation of a red blood cell (RBC) in bounded two-dimensional Poiseuille flows is studied by using an immersed boundary method (IBM). An elastic spring model is applied to simulate the skeleton structure of a RBC membrane. As a benchmarking test, the dynamical behavior of a single RBC under a simple shear flow has been validated. Then we focus on investigating the motion and the deformation of a single RBC in Poiseuille flows by varying the swelling ratio ($s^{*}$), the initial angle of the long axis of the cell at the centerline ($\varphi$), the maximum velocity at the centerline of fluid flow ($u_{\text{max}}$), the membrane bending stiffness of a RBC ($k_b$), and the height of the microchannel ($H$). Two motions of oscillation and vacillating breathing (swing) of a RBC are observed in both narrow and wide channels. The strength of the vacillating-breathing motion depends on the degree of confinement and the value of $u_{\text{max}}$. A RBC exhibits a strong vacillating-breathing motion as the degree of confinement is larger or the value of $u_{\text{max}}$ is higher. For the same degree of confinement, the vacillating-breathing motion appears to be relatively weaker but persists longer as the value of $u_{\text{max}}$ is lower. The continuation of shape change from the slippery to the parachute by varying the value of $u_{\text{max}}$ is obtained for the biconcave shape cell in a narrower channel. In particular, parachute shape and bulletlike shape, depending on the angle $\varphi$, coexist for the elliptic shape cell given initially with lower $u_{\text{max}}$ in a narrower channel.

We derive an analytical expression for the frequency of the shape oscillations of a diamagnetically levitated water droplet, in which the equilibrium shape is not spherical. We give the eigenfrequencies of all modes to first order in the oscillation amplitude and potential energy of the magnetogravitational trap confining the droplet. We compare the result with experimental measurements of the eigenfrequencies.