We study gradient formation of subdiffusive morphogens. The morphogens are produced at a source point at a constant rate. From there they move subdiffusively and are also subject to degradation at a rate that may depend on location and on time. Our analysis is based on a reaction-subdiffusion equation obtained from a continuous time random-walk model with a long-tailed waiting time distribution that also incorporates an evanescence process. Spatially uniform degradation at a constant rate leads to an exponentially decreasing stationary concentration profile hardly distinguishable from that obtained with normal diffusion. On the other hand, with location-dependent degradation we find a rich gamut of profiles, some qualitatively quite different from those occurring with normal diffusion. We conclude that long-time morphogen concentration profiles are very sensitive to the spatial dependence of the reactivity and may also serve as a sensitive measure of the occurrence of anomalous diffusion.

A two-state unit is considered as an abstract modification for an excitable system. Each state is characterized by a different waiting time distribution. This non-Markovian approach allows for a renewal process description of the system dynamics. Exact formulas for the interspike interval distribution and power spectral density are found. In the limit of an infinity ensemble of globally coupled units the mean-field equations for the populations of both states are derived. Depending on the coupling strength and on the noise intensity the ensemble undergoes saddle-node bifurcations and demonstrates bistability, while a pitchfork bifurcation emerges on a cusp point. The ensemble undergoes Hopf bifurcations and bulk oscillations emerge, in the onset of coherent activation events, only when the feedback affects individual units with a certain time delay.

A nonequilibrium extension of Onsager’s canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile $n\left(\mathbf{r},t\right)$ of a colloidal liquid in terms of the coupled time-evolution equations of its mean value $\overline{n}\left(\mathbf{r},t\right)$ and of the covariance $\sigma \left(\mathbf{r},{\mathbf{r}}^{\prime };t\right)\equiv \overline{\delta n\left(\mathbf{r},t\right)\delta n\left({\mathbf{r}}^{\prime },t\right)}$ of its fluctuations $\delta n\left(\mathbf{r},t\right)=n\left(\mathbf{r},t\right)-\overline{n}\left(\mathbf{r},t\right)$. These two coarse-grained equations involve a local mobility function $b\left(\mathbf{r},t\right)$ which, in its turn, is written in terms of the memory function of the two-time correlation function $C\left(\mathbf{r},{\mathbf{r}}^{\prime };t,t^{\prime }\right)\equiv \overline{\delta n\left(\mathbf{r},t\right)\delta n\left({\mathbf{r}}^{\prime },t^{\prime }\right)}$. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance ${\overline{n}}^0\left(\mathbf{r}\right)$ and ${\sigma }^0\left(\mathbf{r},{\mathbf{r}}^{\prime }\right)$ toward its equilibrium state characterized by the equilibrium local concentration profile ${\overline{n}}^{eq}\left(\mathbf{r}\right)$ and equilibrium covariance ${\sigma }^{eq}\left(\mathbf{r},{\mathbf{r}}^{\prime }\right)$. This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities.

The nonequilibrium self-consistent generalized Langevin equation theory of colloid dynamics is used to describe the nonstationary aging processes occurring in a suddenly quenched model colloidal liquid with hard-sphere plus short-ranged attractive interactions, whose static structure factor and van Hove function evolve irreversibly from the initial conditions before the quench to a final dynamically arrested state. The comparison of our numerical results with available simulation data are highly encouraging.

In this paper, we investigate the spectral properties of a cholesteric film presenting a pitch profile with a Gaussian deformation. Using the Berreman $4\times 4$ matrix formalism, we numerically obtain the transmission spectrum at normal and oblique light incidence as a function of width and the position of the deformation. Our results reveal that a pair of resonant modes emerges inside the main stop band of the transmission spectrum as the width of the deformation becomes comparable to the helical pitch length. The mechanism behind the emergence of the resonant modes is discussed. The case of a pitch profile with multiple Gaussian deformations is also analyzed. At this configuration, a crossover from single to multiple band-gap pattern can be observed in the transmission spectrum, depending on the deformation parameters.

In order to explain the speed of Vesicular Stomatitis Virus (VSV) infections, we develop a simple model that improves previous approaches to the propagation of virus infections. For VSV infections, we find that the delay time elapsed between the adsorption of a viral particle into a cell and the release of its progeny has a very important effect. Moreover, this delay time makes the adsorption rate essentially irrelevant in order to predict VSV infection speeds. Numerical simulations are in agreement with the analytical results. Our model satisfactorily explains the experimentally measured speeds of VSV infections.

Beta-sheet protein domains are stabilized by weak hydrogen bonds, yet materials such as silk—whose ultimate tensile strength is controlled primarily by this secondary structure—can exceed the ultimate tensile strength of steel. Earlier work has suggested that this is because hydrogen bonds deform cooperatively within small protein domains to reach the maximum strength. Here we study the atomistic mechanism of this concerted deformation mechanism by applying an elastic structural model, used to solve the deformation field of the chemical bonds in beta-sheet nanostructures under stretching and thereby identify the number of hydrogen bonds that deform cooperatively. Through this analysis, we predict the optimal beta-strand and beta-sheet nanocrystal size associated with reaching the maximum usage of hydrogen bonds under loading applied per unit material volume. Our results, albeit based on a simple model and analytical equations, quantitatively agree with results based on experimental and molecular-dynamics studies and provide physical insight into the underlying molecular mechanisms of weak bond cooperativity. A comparison with the size of hydrogen bond clusters in biology reveals excellent agreement with the cluster sizes predicted by our analysis, suggesting that perhaps the confinement of hydrogen bonds into nanoscale elements is a universal biological design paradigm that turns weakness to strength. The parameters used in this study could be modified and applied to other protein and polymer structures, which imply potential applications of our model in understanding the physics of deformation and failure in a broader range of biological and polymer materials, as well as in de novo biomaterial design.

We consider the stationary and the partially synchronous regimes in an all-to-all coupled neural network consisting of an infinite number of leaky integrate-and-fire neurons. Using analytical tools as well as simulation results, we show that two threshold values for the coupling strength may be distinguished. Below the lower threshold, no synchronization is possible; above the upper threshold, the stationary regime is unstable and partial synchrony prevails. In between there is a range of values for the coupling strength where both regimes may be observed. The assumption of an infinite number of neurons is crucial: simulations with a finite number of neurons indicate that above the lower threshold partial synchrony always prevails—but with a transient time that may be unbounded with increasing system size. For values of the coupling strength in a neighborhood of the lower threshold, the finite model repeatedly builds up toward synchronous behavior, followed by a sudden breakdown, after which the synchronization is slowly built up again. The “transient” time needed to build up synchronization again increases with increasing system size, and in the limit of an infinite number of neurons we retrieve stationary behavior. Similarly, within some range for the coupling strength in this neighborhood, a stable synchronous solution may exist for an infinite number of neurons.

We extend the analysis of the friction factor for turbulent pipe flow reported by G. Gioia and P. Chakraborty [Phys. Rev. Lett. 96, 044502 (2006)] to the case where drag is reduced by polymer additives.

A perturbation study of the suppression of the soliton self-frequency shift by the bandwidth-limited optical amplification is proposed. The stability of the equilibrium point for the soliton amplitude and velocity identified by the adiabatic approximation of the soliton perturbation theory (SPT) is analyzed by a numerical solution of a linearized system in the neighborhood of the equilibrium point. The obtained analytical expressions for the eigenvalues of the linearized system allow the determination of the values of pulse and material parameters for which the equilibrium point is stable. A perturbation approach that leads to the research of the equation of strongly nonlinear Duffing–Van der Pol oscillator is suggested. The last equation is explored by two different methods. First, the recently obtained results for this equation by the hyperbolic perturbation method are used. Next, the hyperbolic Lindstedt-Poincare perturbation method is applied to the exploration of this equation. The equilibrium velocity of the perturbed stationary solution was calculated as a critical value of the control parameter in both methods. It turned out that the coupling of the equilibrium velocity and the amplitude of the perturbed stationary solution in both methods is similar to the relation between the soliton amplitude and velocity derived by the adiabatic approximation of SPT. The change in the form of the perturbed stationary solution has also been identified by means of the hyperbolic Lindstedt-Poincare perturbation method.

We probe the three-dimensional flow structure and rheology of gravitational (nondensity matched) suspensions for a range of driving rates in a split-bottom geometry. We establish that for sufficiently slow flows, the suspension flows as if it were a dry granular medium, and confirm recent theoretical modeling on the rheology of split-bottom flows. For faster driving, the flow behavior is shown to be consistent with the rheological behavior predicted by the recently developed “inertial number” approaches for suspension flows.

We consider a class of single-particle one-dimensional stochastic equations which include external field, additive, and multiplicative noises. We use a parameter $\theta ∊\left[0,1\right]$ which enables the unification of the traditional Itô and Stratonovich approaches, now recovered, respectively, as the $\theta =0$ and $\theta =1/2$ particular cases to derive the associated Fokker-Planck equation (FPE). These FPE is a linear one, and its stationary state is given by a $q$-Gaussian distribution with $q=\frac{\tau +2M\left(2-\theta \right)}{\tau +2M\left(1-\theta \right)}<3$, where $\tau \ge 0$ characterizes the strength of the confining external field and $M\ge 0$ is the (normalized) amplitude of the multiplicative noise. We also calculate the standard kurtosis ${\kappa }_1$ and the $q$-generalized kurtosis ${\kappa }_q$ (i.e., the standard kurtosis but using the escort distribution instead of the direct one). Through these two quantities we numerically follow the time evolution of the distributions. Finally, we exhibit how these quantities can be used as convenient calibrations for determining the index $q$ from numerical data obtained through experiments, observations, or numerical computations.

We extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback. Within this framework, we derive a generalization of the detailed fluctuation theorem, which is modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback. As an application, we extend two nonequilibrium work relations: the nonequilibrium work fluctuation theorem and the relative-entropy work relation.

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

We present a derivation of the recently proposed eighth-order phase-field crystal model [A. Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the crystallization of a solid from an undercooled melt. The model is used to study the planar growth of a two-dimensional hexagonal crystal, and the results are compared against similar results from dynamical density functional theory of Marconi and Tarazona, as well as other phase-field crystal models. We find that among the phase-field crystal models studied, the eighth-order fitting scheme gives results in good agreement with the density functional theory for both static and dynamic properties, suggesting it is an accurate and computationally efficient approximation to the density functional theory.

Empirical evidence is given for a significant difference in the collective trend of the share prices during the stock index rising and falling periods. Data on the Dow Jones Industrial Average and its stock components are studied between 1991 and 2008. Pearson-type correlations are computed between the stocks and averaged over stock pairs and time. The results indicate a general trend: whenever the stock index is falling the stock prices are changing in a more correlated manner than in case the stock index is ascending. A thorough statistical analysis of the data shows that the observed difference is significant, suggesting a constant fear factor among stockholders.

The kinematics of spiral waves with artificially constructed spatial excitability is numerically investigated in the Oregonator model. On an assumption that the rotation center of spiral’s tip drifts at angle $\delta$ to the direction of a local gradient, a kinematic formula of motion of spiral’s tip is derived. To test the formula, we have presented two forms of feedback-related spatial fields with radial gradients (RGs) and concentric circular gradients (CGs) both centering on a reference point. It is found that both rigidly rotating and meandering spiral waves are attracted to the reference point of an inward RG and a clockwise CG perturbation but moved away from it under an outward RG and a counterclockwise CG. Simulations of the drift-velocity formulas provide a quantitative testing of the numerical results.

The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. Orbits can be grouped already on the level of the symbolic dynamics by application of appropriate reconnection rules to the symbolic code in the ternary alphabet. The periodic orbit bunches can significantly improve the efficiency of semiclassical quantization methods for classically chaotic systems, which suffer from the exponential proliferation of orbits. For the diamagnetic hydrogen atom the use of one or few representatives of a periodic orbit bunch in Gutzwiller’s trace formula allows for the computation of semiclassical spectra with a classical data set reduced by up to a factor of 20.

We report the study of enhanced photoacoustic emission from a laser-induced plasma under the influence of the terahertz field up to 100 kV/cm. We theoretically and experimentally investigate the energy transfer from terahertz radiation to molecular translational motion, through terahertz-field-driven electron motion and inelastic electron-molecule collision. The enhanced photoacoustic emission in the frequency range of 1–140 kHz is quadratically dependent on the incident terahertz field. We also demonstrate, as an application, that the enhancement of photoacoustic emission from gases asymmetrically ionized by two-color laser field can be used for coherent terahertz wave detection.

The structure of the system consisting of a self-avoiding polymer chain attracted to the surface of a freely supported soft membrane surface by a short-ranged force is investigated. The adhesion of the polymer to the deformed surface can produce distinctive states such as pancake, pinch, and bud, dependent on the phenomenological parameters in the Helfrich model describing the membrane as well as an adsorption energy describing the attraction between a monomer and a membrane surface.