Biological cells sense external chemical stimuli in their environment using cell-surface receptors. To increase the sensitivity of sensing, receptors often cluster. This process occurs most noticeably in bacterial chemotaxis, a paradigm for sensing and signaling in general. While amplification of weak stimuli is useful in the absence of noise, its usefulness is less clear in the presence of extrinsic input noise and intrinsic signaling noise. Here, exemplified in a bacterial chemotaxis system, we combine the allosteric Monod-Wyman-Changeux model for signal amplification by receptor complexes with calculations of noise to study their interconnectedness. Importantly, we calculate the signal-to-noise ratio, describing the balance of beneficial and detrimental effects of clustering for the cell. Interestingly, we find that there is no advantage for the cell to build receptor complexes for noisy input stimuli in the absence of intrinsic signaling noise. However, with intrinsic noise, an optimal complex size arises in line with estimates of the size of chemoreceptor complexes in bacteria and protein aggregates in lipid rafts of eukaryotic cells.

We studied the responses of three classes of Morris-Lecar neurons to sinusoidal inputs and synaptic pulselike stimuli with deterministic and random interspike intervals (ISIs). It was found that the responses of the output frequency of class 1 and 2 neurons showed similar evolution properties by varying input amplitudes and frequencies, whereas class 3 neuron exhibited substantially different properties. Specifically, class 1 and 2 neurons display complicated phase locking ($p$ : $q$, $p>q$, denoting output action potentials per input spikes) in low-frequency sinusoidal input area when the input amplitude is above their threshold, but a class 3 neuron does not fire action potentials in this area even if the amplitude is much higher. In the case of the deterministic ISI synaptic injection, all the three classes of neurons oscillate spikes with an arbitrary small frequency. When increasing the input frequency (both sinusoidal and deterministic ISI synaptic inputs), all neurons display 1 : 1 phase locking, whereas the response frequency decreases even fall to zero in the high-frequency input area. When the random ISI synaptic pulselike stimuli are injected into the neurons, one can clearly see the low-pass filter behaviors from the return map. The output ISI distribution depends on the mean ISI of input train as well as the ISI variation. Such different responses of three classes of neurons result from their distinct dynamical mechanisms of action potential initiation. It was suggested that the intrinsic dynamical cellular properties are very important to neuron information processing.

We study the discrete nonlinear Schrödinger equation with a random potential in one dimension. It is characterized by the length, the strength of the random potential, and the field density that determines the effect of nonlinearity. Following the time evolution of the field and calculating the largest Lyapunov exponent, the probability of the system to be regular is established numerically and found to be a scaling function of the parameters. This property is used to calculate the asymptotic properties of the system in regimes beyond our computational power.

The paper presents the modifications of the classic Takens-Ellner (TE) algorithm that are necessary to estimate the dimensional complexity ($d$) of the medium- and high-dimensional signals. The main idea is the fitting of the fourth-degree polynomial to the relation $d=\text{fn}(W)$ (where $W$ is window width) in order to find the point of minimum slope in this relation. This point corresponds to the plateau area being the feature of the low-dimensional signals and representing the range of the optimal $W$ used in the calculations. The point of minimum slope is represented by the local minimum in the first derivative function (third-degree polynomial). The exclusion of the attractor pairs of points lying approximately closer than the autocorrelation time removes the tendency to down-estimate $d$ observed in the classic TE algorithm. The procedure of the choice of the embedding parameters was modified: The lag ($L$) was calculated for the given embedding dimension ($m$) and $W$ was calculated by using the formula $L=W/(m-1)$ in order to obtain the desired values of $W$ for generating the precise relation $d=\text{fn}(W)$ being the basis for the polynomial fitting. The cubic interpolation of the signal is proposed for the noninteger $L$’s. Three signals possessing the dimensional complexities $d^A\approx 4$, $d^B\approx 6$, and $d^C\approx 8$ and being the sums of two, three, and four Lorenz signals, respectively, were analyzed. Their lengths were 65 536 points. The applied algorithm gives a precise estimation of $d$ for every signal A, B, and C. Also presented are the results of (a) the method for the estimation of the cubic interpolation error, (b) the analysis for signals contaminated with the white noise, and (c) the comparison between the original signals and the surrogates.

Excitability is a generic prediction for an optically injected semiconductor laser. However, the details of the phenomenon differ depending on the type of device in question. For quantum-well lasers very complicated multipulse trajectories can be found, while for quantum-dot lasers the situation is much simpler. Experimental observations show the marked differences in the pulse shapes while theoretical considerations reveal the underlying mechanism responsible for the contrast, identifying the increased stability of quantum-dot lasers to perturbations as the root.

The present work describes a procedure to calculate the effective diffusivity of a porous composite medium from the three-dimensional reconstruction of its microstructure. We perform Monte Carlo simulations based on the mean-square displacement method on numerical models of composite materials microstructures. First, computations of the effective diffusivity in the bulk diffusion regime account for the effect of the tortuosity of the geometry on gas diffusion. The Bruggeman equation, which is often used in the literature to relate the effective diffusivity to the porosity of the structure, appears to be inaccurate for porosities $\epsilon <0.40$. A more accurate correlation for this range of porosities is provided based on the results of our simulations. Second, the Bosanquet equation, which accounts for the effect of pore confinement on gas diffusion, is validated provided that the definition of the Knudsen number is based on the appropriate characteristic length. The procedure to calculate this characteristic length is demonstrated for analytical geometries. However, in practice, geometries obtained from experimental measurements are discrete. For discrete geometries, we show the effect of the resolution of the geometry on the accuracy of the calculation of the effective diffusivity and other properties of the porous material. In addition, the tesselation of solid surfaces affects the calculation of the chord-length distribution regardless of the resolution. This hinders the accurate estimation of the characteristic length necessary to compute the Knudsen number and the effective diffusivity.

We demonstrate that in significant limiting cases the problem of irreversible energy transfer in an oscillatory system with time-dependent parameters can be efficiently solved in terms of the Fresnel integrals. For definiteness, we consider a system of two weakly coupled linear oscillators in which the first oscillator with constant parameters is excited by an initial impulse, whereas the coupled oscillator with a slowly varying frequency is initially at rest but then acts as an energy trap. We show that the evolution equations of the slow passage through resonance are identical to the equations of the Landau-Zener tunneling problem, and therefore, the suggested asymptotic solution of the classical problem provides a simple analytic description of the quantum Landau-Zener tunneling with arbitrary initial conditions over a finite time interval. A correctness of approximations is confirmed by numerical simulations.

Scattering of a matter-wave single soliton and two-soliton molecule incident on the modified Pöschl-Teller potential well has been studied by means of a collective coordinate approach and numerical simulations of the Gross-Pitaevskii equation. Despite the attractive nature of the potential we observe total reflection of solitons in particular ranges of parameters, which is the signature of quantum behavior displayed by the matter-wave soliton. For other particular sets of parameters unscathed transmission of solitons and molecules through the potential well has been identified. A specific feature of this process is that the soliton passing through the potential well overtakes the freely propagating counterpart; i.e., its mean position appears to have been advanced in time. An array of such potentials makes the “time advance” effect even more pronounced, so that scattered solitons move well ahead of nonscattered ones, fully preserving their initial shape and velocity. A possible application of the obtained results is pointed out.

The effect of ultrafast diffusion is studied on reaction-diffusion processes in heterogeneous media, as encountered in catalysis and field emission microscopy. The reaction-diffusion equations describe adsorption, desorption, and reaction processes for two adspecies, for instance, on a paraboloidal heterogeneous surface in the presence of an external electric field. Using multiscale analysis, we show that the fast adspecies rapidly reaches a quasiequilibrium spatial distribution, characterized by a nonequilibrium chemical potential of the fast adspecies. An ordinary differential equation is derived for the time evolution of the nonequilibrium chemical potential. Numerical simulations are performed under different conditions, which confirm the convergence of the dynamics for finite diffusion toward the ultrafast diffusion limit predicted by our multiscale analysis. The numerical simulations also demonstrate that electric fields may induce important diffusive currents on heterogeneous surfaces under the conditions of field emission microscopy.

The cross-linking of polymer brushes is studied using the bond-fluctuation model. By mapping the cross-linking process into a two-dimensional (2D) percolation problem within the lattice of grafting points, we investigate the gelation transition in detail. We show that the particular properties of cross-linked polymer brushes can be reduced to the distribution of bonds which are formed between the grafted chains, and we propose scaling arguments to relate the gelation threshold to the chain length and the grafting density. The gelation threshold is lower than the percolation threshold for 2D bond percolation because of the longer range and broad distribution of bonds formed by the cross-linking process. We term this type of percolation problem star percolation. We observe a broad crossover from mean-field to critical percolation behavior by analyzing the cluster size distribution near the gelation threshold.

We consider a lattice and structures on it generated by a set of configurations of a cluster. Using some general considerations, we show that there exist linear relations between fractional contents of these configurations in the structures. Such relations can be useful for the determination of the ground states of lattice-gas models (or equivalent spin models). As an illustration we consider a set of configurations of a seven-site cluster on the triangular lattice.

We study the effect of asymmetric coupling strengths on the onset of oscillations in delay-coupled nonlinear systems. Our experiment consists of two wide-band optoelectronic devices that are cross-coupled. We find that oscillations appear in the system when the product of the two coupling strengths exceeds a critical value. Beyond the oscillation threshold, the oscillation amplitudes grow smoothly and we find a scaling law that describes the dependence of the amplitude on the coupling strengths. The observations are in good agreement with predictions from linear stability analysis and normal form theory.

The analytical expressions of the Joule-Thomson coefficient for homogeneous and harmonically trapped three-dimensional ideal anyons which obey Haldane fractional exclusion statistics are derived. For an ideal Fermi gas, the Joule-Thomson coefficient is negative, which means that there is no maximum Joule-Thomson inversion temperature. With careful study, it is found that there exists a Joule-Thomson inversion temperature in the fractional exclusion statistics model. Furthermore, the relations between the Joule-Thomson inversion temperature and the statistical parameter $g$ are investigated.

A new method is devised to derive a thermodynamic perturbation theory that is suitable for short-ranged potentials. We have calculated structure and thermodynamic of short-ranged square-well potential with good agreement with computer simulation data even at low temperatures. We have also compared the results with other perturbation theories. It is found that the proposed theory gives better results when used to compute the structure and thermodynamic of short-ranged hard-core potentials.

In spite of the analogy to the electrostatics, the three-dimensional colloidal nematostatics is substantially different in both its mathematical structure and its physical implications. The general tensorial structure of elastic multipoles derived in V. M. Pergamenshchik and V. O. Uzunova [Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] allows for a classification of different types of colloids in the nematostatics. In comparison to their electrostatic counterparts, the elastic multipoles have one extra tensorial index. Based on this structure, we identify possible types of elastic dipoles. An elastic dipole is characterized by three coefficients—isotropic strength, anisotropy, and chirality—and a two-component vector along the unperturbed director. The relationship between the dipole type and symmetry groups is established and sketches of various representative types of dipolar colloids are given. Instead of a single electric dipole, in the nematostatics there are four different pure types (dipolar singlets) and eight mixed types of elastic dipoles (one quintet, one quartet, two triplets, and four doublets). It is shown that the full symmetry of the colloid-induced director field and the colloid’s shape (body) symmetry determine different dipole components. For instance, a helicoidal component of the anchoring easy axes can make a chiral elastic dipole of a colloid with the quadrupolar shape symmetry. The interaction potentials for different singlet and doublet dipoles are derived and illustrated in terms of the dipolar dyads and elastic Coulomb law. We argue that multipole parameters must be found by pure numerical means, as from ansatz director distributions one can find only orders of their magnitudes.

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, for example, in nanofluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tubelike geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the nonlinear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear $~t^{9/8}$ growth law for the change in end-to-end distance at short times.

We show that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer which is robust against ambient dephasing and associated with strong multisite entanglement. Such optimal, random molecular conformations may explain efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.

This work describes a class of topological phonon modes, that is, mechanical vibrations localized at the edges of special structures that are robust against the deformations of the structures. A class of topological phonons was recently found in two-dimensional structures similar to that of microtubules. The present work introduces another class of topological phonons, this time occurring in quasi-one-dimensional filamentary structures with inversion symmetry. The phenomenon is exemplified using a structure inspired from that of actin microfilaments, present in most live cells. The system discussed here is probably the simplest structure that supports topological phonon modes, a fact that allows detailed analysis in both time and frequency domains. We advance the hypothesis that the topological phonon modes are ubiquitous in the biological world and that living organisms make use of them during various processes.

In the human brain, large-scale neural networks are considered to instantiate the integrative mechanisms underlying higher cognitive, motor, and sensory functions. Computational models of such large-scale networks typically lump thousands of neurons into a functional unit, which serves as the “atom” for the network integration. These atoms display a low dimensional dynamics corresponding to the only type of behavior available for the neurons within the unit, namely, the synchronized regime. Other dynamical features are not part of the unit’s repertoire. With this limitation in mind, here we have studied the dynamical behavior of a neural network comprising “all-to-all” synaptically connected excitatory and inhibitory nonidentical neurons. We found that the network exhibits various dynamical characteristics, synchronization being only a particular case. Then we construct a low-dimensional representation of the network dynamics, and we show that this reduced system captures well the main dynamical features of the entire population. Our approach provides an alternate model for a neurocomputational unit of a large-scale network that can account for rich dynamical features of the network at low computational costs.