The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system.

We study a stochastic process $X_t$ which is a particular case of the Rayleigh process and whose square is the Bessel process, with various applications in physics, chemistry, biology, economics, finance, and other fields. The stochastic differential equation is ${\mathit{dX}}_t=(\mathit{nD}/X_t)\mathit{dt}+\sqrt{2D}\hspace{0.5em}{\mathit{dW}}_t$, where $W_t$ is the Wiener process. The drift term can arise from a logarithmic potential or from taking $X_t$ as the norm of a multidimensional random walk. Due to the singularity of the drift term for $X_t=0$, different natures of boundary at the origin arise depending on the real parameter $n$: entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behavior is observed in the case of a regular boundary.

We study the first-passage time (FPT) distribution to a target site for a random walker evolving in a bounded domain. We show that in the limit of large volume of the confining domain, this distribution falls into universality classes indexed by the walk dimension $d_w$ and the fractal dimension $d_f$ of the medium, which have been recently identified previously [Bénichou et al., Nat. Chem. 2, 472 (2010)]. We present in this paper a complete derivation of these universal distributions, discuss extensively the range of applicability of the results, and extend the method to continuous-time random walks. This analysis puts forward the importance of the geometry, and in particular the position of the starting point, in first-passage statistics. Analytical results are validated by numerical simulations, applied to various models of transport in disordered media, which illustrate the universality classes of the FPT distribution.

One-dimensional transport of an overdamped Brownian particle biased by an external constant force does not exhibit negative mobility. However, when the particle is coupled to another particle, negative mobility can arise. We present a minimal model and propose a scenario in which only one (say, the first) particle is dc biased by a constant force and ac driven by an unbiased harmonic signal. In this way we intend to achieve two aims at once: (i) negative mobility of the first particle, which is exclusively induced by coupling to the second particle and (ii) indirect control of the transport properties of the second particle by manipulating the first particle only. For instance, the sign and amplitude of the averaged stationary velocity of the second particle can be steered by the driving applied to the first particle. As an experimentally realizable system, we propose two coupled resistively shunted Josephson junctions.

The transport process in a molecular chain in a nonequilibrium stationary state is theoretically investigated. The molecule is interacting at both ends with thermal baths of different temperatures, while no dissipation mechanism is contained inside the molecular chain. We have first obtained the nonequilibrium stationary state outside the Hilbert space in terms of the complex spectral representation of Liouvillian. The nonequilibrium stationary state is obtained as an eigenstate of the Liouvillian, which is constructed through the collision invariant of the kinetic equation. The eigenstate of the Liouvillian contains information on the spatial correlation between the molecular chain and the thermal baths. While energy flow in the nonequilibrium state which is due to the first-order correlation can be described by the Landauer formula, the particle current due to the second-order correlation cannot be described by the Landauer formula. The present method provides a simple way to evaluate the energy transport in a molecular chain in a nonequilibrium situation.

Random sequential adsorption of $k$-mers of different sizes and shapes deposited on two types of fractal surfaces (deterministic and statistical) is studied. These kinds of substrates present intrinsic heterogeneities. As a consequence, the average coordination number depends on the topology that characterizes the adsorbent. For discrete models, at the late stage the surface coverage evolves according to $\theta (t)={\theta }_j-A\exp [-\frac{t}{\sigma }]$, where ${\theta }_j$ is the jamming coverage while $A$ and $\sigma$ are fitting parameters. A detailed analysis of how these main quantities [${\theta }_j$, $\sigma$] depend on the relationship between the geometry of the adsorbate and the adsorbent is presented. The results obtained suggest that the symmetry of the substrate may exert a decisive influence on the adsorption kinetics of polyatomic species.

A simple soft-core model potential is proposed to discuss the self-diffusion of biomolecules in solution. Extensive Brownian-dynamics simulations are performed to obtain the long-time self-diffusion coefficient. Then the simulation results are compared with the experimental data from a unified point of view recently obtained for suspensions of hard spheres. Thus, it is shown that the proposed potential can qualitatively well describe the experimental data.

The influence of static correlations beyond the pair level on the dynamics of selected model glass formers is investigated. The pair structure, angular distribution functions, and statistics of Voronoi polyhedra of two well-known Lennard-Jones mixtures as well as of the corresponding Weeks-Chandler-Andersen variants, in which the attractive part of the potential is truncated, are compared. By means of the Voronoi construction, the atomic arrangements corresponding to the locally preferred structures of the models are identified. It is found that the growth of domains formed by interconnected locally preferred structures signals the onset of the slow-dynamics regime and allows the rationalization of the different dynamic behaviors of the models. At low temperature, the spatial extension of the structurally correlated domains, evaluated at fixed relaxation time, increases with the fragility of the models and is systematically reduced by truncating the attractions. In view of these results, proper inclusion of many-body static correlations in theories of the glass transition appears crucial for the description of the dynamics of fragile glass formers.

Structural reordering in monolayers of gold nanoparticles during transfer from water surface to solid substrate has been studied by synchrotron x-ray scattering techniques. Grazing incidence diffraction (GID) and grazing incidence x-ray off-specular scattering (GIXOS) measurements were performed as a function of time to track the in-plane and out-of-plane structural reordering in the transferred monolayers. GID measurements show shift in the in-plane particle-particle correlation peak toward the lower in-plane momentum transfer value, signifying possible expansion of triangular lattice formed on the water surface. However, GIXOS data and supportive microscopy measurements clearly show compactification in the in-plane structure and associated out-of-plane movements. A model that assumes the possibility of a two-dimensional short-range structural reordering from triangular to square-like lattice as a function of time could explain all the data. The observed change in the electron densities of the nanoparticles before and after the structural reordering matches well with the expected change in the calculated electron densities of the nanoparticles arranged in triangular (pretransition) and square-like (post-transition) symmetry.

A cylindrical uniaxial liquid crystal was hydrogen-bonded with a tripod-shaped molecule. As the molecular number ratio of cylindrical liquid crystal to tripod molecule converges to 2:1, |$s$| $=$ 1/2 disclination defects, which are a necessary condition of biaxial nematic phase, appeared predominantly. After the application of an electric field, the |$s$| $=$ 1/2 disclinations converted to |$s$| $=$ 1 disclinations which imply a transition from a biaxial to uniaxial state. IR dichroism measurements support the hypothesis that the liquid crystal-tripod molecule complex undergoes a molecular conformation change from bent shape to parallel shape, and this conformation change is thought to be related to a field-induced biaxial-uniaxial transition.

We investigated membrane-like polymer structures of fractal connectivity such as Sierpinski gaskets and Sierpinski carpets applying the bond fluctuation model in three dimensions. Without excluded volume (phantom), both polymeric fractals obey Gaussian elasticity on larger scales determined by their spectral dimension. On the other hand, the swelling effect due to excluded volume is rather distinct between the two polymeric fractals: Self-avoiding Sierpinski gaskets can be described using a Flory-type mean-field argument. Sierpinski carpets having a spectral dimension closer to perfect membranes are significantly more strongly swollen than predicted. Based on our simulation results it cannot be excluded that Sierpinski carpets in athermal solvent show a flat phase on larger scales. We tested the self-consistency of Flory predictions using a virial expansion to higher orders. From this we conclude that the third virial coefficient contributes marginally to Sierpinski gaskets, but higher order virial coefficients are relevant for Sierpinski carpets.

Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of $N$, the number of motors, provided that $N$ is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.

Neuronal networks exhibit a variety of complex spatiotemporal patterns that include sequential activity, synchrony, and wavelike dynamics. Inhibition is the primary means through which such patterns are implemented. This behavior is dependent on both the intrinsic dynamics of the individual neurons as well as the connectivity patterns. Many neural circuits consist of networks of smaller subcircuits (motifs) that are coupled together to form the larger system. In this paper, we consider a particularly simple motif, comprising purely inhibitory interactions, which generates sequential periodic dynamics. We first describe the dynamics of the single motif both for general balanced coupling (all cells receive the same number and strength of inputs) and then for a specific class of balanced networks: circulant systems. We couple these motifs together to form larger networks. We use the theory of weak coupling to derive phase models which, themselves, have a certain structure and symmetry. We show that this structure endows the coupled system with the ability to produce arbitrary timing relationships between symmetrically coupled motifs and that the phase relationships are robust over a wide range of frequencies. The theory is applicable to many other systems in biology and physics.

Inspired by the gecko's climbing ability, adhesion between an elastic nanofilm with finite length and a rough substrate with sinusoidal roughness is studied in the present paper, considering the effects of substrate roughness and film thickness. It demonstrates that the normal adhesion force of the nanofilm on a rough substrate depends significantly on the geometrical parameters of the substrate. When the film length is larger than the wavelength of the sinusoidal roughness of the substrate, the normal adhesion force decreases with increasing surface roughness, while the normal adhesion force initially decreases then increases if the wavelength of roughness is larger than the film length. This finding is qualitatively consistent with a previously interesting experimental observation in which the adhesion force of the gecko spatula is found to reduce significantly at an intermediate roughness. Furthermore, it is inferred that the gecko may achieve an optimal spatula thickness not only to follow rough surfaces, but also to saturate the adhesion force. The results in this paper may be helpful for understanding how geckos overcome the influence of natural surface roughness and possess such adhesion to support their weights.

Multiphoton fluorescence recovery after photobleaching (MP-FRAP) is a laser microscopy technique used to measure diffusion coefficients of macromolecules in biological systems. The three-dimensional resolution and superior depth penetration within scattering samples offered by MP-FRAP make it an important tool for investigating both in vitro and in vivo systems. However, biological systems frequently confine diffusion within solid barriers, and to date the effect of such barriers on the measurement of absolute diffusion coefficients via MP-FRAP has not been studied. We have used Monte Carlo simulations of diffusion and MP-FRAP to understand the effect of barriers of varying geometries and positions relative to the two-photon focal volume. Furthermore, we supply ranges of barrier positions within which MP-FRAP can confidently be employed to measure accurate diffusion coefficients. Finally, we produce two new MP-FRAP models that can produce accurate diffusion coefficients in the presence of a single plane boundary or parallel infinite plane boundaries positioned parallel to the optical axis, up to the resolution limit of the multiphoton laser scanning microscope.

The opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or nonperiodic. At each time step, all agents move randomly on the lattice, and update their opinions based on those of neighbors with whom the differences of opinion are not greater than a given threshold. Due to the effect of repeated averaging, opinions first converge locally, and eventually reach steady states. As in other models with bounded confidence, steady states in general are those with one or more opinion groups in which all agents have the same opinion. When both the lattice and the opinion are periodic, however, metastable states can emerge, in which the whole spectrum of location-dependent opinions can coexist. This result shows that, when a set of continuous opinions forms a structure like a circle, unlike the typically used linear opinions, rich dynamic behavior can arise. When there are geographical restrictions in real situations, a complete consensus is rarely reached, and metastable states here might be one of the explanations for these situations, especially when opinions are not linear.

We examine multistability of several coexisting bursting patterns in a central pattern generator network composed of three Hodgkin-Huxley type cells coupled reciprocally by inhibitory synapses. We establish that the control of switching between bursting polyrhythms and their bifurcations are determined by the temporal characteristics, such as the duty cycle, of networked interneurons and the coupling strength asymmetry. A computationally effective approach to the reduction of dynamics of the nine-dimensional network to two-dimensional Poincaré return mappings for phase lags between the interneurons is presented.

We study the short-time stability of quantum dynamics in quasi-one-dimensional systems with respect to small localized perturbations of the potential. To this end, we analytically and numerically address the decay of the Loschmidt echo (LE) during times that are short compared to the Ehrenfest time. We find that the LE is generally a nonmonotonic function of time and exhibits strongly pronounced minima and maxima at the instants when the corresponding classical particle traverses the perturbation region. We also show that, under general conditions, the envelope decay of the LE is well approximated by a Gaussian, and we derive explicit analytical formulas for the corresponding decay time. Finally, we demonstrate that the observed nonmonotonic nature of the LE decay is only pertinent to one-dimensional (and, more generally, quasi-one-dimensional) systems, and that the short-time decay of the LE can be monotonic in a higher number of dimensions.

We study a nonlinear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a nonlinear diffusion predicts the existence of fronts as well as shock fronts. Despite the absence of memory effects, solutions in the case of pure nonlinear diffusion exhibit an anomalous subdiffusive scaling. Due to a balance between nonlinear diffusion and convection we, in particular, show that solitary waves appear. For large times they merge into a single solitary wave exhibiting a topological stability. Even though our results concern a specific equation, numerical simulations support the view that anomalous diffusion and the solitary waves disclosed will be general features in such nonlinear convective-diffusive dynamics.

A planar sheet immersed in an electrically polar liquid like water can propel itself by means of a plane wave charge density propagating in the sheet. The corresponding running electric wave polarizes the fluid and causes an electrical torque density to act on the fluid. The sheet is convected by the fluid motion resulting from the conversion of rotational particle motion, generated by the torque density, into translational fluid motion by the mechanism of friction and spin diffusion. Similarly, a planar sheet immersed in a magnetic ferrofluid can propel itself by means of a plane wave current density in the sheet and the torque density acting on the fluid corresponding to the running wave magnetic field and magnetization. The effect is studied on the basis of the micropolar fluid equations of motion and Maxwell’s equations of electrostatics or magnetostatics, respectively. An analytic expression is derived for the velocity of the sheet by perturbation theory to second order in powers of the amplitude of the driving charge or current density. Under the assumption that the equilibrium magnetic equation of state may be used in linearized form and that higher harmonics than the first may be neglected, a set of self-consistent integral equations is derived which can be solved numerically by iteration. In typical situations the second-order perturbation theory turns out to be quite accurate.