Sperm swimming at low Reynolds number have strong hydrodynamic interactions when their concentration is high in vivo or near substrates in vitro. The beating tails not only propel the sperm through a fluid, but also create flow fields through which sperm interact with each other. We study the hydrodynamic interaction and cooperation of sperm embedded in a two-dimensional fluid by using a particle-based mesoscopic simulation method, multiparticle collision dynamics. We analyze the sperm behavior by investigating the relationship between the beating-phase difference and the relative sperm position, as well as the energy consumption. Two effects of hydrodynamic interaction are found, synchronization and attraction. With these hydrodynamic effects, a multisperm system shows swarm behavior with a power-law dependence of the average cluster size on the width of the distribution of beating frequencies.

A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic cellular Potts model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.

Replica exchange simulations have become the method of choice in computational protein science, but they still often do not allow an efficient sampling of low-energy protein configurations. Here, we reconstruct replica flow in the temperature ladder from first passage times and use it for temperature optimization, thereby maximizing sampling. The method is applied in simulations of folding thermodynamics for a number of proteins starting from the pentapeptide Met-enkephalin, through the 36-residue HP-36, up to the 67-residue protein $\mathrm{GS}\text{−}{\alpha }_3\mathrm{W}$.

We investigate the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We find spike death phenomena: namely, the state of neurons transits from the limit cycle to a fixed point or transient state. The phenomena occur under the perturbation of an excitatory synaptic interaction, which has a high efficacy. We show that the decrease of synaptic current results in spike death through depressing the feedback of the sodium ionic current. In the networks with the spike death property the degree of synchronization is lower and insensitive to the heterogeneity of neurons. The mechanism of the influence is that the transition of the neuron state disrupts the adjustment of the rhythm of the neurons oscillation and prevents a further increase of the firing synchronization.

In a variety of biological situations, swimming cells have to move through complex fluids. Similarly, mucociliary clearance involves the transport of polymeric fluids by beating cilia. Here, we consider the extent to which complex fluids could be exploited for force generation on small scales. We consider a prototypical reciprocal motion (i.e., identical under time-reversal symmetry): the periodic flapping of a tethered semi-infinite plane. In the Newtonian limit, such motion cannot be used for force generation according to Purcell’s scallop theorem. In a polymeric fluid (Oldroyd-B, and its generalization), we show that this is not the case and calculate explicitly the forces on the flapper for small-amplitude sinusoidal motion. Three setups are considered: a flapper near a wall, a flapper in a wedge, and a two-dimensional scalloplike flapper. In all cases, we show that at quadratic order in the oscillation amplitude, the tethered flapping motion induces net forces, but no average flow. Our results demonstrate therefore that the scallop theorem is not valid in polymeric fluids. The reciprocal component of the movement of biological appendages such as cilia can thus generate nontrivial forces in polymeric fluid such as mucus, and normal-stress differences can be exploited as a pure viscoelastic force generation and propulsion method.

A clarification is due about the paper by Chelminiak et al. [Phys. Rev. E 72, 031903 (2005)]. In changing notation at the beginning, the authors incur an unfortunate error that significantly impacts the rest of the paper.

An original approach is developed for the description of spectral coherence and time-domain transport of wave fields scattered in random media. This approach accounts explicitly for the correlation properties of the disorder and is universal with respect to the dimensionality of the system. Specifically, a two-frequency mutual coherence function is evaluated by using a procedure of embedding the initial Helmholtz equation into an auxiliary problem of a directed wave propagating in a higher-dimensional space. The resulting Schrödinger-like equation is solved perturbatively by means of a cumulant path integral technique. Mean intensity profiles and temporal moments of a narrowband wave packet scattered in a random medium are calculated by using the Fourier transformation of the coherence function. The theory describes the ballistic to diffusive transition in wave transport, and is consistent with experimental results. Since the coherence function is expressed via an arbitrary form power spectrum, the results obtained open a new avenue for studying wave transport in anisotropic and/or fractally correlated systems.

By measuring or calculating coalescence times for several models of coalescence or evolution, with and without selection, we show that the ratios of these coalescence times become universal in the large size limit and we identify a few universality classes.

We compare two effective phonon theories, which have both been applied recently to study heat conduction in anharmonic lattices. In particular, we study the temperature dependence of the thermal conductivity of the Fermi-Pasta-Ulam $\beta$ model via the Debye formula, showing the equivalence of both approaches. The temperature for the minimum of the thermal conductivity and the corresponding scaling behavior are analytically calculated, which agree well with the result obtained from nonequilibrium simulations. We also give quantum corrections for the thermal conductivity from quantum self-consistent phonon theory. The vanishing behavior at the low temperature regime and the existence of an umklapp peak are qualitatively consistent with experimental studies.

The density profiles of a supercritical Lennard-Jones fluid near a weakly attractive surface are used to study the excess adsorption $\Gamma$ of supercritical fluid in a wide density range. We report the observation of two extrema of $\Gamma$ along the isotherm as a function of density. The attractive fluid-wall interaction potential tends to make $\Gamma$ positive, whereas the missing neighbor effect tends to make $\Gamma$ negative. The latter effect enhances with increasing fluid density due to the growth of the fluid-fluid attraction that results in the crossover from adsorption to depletion $(\Gamma =0)$ at some particular fluid density. With approaching the critical point, $\Gamma$ decreases as the bulk correlation length and passes through a minimum when the average density of confined fluid is close to the bulk critical density. Variation of $\Gamma$ with temperature and density is determined by the monotonic trend from adsorption to desorption upon increasing fluid density and by the increase of the absolute value of $\Gamma$ when approaching the critical point. Interplay of these trends results in two extrema of $\Gamma$ in the temperature-density plane. This effect may be responsible for the crossover from adsorption to desorption with approaching the critical temperature observed experimentally along the isotherms and along the critical isochore. The density profiles of a supercritical fluid are found to be exponential and the power law behavior predicted theoretically was not detected even when the bulk correlation length $\xi$ achieves 11 molecular diameters.

We model how polarized and unpolarized light can cause mechanical response in polydomain nematic and related photoelastomers. The reduction of order by heating and the consequential large strains that are known from nematic elastomers can alternatively be caused by light-induced bending of rodlike dye molecules which then equally reduce the order of their nematic hosts. While there is no mechanical response to heating of polydomain elastomers, mechanical response to light is possible by the selective absorption of light according to how domains are aligned with respect to the polarization direction or with respect to the propagation direction in the case of unpolarized light. We find large contractions or elongations, depending on the nature of polarization. The responses are nonmonotonic with light intensity.

We study how cells can optimize fitness in variable environments by tuning the internal fluctuations of protein expression of a bistable genetic switch. We model cells as bistable toggle switches whose dynamics are governed by a delayed stochastic simulation algorithm. Each state of the toggle switch makes the cell more fit in one of two environmental conditions. Different noise levels in protein expression yield different fitness values for cells in an environment that randomly switches between the two conditions. We compare the behavior of two cell types, one that can sense the environmental condition and one that cannot. In fast changing environments both cell types evolve to be as noisy as possible while maintaining bistability of the toggle switch. In slowly changing environments, evolved nonsensing cells are less noisy while sensing cells evolve the same noise level as in fast changing environments. Sensing removes the need of genotypic changes to adapt to changes in the environment fluctuation rate, providing an evolutionary advantage in unpredictable environments.

We present detailed numerical studies of the dynamics of three semiconductor lasers when interacting in a linear chain through the mutual injection of their optical fields. In particular, we focus on the synchronization properties of the coupling-induced dynamics and the role of the delay in the interaction between the lasers. The recently experimentally and numerically demonstrated zero-lag synchronization [Fischer et al., Phys. Rev. Lett. 97, 123902 (2006)] between the outer lasers in the chain is here further analyzed in detail along with a study of the robustness of this phenomenon. In addition, the propagation properties of perturbing pulses and of harmonic modulation are discussed.

We present a set of three-dimensional direct numerical simulations of incompressible decaying magnetohydrodynamic turbulence in which we investigate the influence of an external uniform magnetic field ${\mathbf{B}}_{\mathbf{0}}$. A parametric study in terms of $B_0$ intensity is made where, in particular, we distinguish the shear-from the pseudo-Alfvén waves dynamics. The initial kinetic and magnetic energies are equal with a negligible cross correlation. Both the temporal and spectral effects of ${\mathbf{B}}_{\mathbf{0}}$ are discussed. A subcritical balance is found between the Alfvén and nonlinear times with both a global and a spectral definition. The nonlinear dynamics of strongly magnetized flows is characterized by a different $k_{\perp }$ spectrum (where ${\mathbf{B}}_{\mathbf{0}}$ defines the parallel direction) if it is plotted at a fixed $k_{\parallel }$ (two-dimensional spectrum) or if it is integrated (averaged) over all $k_{\parallel }$ (one-dimensional spectrum). In the former case a much wider inertial range is found with a steep power law, closer to the wave turbulence prediction than the Kolmogorov one such as in the latter case. It is believed that the averaging effect may be a source of difficulty to detect the transition towards wave turbulence in natural plasmas. Another important result of this paper is the formation of filaments reported within current and vorticity sheets in strongly magnetized flows, which modifies our classical picture of dissipative sheets in conductive flows.

We propose two sets of initial conditions for magnetohydrodynamics (MHD) in which both the velocity and the magnetic fields have spatial symmetries that are preserved by the dynamical equations as the system evolves. When implemented numerically they allow for substantial savings in CPU time and memory storage requirements for a given resolved scale separation. Basic properties of these Taylor-Green flows generalized to MHD are given, and the ideal nondissipative case is studied up to the equivalent of ${2048}^3$ grid points for one of these flows. The temporal evolution of the logarithmic decrements $\delta$ of the energy spectrum remains exponential at the highest spatial resolution considered, for which an acceleration is observed briefly before the grid resolution is reached. Up to the end of the exponential decay of $\delta$, the behavior is consistent with a regular flow with no appearance of a singularity. The subsequent short acceleration in the formation of small magnetic scales can be associated with a near collision of two current sheets driven together by magnetic pressure. It leads to strong gradients with a fast rotation of the direction of the magnetic field, a feature also observed in the solar wind.

Visualization of turbulent flows is a powerful tool to help understand the turbulence dynamics and induced transport. However, it does not provide a quantitative description of the observed structures. In this paper, an approach to characterize quantitatively the topology of the flows is given. The technique, which can be applied to any type of turbulence dynamics, is illustrated through the example of resistive ballooning instabilities.

We present a method for the rankwise distributed multipole analysis of an arbitrary distribution of charge and its surrounding field. Using the superposition principle, the electrostatic field created by a distribution of charge can be resolved recursively into the contributions of a set of intrinsic multipole moments “tied to” their rank-specific multipole centers. The positions of the multipole centers, which are fixed with respect to the distribution of charge, are determined from a term-by-term optimization of the Taylor’s expansion of the electrostatic potential with respect to the charge coordinates. We describe the recursive construction of the intrinsic multipole moments and derive the algebraic expression of the multipole centers. The resulting distributed multipole expansion provides a conceptual framework for the analysis and modeling of the electrostatic field and of its associated distribution of charge.

The ability to exert a significant degree of pore structure control in porous silicon materials has made them attractive materials for the experimental investigation of the relationship between pore structure, capillary condensation, and hysteresis phenomena. Using both experimental measurements and a lattice gas model in mean field theory, we have investigated the role of pore size inhomogeneities and surface roughness on capillary condensation of ${\mathrm{N}}_2$ at $77\mathrm{K}$ in porous silicon with linear pores. Our results resolve some puzzling features of earlier experimental work. We find that this material has more in common with disordered materials such as Vycor glass than the idealized smooth-walled cylindrical pores discussed in the classical adsorption literature. We provide strong evidence that this behavior comes from the complexity of the processes within independent linear pores, arising from the pore size inhomogeneities along the pore axis, rather than from cooperative effects between different pores.

In this work we introduce a scheme for the calculation of an approximate closed expression for the time-dependent probability density function for overdamped particles in tilted periodic potentials. Our derivation is based on an ansatz for the solution of the corresponding Fokker-Planck equation and on a self-consistent cumulant calculation. The high accuracy of our expression for the time-dependent probability density function is exhibited by comparisons with Langevin dynamics simulations and exact analytic results for the drift and diffusion coefficients. Good agreement is found both, for large and intermediate times.

Molecular dynamics simulations have revealed a dramatic increase, with increasing temperature, of the amplitude of electrostatic fluctuations caused by water at the active site of metalloprotein plastocyanin. The increased breadth of electrostatic fluctuations, expressed in terms of the reorganization energy of changing the redox state of the protein, is related to the formation of the hydrophobic protein-water interface, allowing large-amplitude collective fluctuations of the water density in the protein’s first solvation shell. On top of the monotonic increase of the reorganization energy with increasing temperature, we have observed a spike at $\simeq 220\mathrm{K}$ also accompanied by a significant slowing of the exponential collective Stokes shift dynamics. In contrast to the local density fluctuations of the hydration-shell waters, these spikes might be related to the global property of the water solvent crossing the Widom line or undergoing a weak first-order transition.