We investigate the role of hydrodynamics in the evolution of the morphology and the selection of kinematics in simple uniflagellated microorganisms. We find that the most efficient swimming strategies are characterized by symmetrical, nonsinusoidal bending waves propagating from the base of the head to the tip of the tail. In addition, we show that the ideal tail-to-head length ratio for such a swimmer is $\approx 12$ and that this predicted ratio is consistent with data collected from over 400 species of mammalian sperm.

Simulation of noncontinuum gas flows presents tremendous challenges, especially for nanoscale devices that usually exhibit low speeds and isothermal conditions. Such simulations are often achieved through use of the Boltzmann Bhatnagar-Gross-Krook equation, which forms the foundation for the lattice Boltzmann (LB) method. Accuracy of the LB method in noncontinuum flows is widely assumed to depend on the order of quadrature used. Here, we study noncontinuum Couette flow and discover that interaction of the lattice with the solid boundaries is the dominant mechanism controlling accuracy—quadrature order plays a comparatively minor role. This suggests the applicability of low-order quadrature in LB simulation of wall bounded isothermal noncontinuum flows, and leads to a framework and rationale for accurate implementation of LB models in noncontinuum flows.

We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting-time distributions have a power-law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasibrittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.

We analyze the citation distributions of all papers published in Physical Review journals between $1985$ and $2009$. The average number of citations received by papers published in a given year and in a given field is computed. Large variations are found, showing that it is not fair to compare citation numbers across fields and years. However, when a rescaling procedure by the average is used, it is possible to compare impartially articles across years and fields. We make the rescaling factors available for use by the readers. We also show that rescaling citation numbers by the number of publication authors has strong effects and should therefore be taken into account when assessing the bibliometric performance of researchers.

In the study of small and large networks it is customary to perform a simple random walk where the random walker jumps from one node to one of its neighbors with uniform probability. The properties of this random walk are intimately related to the combinatorial properties of the network. In this paper we propose to use the Ruelle-Bowens random walk instead, whose probability transitions are chosen in order to maximize the entropy rate of the walk on an unweighted graph. If the graph is weighted, then a free energy is optimized instead of the entropy rate. Specifically, we introduce a centrality measure for large networks, which is the stationary distribution attained by the Ruelle-Bowens random walk; we name it entropy rank. We introduce a more general version, which is able to deal with disconnected networks, under the name of free-energy rank. We compare the properties of those centrality measures with the classic PageRank and hyperlink-induced topic search (HITS) on both toy and real-life examples, in particular their robustness to small modifications of the network. We show that our centrality measures are more discriminating than PageRank, since they are able to distinguish clearly pages that PageRank regards as almost equally interesting, and are more sensitive to the medium-scale details of the graph.

Observations suggest that contemporary wildfire suppression practices in the United States have contributed to conditions that facilitate large, destructive fires. We introduce a forest-fire model with natural fire resistance that supports this theory. Fire resistance is defined with respect to the size and shape of clusters; the model yields power-law frequency-size distributions of model fires that are consistent with field observations in the United States, Canada, and Australia.

Particle motion in a smoothly oscillating nonintegrable billiard is known to result in unbounded energy growth. The asymptotic energy growth rate of an ensemble of particles in a smoothly oscillating chaotic billiard is known to be quadratic in time. In this paper, it is shown that although this holds for the case of small oscillations, large oscillations in chaotic billiards can lead to faster than quadratic-in-time energy growth. It is also shown that the energy growth rate in oscillating pseudo-integrable billiards could be exponential in time. This is important for applications since slower than exponential-in-time energy growth can be annihilated by dissipation.

The numerically observed approximate functional forms for the transverse and longitudinal-momentum proportional (LP) Gram-Schmidt Lyapunov modes have been studied for some time. We construct a field theory for a system where the number of particles is large enough so the Lyapunov mode contributions from each particle can be considered to change continuously with particle position, whose solution gives the observed functional forms for all modes. The wave equations obtained as solutions of the field theory are derived either phenomenologically or from the exact dynamics of two-dimensional hard particles. The wave speed of the LP modes is predicted to reasonable accuracy for a range of densities and system sizes.

We examine the finite surface tension radial viscous fingering problem in a rotating Hele-Shaw cell, and focus on the action of inertial effects on the stability and morphology of the emerging patterns. To study such a flow we use an alternative version of the usual Darcy’s law derived by gap-averaging the Navier-Stokes equation, but retaining its inertial terms. The importance of inertial forces is pertinently characterized by a rotational Reynolds number. Linear and weakly nonlinear stages of the dynamics are described analytically through a mode coupling approach. The linear stability results indicate that inertia has a stabilizing role. However, the characteristic number of fingers and the width of the band of linearly unstable modes are not altered by inertia. In the early nonlinear regime we find that inertia acts to favor the development of fingers with narrower tips than those obtained in its absence. We have also verified that finger competition events are affected by inertial effects which tend to restrain finger length variability among inward-moving fingers.

Using scaling, we show that the stability of a buoyant boundary layer in a porous medium in the presence of a first-order chemical reaction is fully determined by the nondimensional number $\mathrm{Da}/{\mathrm{Ra}}^2=k_r\mathit{aD}\varphi {\mu }^2/(k\Delta {\rho }_{0}g){}^2$, where $\mathrm{Da}=k_{\mathrm{r}}{\mathit{aL}}_{\mathrm{Z}}^2/k_{\mathrm{r}}{\mathit{aL}}_{\mathrm{Z}}^2(D\varphi )$ is the Damköhler number and $\mathrm{Ra}=k\Delta {\rho }_0{\mathit{gL}}_{\mathrm{Z}}/k\Delta {\rho }_0{\mathit{gL}}_{\mathrm{Z}}(\mu D\varphi )$ is the solutal Rayleigh number. The time for onset of convection is shown to increase with rising $\mathrm{Da}/{\mathrm{Ra}}^2$. Above a critical $\mathrm{Da}/\mathrm{Da}{\mathrm{Ra}}^2\approx 2\times {10}^{-3}\hspace{0.5em}{\mathrm{Ra}}^2\approx 2\times {10}^{-3}$, no convection occurs as reaction stabilizes the diffusive layer at a finite thickness. This thickness decreases with increasing $\mathrm{Da}/{\mathrm{Ra}}^2$, becoming zero at $\mathrm{Da}/{\mathrm{Ra}}^2\approx \mathrm{O}(1)$. As applied to CO${}_2$ geostorage, our results suggest distinct regimes for CO${}_2$ transport in saline aquifers.

This study reports the presence of two different stable modes of bifurcation in the near field of a three-dimensional sudden contraction. To be precise, flow downstream of a symmetric sudden contraction undergoes a transition from a symmetric state to an asymmetric state through a symmetry-breaking pitchfork bifurcation following an increase in the channel aspect ratio or the Reynolds number. In addition, the oncoming (upstream) symmetry-plane flow exhibits spanwise bifurcations along the topological core lines of each of the salient roof and floor eddies. Small aspect-ratio (contraction) channels are noted to facilitate interesting splitting of the salient roof and floor eddies into multicore forms with accompanying spanwise flow bifurcations along the respective vortical core lines. Herein extensive three-dimensional simulations performed with various aspect and contraction ratios and Reynolds numbers clearly suggest that flow transition in the sudden-contraction channels should indeed occur primarily through these two generically distinct modes of bifurcation.

A special cavity based on effective near-zero-index paired structures containing $\varepsilon$-negative and μ-negative materials is realized by using composite right- or left-handed transmission lines. When an artificial magnetic “atom” is put into the cavity, unusual Rabi-type splitting appears because of the strong coupling between the artificial atom and the localized tunneling mode. The direct time domain energy exchanges between the cavity and the “atom” are experimentally observed after excited by a short pulse signal. Within the “atom” field attenuation time, more than one oscillations appear. Rabi-type splitting and the Rabi-type oscillation period are invariant with the scaling changes of the length but vary with the positions where the “atom” is put with different field intensity. Moreover, the decay time of Rabi-type oscillation becomes longer when the tunneling mode possesses smaller linewidth, which is in good agreement with numerical simulations.

We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low-frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wavenumber of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the independent scattering approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this “polydisperse correlation” into account and show that our model better describes the experimental results than the ISA.

We investigate the critical properties of the two-dimensional Z(5) vector model. For this purpose, we propose a cluster algorithm, valid for Z($N$) models with odd values of $N$. The two-dimensional Z(5) vector model is conjectured to exhibit two phase transitions with a massless intermediate phase. We locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices and compare the results with analytical predictions.

We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has $N$ positional degrees of freedom, of which $N_L$ are connected to a bath at temperature $T_L$ and $N_R$ are connected to a bath at temperature $T_R$. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for $N_L\ne N_R$ and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.

We present here the dielectric and electro-optical studies of cadmium telluride quantum dots (CdTe QDs) doped ferroelectric liquid crystals (FLCs). It has been observed that the doping of CdTe QDs not only induced a pronounced memory effect but also affected the physical parameters of FLC material (LAHS19). The modifications in the physical parameters and memory effect of LAHS19 are found to depend on the concentration ratio of CdTe QDs. The lower concentration of CdTe QDs (1–3 wt%) enhanced the values of spontaneous polarization and rotational viscosity of LAHS19 material but did not favor the memory effect, whereas a higher concentration of CdTe QDs (>5 wt%) degraded the alignment of LAHS19 material. The doping of ∼5 wt% of CdTe QDs is found to be the most suitable for achieving good memory effect without significantly affecting the material parameters.

We investigate the electrostatics of a partially formed, charged spherical shell in a salt solution. We solve the problem numerically at the Poisson-Boltzmann level and analytically in the Debye-Hückel regime. From the results on energetics of partially formed shells we examine the stability of tethered (crystalline) and fluid shells toward rupture. We delineate different regimes of stability, where, for fluid shells, we also include the effects of bending elasticity of the shells. Our analysis shows how charging of the shell induces its instability toward rupture but also provides insight regarding growth of charged shells.

We theoretically study the structure of periodic bulk assemblies of identical lipid vesicles. In our model, each vesicle is represented as a convex polyhedron with flat faces, rounded edges, and rounded vertices. Each vesicle carries an elastic and an adhesion energy and in the limit of strong adhesion, the minimal-energy shape of cells minimizes the weighted total edge length. We calculate exactly the shape of the rounded edge and show that it can be well described by a cylindrical surface. By comparing several candidate space-filling polyhedra, we find that the oblate shapes are preferred over prolate shapes for all volume-to-surface ratios. We also study periodic assemblies of vesicles whose adhesion strength on lateral faces is different from that on basal or apical faces. The anisotropy needed to stabilize prolate shapes is determined and it is shown that, at any volume-to-surface ratio, the transition between oblate and prolate shapes is very sharp. The geometry of the model vesicle assemblies reproduces the shapes of cells in certain simple animal tissues.

Current-voltage ($I$-$V$) characteristics in proteins are sensitive to conformational changes induced by an external stimulus (photons, chemical, etc.). This sensitivity can be used in medical and industrial applications as well as shedding new light on the microscopic structure of biological materials. Here, we show that a sequential tunneling model of carrier transfer between neighboring amino acids in a single protein is the basic mechanism responsible for the electrical properties measured over a wide range of applied potentials. We also show that such a strict correlation between the protein structure and the electrical response can lead to a new generation of nanobiosensors that mimic the sensorial activity of living species. To demonstrate the potential usefulness of protein electrical properties, we provide a microscopic interpretation of recent $I$-$V$ experiments carried out in bacteriorhodopsin at a nanoscale length.

A simple measure for the efficiency of protein synthesis by ribosomes is provided by the steady state amount of protein per messenger RNA (mRNA), the so-called translational ratio, which is proportional to the translation rate. Taking the degradation of mRNA into account, we show theoretically that both the translation rate and the translational ratio decrease with increasing mRNA length, in agreement with available experimental data for the prokaryote Escherichia coli. We also show that, compared to prokaryotes, mRNA degradation in eukaryotes leads to a less rapid decrease of the translational ratio. This finding is consistent with the fact that, compared to prokaryotes, eukaryotes tend to have longer proteins.