Random networks of semiflexible filaments play a crucial role in the mechanics of many systems, including the cell. To understand the response of semiflexible networks to stress, a strain-based measure of nonaffine deformation is introduced and used to probe the mechanics on various scales. This measure provides a unified description of nonaffinity in both strain and rotation and indicates that the level of nonaffinity in these quantities in a given system is comparable. The degree of nonaffinity decreases as the scale of observation increases. This scaling is a power law with different exponents for length scales smaller and larger than a characteristic length scale proportional to the fiber length. The fiber bending stiffness controls the scaling at small length scales, while the large length scale scaling exponent is independent of fiber density and stiffness.

Random sequential adsorption of mixed convex plus concave contour (MC) objects exhibits some distinctly different peculiar characteristics than the cases of purely convex objects. Though the substrate coverage approaches the jamming limit with time $t$ as $t^{-p}$, same as that for convex objects, the law $p\sim 1∕d_f$, valid for convex objects with $d_f$ degrees of freedom, does not hold for MC objects. Interestingly, for a fixed number of degrees of freedom, the exponent $p$ changes with the degree of nonconvexity and bears a near perfect correlation with the same.

We characterize some intriguing aspects of the entrainment behavior of coupled oscillators by means of a perturbation analysis of the partially synchronized solution of the classical Kuramoto-Sakaguchi model. The analysis reveals that partial entrainment may disappear with increasing coupling strength. It also predicts the occurrence of resonances: partial entrainment is induced in oscillators with natural frequencies in specific intervals not corresponding to high oscillator densities. The results are illustrated by simulations.

We study the control of transport properties in a deterministic inertia ratchet system via the extended delay feedback method. A chaotic current of a deterministic inertia ratchet system is controlled to a regular current by stabilizing unstable periodic orbits embedded in a chaotic attractor of the unperturbed system. By selecting an unstable periodic orbit, which has a desired transport property, and stabilizing it via the extended delay feedback method, we can control transport properties of the deterministic inertia ratchet system. Also, we show that the extended delay feedback method can be utilized for separation of particles in the deterministic inertia ratchet system as a particle’s initial condition varies.

We report experimental results concerning observation of a pattern forming system, subject to directional viscous fingering (printer’s instability). This system was excited by a time-dependent, periodic perturbation. A variety of spatiotemporal effects was observed, including pattern transient dynamics, wave vector selection, and morphological transitions. Detailed measurement of pattern shape and its associated Fourier modes assured the detection of a crossover between different regimes of the pattern evolution.

In this paper we investigate the spatiotemporal dynamics of a diatomic fluid undergoing zero mean oscillatory flow in a slit pore. The study is based on nonequilibrium molecular dynamics simulations together with two limiting solutions to the Navier-Stokes equations which include the effect of molecular rotation. By examining the viscoelastic properties of the system we can estimate the extent of the Newtonian regime, and a direct comparison between the molecular dynamics data and the solutions to the Navier-Stokes equations is then possible. It is found that the agreement is excellent, and that the vortex viscosity can be estimated by fitting the data obtained in the molecular dynamics simulations to the solutions to the Navier-Stokes equations. The quantitative effect of the coupling between the linear momentum and the spin angular momentum on flow is also investigated. We find that the maximum flow can be reduced up to 3–4 % due to the coupling.

We explore six classes of fractal probability laws defined on the positive half-line: Weibull, Frechét, Lévy, hyper Pareto, hyper beta, and hyper shot noise. Each of these classes admits a unique statistical power-law structure, and is uniquely associated with a certain operation of renormalization. All six classes turn out to be one-dimensional projections of underlying Poisson processes which, in turn, are the unique fixed points of Poissonian renormalizations. The first three classes correspond to linear Poissonian renormalizations and are intimately related to extreme value theory (Weibull, Frechét) and to the central limit theorem (Lévy). The other three classes correspond to nonlinear Poissonian renormalizations. Pareto’s law––commonly perceived as the “universal fractal probability distribution”––is merely a special case of the hyper Pareto class.

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortexlike flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads superdiffusively, depending on the shear modulus of the medium.

We study the effects of two kinds of interactions in tubelike polymers and demonstrate that they result in the formation of secondary motifs. The first has an entropic origin and is a measure of the effective space available to the solvent. The second arises from solvophobic interactions of the solvent with the polymers and leads to an energy proportional to the contact surface between the tube and solvent particles. The solvent molecules are modeled as hard spheres and the two interactions are considered separately with the solvent density affecting their relative strength. In addition to analytical calculations, we present the results of numerical simulations in order to understand the role played by the finite length of short polymers and the discrete versus continuum descriptions of the system in determining the preferred conformation.

We investigate theoretically the kinetics of the folding transition of a single semiflexible polymer. In the folding transition, the growth rate decreases with an increase in the number of monomers in the collapsed domain, suggesting that the main contribution to dissipation is from the motion of the domain. In the unfolding transition, the dynamic scaling exponents 1/8 and 1/4 were determined for the disentanglement and relaxation steps, respectively. We performed Langevin dynamics simulations to test our theory. It is found that our theory is in good agreement with simulations. We also propose the kinetics of the transitions in the presence of a hydrodynamic interaction.

DNA microarrays are devices that are able, in principle, to detect and quantify the presence of specific nucleic acid sequences in complex biological mixtures. The measurement consists in detecting fluorescence signals from several spots on the microarray surface onto which different probe sequences are grafted. One of the problems of the data analysis is that the signal contains a noisy background component due to nonspecific binding. We present a physical model for background estimation in Affymetrix Genechips. It combines two different approaches. The first is based on the sequence composition, specifically its sequence-dependent hybridization affinity. The second is based on the strong correlation of intensities from locations which are the physical neighbors of a specific spot on the chip. Both effects are incorporated in a background estimator which contains 24 free parameters, fixed by minimization on a training data set. In all data analyzed the sequence-specific parameters, obtained by minimization, are found to strongly correlate with empirically determined stacking free energies for RNA-DNA hybridization in solution. Moreover, there is an overall agreement with experimental background data and we show that the physics-based model that we propose performs on average better than purely statistical approaches for background calculations. The model thus provides an interesting alternative method for background subtraction schemes in Affymetrix Genechips.

Semiflexible polymer networks, such as cell cytoskeleton, differ significantly from their flexible counterparts in their deformation energy storage mechanism. As a result, the network elasticity is governed by both enthalpic and entropic variations. In addition, the enthalpic effect shows two distinct regimes of energy storage mechanism, the affine and nonaffine regimes. In the past, computation-based modeling on random networks, such as the Mikado model, was used to demonstrate the physical mechanism of mechanical deformation of semiflexible networks. These models are computationally intensive and hence are difficult to apply to studying whole cells. In this paper, we develop a micromechanical model to predict the average macroscopic elastic properties of a random, semiflexible, biopolymer network. The model employs a unit cell consisting of four semiflexible chains and four equivalent axial-bending springs. The proposed unit-cell-based micromechanical model represents a statistically average realization of the actual network and gives the average mechanical properties, such as the shear modulus. Comparisons between the model predictions and Mikado model results confirm that this micromechanical model captures the essential deformation physics revealed from previous studies on the actual network and is capable of predicting the transition between nonaffine and affine deformations. This model can be used to develop efficient continuum constitutive models of the cytoskeleton in the future.

We study a set of linearized catalytic reactions to model gene and protein interactions. The model is based on experimentally motivated interaction network topologies and is designed to capture some key properties of gene expression statistics. We impose a nonlinearity to the system by enforcing a boundary condition which guarantees non-negative concentrations of chemical substances. System stability is quantified by maximum Lyapunov exponents. We find that the non-negativity constraint leads to a drastic inflation of those regions in parameter space where the Lyapunov exponent exactly vanishes. Within the model this finding can be fully explained as a result of a symmetry breaking mechanism induced by the positivity constraint. The robustness of this finding with respect to network topologies and the role of intrinsic molecular and external noise is discussed. We argue that systems with inflated “edges of chaos” could be much more easily favored by natural selection than systems where the Lyapunov exponent vanishes only on a parameter set of measure zero.

On a Si(111) surface, which is covered with the $1\times 1$ structure at high temperature, the $7\times 7$ structure appears when temperature is lower than the structural transition temperature $\left(860°\text{C}\right)$. On the vicinal face, the $7\times 7$ structure spreads from the upper side of the step edge. The diffusion coefficient on the $1\times 1$ structure is larger than that on the $7\times 7$ structure. During growth, due to the difference in the diffusion coefficient, step wandering occurs and grooves perpendicular to the steps are formed. When the direct electric current is added parallel to the step, the grooves are tilted. In this paper, with taking account of the drift of adatoms caused by the direct current, we study the possibility of tilting of the grooves.

The orientational ordering of the nematic phase of a polyethylene glycol (PEG)–peptide block copolymer in aqueous solution is probed by small-angle neutron scattering (SANS), with the sample subjected to steady shear in a Couette cell. The PEG-peptide conjugate forms fibrils that behave as semiflexible rodlike chains. The orientational order parameters ${\overline{P}}_2$ and ${\overline{P}}_4$ are obtained by modeling the data using a series expansion approach to the form factor of uniform cylinders. The method used is independent of assumptions on the form of the singlet orientational distribution function. Good agreement with the anisotropic two-dimensional SANS patterns is obtained. The results show shear alignment starting at very low shear rates, and the orientational order parameters reach a plateau at higher shear rates with a pseudologarithmic dependence on shear rate. The most probable distribution functions correspond to fibrils parallel to the flow direction under shear, but a sample at rest shows a bimodal distribution with some of the rodlike peptide fibrils oriented perpendicular to the flow direction.

We consider the task of identification of a cluster structure in random networks. The results of two methods are presented: (i) the Newman algorithm [M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004)]; and (ii) our method based on differential equations. A series of computer experiments is performed to check if in applying these methods we are able to determine the structure of the network. The trial networks consist initially of well-defined clusters and are disturbed by introducing noise into their connectivity matrices. Further, we show that an improvement of the previous version of our method is possible by an appropriate choice of the threshold parameter $\beta$. With this change, the results obtained by the two methods above are similar, and our method works better, for all the computer experiments we have done.

We propose a method called multifractal detrended cross-correlation analysis to investigate the multifractal behaviors in the power-law cross-correlations between two time series or higher-dimensional quantities recorded simultaneously, which can be applied to diverse complex systems such as turbulence, finance, ecology, physiology, geophysics, and so on. The method is validated with cross-correlated one- and two-dimensional binomial measures and multifractal random walks. As an example, we illustrate the method by analyzing two financial time series.

We experimentally investigated the effects of a chemical reaction involving precipitation on the miscible viscous fingering pattern formed in a Hele-Shaw cell. The precipitation concentration, the ratio of the reactant concentrations initially included in the more- and less-viscous liquids, and the Péclet number were varied. For a Péclet number at the stoichiometric ratio the precipitation had significant effects on the fingering pattern when its concentration exceeded a threshold value. Interestingly, the type of effect of the precipitation on the pattern depended on its concentration. At moderate concentration, a straight-shaped finger was observed. At high concentration, the finger was bent in an almost perpendicular direction. The effect of precipitation on the pattern also depended on the ratio of reactant concentrations.

Temporal evolution of a distribution function $P\left(X,t\right)$ for $\mathit{X}$ clusters is analyzed in aggregation-chipping processes, which is a model incorporating simultaneously aggregation and the chipping off of a monomeric unit from a randomly chosen aggregate. Numerical simulations show that $P\left(1,t\right)$ exhibits the singular time dependence $P\left(1,t\right)-P\left(1,\infty \right)\propto t^{-2/3}$. Using this time dependence, we find a notable double power-law distribution of $P\left(X,t\right)$ with universal exponents $-5/2$ and $-3/2$ at a sufficiently large $t$. In finite systems, clusters in the second power law with the exponent $-3/2$ eventually coagulate into one “monopolized” cluster. These analyses are in good agreement with the results of the simulation.

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over Galois fields $\text{GF}\left(q\right)$, with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of $\text{GF}\left(q\right)$ matrices onto spin systems using the representation of the cyclic group of order $q$ as the $q$th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica-symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average numbers of random matrices for any general connectivity profile. We present numerical results for particular distributions.