We theoretically investigated the temperature fluctuations of DNA close to denaturation and observed a strong enhancement of these fluctuations at the critical temperature. Although in a much lower frequency range, such a sharp increase was also reported in the recent experimental work of Nagapriya et al. [Phys. Rev. Lett. 96, 038102 (2006)]. We showed that there is instead no enhancement of temperature fluctuations when the dissipation coefficient $\gamma$ in Langevin equations is assumed to be larger than a few tens of ${\mathrm{ps}}^{-1}$, and pointed out the possible role of the solvent in real experiments. We sought for a possible correlation between the growth of large bubbles and the enhancement of temperature fluctuations but found no direct evidence thereof. Finally, we showed that neither the enhancement of fluctuations nor the $1∕f$ dependence are observed at the scale of a single base pair, while these properties show up when summing the contributions of a large number of base pairs. We therefore conclude that both effects result from collective motions that are facilitated by the divergence of the correlation length at denaturation.

Forced packing of a long metallic wire injected into a two-dimensional cavity leads to crushed structures involving a hierarchical cascade of loops with varying curvature radii. We study the distribution of elastic energy stored in such systems from experiments, and high-resolution digital techniques. It is found that the set where the elastic energy of curvature is concentrated has dimension $D_{\mathcal{S}}=1.0\pm 0.1$, while the set where the mass is distributed has dimension $D=1.9\pm 0.1$.

Many important real-world networks manifest small-world properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is preferential attachment, where nodes acquire new links with probability proportional to the number of links they already have. We show that preferential attachment is a special case of the process of molecular evolution. We present a single-parameter model of network growth that unifies varieties of preferential attachment with the quasispecies equation (which models molecular evolution), and also with the Erdős-Rényi random graph model. We suggest some properties of evolutionary models that might be applied to the study of networks. We also derive the form of the degree distribution resulting from our algorithm, and we show through simulations that the process also models aspects of network growth. The unification allows mathematical machinery developed for evolutionary dynamics to be applied in the study of network dynamics, and vice versa.

Based on a two-dimensional small-world network model, we propose an efficient routing strategy that enhances the network capacity while keeping the average packet travel time low. We deterministically increase the weight of the links attached to the “congestible nodes” and compute the effective distance of a path by summing up the weight of the links belong to that path. The routing cost of a node is a linear combination of the minimum effective distance from the node to the target and its queue length. The weight assignment reduces the maximum load of the network, while the incorporation of dynamic information further balances the traffic on the network. Simulation results show that the network capacity is much improved compared with the reference strategies, while the average packet travel time is relatively small.

Recently, there has been a growing interest in using induced electro-osmosis to pump fluids in microfluidic devices. We show that induced electroosmosis can also be used to promote stirring and chaotic advection. To this end, we study theoretically a stirrer in which the flow patterns are alternated in time. We first analyze an idealized embodiment of the stirrer that admits a simple analytical solution for the flow patterns. The stirrer consists of a concentric annulus whose outer surface is defined by an array of electrodes that provide a spatially varying potential distribution. The resulting electric field induces quadruple electro-osmotic flow around the inner cylinder. By timewise alternating the potential distribution around the outer cylinder, we induce chaotic advection in the cavity. Subsequently, we carry out numerical simulations for a more realistic design that can be readily constructed, and demonstrate that it is possible to induce chaotic advection also in this case.

We present a concept for and experimental demonstration of an active microfluidic mixer that uses microvalves to control periodic flow deviation. This active design allows the degree of mixing to be varied independently of flow rate. The mixer is compact and efficient, achieving mixing of different fluids through chaotic advection by stretching and folding the interface of the fluids.

The influence of white noise on the dynamics of a delayed electrically coupled pair of Hidmarsh-Rose bursting neurons is studied. In particular a simple method to predict the intensity of noise that can destabilize the quiescent state is proposed and compared with numerical computations. Furthermore, it is demonstrated that quite small noise completely destroys the exact synchronization of bursting dynamics, and a qualitative explanation of this effect is discussed.

Formation of microstructure in homogeneous associated liquids is analyzed through the density-density pair correlation functions, both in direct and reciprocal space, as well as an effective local one-body density function. This is illustrated through a molecular dynamics study of two neat alcohols, namely, methanol and tert-butanol, which have a rich microstructure: chainlike molecular association for the former and micellelike for the latter. The relation to hydrogen bonding interaction is demonstrated. The apparent failure to find microstructure in water—a stronger hydrogen bonding liquid—with the same tools is discussed.

We develop both phenomenological and molecular-statistical theory of smectic-$A$–smectic-$C$ phase transition with anomalously weak smectic layer contraction. Using a general mean-field molecular model, we demonstrate that a relatively simple interaction potential suffices to describe the transition both in conventional and de Vries type smectics. The theoretical results are in excellent agreement with experimental data. The approach can be used to describe tilting transitions in other soft matter systems.

We perform a time-dependent study of the driven dynamics of overdamped particles that are placed in a one-dimensional, piecewise linear random potential. This setup of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function for the position of the particles and transform this quantity of interest into the form of a Fourier integral. In doing so, the evolution of the probability density can be investigated analytically for finite times. It is demonstrated that the probability density contains both a $\delta$-singular contribution and a regular part. While the former part plays a dominant role at short times, the latter rules the behavior at large evolution times. The slow approach of the probability density to a limiting Gaussian form as time tends to infinity is elucidated in detail.

We show by numerical simulations that a nonrotationally symmetric body, whose orientation is fixed and whose center of mass can slide along a rectilinear guide, under the effect of inelastic collisions with a surrounding gas of particles, displays directed motion. We present a theory which explains how the lack of time reversal induced by the inelasticity of collisions can be exploited to generate a steady average drift. In the limit of a heavy ratchet, we derive an effective Langevin equation whose parameters depend on the microscopic properties of the system and obtain a fairly good quantitative agreement between the theoretical predictions and simulations concerning effective friction, diffusivity, and average velocity.

The basic ingredient of osmotic pressure is a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van ’t Hoff law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length scale associated with the solute-wall interactions or solute molecular interactions. In each of these cases, the assumptions underlying the classical van ’t Hoff law may no longer hold. We develop a general theoretical framework which captures corrections to the classical theory for osmotic pressure under more general relationships between the size of the chamber and the interaction length scales. We also show that notions of osmotic pressure based on the hydrostatic pressure of the fluid and the mechanical pressure on the bounding walls of the chamber must be distinguished for microscopic systems. To demonstrate how the theoretical framework can be applied, numerical results are presented for the osmotic pressure associated with a polymer of $N$ monomers confined in a spherical chamber as the bond strength is varied.

The onset and dynamics of flow in shallow horizontally oscillating granular layers are studied as a function of the depth of the layer and imposed acceleration. Measurements of the flow velocity made from the top and side are presented in the frame of reference of the container. As is also found for avalanches of inclined layers, the thresholds for starting and stopping of flow are slightly different. The variation with depth of the starting acceleration ${\Gamma }_{\mathrm{start}}$ for the oscillating layer is similar to the corresponding variation of the tangent of the starting angle $\tan \left({\theta }_{\mathrm{start}}\right)$ for avalanches in the same container at low frequencies, but deviates as the frequency is increased. However, the threshold behavior depends significantly on the measurement protocol. Just above ${\Gamma }_{\mathrm{start}}$, the motion decays with time as the material reorganizes over a minute or so, causing the apparent threshold to increase. Furthermore, the rms velocity as a function of acceleration rises more sharply above the starting threshold if the first minute or so of excitation is discarded. Once excited, the rheology of the material is found to vary in time during the cycle in surprising ways. If the maximum inertial force (proportional to the container acceleration amplitude) is slightly higher than that required to produce flow, the flow velocity grows as soon as the inertial force exceeds zero in each cycle, but jamming occurs long before the inertial force returns to zero. At higher $\Gamma$, the motion is fluidlike over the entire cycle. However, the fraction of the cycle during which the layer is mobile is typically far higher than what one would predict from static considerations or the behavior of the inclined layer. Finally, we consider the flow profiles as a function of both the transverse distance across the cell at the free surface and also as a function of the vertical coordinate in the boundary layer near the sidewall. These profiles have time-dependent shapes and are therefore significantly different from profiles previously measured for avalanche flows.

In this paper, the affine connection approach [D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)] will be defined in terms of a local transformation. Accordingly, the macroscopic anisotropy of the nematic medium will be conceived as resulting from a local transformation where, at each point of the sample, the spherical molecules of an idealized hypothetic isotropic liquid have their shape changed to the ellipsoidal form of the nematic liquid crystals molecules. When such local character is imposed to this transformation, the patterns determined by the director configuration of the nematic medium acquire an intrinsic curvature whose correct treatment requires the replacement of the techniques and methods of the usual calculus by those of the differential geometry of nonflat surfaces. Such an approach will be used in the calculus of the nematic elastic constants. As a result, the dependence of the elastic constants on the scalar order parameter, on the eccentricity of the nematic molecules, and on the interaction between them will be determined and compared with the experimental data of the 4-methoxybenzylidene-4-n-butylaniline.

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example, at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension $D_0$ of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.

We propose numerical methods to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erdős-Rényi networks and in scale-free networks with degree distribution $\mathcal{P}\left(k\right)\sim k^{-\lambda }$, where $k$ is the degree of a node and $\lambda$ is the broadness of the degree distribution. Our results support the theoretical prediction, $d_c=2(\lambda -1)∕(\lambda -3)$ for scale-free networks with $3<\lambda <4$ and $d_c=6$ for Erdős-Rényi networks and scale-free networks with $\lambda >4$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain $d_c=6$ for all $\lambda >2$. Our method also yields a better numerical evaluation of the critical percolation threshold $p_c$ for scale-free networks. Our results suggest that the finite size effects increases when $\lambda$ approaches 3 from above.

We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting from a sharp interface formulation we derive the elastic equations and the dissipative interface kinetics. We develop a phase field model to simulate these processes numerically; in the sharp interface limit, it reproduces the desired equations of motion and boundary conditions. We perform large scale simulations of fracture processes to eliminate finite-size effects and compare the results to a recently developed sharp interface method. Details of the numerical simulations are explained, and the generalization to multiphase simulations is presented.

Transportation networks play a vital role in modern societies. Structural optimization of a transportation system under a given set of constraints is an issue of great practical importance. For a general transportation system whose total cost $C$ is determined by $C={\sum }_{i<j}{C}_{ij}\left(I_{ij}\right)$, with $C_{ij}\left(I_{ij}\right)$ being the cost of the flow $I_{ij}$ between node $i$ and node $j$, Banavar and co-workers [Phys. Rev. Lett. 84, 4745 (2000)] proved that the optimal network topology is a tree if $C_{ij}\propto {\left|I_{ij}\right|}^{\gamma }$ with $0<\gamma <1$. The same conclusion also holds in the more general case where all the flow costs are strictly concave functions of the flow $I_{ij}$. To further understand the qualitative difference between systems with concave and convex cost functions, a loop analysis of transportation cost is performed in the present paper, and an alternative mathematical proof of the optimality of tree-formed networks is given. The simple intuitive picture of this proof then leads to an efficient global algorithm for the searching of optimal structures for a given transportation system with concave cost functions.

Chaotic orbits of the mushroom billiards display intermittent behaviors. We investigate statistical properties of this system by constructing an infinite partition on the chaotic part of a Poincaré surface, which illustrates details of chaotic dynamics. Each piece of the infinite partition has a unique escape time from the half disk region, and from this result it is shown that, for fixed values of the system parameters, the escape time distribution obeys a power law $1∕t_{\mathrm{esc}}^3$.

We present an experimental investigation of the agglomeration of bubbles obtained from a nozzle working in different bubbling regimes. This experiment consists of a continuous production of bubbles from a nozzle at the bottom of a liquid column, and these bubbles create a two-dimensional (2D) foam (or a bubble raft) at the top of this column. The bubbles can assemble in various dynamically stable arrangement, forming different kinds of foams in a liquid mixture of water and glycerol, with the effect that the bubble formation regimes influence the foam obtained from this agglomeration of bubbles. The average number of bubbles in the foam is related to the bubble formation frequency and the bubble mean lifetime. The periodic bubbling can generate regular or irregular foam, while a chaotic bubbling only generates irregular foam.