DNA loop formation is one of several mechanisms used by organisms to regulate genes. The free energy of forming a loop is an important factor in determining whether the associated gene is switched on or off. In this paper we use an elastic rod model of DNA to determine the free energy of forming short (50–100 basepair), protein mediated DNA loops. Superhelical stress in the DNA of living cells is a critical factor determining the energetics of loop formation, and we explicitly account for it in our calculations. The repressor protein itself is regarded as a rigid coupler; its geometry enters the problem through the boundary conditions it applies on the DNA. We show that a theory with these ingredients is sufficient to explain certain features observed in modulation of in vivo gene activity as a function of the distance between operator sites for the lac repressor. We also use our theory to make quantitative predictions for the dependence of looping on superhelical stress, which may be testable both in vivo and in single-molecule experiments such as the tethered particle assay and the magnetic bead assay.

In this work, through the Z-scan technique, we report on measurements of the nonlinear refractive index $\left(n_2\right)$ in discotic and calamitic nematic phases at room temperature in lyotropic mixtures of potassium laurate, decanol and ${\mathrm{D}}_2\mathrm{O}$. This technique presents high sensitivity when compared to conventional interferometry. The nonlinear optical birefringence $\left(\mathrm{\Delta }{n}_2\right)$ of these nematic phases was also determined. The sign and absolute value of this relevant nonlinear parameter are discussed in terms of structural changes in the micellar configuration which takes place in each nematic lyotropic phase.

The results presented in [] are mathematically incomplete and physically faulty. Contrary to their claim, there exists a fluctuation theorem for the heat probability distribution function in Brownian transducers operating between two heat reservoirs. The corresponding large deviation function is determined exactly.

In this Reply we show that to characterize our paper as “mathematically incomplete and physically faulty” is incorrect. Moreover, we never claimed that there is not a fluctuation theorem for the heat probability distribution in Brownian transducers operating between two heat reservoirs. We studied the conditions of observability of the Jarzynski-Wojcik fluctuation theorem [] in a model system in which the coupling term is relevant and the observation time is necessarily finite.

We use the theory of complex networks in order to quantitatively characterize the formation of communities in a particular financial market. The system is composed by different banks exchanging on a daily basis loans and debts of liquidity. Through topological analysis and by means of a model of network growth we can determine the formation of different group of banks characterized by different business strategy. The model based on Pareto’s law makes no use of growth or preferential attachment and it reproduces correctly all the various statistical properties of the system. We believe that this network modeling of the market could be an efficient way to evaluate the impact of different policies in the market of liquidity.

We study the nonequilibrium phase transition in a model for epidemic spreading on scale-free networks. The model consists of two particle species $A$ and $B$, and the coupling between them is taken to be asymmetric; $A$ induces $B$ while $B$ suppresses $A$. This model describes the spreading of an epidemic on networks equipped with a reactive immune system. We present analytic results on the phase diagram and the critical behavior, which depends on the degree exponent $\gamma$ of the underlying scale-free networks. Numerical simulation results that support the analytic results are also presented.

I study the spreading of infectious diseases in heterogeneous populations. The population structure is described by a contact graph where vertices represent agents and edges represent disease transmission channels among them. The population heterogeneity is taken into account by the agent’s subdivision in types and the mixing matrix among them. I introduce a type-network representation for the mixing matrix, allowing an intuitive understanding of the mixing patterns and the calculations. Using an iterative approach I obtain recursive equations for the probability distribution of the outbreak size as a function of time. I demonstrate that the expected outbreak size and its progression in time are determined by the largest eigenvalue of the reproductive number matrix and the characteristic distance between agents on the contact graph. Finally, I discuss the impact of intervention strategies to halt epidemic outbreaks. This work provides both a qualitative understanding and tools to obtain quantitative predictions for the spreading dynamics of heterogeneous populations.

Hydrodynamic dispersion of water flowing through porous glasses with nominal pore sizes in the range $40\text{to}160\text{micrometers}$ was studied with the aid of a pulsed gradient nuclear magnetic resonance technique compensating for coherent flow velocities. The crossover from effectively subdiffusive mean square displacement, $⟨Z^2⟩\propto t^{0.84}$, in the absence of hydrodynamic flow to a superdiffusive, almost ballistic power law, $⟨Z^2⟩\propto t^{1.95}$, at the highest flow rates was observed. At intermediate flow rates, a gradual conversion between these two limiting power laws occurs. As a function of the Péclet number, the effective dispersion coefficient is in accordance with a power law with an exponent 1.2.

We introduce periodic photonic structures where the strength of diffraction can be managed in a very broad frequency range. We show how to design arrays of curved waveguides where light beams experience wavelength-independent normal, anomalous, or zero diffraction. Our results suggest opportunities for efficient self-collimation, focusing, and reshaping of beams produced by white-light and supercontinuum sources. We also predict a possibility of multicolor Talbot effect, which is not possible in free space or conventional photonic lattices.

A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics exhibits anomalous behavior which is characterized by ballistic diffusion and accelerated transport. We also investigate the role of a possible initial correlation between the system degrees of freedom and the heat-bath degrees of freedom for the asymptotic long-time behavior of the system dynamics. As two test beds we investigate (i) the anomalous energy relaxation of free non-Markovian Brownian motion that is driven by a harmonic velocity noise and (ii) the phenomenon of a net directed acceleration in noise-induced transport of an inertial rocking Brownian motor.

Sphere packings in high dimensions have been the subject of recent theoretical interest. Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ in the infinite-time or saturation limit for the first six space dimensions $(1\le d\le 6)$. Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each of these dimensions. We find that for $2\le d\le 6$, the saturation density ${\varphi }_s$ scales with dimension as ${\varphi }_s=c_1∕2^d+c_{2}d∕2^d$, where $c_1=0.202048$ and $c_2=0.973872$. We also show analytically that the same density scaling is expected to persist in the high-dimensional limit, albeit with different coefficients. A byproduct of this high-dimensional analysis is a relatively sharp lower bound on the saturation density for any $d$ given by ${\varphi }_s\ge (d+2)(1-S_0)∕2^{d+1}$, where $S_0∊[0,1]$ is the structure factor at $k=0$ (i.e., infinite-wavelength number variance) in the high-dimensional limit. We demonstrate that a Palàsti-type conjecture (the saturation density in ${\mathbb{R}}^d$ is equal to that of the one-dimensional problem raised to the $d$th power) cannot be true for RSA hyperspheres. We show that the structure factor $S\left(k\right)$ must be analytic at $k=0$ and that RSA packings for $1\le d\le 6$ are nearly “hyperuniform.” Consistent with the recent “decorrelation principle,” we find that pair correlations markedly diminish as the space dimension increases up to six. We also obtain kissing (contact) number statistics for saturated RSA configurations on the surface of a $d$-dimensional sphere for dimensions $2\le d\le 5$ and compare to the maximal kissing numbers in these dimensions. We determine the structure factor exactly for the related “ghost” RSA packing in ${\mathbb{R}}^d$ and demonstrate that its distance from “hyperuniformity” increases as the space dimension increases, approaching a constant asymptotic value of $1∕2$. Our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions.

We report on the behavior of a single-wavelength Rayleigh-Taylor flow at late times. The calculations were performed in a long square duct $(\lambda \times \lambda \times 8\lambda )$, using four different numerical simulations. In contradiction with potential flow theories that predict a constant terminal velocity, the single-wavelength Rayleigh-Taylor problem exhibits late-time acceleration. The onset of acceleration occurs as the bubble penetration depth exceeds the diameter of bubbles, and is observed for low and moderate density differences. Based on our simulations, we provide a phenomenological description of the observed acceleration, and ascribe this behavior to the formation of Kelvin-Helmholtz vortices on the bubble-spike interface that diminish the friction drag, while the associated induced flow propels the bubbles forward. For large density ratios, the formation of secondary instabilities is suppressed, and the bubbles remain terminal consistent with potential flow models.

Three-dimensional two-component solitons, propagating in long-short wave resonance mode, are predicted. If the spectrum of the short-wave component lies in the area of normal group velocity dispersion, these solitons have transverse structure in the form of hole-vortex field defects on an infinite background. In the opposite case two-component “bullets” or the “bright” vortex and the “bullet” with a hole in the center can exist. The stability region of the considered objects is estimated on the basis of a variational approach. As a concrete physical model we consider the propagation of electromagnetic pulses in a uniaxial crystal. Here the ordinary component of the pulse is the short wave, and its extraordinary component is the long wave.

We show how applying field conjugated to the order parameter may act as a very precise probe to explore the probability distribution function of the order parameter. Using this “magnetic-field scanning” on large-scale numerical simulations of the critical two-dimensional $XY$ model, we are able to discard the conjectured double-exponential form of the large-magnetization asymptote.

One of the consequences of sedimentation in colloidal aggregation is the stratification of the system in the sense that, after a sufficiently long elapsed time, the large clusters lie preferentially at the bottom zones of the confinement prism, and the structural and dynamical quantities describing the aggregates depend on the depth at which they are measured. A few years ago a computer simulation using particles for colloidal aggregation coupled with sedimentation was proposed by the author [A. E. González, Phys. Rev. Lett. 86, 1243 (2001)]. In that simulation, due to computational limitations, the mentioned quantities were averaged over all clusters in the prism, independently of the depth at which they were located, in order to have good statistics for the evaluation of the cluster fractal dimension and the cluster size distribution function. In this work we present a computer simulation using particles of colloidal aggregation coupled with sedimentation, for which the clusters in the simulation box represent those clusters inside a layer at a fixed depth and of arbitrary thickness in the prism. It would then be possible to compare the results with an eventual validation experiment, in which an aggregating sample is sipped out with a pipette at a fixed depth in the prism and subjected to further studies, or with a light scattering study in which the laser beam is focused at a fixed depth in the system. We confirm the acceleration of the aggregation rate, followed by a slowing down, compared with an aggregating system driven purely by diffusion (DLCA). In the present system, the large clusters when drifting downwards sweep smaller ones, which in turn occlude the holes and cavities of these large clusters, increasing in this way their compacticity. We also confirm that (i) in some cases of sedimentation strengths and layer depths, the mean width (perpendicular to the gravitational field direction) and the mean height of the large settling clusters scale with the size as a power law, with the same scaling power, in some range of cluster sizes. This leads to self-similar clusters with an appreciably higher fractal dimension $\left(d_f\right)$ than the $d_f$ of DLCA clusters, a case that we called the “sweeping scaling regime” in earlier works. However, the present system is much richer than DLCA in that (ii) there are some other cases for which the parallel and perpendicular scaling powers differ, leading to anisotropic self-affine clusters. (iii) There are further cases for which only the mean width or the mean height scale as a power law, leading again to anisotropic clusters. Finally, (iv) there are still some cases for which neither the mean width nor mean height scale as a power law with the size. In the last (ii), (iii), and (iv) cases the large settling clusters are anisotropic and non-self-similar, and a fractal dimension cannot be defined for them, as found recently by some other authors for case (iii); however, their “compacticity” should be greater than that for DLCA clusters, in a yet undefined way.

The influence of flexibility on the phase behavior of bent core biaxial nematic liquid crystals is investigated using Monte Carlo simulation. A generic model for rigid V-shaped molecules is extended to include a bending potential, which allows us to investigate the relationship between the flexibility of a bent core molecule and its ability to form a biaxial nematic phase. The simulation results indicate that, as the flexibility is increased, the biaxial nematic phase is typically forced to lower temperatures. In contrast, the stability of the uniaxial nematic phase with respect to the isotropic phase is not significantly affected. The Landau point is split into a line of first order phase transitions between two different uniaxial phases. In some cases, the uniaxial nematic to biaxial nematic transition becomes first order, and a shape change is observed at this transition.

The Hindmarsh-Rose (HR) system of equations is a model that captures the essential of the spiking activity of biological neurons. In this work we present an exploratory numerical study of the time activities of two HR neurons interacting through electrical synapses. The knowledge of this simple system is a first step towards the understanding of the cooperative behavior of large neural assemblies. Several periodic and chaotic attractors where identified, as the coupling strength is increased from zero until the perfect synchronization regime. In addition to the known phase locking synchronization at weak coupling, electrical synapses also allow for both in-phase and antiphase synchronization from moderate to strong coupling. A regime where the system changes apparently randomly between in-phase and antiphase locking evolves to a bistability regime, where both in-phase and antiphase periodic attractors are locally stable. At the strong coupling regime in-phase chaotic evolution dominates, but windows with complex periodic behavior are also present.

We study the interactions of velocity-locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We reveal that the inelastic scattering between three-wave solitons and linear waves may be described in terms of analytical solutions with dynamically varying group velocity, or boomerons. Moreover, we demonstrate the elastic nature of three-wave soliton-soliton collisions and interactions.

Experimental evidence and theoretical models are presented supporting the conjecture that dry friction stick-slip is described by self-organized criticality. We use the data, obtained with a pin-on-disk tribometer set to measure lateral force, to examine the variation of the friction force as a function of time. We study nominally flat surfaces of matching aluminum and steel. The probability distribution of force drops follows a negative power law with exponents $\mu$ in the range 3.2–3.5. The frequency power spectrum follows a $1∕f^{\alpha }$ pattern with $\alpha$ in the range 1–1.8. We first compare these experimental results with the well-known Robin Hood model of self-organized criticality. We find good agreement between theory and experiment for the force-drop distribution but not for the power spectrum. We explain this on a physical basis and propose a model which takes explicitly into account the stiffness and inertia of the tribometer. Specifically, we numerically solve the equation of motion of a block on a friction surface pulled by a spring and show that for certain spring constants the motion is characterized by the same power law spectrum as in experiments. We propose a physical picture relating the fluctuations of the force drops to the microscopic geometry of the surface.

The cascade failures in scale-free networks with community structure are studied and cascade propagation of such networks with different modularity parameters is simulated. It is found that the network with small modularity is much easier to trigger cascade failures than that of the larger one. Furthermore, different removal strategies have some what large effects on the cascade failures aftereffect. The simulations also show that larger modularity and reserve capacity coefficient will delay the breakdown caused by a cascade of network. This is particularly important for such real networks with community as traffic networks, distribution networks, and electrical power grids.