One issue in genome maintenance is how DNA repair proteins find lesions at rates that seem to exceed diffusion-limited search rates. We propose a phenomenon where DNA damage induces nucleosomal rearrangements which move lesions to potential rendezvous points in the chromatin structure. These rendezvous points are the dyad and the linker DNA between histones, positions in the chromatin which are more likely to be accessible by repair proteins engaged in a random search. The feasibility of this mechanism is tested by considering the statistical mechanics of DNA containing a single lesion wrapped onto the nucleosome. We consider lesions which make the DNA either more flexible or more rigid by modeling the lesion as either a decrease or an increase in the bending energy. We include this energy in a partition function model of nucleosome breathing. Our results indicate that the steady state for a breathing nucleosome will most likely position the lesion at the dyad or in the linker, depending on the energy of the lesion. A role for DNA binding proteins and chromatin remodelers is suggested based on their ability to alter the mechanical properties of the DNA and DNA-histone binding, respectively. We speculate that these positions around the nucleosome potentially serve as rendezvous points where DNA lesions may be encountered by repair proteins which may be sterically hindered from searching the rest of the nucleosomal DNA. The strength of the repositioning is strongly dependent on the structural details of the DNA lesion and the wrapping and breathing of the nucleosome. A more sophisticated evaluation of this proposed mechanism will require detailed information about breathing dynamics, the structure of partially wrapped nucleosomes, and the structural properties of damaged DNA.

We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.

We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity-driven-network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework based on a mapping to hidden variables networks, we provide expressions for the percolation time $T_p$ marking the onset of a giant connected component in the integrated network. In particular, we consider both the generating function formalism, valid for degree-uncorrelated networks, and the general case of networks with degree correlations. We discuss the different limits of the two approaches, indicating the parameter regions where the correlated threshold collapses onto the uncorrelated case. Our analytical predictions are confirmed by numerical simulations of the model. The temporal percolation concept can be fruitfully applied to study epidemic spreading on temporal networks. We show in particular how the susceptible-infected-removed model on an activity-driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process. This mapping allows us to obtain additional information on this process, not available for previous approaches.

In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.

In the present work we approach the hydrodynamic problem of discriminating the state of the turbulent fluid region as a function of the distance from the axis of a turbulent jet axis. More specifically, we analyzed temperature fluctuations in vertical turbulent heated jets where temperature time series were recorded along a horizontal line through the jet axis. We employed data from different sets of experiments with various initial conditions out of circular and elliptical shaped nozzles in order to identify time series taken at the jet axis, and discriminate them from those taken near the boundary with ambient fluid using nonconventional hydrodynamics methods. For each temperature time series measured at a different distance from jet axis, we estimated mainly nonlinear measures such as mutual information combined with descriptive statistics measures, as well as some linear and nonlinear dynamic detectors such as Hurst exponent, detrended fluctuation analysis, and Hjorth parameters. The results obtained in all cases have shown that the proposed methodology allows us to distinguish the flow regime around the jet axis and identify the time series corresponding to the jet axis in agreement with the conventional statistical hydrodynamic method. Furthermore, in order to reject the null hypothesis that the time series originate from a stochastic process, we applied the surrogate data method.

Nonadiabatic transitions between the acoustic and the vorticity modes perturbing a plane Couette flow are examined in the context of higher-order WKB asymptotics. In the case of the Schrödinger equation, it is known that looking at the solution expressed in the superadiabatic base, composed of higher-order asymptotic solutions, smoothes quantum state transitions. Then, increasing the order of the superadiabatic base causes these transitions to tend to the Gauss error function, and, once an optimal order is reached, the asymptotic process starts to diverge. We show that for perturbations in Couette flow, similar results can be applied on the amplitudes of the vorticity and acoustic modes. This allows us to more closely track the emergence of the acoustic modes in the presence of the vorticity mode.

Small-scale anisotropic intermittency is examined in three-dimensional incompressible magnetohydrodynamic turbulence subjected to a uniformly imposed magnetic field. Orthonormal wavelet analyses are applied to direct numerical simulation data at moderate Reynolds number and for different interaction parameters. The magnetic Reynolds number is sufficiently low such that the quasistatic approximation can be applied. Scale-dependent statistical measures are introduced to quantify anisotropy in terms of the flow components, either parallel or perpendicular to the imposed magnetic field, and in terms of the different directions. Moreover, the flow intermittency is shown to increase with increasing values of the interaction parameter, which is reflected in strongly growing flatness values when the scale decreases. The scale-dependent anisotropy of energy is found to be independent of scale for all considered values of the interaction parameter. The strength of the imposed magnetic field does amplify the anisotropy of the flow.

The metric signature topological transitions associated with the propagation of electromagnetic waves in a dispersive metamaterial with frequency-dependent and anisotropic dielectric and magnetic responses are examined in the present work. The components of the reciprocal-space metric tensor depend upon both the electric permittivity and magnetic permeability of the metamaterial, which are taken as Drude-like dispersive models. A thorough study of the frequency dependence of the metric tensor is presented which leads to the possibility of topological transitions of the isofrequency surface determining the wave dynamics inside the medium, to a diverging photonic density of states at some range of frequencies, and to the existence of large wave vectors' modes propagating through the metamaterial.

Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.

We propose a method to reconstruct the density of a luminescent source in a highly scattering medium from ultrasound-modulated optical measurements. Our approach is based on the solution to a hybrid inverse source problem for the diffusion equation.

Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned—fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.

The time evolution of the one-particle distribution function of an $N$-particle classical Hamiltonian system with long-range interactions satisfies the Vlasov equation in the limit of infinite $N$. In this paper we present a new derivation of this result using a different approach allowing a discussion of the role of interparticle correlations on the system dynamics. Otherwise for finite N collisional corrections must be introduced. This has allowed a quite comprehensive study of the quasistationary states (QSSs) though many aspects of the physical interpretations of these states still remain unclear. In this paper a proper definition of time scale for long time evolution is discussed, and several numerical results are presented for different values of $N$. Previous reports indicate that the lifetimes of the QSS scale as $N^{1.7}$ or even the system properties scale with $exp\left(N\right)$. However, preliminary results presented here indicates that time scale goes as $N^2$ for a different type of initial condition. We also discuss how the form of the interparticle potential determines the convergence of the $N$-particle dynamics to the Vlasov equation. The results are obtained in the context of the following models: the Hamiltonian mean field, the Self-gravitating ring model, and one- and two-dimensional systems of gravitating particles. We have also provided information of the validity of the Vlasov equation for finite $N$.

We analytically calculate the correlation potential of a test ion near a strongly charged plate inside a dilute $m\text{:}$$-n$ electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear background potential, the latter having been obtained using the nonlinear Poisson-Boltzmann theory. We consider the general case where the dielectric constants of the plate and the electrolyte are distinct. The following generic results emerge from our analyses: (1) If the distance to the plate $\Delta z$ is much larger than a Gouy-Chapman length, the plate surface will behave effectively as an infinitely charged surface, and the dielectric constant of the plate effectively plays no role. (2) If $\Delta z$ is larger than a Gouy-Chapman length but shorter than a Debye length, the correlation potential can be interpreted in terms of an image charge that is three times larger than the source charge. This behavior is independent of the valences of the ions. (3) The Green's function vanishes inside the plate if the surface charge density is infinitely large; hence the electrostatic potential is constant there. In this respect, a strongly charged plate behaves like a conductor plate. (4) If $\Delta z$ is smaller than a Gouy-Chapman length, the correlation potential is dominated by the conventional image charge due to the dielectric discontinuity at the interface. (5) If $\Delta z$ is larger than a Debye length, the leading order behavior of the correlation potential will depend on the valences of the ions in the electrolyte. Furthermore, inside an asymmetric electrolyte, the correlation potential is singly screened, i.e., it undergoes exponential decay with a decay width equal to the Debye length.

Diffusive properties of interacting magnetic dipoles confined in a parabolic narrow channel and in the presence of a periodic modulated (corrugated) potential along the unconfined direction are studied using Brownian dynamics simulations. We compare our simulation results with the analytical result for the effective diffusion coefficient of a single particle by Festa and d'Agliano [Physica A 90, 229 (1978)] and show the importance of interparticle interaction on the diffusion process. We present results for the diffusion of magnetic dipoles as a function of linear density, strength of the periodic modulation and commensurability factor.

We study the gross domestic product (GDP) per capita together with the market capitalization (MCAP) per capita as two indicators of the effect of globalization. We find that $g$, the GDP per capita, as a function of $m$, the MCAP per capita, follows a power law with average exponent close to 1/3. In addition, the Zipf ranking approach confirms that the $m$ for countries with initially lower values of $m$ tends to grow more rapidly than for countries with initially larger values of $m$. If the trends over the past 20 years continue to hold in the future, then the Zipf ranking approach leads to the prediction that in about 50 years, all countries participating in globalization will have comparable values of their MCAP per capita. We call this economic state “capital death,” in analogy to the physics state of “heat death” predicted by thermodynamic arguments.

Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be $\mathcal{P}\mathcal{T}$ invariant under the combined operation of parity ($\mathcal{P}$) and time reversal ($\mathcal{T}$) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of $\mathcal{P}\mathcal{T}$ occurs.

This article analyzes the properties of rotationally symmetric self-localized solutions with different radial quantum numbers in the simplest one- and two-component reaction-diffusion systems. The consideration is made in one and two dimensions with the focus on the fundamental and first higher-order solutions showing zero and one intersections of the radial profile with zero. It is demonstrated that the solution with one intersection does not exist for the case of the quadratic-cubic nonlinearity, while the cubic-quintic extension of the models does allow existence. I show additionally that the cubic-quintic reaction diffusion system supports the existence and stability of the states with zero quantum numbers, as well as their antistates, state-antistate pairs, and clusters, which can be interpreted as the states with nonzero azimuthal quantum number.

Can one hear the shape of a graph? This is a modification of the famous question of Mark Kac “Can one hear the shape of a drum?” which can be asked in the case of scattering systems such as quantum graphs and microwave networks. It addresses an important mathematical problem whether scattering properties of such systems are uniquely connected to their shapes? Recent experimental results based on a characteristics of graphs such as the cumulative phase of the determinant of the scattering matrices indicate a negative answer to this question [O. Hul, M. Ławniczak, S. Bauch, A. Sawicki, M. Kuś, and L. Sirko, Phys. Rev. Lett. 109, 040402 (2012)]. In this paper we consider important local characteristics of graphs such as structures of resonances and poles of the determinant of the scattering matrices. Using these characteristics we study experimentally and theoretically properties of graphs and directly confirm that the pair of graphs considered in the cited paper is isoscattering. The experimental results are compared to the theoretical ones for a broad frequency range from 0.01 to 3 GHz. In the numerical calculations of the resonances of the graphs absorption present in the experimental networks is taken into account.

The evolution of a perfectly conducting and nonviscous fluid, under the action of an electric field (uniform at infinity), is studied numerically. Level set techniques are employed to develop an Eulerian potential flow model that can follow the drop evolution past breakup, while the free surface fluid velocity and the electric field force are obtained via axisymmetric boundary integral calculations. Numerical results are presented for neutral and charged droplets and for free charged droplets. In all cases, the evolution droplet aspect ratio, progeny droplet size, Taylor cone angles, jet shapes, and self-similar scaling exponents are reported. In particular, for free charged water droplets, the bursting frequency and other jetting characteristics have been carefully analyzed. Wherever possible, these results are compared with previously reported experiments and simulations.

The spatial expansion of a population in a nonuniform environment may benefit from phenotypic heterogeneity with interconverting subpopulations using different survival strategies. We analyze the crossing of an antibiotic-containing environment by a bacterial population consisting of rapidly growing normal cells and slow-growing, but antibiotic-tolerant persister cells. The dynamics of crossing is characterized by mean first arrival times and is found to be surprisingly complex. It displays three distinct regimes with different scaling behavior that can be understood based on an analytical approximation. Our results suggest that a phenotypically heterogeneous population has a fitness advantage in nonuniform environments and can spread more rapidly than a homogeneous population.