The squared reciprocal tortuosity ${\kappa }^{-2}=D/D_0$ for linear diffusion on lattices and in pores in the Knudsen regime is calculated analytically for a large variety of disordered systems. Here, $D_0$ and $D$ are the self-diffusion coefficients of the smooth and the corresponding disordered system, respectively. To this end, a building-block principle is developed that composes the systems into substructures without cross correlations between them. It is shown how the solutions of the different building blocks can be combined to gain $D/D_0$ for pores of high complexity from the geometrical properties of the systems, i.e., from the volumes of the different substructures. As a test, numerical simulations are performed that agree perfectly with the theory.

The variance of the advection-diffusion processes with variable coefficients is exactly decomposed as a sum of dispersion terms and memory terms consisting of correlations between velocity and initial positions. For random initial conditions, the memory terms quantify the departure of the preasymptotic variance from the time-linear diffusive behavior. For deterministic initial conditions, the memory terms account for the memory of the initial positions of the diffusing particles. Numerical simulations based on a global random walk algorithm show that the influence of the initial distribution of the cloud of particles is felt over hundreds of dimensionless times. In case of diffusion in random velocity fields with finite correlation range the particles forget the initial positions in the long-time limit and the variance is self-averaging, with clear tendency toward normal diffusion.

We investigate the model of “reversible ratchet” with interacting particles, presented by us earlier [F. Slanina, EPL 84, 50009 (2008)]. We further clarify the effect of efficiency enhancement due to interaction and show that it is of energetic origin, rather than a consequence of reduced fluctuations. We also show complicated structures emerging in the interaction and density dependence of the current and response function. The fluctuation properties of the work and input energy indicate in detail the far-from-equilibrium nature of the dynamics.

In this work we present a molecular-dynamics study of a coarse-grained (CG) model for a system of planar shape-persistent macrocycles (SPMs). SPMs are synthetic organic rigid macromolecules typically comprised of meta- and para-aromatics groups connected by acetylene and/or diacetylene units. In the CG model, each SPM is represented as a rigid hexagonal arrangement of 24 soft-repulsive spheres, resembling a large ring or hoop. The supramolecular arrangement of these macrocycles at high pressures is studied using $N\text{−}P\text{−}T$ molecular-dynamics simulation both by expansion of an initial hexagonal lattice structure and also by compression of an isotropic phase. In both cases, systems under consideration exhibit an isotropic-smectic-$A$ phase transition, which is detected by monitoring relevant order parameters and analyzing snapshots of equilibrium configurations. The smectic-$A$ phase is unique; although the molecules form layers, the system presents antinematic order where the orientation of the molecular axes is perpendicular to the direction of the layers themselves. Due to their planar geometry, the SPM molecules would be expected to form columnar or nematic phases. On the contrary, these phases seem suppressed by a novel smectic-$A$ phase, formed by the mutual interpenetration of the cycles. These results are a unique example of how molecular nonconvexity can, by itself, induce mesomorphism in anisotropic systems.

We present a theoretical and numerical investigation of streamlines and mixing within drops flowing in capillaries. We first study theoretically the limit case of purely viscous flow around a drop of negligible radius, and find that, owing to geometrical constraints, recirculating regions are always present at the front and back of such drops. Using two-dimensional simulations, we visualize streamlines for larger drops, showing that the extent of these recirculating torii increases with drop size and decreases with Reynolds number. We study the mixing within drops as they are subjected to time-dependent shear, thus modeling a sinusoidal channel, and find that while cross-stream mixing is efficient, streamwise mixing is hindered by the front and back recirculating regions.

Microscale gas flows between two rotating coaxial circular cylinders of infinite length with different temperatures are investigated. Navier-Stokes-Fourier (NSF) and regularized 13-moment (R13) equations in their linear form are used to independently analyze velocity and temperature fields in shear-driven rotary flows, i.e., cylindrical Couette flows. Knudsen boundary layers, which present non-Newtonian stress and non-Fourier heat flow, are predicted as the dominant rarefaction effects in the linear theory. We show that the R13 system yields more accurate results for this boundary value problem by predicting the Knudsen boundary layers, which are not accessible for NSF equations. Furthermore, a set of second-order boundary conditions for velocity slip and temperature jump are derived for the NSF system. It is shown that the proposed boundary conditions effectively improve the classical hydrodynamics. The accuracy of NSF and R13 equations is discussed based on their comparison with available direct simulation Monte Carlo data.

We obtain the pairwise summation approximation (PSA) of the Casimir energy from first principles in the soft dielectric and soft diamagnetic limit, this analysis let us find that the PSA is an asymptotic approximation of the Casimir energy valid for large distances between the objects. We also obtain the PSA for the electromagnetic coupling part of the Casimir energy, so we are able to complete the PSA limit for the first time for the complete electromagnetic field.

Motivated by the growing interest in the nanophysics and the field of quantum thermodynamics we study an open quantum system consisting of two spatially separated two-level atoms (spins) coupled to a quantum oscillator (resonator field mode). There is no external driving. The spins of different energy splittings are each linked to a heat bath with different temperature. We find that the temperature gradient imposed on the system together with the oscillator operating as a kind of work reservoir makes this system act as a thermodynamic machine, in particular, as a heat engine (laser). We analyze the properties of the resulting resonator field and of the engine functionality. For the latter problem we use recently developed definitions of heat flux and power as well as a test, in which the resulting field is used as an input for a heat pump.

Molecular dynamics simulations are performed on a Lennard Jones binary mixture confined in off lattice matrices of soft spheres with increasing radius. We focus on dynamics upon supercooling and in particular on testing the mode coupling theory properties of the confined mixture. Parameters of mode coupling theory in going from bulk to weak confinement, and from weak to strong confinement are extracted from simulations and analyzed. We focus on the study of the behavior of the single particle density correlators. We find that the mode coupling theory retains its validity also in the case of strong confinement, with a reduction of range of validity. The role of hopping is discussed in relation with the differences between the results obtained from the diffusion coefficients and the mode coupling theory predictions.

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to criticality. This is further supported by the observation of power-law distributions, which are a hallmark of phase transitions. An important open question is how neural networks could remain close to a critical point while undergoing a continual change in the course of development, adaptation, learning, and more. An influential contribution was made by Bornholdt and Rohlf, introducing a generic mechanism of robust self-organized criticality in adaptive networks. Here, we address the question whether this mechanism is relevant for real neural networks. We show in a realistic model that spike-time-dependent synaptic plasticity can self-organize neural networks robustly toward criticality. Our model reproduces several empirical observations and makes testable predictions on the distribution of synaptic strength, relating them to the critical state of the network. These results suggest that the interplay between dynamics and topology may be essential for neural information processing.

In human societies, opinion formation is mediated by social interactions, consequently taking place on a network of relationships and at the same time influencing the structure of the network and its evolution. To investigate this coevolution of opinions and social interaction structure, we develop a dynamic agent-based network model by taking into account short range interactions like discussions between individuals, long range interactions like a sense for overall mood modulated by the attitudes of individuals, and external field corresponding to outside influence. Moreover, individual biases can be naturally taken into account. In addition, the model includes the opinion-dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation. With this model, comprehensive numerical simulations and mean field calculations have been carried out and they show the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.

We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance, in power-grids where energy is either generated or consumed at different locations, we assume that the frequencies can take only two different values. Correlations between the value of the frequency of a given node and its topological localization are considered in both regular and random topologies. Synchronization is enhanced when nodes are surrounded by nodes of the opposite frequency. The theoretical result presented in this paper is an analytical estimation for the minimum value of the coupling strength between oscillators that guarantees the achievement of a globally synchronized state. This analytical estimation, which is in a very good agreement with numerical simulations, provides a better understanding of the effect of topological localization of natural frequencies on synchronization dynamics.

We study the consensus problem in directed static networks with arbitrary finite communication delays and consider both linear and nonlinear coupling. For the considered networked system, only locally delayed information is available for each node and also the information flow is directed. We find that consensus can be realized whatever the communications delays are. In fact, we do not even need to know the explicit values of the communication delays. One well-informed leader is proved to be enough for the regulation of all nodes’ final states, even when the external signal is very weak. Numerical simulations for opinion formation in small-world and scale-free networks are given to demonstrate the potentials of our analytic results.

We investigated flows of visitors migrating between different portal subpages. Two various portals were studied as weighted networks where nodes are portal subpages and edge weights are numbers of user transitions. Such networks differ from networks of portal subpages connected by hyperlinks prepared by portal designers. Distributions of link weights, node strengths, and times spent by visitors at one subpage follow power laws over several decades for data collected during two different days and for weekly data. The distribution of numbers $P\left(z\right)$ of unique subpages visited during one session is exponential and there is a square-root dependence between the total number of transitions $n$ during a single visit and the average $z$. A model of portal surfing is developed where the browsing process corresponds to a self-attracting walk on the weighted network with a short memory. Results of numerical simulation are in agreement with weekly and daily portal data, and our analytical approach fits empirical data in the center part of scaling regime.

We investigate the stickiness of the two-dimensional piecewise linear map with a family of marginal unstable periodic orbits (FMUPOs), and show that a series of unstable periodic orbits accumulating to FMUPOs plays a significant role to give rise to the power law correlation of trajectories. We can explicitly specify the sticky zone in which unstable periodic orbits whose stability increases algebraically exist, and find that there exists a hierarchy in accumulating periodic orbits. In particular, the periodic orbits with linearly increasing stability play the role of fundamental cycles as in the hyperbolic systems, which allows us to apply the method of cycle expansion. We also study the recurrence time distribution, especially discussing the position and size of the recurrence region. Following the definition adopted in one-dimensional maps, we show that the recurrence time distribution has an exponential part in the short time regime and an asymptotic power law part. The analysis on the crossover time $T_c^{\ast }$ between these two regimes implies $T_c^{\ast }\sim -\text{log}\left[\mu \left(R\right)\right]$ where $\mu \left(R\right)$ denotes the area of the recurrence region.

We study experimentally the acoustic signal associated with a continuous bubble bursting at the free surface of a non-Newtonian fluid. Due to the fluid rheological properties, the bubble shape is elongated, and, when bursting at the free surface, acts as a resonator. For a given fluid concentration, at constant flow rate, repetitive bubble bursting occurs at the surface. We report a modulation pattern of the acoustic waveform through time. Moreover, we point out the existence of a precursor acoustic signal, recorded on the microphone array, previous to each bursting. The time delay between this precursor and the bursting signal is well correlated with the bursting signal frequency content. Their joint modulation through time is driven by the fluid rheology, which strongly depends on the presence of small satellite bubbles trapped in the fluid due to the yield stress.

We study large-scale dynamo action due to turbulence in the presence of a linear shear flow. Our treatment is quasilinear and equivalent to the standard “first-order smoothing approximation.” However it is non perturbative in the shear strength. We first derive an integrodifferential equation for the evolution of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We show that, for nonhelical turbulence, the time evolution of the cross-shear components of the mean field do not depend on any other components excepting themselves; this is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence, to all orders in the shear parameter, there is no shear-current-type effect for non helical turbulence in a linear shear flow in quasilinear theory in the limit of zero resistivity. We then develop a systematic approximation of the integro-differential equation for the case when the mean magnetic field varies slowly compared to the turbulence correlation time. For nonhelical turbulence, the resulting partial differential equations can again be solved by making a shearing coordinate transformation in Fourier space. The resulting solutions are in the form of shearing waves, labeled by the wave number in the sheared coordinates. These shearing waves can grow at early and intermediate times but are expected to decay in the long time limit.

We analyze the response of a classical system with $N\ge 2$ internal degrees of freedom satisfying $R\le \left(N-1\right)$ approximated resonance conditions to an external perturbative transient interaction. Under certain assumptions on the system internal frequencies and on the coupling interaction, we show the precise $N-R$ adiabatic invariants and obtain an estimate of the span of the domain defined by the intersecting resonances. The results are illustrated considering a system of three anharmonic oscillators transiently coupled by an explicitly time-dependent interaction, and applied to the low energy vibro-rotationally inelastic collisions between two diatomic molecules.

We present a simple lattice model showing a glassy behavior. $R$ matrix analysis predicts critical termination of the supercooled fluid branch at density ${\rho }_g=0.1717$. This prediction is confirmed by dynamical numerical simulations, showing power-law divergences of relaxation time ${\tau }_{1/2}$, as well as the four-susceptibility ${\chi }_4$ peak’s location and height exactly at the predicted density. The power-law divergence of ${\chi }_4$ continues up to ${\chi }_4$ as high as ${10}^4$. Finite-size scaling study reveals the divergence of the correlation length accompanying the transition.