Characterizing the community structure of complex networks is a key challenge in many scientific fields. Very diverse algorithms and methods have been proposed to this end, many working reasonably well in specific situations. However, no consensus has emerged on which of these methods is the best to use in practice. In part, this is due to the fact that testing their performance requires the generation of a comprehensive, standard set of synthetic benchmarks, a goal not yet fully achieved. Here, we present a type of benchmark that we call “closed,” in which an initial network of known community structure is progressively converted into a second network whose communities are also known. This approach differs from all previously published ones, in which networks evolve toward randomness. The use of this type of benchmark allows us to monitor the transformation of the community structure of a network. Moreover, we can predict the optimal behavior of the variation of information, a measure of the quality of the partitions obtained, at any moment of the process. This enables us in many cases to determine the best partition among those suggested by different algorithms. Also, since any network can be used as a starting point, extensive studies and comparisons can be performed using a heterogeneous set of structures, including random ones. These properties make our benchmarks a general standard for comparing community detection algorithms.

We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.

We present an analytical model that describes the linear interaction of a planar shock wave with an isotropic random sonic field. First, we study the interaction with a single-mode acoustic field. We present the exact evolution for the pressure, velocity, vorticity, and density field generated behind the shock wave, and we also calculate exact and closed analytical expressions for the asymptotic behavior of these modes. Applying superposition, we use the results obtained from the single-mode analysis in order to compute the interaction with 2D/3D isotropic random acoustic fields. We present analytical expressions for the average turbulent kinetic energy generated behind the shock, as well as the averaged vorticity and the density perturbations as a function of the shock strength $M_1$ and the gas compressibility $\gamma$. We also study the acoustic energy flux emitted by the shock front. Exact asymptotic analytical scaling laws are given for all the 3D averages downstream. A detailed comparison with previous works is shown.

We report the first experimental demonstration of a slippage-dominant free-electron laser (FEL) amplifier using a 140-fs full width at half maximum broadband seed laser pulse. The evolution of the longitudinal phase space of a laser seeded FEL amplifier in the slippage-dominant regime was experimentally characterized. We observed, for the first time, that the pulse duration of the FEL is primarily determined by the slippage between the seed laser and the electron beam. With a $\pm$1$\%$ variation in the electron-beam energy, we demonstrated reasonably good longitudinal coherence and a $\pm$2$\%$ spectral tuning range. The experimentally observed temporal and spectral evolution of the slippage-dominant FEL was verified by the numerical simulations.

The present paper investigates the interaction of an acoustic Bessel vortex beam centered on a viscoelastic polyethylene sphere and spherical shells filled with air or water immersed in nonviscous water and mercury, and the induced axial acoustic radiation torque (ART) resulting from the transfer of angular momentum. Closed-form series expansions for the axial ART are derived for the case of progressive, standing, and quasistanding waves. The ART is shown to be the result of acoustic absorption inside the particle's material. Numerical predictions shown in the form of two-dimensional (2D) plots illustrate the theory, and reveal new properties related to the ART of Bessel vortex beams. Potential applications are in particle rotation and manipulation. Other applications, such as the characterization of fluids from induced angular accelerations (produced by the ART) and containerless processing, may benefit from the analysis developed here.

A Monte Carlo method to sample the classical configurational canonical ensemble is introduced. In contrast to the Metropolis algorithm, where trial moves can be rejected, in this approach collisions take place. The implementation is event-driven; i.e., at scheduled times the collisions occur. A unique feature of the new method is that smooth potentials (instead of only step-wise changing ones) can be used. In addition to an event-driven approach, where all particles move simultaneously, we introduce a straight event-chain implementation. As proof of principle, a system of Lennard-Jones particles is simulated.

We present accurate measurements of the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell. Although the second injected bubble was smaller, we observed that, in all cases, it accelerated and caught up with the leading bubble. This acceleration is related to the wake of the leading bubble, which also induces significant changes in the width and curvature of the trailing bubble. On the contrary, the velocity of the leading bubble is unaltered during the whole interaction and coalescence process. Shape adaptation of the two bubbles is observed just prior to coalescence. After pinch-off, the liquid film is drained at a constant velocity.

We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation description of the activated jump dynamics among the local minima of the potential energy (the so-called inherent structures) that characterize the potential energy landscape of the system. We study the dynamics of a small atomic cluster using this description as well as molecular dynamics simulations and demonstrate the usefulness of our approach for this system. Many of the remarkable features of the complex dynamics of glassy systems emerge from the activated dynamics in the potential energy landscape of the atomic cluster. The dynamics of the system exhibits typical characteristics of a strong supercooled liquid when the system is allowed to explore the full configuration space. This behavior arises because the dynamics is dominated by a few lowest-lying minima of the potential energy and the potential energy barriers between these minima. When the system is constrained to explore only a limited region of the potential energy landscape that excludes the basins of attraction of a few lowest-lying minima, the dynamics is found to exhibit the characteristics of a fragile liquid.

The multiplet structure of the optical defect modes generated within the bandgap are analyzed by a finite number of identical equispaced twist defects in axially elongated cholesteric elastomers. It is shown that $n_0$ defect modes induced by $n_0$ twist defects can be mechanically tuned. The transfer matrix is obtained and the defect frequencies when $n_0=1,2$ are expressed in terms of twist angle, fractional shape anisotropy, and longitudinal deformation. For $n_0=2$, the coupling between modes is analytically studied and it is shown that when the separation between defects is much larger than the line width, the defect modes do not interact and become degenerated.

In this work we develop an approach for predicting the tertiary structures of RNA fragments by combining an RNA nucleobase discrete state (RNAnbds) model, a sequential Monte Carlo method, and a statistical potential. The RNAnbds model is designed for optimizing the configuration of nucleobases with respect to their preceding ones along the sequence and their spatial neighbors, in contrast to previous works that focus on RNA backbones. The tests of our approach with the fragments taken from a small RNA pseudoknot and a 23S ribosome RNA show that for short fragments ($<10$ nucleotides), the root mean square deviations (RMSDs) between the predicted and the experimental ones are generally smaller than 3 Å; for slightly longer fragments (10–15 nucleotides), most RMSDs are smaller than 4 Å. The comparison of our method with another physics-based predictor with a testing set containing nine loops shows that ours is superior in both accuracy and efficiency. Our approach is useful in facilitating RNA three-dimensional structure prediction as well as loop modeling. It also holds the promise of providing insight into the structural ensembles of RNA loops.

We analyze the effects of transient stimulation on traveling waves in neural field equations. Neural fields are modeled as integro-differential equations whose convolution term represents the synaptic connections of a spatially extended neuronal network. The adjoint of the linearized wave equation can be used to identify how a particular input will shift the location of a traveling wave. This wave response function is analogous to the phase response curve of limit cycle oscillators. For traveling fronts in an excitatory network, the sign of the shift depends solely on the sign of the transient input. A complementary estimate of the effective shift is derived using an equation for the time-dependent speed of the perturbed front. Traveling pulses are analyzed in an asymmetric lateral inhibitory network and they can be advanced or delayed, depending on the position of spatially localized transient inputs. We also develop bounds on the amplitude of transient input necessary to terminate traveling pulses, based on the global bifurcation structure of the neural field.

Recent studies of photosynthetic bacteria living in geothermal hot spring environments have revealed surprisingly complex ecosystems with an unexpected level of genetic diversity. One case of particular interest involves the distribution along hot spring thermal gradients of genetically distinct bacterial strains that differ in their preferred temperatures for reproduction and photosynthesis. In such systems, a single variable, temperature, defines the relevant environmental variation. In spite of this, each region along the thermal gradient exhibits multiple strains of photosynthetic bacteria adapted to several distinct thermal optima, rather than a single thermal strain adapted to the local environmental temperature. Here we analyze microbiology data from several ecological studies to show that the thermal distribution data exhibit several universal features independent of location and specific bacterial strain. These include the distribution of optimal temperatures of different thermal strains and the functional dependence of the net population density on temperature. We present a simple population dynamics model of these systems that is highly constrained by biophysical data and by physical features of the environment. This model can explain in detail the observed thermal population distributions, as well as certain features of population dynamics observed in laboratory studies of the same organisms.

Understanding the physical mechanisms behind the folding and conformational dynamics of biomolecules is one of the major unsolved challenges of soft matter theory. In this contribution, a theoretical framework for biomolecular dynamics is introduced, employing selected aspects of statistical mechanics, dimensionality reduction, the perturbation theory, and the theory of matrices. Biomolecular dynamics is represented by time-dependent orthogonal conformational modes, the dynamics of the modes is investigated, and invariant properties that persist are identified. As an example, the dynamics of a human prion protein is considered. The theory provides a rigorous background for assessing the stable dynamical properties of biomolecules, such as their coarse-grained structure, through a multiscale approach using short subnanosecond segments of molecular dynamics trajectories. Furthermore, the paper offers a theoretical platform for models of conformational changes in macromolecules, which may allow complementing molecular dynamics simulations.

Dynamical systems driven by a general Lévy stable noise are considered. The inertia is included and the noise, represented by a generalized Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive noise) is solved: the resulting distribution converges with time to the distribution for the white-noise, massless case. Moreover, a multiplicative noise is discussed. It can make the distribution steeper and the variance, which is finite, depends sublinearly on time (subdiffusion). For a small mass, a white-noise limit corresponds to the Stratonovich interpretation. On the other hand, the distribution tails agree with the Itô interpretation if the inertia is very large. An escape time from the potential well is calculated.

This paper proposes a cellular automata model of pedestrian flow that defines a cost potential field, which takes into account the costs of travel time and discomfort, for a pedestrian to move to an empty neighboring cell. The formulation is based on a reconstruction of the density distribution and the underlying physics, including the rule for resolving conflicts, which is comparable to that in the floor field cellular automaton model. However, we assume that each pedestrian is familiar with the surroundings, thereby minimizing his or her instantaneous cost. This, in turn, helps reduce the randomness in selecting a target cell, which improves the existing cellular automata modelings, together with the computational efficiency. In the presence of two pedestrian groups, which are distinguished by their destinations, the cost distribution for each group is magnified due to the strong interaction between the two groups. As a typical phenomenon, the formation of lanes in the counter flow is reproduced.

Particle trajectories and size sorting above an artificial rippled bed under standing surface waves are experimentally and theoretically studied. It is observed that fine particles may be trapped in a very thin region near the ripple crests. When the surface waves damp, fine particles concentrate on the top of ripple crests forming narrow strips, while coarse particles settle more uniformly along the rippled bed. Measurements of particle concentrations before their deposition confirm this size segregation. The present experimental results are explained with a theoretical approach.

We investigate the rheology of granular materials via molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional, noncohesive spheres. In agreement with previous results for frictionless particles, we observe three flow regimes existing in different domains of particle volume fraction and shear rate, with all stress data collapsing upon scaling by powers of the distance to the jamming point. Though this jamming point is a function of the interparticle friction coefficient, the relation between pressure and strain rate at this point is found to be independent of friction. We also propose a rheological model that blends the asymptotic relations in each regime to obtain a general description for these flows. Finally, we show that departure from inertial number scalings is a direct result of particle softness, with a dimensionless shear rate characterizing the transition.

A molecular field theory of the smectic-$A$$-$smectic-$C$ transition has been developed for smectics with a diffused cone orientational distribution of molecules (volcano-like distribution function) in the smectic-$A$ phase and anomalously weak layer contraction in the smectic-$C$ phase. Orientational order parameters and smectic layer spacing have been calculated numerically as functions of temperature and compared with the results obtained using a model with a standard Maier-Saupe–type distribution function that has been considered before. A molecular theory of the electroclinic effect in chiral smectics has also been developed using the recently proposed simple biaxial interaction potential. A comparison has been made between the absolute values and temperature variations of the electroclinic coefficient obtained using the volcano model, the model with Maier-Saupe–type distribution, and the orthodox cone model proposed by de Vries. It has been shown that the model with a conventional “sugar loaf” type orientational distribution function in the smectic-$A$ phase is sufficient to describe the main properties of smectics with anomalously weak layer contraction.

We consider the coarse-grained approach in which star polymers are mapped onto atoms located at the centers of the stars interacting by means of ultrasoft potentials. We generalize the Witten-Pincus formula to all $n$-body potentials: in the good-solvent regime all potentials show an ultrasoft logarithmic divergence when the relative distance of all $n$ stars goes to zero, with coefficients that can be related to the partition-function exponents ${\gamma }_f$.

Continuous-time modeling of random searches is designed to be robust to the sampling rate while the spatial model is required to be of rotation-invariant type, which is often computationally prohibitive. Such computational difficulty may be circumvented by employing a model with independent components. We demonstrate that its disadvantages in statistical properties are blurred under lower frequency. We propose a quantitative criterion for choice of the sampling rate at which a spatial model with independent components resembles a rotation-invariant model. Our findings have the potential to assist the observer to employ simpler models in the continuous-time framework to avoid expensive computation required for statistical inference.