The finite-element method (FEM) has already been extended to analyze transport properties of electron waves of two-dimensional electron systems in magnetic fields. Although many researchers have created new formulations or improvements to this method, few have analyzed how this method is applied to realistic systems. The present paper suggests that conventional formulations of the FEM do not give accurate results for large systems or for strong magnetic fields; in addition, it suggests that the selected gauge significantly influences the numerical results. Furthermore, this paper proposes a conceptually different formulation of the FEM that solves the poor convergence problem. This formulation is simple: matrix elements are multiplied by the Peierls phase in the absence of a magnetic field. To show the advantages of this formulation, numerical examples are presented.

Laser-induced bubbles provide an effective vehicle to achieve high-energy concentrations and maximum temperatures in bubble luminescence phenomena. One limitation to the temperatures that can be achieved is the development of the Rayleigh-Taylor instability (RTI) during the instants previous to the bubble maximum compression. For a given fluid, the control parameters of the experiment are: the bubble maximum radius, the bubble ambient radius, the initial perturbations of the bubble, and the liquid pressure at infinity. In this work, experiments using laser-induced bubbles in a highly viscous phosphoric acid were performed in order to determine the achievable parameters values in the phase space. The effect of $R_{\max }$, $R_0$, $a_2^i$, $a_3^i$, and $p_{\infty }$ on the maximum temperature achieved by the gas contents inside the bubble were numerically determined. The results show for each static pressure an optimum region for maximum temperatures of the gas contents bounded by the RTI.

We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a distributional limit theorem to provide both a powerful tool for calculating thermodynamic potentials as also an understanding of the dynamic characteristics at each instability phase. In particular, topological pressure and Rényi entropy are calculated exactly for such systems. Finally, we show the connection of the distributional limit theorem with non-Gaussian fluctuations of the algorithmic complexity proposed by Gaspard and Wang [Proc. Natl. Acad. Sci. USA 85, 4591 (1988)].

The temporal evolution of patterns within the driving period of the ac voltage was studied in the 10-mHz–250-Hz frequency range. It was shown that the stationary electroconvection pattern of the conductive regime transforms into a flashing one at ultralow frequencies, existing only in narrow time windows within the period. Furthermore a transition between electroconvection and flexoelectric domains was detected which is repeating in each half period. The two patterns are well separated in time and in Fourier space. Simultaneous current measurements uncovered that the electric properties of the polyimide orienting layers influence the redistribution of the applied voltage. The experimental findings are in good qualitative agreement with the theoretical predictions based on an extended standard model including flexoelectricity.

We have developed a theoretical formulation for excitation energy transfer between structurally fluctuating dimer molecules in surrounding environments. On the basis of a generalized master equation in which a memory function plays a vital role, the temporal evolutions of the population densities of exciton at the donor and acceptor sites are described. By employing an ansatz form for the memory function, the competitive effects of dimeric coupling and bath modes are analyzed quantitatively, where the roles of oscillating electronic coupling are highlighted.

Observational learning is an important information aggregation mechanism. However, it occasionally leads to a state in which an entire population chooses a suboptimal option. When this occurs and whether it is a phase transition remain unanswered. To address these questions we perform a voting experiment in which subjects answer a two-choice quiz sequentially with and without information about the prior subjects’ choices. The subjects who could copy others are called herders. We obtain a microscopic rule regarding how herders copy others. Varying the ratio of herders leads to qualitative changes in the macroscopic behavior of about 50 subjects in the experiment. If the ratio is small, the sequence of choices rapidly converges to the correct one. As the ratio approaches 100%, convergence becomes extremely slow and information aggregation almost terminates. A simulation study of a stochastic model for ${10}^6$ subjects based on the herder’s microscopic rule shows a phase transition to the two-peak phase, where the convergence completely terminates as the ratio exceeds some critical value.

It is known that the reconstructed phase portrait of a given system strongly depends on the choice of the observable. In particular, the ability to obtain a global model from a time series strongly depends on the observability provided by the measured variable. Such a dependency results from (i) the existence of a singular observability manifold, ${\mathcal{M}}_s^{\mathrm{obs}}$, for which the coordinate transformation between ${\text{R}}^m$ and the reconstructed space is not defined and (ii) how often the trajectory visits the neighborhood ${\mathcal{U}}_{{\mathcal{M}}_s^{\mathrm{obs}}}$ of ${\mathcal{M}}_s^{\mathrm{obs}}$. In order to clarify how these aspects contribute to the observability coefficients, we introduce the probability of visits of ${\mathcal{M}}_s^{\mathrm{obs}}$ and the relative time spent in ${\mathcal{U}}_{{\mathcal{M}}_s^{\mathrm{obs}}}$ to construct a new coefficient. Combined with the symbolic observability coefficients previously introduced [Letellier and Aguirre, Phys. Rev. E 79, 066210 (2009)] (only taking into account the existence of ${\mathcal{M}}_s^{\mathrm{obs}}$), this new coefficient helps to determine the specific role played by the location of ${\mathcal{M}}_s^{\mathrm{obs}}$ with respect to the attractor, in phase portrait reconstruction and in any analysis technique.

We report on the measurement and computer simulation of the divergence of fast electrons generated in an ultraintense laser-plasma interaction (LPI) and the subsequent propagation in a nonrefluxing target. We show that, at $I{\lambda }^2$ of ${10}^{20}$ Wcm${}^{-2}\mu$m${}^2$, the time-integrated electron beam full divergence angle is ${(60\pm 5)}^{\circ }$. However, our time-resolved 2D particle-in-cell simulations show the initial beam divergence to be much smaller ($\le {30}^{\circ }$). Our simulations show the divergence to monotonically increase with time, reaching a final value of ${(68\pm 7)}^{\circ }$ after the passage of the laser pulse, consistent with the experimental time-integrated measurements. By revealing the time-dependent nature of the LPI, we find that a substantial fraction of the laser energy ($\sim 7\%$) is transported up to $100\mu$m with a divergence of 32${}^{\circ }$.

Existing studies on network synchronization focused on complex networks possessing either identical or nonidentical but simple nodal dynamics. We consider networks of both complex topologies and heterogeneous but chaotic oscillators, and investigate the onset of global phase synchronization. Based on a heuristic analysis and by developing an efficient numerical procedure to detect the onset of phase synchronization, we uncover a general scaling law, revealing that chaotic phase synchronization can be facilitated by making the network more densely connected. Our methodology can find applications in probing the fundamental network dynamics in realistic situations, where both complex topology and complicated, heterogeneous nodal dynamics are expected.

Transport of suspended Brownian particles dc driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. With such a diffusion length being inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility, and diffusivity markedly differ for smoothly and sharply corrugated channels.

Continuous time random walk (CTRW) subdiffusion along with the associated fractional Fokker-Planck equation (FFPE) is traditionally based on the premise of random clock with divergent mean period. This work considers an alternative CTRW and FFPE description which is featured by finite mean residence times (MRTs) in any spatial domain of finite size. Transient subdiffusive transport can occur on a very large time scale ${\tau }_c$ which can greatly exceed mean residence time in any trap, ${\tau }_c\gg \langle \tau \rangle$, and even not being related to it. Asymptotically, on a macroscale transport becomes normal for $t\gg {\tau }_c$. However, mesoscopic transport is anomalous. Differently from viscoelastic subdiffusion no long-range anticorrelations among position increments are required. Moreover, our study makes it obvious that the transient subdiffusion and transport are faster than one expects from their normal asymptotic limit on a macroscale. This observation has profound implications for anomalous mesoscopic transport processes in biological cells because the macroscopic viscosity of cytoplasm is finite.

We provide a detailed derivation of a recently developed first-principles approach to calculating averages in systems of interacting, spherical Brownian particles under time-dependent flow. Although we restrict ourselves to flows which are both homogeneous and incompressible, the time dependence and geometry (e.g., shear and extension) are arbitrary. The approximations formulated within mode-coupling theory are particularly suited to dense colloidal suspensions and capture the slow relaxation arising from particle interactions and the resulting glass transition to an amorphous solid. The delicate interplay between slow structural relaxation and time-dependent external flow in colloidal suspensions thus may be studied within a fully tensorial theory.

We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available.

Using a Gaussian model, we study the transmission of time-varying biochemical signals through feed-forward motifs and diamond motifs. To this end, we compute the frequency dependence of the gain, the noise, as well as their ratio, the gain-to-noise ratio, which measures how reliably a network transmits signals at different frequencies. We find that both coherent and incoherent feed-forward motifs can either act as low-pass or high-pass filters for information: The frequency dependence of the gain-to-noise ratio increases or decreases with increasing frequency, respectively. Our analysis of diamond motifs reveals that cooperative activation of the output component can increase the gain-to-noise ratio. This means that from the perspective of information transmission, it can be beneficial to split the input signal in two and recombine the two propagated signals at the output. Cooperative activation can be implemented via the formation of homo- or heteromultimers that then bind and activate the output component or via the binding of individual molecules of the intermediate species to the output component.

We investigate the time evolution of the scores of the second most popular sport in the world: the game of cricket. By analyzing, event by event, the scores of more than 2000 matches, we point out that the score dynamics is an anomalous diffusive process. Our analysis reveals that the variance of the process is described by a power-law dependence with a superdiffusive exponent, that the scores are statistically self-similar following a universal Gaussian distribution, and that there are long-range correlations in the score evolution. We employ a generalized Langevin equation with a power-law correlated noise that describes all the empirical findings very well. These observations suggest that competition among agents may be a mechanism leading to anomalous diffusion and long-range correlation.

We show that the front factor appearing in the shear modulus of a phantom network, $G_{\mathrm{ph}}=(1-2/f)\left(\rho k_{B}T\right)/N_s$, also controls the ratio of the strand length, $N_s$, and the number of monomers per Kuhn length of the primitive paths, $N_{\mathrm{ph}}^{\mathrm{PPKuhn}}$, characterizing the average network conformation. In particular, $N_{\mathrm{ph}}^{\mathrm{PPKuhn}}=N_s/(1-2/f)$ and $G_{\mathrm{ph}}=\left(\rho k_{B}T\right)/N_{\mathrm{ph}}^{\mathrm{PPKuhn}}$. Neglecting the difference between cross-links and slip-links, these results can be transferred to entangled systems and the interpretation of primitive path analysis data. In agreement with the tube model, the analogy to phantom networks suggest that the rheological entanglement length, $N_e^{\mathrm{rheo}}=\left(\rho k_{B}T\right)/G_e$, should equal $N_e^{\mathrm{PPKuhn}}$. Assuming binary entanglements with $f=4$ functional junctions, we expect that $N_e^{\mathrm{rheo}}$ should be twice as large as the topological entanglement length, $N_e^{\mathrm{topo}}$. These results are in good agreement with reported primitive path analysis results for model systems and a wide range of polymeric materials. Implications for tube and slip-link models are discussed.

We show that multiscaling properties of developed turbulence in shell models, which lead to anomalous scaling exponents in the inertial range, are determined exclusively by instanton dynamics. Instantons represent correlated extreme events localized in space-time, whose structure is described by self-similar statistics with a single universal scaling exponent. We show that anomalous scaling exponents appear due to the process of instanton creation. A simplified model of instanton creation is suggested, which adequately describes this anomaly.

We explore how the social dynamics of communication and learning can bring about the rise of a syntactic communication in a population of speakers. Our study is developed starting from a version of the Naming Game model in which an elementary syntactic structure is introduced. This analysis shows how the transition from nonsyntactic to syntactic communication is socially favored in communities which need to exchange a large number of concepts.

Network structure is a product of both its topology and interactions between its nodes. We explore this claim using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state, nodes synchronize in stages, revealing the network's underlying community structure. Traditional models of synchronization assume that interactions between nodes are mediated by a conservative process similar to diffusion. However, social and biological processes are often nonconservative. We propose a model of synchronization in a network of oscillators coupled via nonconservative processes. We study the dynamics of synchronization of a synthetic and real-world networks and show that the traditional and nonconservative models of synchronization reveal different structures within the same network.