The discharge flow in a cylindrical and a rectangular silo using both monodisperse and bidisperse mixtures of spherical glass beads is studied experimentally. The flow rate is measured using a precision balance for a large range of particle diameters, size ratios, and outlet diameters. A simple physical model is proposed to describe the flow of bidisperse mixtures. It gives an expression for the flow rate and predicts that the bulk velocity follows a simple mixture law. This model implies that a mixture diameter cannot be simply defined. Moreover it is shown that bidisperse granular media allow for the transport of coarse particles below their jamming conditions.

By means of high-resolution ac calorimetry and polarizing optical microscopy, it is demonstrated that surface-functionalized spherical CdSSe nanoparticles induce a twist-grain boundary phase when dispersed in a chiral liquid crystal. These nanoparticles can effectively stabilize the one-dimensional lattice of screw dislocations, thus establishing the twist-grain boundary order between the cholesteric and the smectic-$A$ phases. A Landau–de Gennes–Ginzburg model is used to analyze the impact of nanoparticles on widening the temperature range of molecular organizations possessing a lattice of screw dislocations. We show that in addition to the defect-core-replacement mechanism, the saddle-splay elasticity may also play a significant role.

Transcription factors perform facilitated diffusion [three-dimensional (3D) diffusion in the cytosol and 1D diffusion on the DNA] when binding to their target sites to regulate gene expression. Here, we investigated the influence of this binding mechanism on the noise in gene expression. Our results showed that, for biologically relevant parameters, the binding process can be represented by a two-state Markov model and that the accelerated target finding due to facilitated diffusion leads to a reduction in both the mRNA and the protein noise.

Covariant Lyapunov vectors for scale-free networks of Hénon maps are highly localized. We revealed two mechanisms of the localization related to full and phase cluster synchronization of network nodes. In both cases the localization nodes remain unaltered in the course of the dynamics, i.e., the localization is nonwandering. Moreover, this is predictable: The localization nodes are found to have specific dynamical and topological properties and they can be found without computing of the covariant vectors. This is an example of explicit relations between the system topology, its phase-space dynamics, and the associated tangent-space dynamics of covariant Lyapunov vectors.

We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter—the propagation constant $k$. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant $k$, showing that probability of appearance of rogue waves depends on $k$.

The Rayleigh instability (also called the Plateau-Rayleigh instability) of a nanosized liquid propane thread is investigated using molecular dynamics (MD). The validity of classical predictions at small length scales is verified by comparing the temporal evolution of liquid thread simulated by MD against classical predictions. Previous works have shown that thermal fluctuations become dominant at small length scales. The role and influence of the stochastic nature of thermal fluctuations in determining the instability at small length scale is also investigated. Thermal fluctuations are seen to dominate and accelerate the breakup process only during the last stages of breakup. The simulations also reveal that the breakup profile of nanoscale threads undergo modification due to reorganization of molecules by the evaporation-condensation process.

Understanding the agglomeration of dust particles in complex plasmas requires knowledge of basic properties such as the net electrostatic charge and dipole moment of the dust. In this study, dust aggregates are formed from gold-coated mono-disperse spherical melamine-formaldehyde monomers in a radiofrequency (rf) argon discharge plasma. The behavior of observed dust aggregates is analyzed both by studying the particle trajectories and by employing computer models examining three-dimensional structures of aggregates and their interactions and rotations as induced by torques arising from their dipole moments. These allow the basic characteristics of the dust aggregates, such as the electrostatic charge and dipole moment, as well as the external electric field, to be determined. It is shown that the experimental results support the predicted values from computer models for aggregates in these environments.

We calculate interdiffusion coefficients in a two-component, weakly or strongly coupled ion plasma (gas or liquid, composed of two ion species immersed into a neutralizing electron background). We use an effective potential method proposed recently by Baalrud and Daligaut [Phys. Rev. Lett. 110, 235001 (2013)]. It allows us to extend the standard Chapman-Enskog procedure of calculating the interdiffusion coefficients to the case of strong Coulomb coupling. We compute binary diffusion coefficients for several ionic mixtures and fit them by convenient expressions in terms of the generalized Coulomb logarithm. These fits cover a wide range of plasma parameters spanning from weak to strong Coulomb couplings. They can be used to simulate diffusion of ions in ordinary stars as well as in white dwarfs and neutron stars.

The complete Kubo conductivity tensor is computed in two- and three-dimensional linear magnetic null systems using collisionless single-particle simulations. Regions of chaotic charged-particle dynamics are constructed for each case. It is found that stochastic frequency mixing of particle bounce motion, as well as gyromotion, contribute significantly to the conductivity. The conductivity curves are well approximated by power laws over a certain frequency range and the ac conductivity is found to be an order of magnitude smaller than the dc value, leading to enhanced resistivity, particularly near the cyclotron frequency. The ac conductivities must be accounted for in computation of the total dissipation.

A partial-bounce-back lattice Boltzmann model has been used to simulate flow on a lattice consisting of cubic voxels with a locally varying effective percolating fraction. The effective percolating fraction of a voxel is the total response to the partial-bounce-back techniques for porous media flow due to subvoxel fine structures. The model has been verified against known analytic solutions on two- and three-dimensional regular geometries, and has been applied to simulate flow and permeabilities of two real-world rock samples. This enables quantitative determination of permeability for problems where voxels cannot be adequately segmented as discrete compositions. The voxel compositions are represented as volume fractions of various material phases and void. The numerical results have shown that, for the tight-sandstone sample, the bulk permeability is sensitive to the effective percolating fraction of calcite. That is, the subvoxel flow paths in the calcite phase are important for bulk permeability. On the other hand, flow in the calcite phase in the sandstone sample makes an insignificant contribution to the bulk permeability. The calculated permeability value for the sandstone sample is up to two orders of magnitude greater than the tight sandstone. This model is generic and could be applied to other oil and gas reservoir media or to material samples.

Studies of temperature-dependent phase behaviors of discotic colloids are found infrequently in the literature. We establish here the isotropic-to-nematic (I-N) transition phase diagram of charged platelets in the temperature-versus-volume fraction plane. We discover that the N phase can be melted by increasing temperature, and that coexistent samples are more sensitive to polydispersity at higher temperature and higher concentration.

The transport of biomolecules across biomembranes occurs in a complex environment where the fluid on both sides of the membrane contains many inclusions. We investigate the translocation of a polymer through a nanopore in such crowded environments via computer simulations. Modeling intracellular and extracellular inclusions as spherical obstacles, the emergence of an entropic driving force is demonstrated for (i) a gradient in the number of obstacles on either side of the pore and (ii) having the obstacles in an ordered arrangement on one side and disordered on the other. With a directional preference of $\approx 90\%$ of events occurring towards the disordered side and a reduction in the translocation time of $\approx 30\%$, the latter case represents a manifestation of entropic trapping. Simple estimates for the magnitude of the driving force are developed for both cases. The effect of allowing the obstacles to move as well as systems containing opposing concentration and disorder gradients are also explored. Demonstrating a robust conclusion that translocation to lower obstacle densities and higher degrees of disorder will be accelerated, these results suggest that accounting for such effects will be critical in developing a realistic model of in vivo translocation.

We study a series of $N$ oscillators, each coupled to its nearest neighbors, and linearly to a phonon field through the oscillator's number operator. We show that the Hamiltonian of a pair of adjacent oscillators, or a dimer, within the series of oscillators can be transformed into a form in which they are collectively coupled to the phonon field as a composite unit. In the weak coupling and rotating-wave approximation, the system behaves effectively as the trilinear boson model in the one excitation subspace of the dimer subsystem. The reduced dynamics of the one excitation subspace of the dimer subsystem coupled weakly to a phonon bath is similar to that of a two-level system, with a metastable state against the vacuum. The decay constant of the subsystem is proportional to the dephasing rate of the individual oscillator in a phonon bath, attenuated by a factor that depends on site asymmetry, intersite coupling, and the resonance frequency between the transformed oscillator modes, or excitons. As a result of the collective effect, the excitation relaxation lifetime is prolonged over the dephasing lifetime of an individual oscillator coupled to the same bath.

Work can be extracted from a single bath beyond the limit set by the second law of thermodynamics by performing measurement on the system and utilizing the acquired information. This imposes an upper bound on extracted work and maintains a generalized (i.e., with information) second law. As an example, we studied a Brownian particle confined in a two-dimensional harmonic trap in the presence of a magnetic field, whose position coordinates are measured with finite precision. Two separate cases are investigated in this study: (A) moving the center of the potential and (B) varying the stiffness of the potential. Optimal protocols that extremize the work in a finite-time process are explicitly calculated for these two cases. For case A, we show that even though the optimal protocols depend on magnetic field, surprisingly, extracted work is independent of the field. For case B, both the optimal protocol and the extracted work depend on the magnetic field. However, the presence of a magnetic field always reduces the extraction of work for the latter case.

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum $XY$ models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently when, in a new so-called “explosive percolation” problem for a competition-driven process, a discontinuous phase transition was reported. The analysis of evolution equations for this process showed, however, that this transition is actually continuous, though with surprisingly tiny critical exponents. For a wide class of representative models, we develop a strict scaling theory of this exotic transition which provides the full set of scaling functions and critical exponents. This theory indicates the relevant order parameter and susceptibility for the problem and explains the continuous nature of this transition and its unusual properties.

We consider the phase behavior of a simple model of a liquid crystal by means of modified mean-field density-functional theory (MMF DFT) and Monte Carlo simulations in the grand canonical ensemble (GCEMC). The pairwise additive interactions between liquid-crystal molecules are modeled via a Lennard-Jones potential in which the attractive contribution depends on the orientation of the molecules. We derive the form of this orientation dependence through an expansion in terms of rotational invariants. Our MMF DFT predicts two topologically different phase diagrams. At weak to intermediate coupling of the orientation dependent attraction, there is a discontinuous isotropic-nematic liquid-liquid phase transition in addition to the gas-isotropic liquid one. In the limit of strong coupling, the gas-isotropic liquid critical point is suppressed in favor of a fluid- (gas- or isotropic-) nematic phase transition which is always discontinuous. By considering three representative isotherms in parallel GCEMC simulations, we confirm the general topology of the phase diagram predicted by MMF DFT at intermediate coupling strength. From the combined MMF DFT-GCEMC approach, we conclude that the isotropic-nematic phase transition is very weakly first order, thus confirming earlier computer simulation results for the same model [see M. Greschek and M. Schoen, Phys. Rev. E 83, 011704 (2011)].

A form of activity that is highly studied in cultured cortical networks is the neuronal avalanche, characterized by bursts whose distribution follows a power law. While the statistics of neuronal avalanches are well characterized, much less is known about the neuronal interactions from which they arise. We examined statistical dependencies between pairs of cells in spontaneously active cultures of cortical neurons using an information measure of transfer entropy. We show that the distribution of transfer entropy follows a power law with a slope near 3/2. Using graph-theoretic approaches of weighted networks, we demonstrate that this power law maximizes a measure of global economy that accounts for both the efficiency of neuronal interactions as well as the overall traffic in the network. Finally, we describe a pairwise Poisson model that captures the statistics of information transfer in a population of spiking neurons. Using this model, we show that avalanches can occur in systems with weak pairwise interactions, and that strong pairwise interactions can arise without avalanches, suggesting that these two measures capture distinct properties of brain dynamics.

Cochlear implants, also called bionic ears, are implanted neural prostheses that can restore lost human hearing function by direct electrical stimulation of auditory nerve fibers. Previously, an information-theoretic framework for numerically estimating the optimal number of electrodes in cochlear implants has been devised. This approach relies on a model of stochastic action potential generation and a discrete memoryless channel model of the interface between the array of electrodes and the auditory nerve fibers. Using these models, the stochastic information transfer from cochlear implant electrodes to auditory nerve fibers is estimated from the mutual information between channel inputs (the locations of electrodes) and channel outputs (the set of electrode-activated nerve fibers). Here we describe a revised model of the channel output in the framework that avoids the side effects caused by an “ambiguity state” in the original model and also makes fewer assumptions about perceptual processing in the brain. A detailed comparison of how different assumptions on fibers and current spread modes impact on the information transfer in the original model and in the revised model is presented. We also mathematically derive an upper bound on the mutual information in the revised model, which becomes tighter as the number of electrodes increases. We found that the revised model leads to a significantly larger maximum mutual information and corresponding number of electrodes compared with the original model and conclude that the assumptions made in this part of the modeling framework are crucial to the model's overall utility.