We study the flow of elongated grains (wooden pegs of length $L=20$ mm with circular cross section of diameter $d_c=6$ and 8 mm) from a silo with a rotating bottom and a circular orifice of diameter $D$. In the small orifice range ($D/d<5$) clogs are mostly broken by the rotating base, and the flow is intermittent with avalanches and temporary clogs. Here $d\equiv {\left(\frac{3}{2}{d}_c^{2}L\right)}^{1/3}$ is the effective grain diameter. Unlike for spherical grains, for rods the flow rate $W$ clearly deviates from the power law dependence $W\propto {(D-kd)}^{2.5}$ at lower orifice sizes in the intermittent regime, where $W$ is measured in between temporary clogs only. Instead, below about $D/d<3$ an exponential dependence $W\propto e^{\kappa D}$ is detected. Here $k$ and $\kappa$ are constants of order unity. Even more importantly, rotating the silo base leads to a strong—more than 50%—decrease of the flow rate, which otherwise does not depend significantly on the value of $\omega$ in the continuous flow regime. In the intermittent regime, $W\left(\omega \right)$ appears to follow a nonmonotonic trend, although with considerable noise. A simple picture, in terms of the switching from funnel flow to mass flow and the alignment of the pegs due to rotation, is proposed to explain the observed difference between spherical and elongated grains. We also observe shear-induced orientational ordering of the pegs at the bottom such that their long axes in average are oriented at a small angle $\langle \theta \rangle \approx {15}^{\circ }$ to the motion of the bottom.

In this paper, we account for the many critical exponents derived from the studies of the electrical conductivity in porous media by applying analysis of the well-known relation known as Archie's law. In spite of its seeming simplicity this law is considered to be “poorly understood,” and the question that was and still is debated in the literature is whether there is some “hidden physics” in this law, or if it is “strictly a parametrization use for curve fitting with a priori no physical meaning.” Our solution to the corresponding long-debated 78 years old puzzle is based on the classical percolation theory, but it also involves a principle that is based on continuum percolation. This principle is that the electrical properties of a percolation system are determined by the interplay between the connectivity of the conducting objects in that system, and the connectivity of the intersections between pairs of them. We thus propose a general concept that we call an electrically affected connectivity, and we predict the corresponding evolvement of the conductivity critical exponent with the increase of the content of the electrically conducting phase. Then, we show that the zerolike threshold that characterizes Archie's law is what enables the observation of this evolution. Combining the above principle and the latter feature, we provide a holistic, yet simple, solution to the longstanding controversy surrounding this law and its practical applications. In contrast with many previous claims that Archie's law lacks a physical basis, and the commonly suggested experiential explanations for it, we provide a solution that is physically based and thus elucidates Archie's law by showing clearly that it represents a bona fide phase transition phenomenon. This conclusion and its generality are strongly supported by the fact that it also explains the behavior of the electrical conductivity exponents in nonporous systems such as composite materials. The predicted ability to extract the long sought microgeometrical information from Archie's-law data, within the framework of the percolation phase transition, is expected to open a new direction in the understanding and the applications of this law.

Newtonian turbulence is characterized by interscale transport of energy from the forcing scales to the dissipation scales. In elastoinertial turbulence, this interscale energy flux is weakened. Here, we explain this phenomenon by numerically showing that elastoinertial energy is predominantly dissipated through polymer chain relaxation. As opposed to Newtonian dissipation, chain relaxation is neither restricted to small nor to large scales but instead it is effective on all the scales. Chain relaxation does not therefore require interscale transport of elastoinertial energy from the forcing scales to the dissipation scales.

Competition between ion trapping and collisional detrapping is considered to be an important issue in the stabilization of the ion flow instability. The saturation amplitudes in terms of the particle density are derived and compared to the experimental data.

The ionic dynamic structure factor is examined to assess the relative roles of dissipation and the effective ionic interaction. Two disparate physically based models of dissipation, which can differ numerically by orders of magnitude, are used in molecular dynamics. We find a negligible impact on the amplitudes of the dynamic structure factors for physically realistic parameter values. We then examine the effective ionic interaction by varying its strength, the size of the atomic core (through a pseudopotential), and the screening model. We find that “diffusive” peaks in the dynamic structure factor are very sensitive to the form of the ionic interaction, and this sensitivity arises primarily from atomic physics through the pseudopotential. This suggests that it would be useful to employ the measured zero-frequency dynamic structure factor $S_{ii}(k,0)$ as a constraint on the effective interaction, which in turn can be used to compute physical properties.

Collisional excitation kinetics for atomic oxygen is studied behind reflected shock waves in $1\%{\mathrm{O}}_2/\mathrm{Ar}$ mixtures over 10 000–11 000K using laser absorption spectroscopy of the O($3s{}^{5}S^o$) to $\mathrm{O}(3p{}^{5}P_3$) transition at 777 nm and the $\mathrm{O}(3p{}^{5}P_3$) to O($3d {}^{5}D_{2,3,4}^{\mathrm{o}}$) transitions at 926 nm. Four time histories are inferred simultaneously from the absorbance of the two transitions: the population density of level 4 of atomic oxygen, i.e., the O($3s {}^{5}S^o$) state, $n_4$; the population density of level 6 of atomic oxygen, i.e., the $\mathrm{O}(3p{}^{5}P_3$) state, $n_6$; the electron number density, $n_e$; and the heavy-particle translational temperature, $T_{\text{tr}}$. Atomic oxygen in the levels 4 and 6 are not in equilibrium with the ground-state atomic oxygen as the measurements of $n_4$ and $n_6$ are generally 3–20 times smaller than the corresponding values under Boltzmann equilibrium at $T_{\text{tr}}$. However, these two states are close to partial equilibrium with each other within the test time, indicating strong heavy-particle cross coupling between levels 4 and 6 of atomic oxygen. A simplified two-temperature collisional-radiative (CR) model is developed to study the thermal and chemical nonequilibrium of atomic oxygen following shock heating. The four measured time histories are used to optimize the 12 collisional rate constants in the CR model using a stochastic gradient descent (SGD) algorithm. The time-history results, diagnostic methods, and collisional-radiative model presented in the current study are potentially useful in studies of high-enthalpy air, plasma processing, or other applications involving weakly ionized oxygen.

Microparticle suspensions in a polarity-switched discharge plasma of the Plasmakristall-4 facility on board the International Space Station exhibit string-like order. As pointed out in [Phys. Rev. Research 2, 033314 (2020)], the string-order is subject to evolution on the timescale of minutes at constant gas pressure and constant parameters of polarity switching. We perform a detailed analysis of this evolution using the pair correlations and length spectrum of the string-like clusters (SLCs). Average exponential decay rate of the SLC length spectrum is used as a measure of string order. The analysis shows that the improvement of the string-like order is accompanied by the decrease of the thickness of the microparticle suspension, microparticle number density, and total amount of microparticles in the field of view. This suggests that the observed long-term evolution of the string-like order is caused by the redistribution of the microparticles, which significantly modifies the plasma conditions.

The stochastic dynamics of an electron in counterpropagating linearly polarized laser beams is analyzed using a recently developed 3/2-dimensional Hamiltonian approach. It is shown that perpendicular canonical momenta suppress stochasticity, helping to explain the results from recently reported numerical studies of stochastic dynamics in a similar setting. The stochasticity in a perpendicular polarization setup is demonstrated. Lastly, the impact of radiation friction effects is considered, and shown to be negligible in the classical radiation reaction limit.

The three-dimensional Ising model in an external field is used as a mathematical model for price dynamics of financials market. The model allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the stylized facts of the financial markets. We obtain the price dynamics in terms of the strength of the field that reinforces the sensitivity of the agent's sentiment to external news. The exponent of long-tail cumulative probability density is determined and satisfies the inverse of the cubic law. Furthermore, the long range memory of the model is studied using different methods to determine the Hurst index of the model. The results obtained display that the model does serve as a mathematical model for financial markets.

Networks provide a mathematically rich framework to represent social contacts sufficient for the transmission of disease. Social networks are often highly clustered and fail to be locally treelike. In this paper, we study the effects of clustering on the spread of sequential strains of a pathogen using the generating function formulation under a complete cross-immunity coupling, deriving conditions for the threshold of coexistence of the second strain. We show that clustering reduces the coexistence threshold of the second strain and its outbreak size in Poisson networks, while exhibiting the opposite effects on uniform-degree models. We conclude that clustering within a population must increase the ability of the second wave of an epidemic to spread over a network. We apply our model to the study of multilayer clustered networks and observe the fracturing of the residual graph at two distinct transmissibilities.

A fluid composed of two molecular species may undergo phase segregation via spinodal decomposition. However, if the two molecular species can interconvert, e.g., change their chirality, then a phenomenon of phase amplification, which has not been studied so far to our best knowledge, emerges. As a result, eventually, one phase will completely eliminate the other one. We model this phenomenon on an Ising system which relaxes to equilibrium through a hybrid of Kawasaki-diffusion and Glauber-interconversion dynamics. By introducing a probability of Glauber-interconversion dynamics, we show that the particle conservation law is broken, thus resulting in phase amplification. We characterize the speed of phase amplification through scaling laws based on the probability of Glauber dynamics, system size, and distance to the critical temperature of demixing.

Recently we introduced the generalized energy-conserving dissipative particle dynamics method (GenDPDE) [J. Bonet Avalos, M. Lísal, J. P. Larentzos, A. D. Mackie, and J. K. Brennan, Phys. Chem. Chem. Phys. 21, 24891 (2019)], which has been formulated for an emerging class of density- and temperature-dependent coarse-grain models. In the original work, GenDPDE was formulated to ensure a fundamental link is maintained with the underlying physical system at the higher resolution scale. In this paper, we revisit the formulation of the GenDPDE method, and rederive the particle thermodynamics to ensure consistency at the opposing scale extreme, i.e., between the local thermodynamics in the mesoscopic systems and the corresponding macroscopic properties. We demonstrate this consistency by introducing unambiguous, physically meaningful definitions of the heat and work, which lead to the formulation of an alternative heat flow model that is analogous to Fourier's law of heat conduction. We present further analysis of the internal, unresolved degrees-of-freedom of the mesoparticles by considering the thermodynamics of an individual mesoparticle within the GenDPDE framework. Several key outcomes of the analysis include: (i) demonstration that the choice of the independent variables alters the particle thermodynamic description; (ii) demonstration that the mesoscopic thermodynamic transformations introduce additional terms of the order of the size of the local fluctuations, which prevent an unambiguous definition of both the heat and work; (iii) an emphasis on the importance of the choice of the proper estimators of the thermodynamic properties that are embedded in the chosen thermodynamic description; and (iv) a clearly defined path for determining any thermodynamic quantity dressed by the fluctuations. The further insight provided by this deeper analysis is useful for both readers interested in the GenDPDE theoretical framework, as well as readers interested in the practical ramifications of the analysis, namely, the alternative heat flow model.

We propose a stochastic order parameter model for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a nonequilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in nonequilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a superheated ordered (supercooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in Nakagawa and Sasa [Liquid-Gas Transitions in Steady Heat Conduction, Phys. Rev. Lett. 119, 260602 (2017).]

In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.

Microtubules are an essential physical building block of cellular systems. They are organized using specific crosslinkers, motors, and influencers of nucleation and growth. With the addition of antiparallel crosslinkers, microtubule self-organization patterns go through a transition from fanlike structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To create these organizations, we previously used polymer crowding agents. Here we study how altering the properties of the crowders, such as type, size, and molecular weight, affects microtubule organization. Comparing simulations with experiments, we observe a scaling law associated with the fanlike patterns in the absence of crosslinkers. Tactoids formed in the presence of crosslinkers show variable length, depending on the crowders. We correlate the subtle differences to filament contour length changes, affected by nucleation and growth rate changes induced by the polymers in solution. Using quantitative image analysis, we deduce that the tactoids differ from traditional liquid crystal organization, as they are limited in width irrespective of crowders and surfaces, and behave as solidlike condensates.

Single-filament tracing has been a valuable tool to directly determine geometrical and mechanical properties of entangled polymer networks. However, systematically verifying how the stiffness of the tracer filament or its molecular interactions with the surrounding network impacts the measurement of these parameters has not been possible with the established experimental systems. Here we use mechanically programmable DNA nanotubes embedded in crosslinked and entangled F-actin networks, as well as in synthetic DNA networks, in order to measure fundamental, structural network properties like tube width and mesh size with respect to the stiffness of the tracers. While we confirm some predictions derived from models based purely on steric interactions, our results indicate that these models should be expanded to account for additional interfilament interactions, thereby describing the behavior of real polymer networks.

This paper describes an attempt to construct a first-principles theory of the fracture toughness of crystalline solids. It is based on the thermodynamic dislocation theory (TDT), which starts with the assertion that dislocations in solids must obey the second law of thermodynamics. A second starting assumption is that fracture is initiated when the tip of a notch is driven to undergo a dynamic shape instability. The results of this analysis are developed in comparison with measurements by Gumbsch and colleagues of the notch toughness of both predeformed and non-predeformed tungsten crystals. The theory includes a simple ad hoc conjecture regarding tip dynamics at small dislocation densities. Nevertheless, its predictions agree quantitatively with the experimental data, including both brittle and ductile fracture, over a wide range of temperatures, loading rates, and initial conditions.

As an alternative inertial confinement fusion scheme, shock ignition requires a strong converging shock driven by a high-intensity laser pulse to ignite a precompressed fusion capsule. Understanding nonlinear laser-plasma instabilities is crucial to assess and improve the laser-shock energy coupling. Recent experiments conducted on the OMEGA EP laser facility have demonstrated that such instabilities can $\sim 100$% deplete the first 0.5 ns of the high-intensity laser. Analyses of the observed laser-generated blast wave suggest that this pump-depletion starts at $\sim 0.02$ critical density and progresses to 0.1–0.2 critical density, which is also confirmed by the time-resolved stimulated Raman backscattering spectra. The pump-depletion dynamics can be explained by the breaking of ion-acoustic waves in stimulated Brillouin scattering. Such pump depletion would inhibit the collisional laser energy absorption but may benefit the generation of hot electrons with moderate temperatures for electron shock ignition [Phys. Rev. Lett. 119, 195001 (2017)].

Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states, i.e., states of coexisting synchronized and unsynchronized elements. We address the ${\mathbb{S}}_4$ permutation symmetry of four globally coupled Stuart-Landau oscillators and uncover an interconnected web of solutions with different symmetries. Among these are chaotic $2-1-1$ minimal chimeras that arise from $2-1-1$ periodic solutions in a period-doubling cascade, as well as fully asymmetric chaotic states arising similarly from periodic $1-1-1-1$ solutions. A backbone of equivariant pitchfork bifurcations mediate between the two cascades, culminating in equivariant pitchforks of chaotic attractors.