We study periodic, quasiperiodic (Thue-Morse, Fibonacci, period doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski, and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system. All sequences have purines, guanine (G) or adenine (A), on the same strand, i.e., our prototype binary alphabet is $\{\mathrm{G},\mathrm{A}\}$. Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization, and charge transport. We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients, and current-voltage curves. We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties. Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category.

Near the thermodynamic critical point, the physical properties of binary fluids exhibit large variations in response to small temperature and concentration differences, whose effects on the onset of double-diffusive convection are reported here. The vertical symmetry is broken, irregular penetrative instability occurs, and cat's eye patterns are identified in the fingering regime and oscillatory regime, respectively. A new parameter $\mathrm{\Theta }$ is defined which indicates how the variations of physical properties influence flow fields. It is seen through numerical simulations that the Boussinesq approximation with constant physical properties has limited applicability, and that the Boussinesq equations with variable properties and density will describe all features seen. This conclusion is based on comparisons with the fully compressible, variable-property system.

A spectral collocation method using Chebyshev polynomials is applied to compute the electromagnetic fields and the collisional power absorption in radially inhomogeneous helicon plasmas. The governing equation has a singularity at the cylindrical axis, which has been resolved by imposing the appropriate boundary conditions. The results are compared with those of the finite difference method. The present work not only shows the superior accuracy of the spectral collocation method with a proper treatment of the singularity, but also discusses the advantages of using Chebyshev nodes for helicon plasmas in particular. It is possible to extend the range of parameters efficiently in cases for which the finite difference method fails to obtain reliable solutions without drastically decreasing the grid size. The spectral collocation method is shown to be especially useful near the lower hybrid resonance condition.

We study classical Markovian stochastic systems with discrete states, coupled to randomly switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of infinite timescale separation. We show that this can lead to master equations with bursting events. Negative transition rates can result in the reduced master equation, leading to unphysical short-time behavior. However, the reduced master equation can describe stationary states better than a leading-order adiabatic calculation, similar to what is known for Kramers-Moyal expansions in the context of the Pawula theorem [R. F. Pawula, Phys. Rev. 162, 186 (1967); H. Risken and H. Vollmer, Z. Phys. B 35, 313 (1979)]. We provide an interpretation of the reduced dynamics in discrete time and a criterion for the occurrence of negative rates for systems with two environmental states.

We study stochastic population dynamics coupled to fast external environments and combine expansions in the inverse switching rate of the environment and a Kramers–Moyal expansion in the inverse size of the population. This leads to a series of approximation schemes, capturing both intrinsic and environmental noise. These methods provide a means of efficient simulation and we show how they can be used to obtain analytical results for the fluctuations of population dynamics in switching environments. We place the approximations in relation to existing work on piecewise-deterministic and piecewise-diffusive Markov processes. Finally, we demonstrate the accuracy and efficiency of these model-reduction methods in different research fields, including systems in biology and a model of crack propagation.

We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and nonergodic systems. In particular we look at the quantum kicked top and kicked rotor as multispin systems and investigate the single-spin EE which characterizes bipartite entanglement of this spin with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems and local chaos in nonergodic systems. In particular, we show that EE can be maximized even when systems are highly nonergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analog of Kolmogorov-Arnol'd-Moser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.

We present an experimental realization of the collective trapping phase transition [Kaiser et al., Phys. Rev. Lett. 108, 268307 (2012)], using motile polar granular rods in the presence of a V-shaped obstacle. We offer a theory of this transition based on the interplay of motility-induced condensation and liquid-crystalline ordering and show that trapping occurs when persistent influx overcomes the collective expulsion of smectic defect structures. In agreement with the theory, our experiments find that a trap fills to the brim when the trap angle $\theta$ is below a threshold ${\theta }_c$, while all particles escape for $\theta >{\theta }_c$. Our simulations support a further prediction, that ${\theta }_c$ goes down with increasing rotational noise. We exploit the sensitivity of trapping to the persistence of directed motion to sort particles based on the statistical properties of their activity.

The recent paper “Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices” by G. S. Dhesi and M. Ausloos [Phys. Rev. E 93, 062115 (2016)] uses the replica method to compute the $1/N$ correction to the Wigner semicircle law for the ensemble of real symmetric random matrices with 0's down the diagonal, and upper triangular entries independently chosen from the values $\pm w$ with equal probability. We point out that the results obtained are inconsistent with known results in the literature, as well as with known large $N$ series expansions for the trace of powers of these random matrices. An incorrect assumption relating to the role of the diagonal terms at order $1/N$ appears to be the cause for the inconsistency. Moreover, results already in the literature can be used to deduce the $1/N$ correction to the Wigner semicircle law for real symmetric random matrices with entries drawn independently from distributions ${\mathcal{D}}_1$ (diagonal entries) and ${\mathcal{D}}_2$ (upper triangular entries) assumed to be even and have finite moments. Large $N$ expansions for the trace of the $2k\mathrm{th}$ power $\left(k=1,2,3\right)$ for these matrices can be computed and used as checks.

Trachenko [Trachenko, Phys. Rev. E 96, 062134 (2017)] has argued for creating a Lagrangian formulation of liquid dynamics. This Comment shows that the proposed two-field Lagrangian does not describe dynamics of liquid in a correct way. Other claims on the symmetric description of liquid dynamics and on the similarity of Maxwell and Frenkel characteristic times are discussed.

We make three remarks in reply to the comment by Bryk, Duviryak, and Mryglod (BDM) [Bryk, Duviryak, and Mryglod, Phys. Rev. E 99, 036102 (2019)]: (a) the discussion of shear liquid dynamics cannot be incorrect for the reason that this discussion does not include other effects such as longitudinal fluctuations; (b) the same point of relaxation time has been already discussed and published by Bryk et al. in their earlier comment [Bryk, Mryglod, Ruocco, and Scopigno, Phys. Rev. Lett. 120, 219601 (2018)] and in our related reply [Yang, Dove, Brazhkin, and Trachenko, Phys. Rev. Lett. 120, 219602 (2018)]; and (c) the field transformation for the complex scalar field theory used by BDM is incorrect.

We study the classic problem of dynamical evolution of a polymer in a shear flow. Interestingly, the polymer goes through several distinctly identifiable conformations during its passage from coiled to stretched states back and forth. We identify these conformations assumed by the polymer while tumbling and study the kinetics of the process in terms of the residence and recurrence times of individual conformations. The distribution of residence times exhibits exponentially decaying tails which helps us build an effective Markovian picture of the truly non-Markovian problem. We present the explicit $\mathbb{W}$ matrix for the coarse-grained evolution via a master equation and study its elements as a function of the Weissenberg number. We show that the timescales of decay of the autocorrelation function for the full Langevin dynamics compare quite well with the approximate results from the master equation approach.

This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics on random time durations, whose analytical representation is given by the $\mathrm{It}\widehat{\mathrm{o}}$ stochastic integral. The associated probability density function is given by a generalized Cauchy distribution at the stationary state. A fractional Feynman-Kac formula is utilized to show that weak ergodicity breaking of the FGCP depends on the existence of the subordinator and/or the divergence of variance.

We derive macroscopically deterministic flow equations with regard to the order parameters of the ferromagnetic $p$-spin model with infinite-range interactions. The $p$-spin model has a first-order phase transition for $p>2$. In the case of $p\ge 5$, the $p$-spin model with antiferromagnetic $XX$ interaction has a second-order phase transition in a certain region. In this case, however, the model becomes a nonstoquastic Hamiltonian, resulting in a negative sign problem. To simulate the $p$-spin model with antiferromagnetic $XX$ interaction, we utilize the adaptive quantum Monte Carlo method. By using this method, we can regard the effect of the antiferromagnetic $XX$ interaction as fluctuations of the transverse magnetic field. A previous study [J. Inoue, J. Phys. Conf. Ser. 233, 012010 (2010)] derived deterministic flow equations of the order parameters in the quantum Monte Carlo method. In this study, we derive macroscopically deterministic flow equations for the magnetization and transverse magnetization from the master equation in the adaptive quantum Monte Carlo method. Under the Suzuki-Trotter decomposition, we consider the Glauber-type stochastic process. We solve these differential equations by using the Runge-Kutta method, and we verify that these results are consistent with the saddle-point solution of mean-field theory. Finally, we analyze the stability of the equilibrium solutions obtained by the differential equations.

Spatial linguistic surveys often reveal well-defined geographical zones where certain linguistic forms are dominant over their alternatives. It has been suggested that these patterns may be understood by analogy with coarsening in models of two-dimensional physical systems. Here we investigate this connection by comparing data from the Cambridge Online Survey of World Englishes to the behavior of a generalized zero temperature Potts model with long-range interactions. The relative displacements of linguistically similar population centers reveal enhanced east-west affinity. Cluster analysis reveals three distinct linguistic zones. We find that when the interaction kernel is made anisotropic by stretching along the east-west axis, the model can reproduce the three linguistic zones for all interaction parameters tested. The model results are consistent with a view held by some linguists that, in the USA, language use is, or has been, exchanged or transmitted to a greater extent along the east-west axis than the north-south.

Pointwise zero velocity helicity density is shown not to prevent steady flows from acting as kinematic dynamos. We present numerical evidences that such flows can generate both small-scale magnetic fields as well as, by the magnetic $\alpha$-effect or negative eddy diffusivity mechanisms, large-scale ones. The flows are constructed as curls of analytically defined space-periodic steady solenoidal flows, whose vorticity helicity (i.e., kinetic helicity) density is everywhere zero.

The cascaded production and dynamics of electron-positron plasma in ultimately focused laser fields of extreme intensity are studied by three-dimensional particle-in-cell simulations with the account of the relevant processes of quantum electrodynamics (QED). We show that, if the laser facility provides a total power above 20 PW, it is possible to trigger not only a QED cascade but also pinching in the produced electron-positron plasma. The plasma self-compression in this case leads to an abrupt rise of the peak density and magnetic (electric) field up to at least ${10}^{28}{\mathrm{cm}}^{-3}$ and 1/20 (1/40) of the Schwinger field, respectively. Determining the actual limits and physics of this process might require quantum treatment beyond the used standard semiclassical approach. The proposed setup can thus provide extreme conditions for probing and exploring fundamental physics of the matter and vacuum.

Gut microbes play a key role in colorectal carcinogenesis, yet reaching a consensus on microbial signatures remains a challenge. This is in part due to a reliance on mean value estimates. We present an extreme value analysis for overcoming these limitations. By characterizing a power-law fit to the relative abundances of microbes, we capture the same microbial signatures as more complex meta-analyses. Importantly, we show that our method is robust to the variations inherent in microbial community profiling and point to future directions for developing sensitive, reliable analytical methods.

Diffusion is an important particle behavior in granular flow. Although granular diffusion has been studied for decades, the diffusion of size bidisperse particles has not been well understood. In this paper, discrete element method simulations with the Lees-Edwards boundary condition are performed to quantify the relation between the diffusion coefficient ($D$) and flow parameters for size bidisperse spheres in dense granular flow. The influences of the shear rate ($\dot{\gamma }$), the solids fraction $\left(f\right)$, and the diameter ratio $\left(D_{LS}\right)$ of particles on diffusion are studied. The effects of the friction coefficient (μ) and the restitution coefficient ($e$) are also investigated. The results indicate that while small particles diffuse faster than large particles in a binary system the volume weighted average diffusion coefficient is proportional to the shear rate and the square of the volume weighted average particle diameter, $d^2$, and it is inversely proportional to the solids fraction. The quantified relation is given as $D=k_d\dot{\gamma }{d}^2$, where $k_d=0.0186/f$, and this relation is not sensitive to the diameter ratio for $D_{LS}\le 3$. The diffusion coefficient is not sensitive to the friction coefficient except for the extreme condition where $\mu <0.1$, and it is also not sensitive to the restitution coefficient between 0.3 and 0.9.

It is well known that the turbulence that evolves from the tangles of vortices in quantum fluids at scales larger than the typical quantized vortex spacing $\ell$ has a close resemblance with classical turbulence. The temperature-dependent mutual friction parameter $\alpha \left(T\right)$ drives the turbulent statistics in the hydrodynamic regime of quantum fluids that involves a self-similar cascade of energy. From a simple theoretical analysis, here we show that superfluid ${}^3\mathrm{He}$-B in the presence of mutual damping exhibits a $k^{-5/3}$ Kolmogorov energy spectrum in the entire inertial range $\ell <r<L$ at temperature $T\lesssim 0.2T_c$, while at $T\gtrsim 0.2T_c$ dissipation begins to dominate larger eddies exhibiting a $k^{-3}$ spectrum toward the energy pumping scale $L$. At $T\approx 0.35T_c$, eddies of all size, being highly affected by damping, exhibit a $k^{-3}$ spectrum in the entire inertial range. The consistency of this result with the predictions of recent direct numerical simulations indicates that the present theoretical framework is applicable in quantifying the hydrodynamic regime of quantum turbulence.