Using data from equilibrium molecular dynamics computer simulations we have built up a catalog of response functions for the Coulomb one-component plasma over a wide range of $\mathrm{\Gamma }$ coupling values, including the strongly coupled $\mathrm{\Gamma }>1$ liquid regime. We focus on the domain of negative compressibility ($\mathrm{\Gamma }>3$), where the proper response displays an acausal behavior, implying a modification of the relation between its real and imaginary parts in the Kramers-Kronig relations. We give a description of the details of this acausal feature, in both the frequency and time domains. We show that the viscoelastic pole of the density response function morphs into an imaginary pole in the upper $\omega$ half-plane that is responsible for the anomalous behavior of the response in this coupling range. By examining the plasmon dispersion relation through the dielectric response function, rather than via the peaks of the dynamical structure function, we obtain a more reliable representation for the dispersion. We demonstrate that there is an intimate link between the formation of the roton minimum in the dispersion and the negative compressibility of the system. The feasibility of the extension of our analysis to systems with a short-range interaction is explored.

We present a regime where an ultraintense laser pulse interacting with a foil target results in high $\gamma$-photon conversion efficiency, obtained via three-dimensional quantum-electrodynamics particle-in-cell simulations. A single-cycle laser pulse is used under the tight-focusing condition for obtaining the ${\lambda }^3$ regime. The simulations employ a radially polarized laser as it results in higher $\gamma$-photon conversion efficiency compared to both azimuthal and linear polarizations. A significant fraction of the laser energy is transferred to positrons, while a part of the electromagnetic wave escapes the target as attosecond single-cycle pulses.

We propose to measure the surface charge accumulating at the interface between a plasma and a dielectric by infrared spectroscopy using the dielectric as a multi-internal reflection element. The surplus charge leads to an attenuation of the transmitted signal from which the magnitude of the charge can be inferred. Calculating the optical response perturbatively in first order from the Boltzmann equation for the electron-hole plasma inside the solid, we can show that in the parameter range of interest a classical Drude term results. Only the integrated surface charge enters, opening up thereby a very efficient analysis of measured data.

We describe state-reduction algorithms for the analysis of first-passage processes in discrete- and continuous-time finite Markov chains. We present a formulation of the graph transformation algorithm that allows for the evaluation of exact mean first-passage times, stationary probabilities, and committor probabilities for all nonabsorbing nodes of a Markov chain in a single computation. Calculation of the committor probabilities within the state-reduction formalism is readily generalizable to the first hitting problem for any number of alternative target states. We then show that a state-reduction algorithm can be formulated to compute the expected number of times that each node is visited along a first-passage path. Hence, all properties required to analyze the first-passage path ensemble (FPPE) at both a microscopic and macroscopic level of detail, including the mean and variance of the first-passage time distribution, can be computed using state-reduction methods. In particular, we derive expressions for the probability that a node is visited along a direct transition path, which proceeds without returning to the initial state, considering both the nonequilibrium and equilibrium (steady-state) FPPEs. The reactive visitation probability provides a rigorous metric to quantify the dynamical importance of a node for the productive transition between two endpoint states and thus allows the local states that facilitate the dominant transition mechanisms to be readily identified. The state-reduction procedures remain numerically stable even for Markov chains exhibiting metastability, which can be severely ill-conditioned. The rare event regime is frequently encountered in realistic models of dynamical processes, and our methodology therefore provides valuable tools for the analysis of Markov chains in practical applications. We illustrate our approach with numerical results for a kinetic network representing a structural transition in an atomic cluster.

We present a quantitative analysis of the inertial range statistics produced by entropic lattice Boltzmann method (ELBM) in the context of three-dimensional homogeneous and isotropic turbulence. ELBM is a promising mesoscopic model particularly interesting for the study of fully developed turbulent flows because of its intrinsic scalability and its unconditional stability. In the hydrodynamic limit, the ELBM is equivalent to the Navier-Stokes equations with an extra eddy viscosity term. From this macroscopic formulation, we have derived a new hydrodynamical model that can be implemented as a large-eddy simulation closure. This model is not positive definite, hence, able to reproduce backscatter events of energy transferred from the subgrid to the resolved scales. A statistical comparison of both mesoscopic and macroscopic entropic models based on the ELBM approach is presented and validated against fully resolved direct numerical simulations. Besides, we provide a second comparison of the ELBM with respect to the well-known Smagorinsky closure. We found that ELBM is able to extend the energy spectrum scaling range preserving at the same time the simulation stability. Concerning the statistics of higher order, inertial range observables, ELBM accuracy is shown to be comparable with other approaches such as Smagorinsky model.

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first-order transition from a high-temperature random coil phase to a highly unusual low-temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures [we call these PoSSuM (Planar Structures with Secondary Motifs)] in the phase and protein native state structures.

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of straight rigid rods on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, linear $k$-mers (particles occupying $k$ consecutive sites along one of the lattice directions) are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then the system is diluted by randomly removing sets of $k$ consecutive monomers (linear $k$-mers) from the lattice. Two schemes are used for the depositing/removing process: an isotropic scheme, where the deposition (removal) of the linear objects occurs with the same probability in any lattice direction, and an anisotropic (perfectly oriented) scheme, where one lattice direction is privileged for depositing (removing) the particles. The study is conducted by following the behavior of four critical concentrations with size $k$: $\left(\text{i}\right)$ $\left[\right(\text{ii}\left)\right]$ standard isotropic[oriented] percolation threshold ${\theta }_{c,k}\left[{\vartheta }_{c,k}\right]$, which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. ${\theta }_{c,k}\left[{\vartheta }_{c,k}\right]$ is reached by isotropic[oriented] deposition of straight rigid $k$-mers on an initially empty lattice; and $\left(\text{iii}\right)$ $\left[\right(\text{iv}\left)\right]$ inverse isotropic[oriented] percolation threshold ${\theta }_{c,k}^i\left[{\vartheta }_{c,k}^i\right]$, which corresponds to the maximum concentration of occupied sites for which connectivity disappears. ${\theta }_{c,k}^i\left[{\vartheta }_{c,k}^i\right]$ is reached after removing isotropic [completely aligned] straight rigid $k$-mers from an initially fully occupied lattice. ${\theta }_{c,k}$, ${\vartheta }_{c,k}$, ${\theta }_{c,k}^i$, and ${\vartheta }_{c,k}^i$ are determined for a wide range of $k$ ($2\le k\le 512$). The obtained results indicate that $\left(1\right){\theta }_{c,k}\left[{\theta }_{c,k}^i\right]$ exhibits a nonmonotonous dependence on the size $k$. It decreases[increases] for small particle sizes, goes through a minimum[maximum] at around $k=11$, and finally increases and asymptotically converges towards a definite value for large segments ${\theta }_{c,k\to \infty }=0.500\left(2\right)$ $[{\theta }_{c,k\to \infty }^i=0.500\left(1\right)]$; $\left(2\right){\vartheta }_{c,k}\left[{\vartheta }_{c,k}^i\right]$ depicts a monotonous behavior in terms of $k$. It rapidly increases[decreases] for small particle sizes and asymptotically converges towards a definite value for infinitely long $k$-mers ${\vartheta }_{c,k\to \infty }=0.5334\left(6\right)$ $[{\vartheta }_{c,k\to \infty }^i=0.4666\left(6\right)]$; (3) for both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line $\theta \left(\vartheta \right)=0.5$. Thus a complementary property is found ${\theta }_{c,k}+{\theta }_{c,k}^i=1$ (and ${\vartheta }_{c,k}+{\vartheta }_{c,k}^i=1$) which has not been observed in other regular lattices. This condition is analytically validated by using exact enumeration of configurations for small systems, and (4) in all cases, the critical concentration curves divide the $\theta$ space in a percolating region and a nonpercolating region. These phases extend to infinity in the space of the parameter $k$ so that the model presents percolation transition for the whole range of $k$.

Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is that small interparticle forces $\left(f\right)$ and gaps $\left(h\right)$ are distributed according to nontrivial power laws. A recently developed mean-field (MF) theory predicts the characteristic exponents of these distributions in the limit of very high spatial dimension, $d\to \infty$ and, remarkably, their values seemingly agree with numerical estimates in physically relevant dimensions, $d=2$ and 3. These exponents are further connected through a pair of inequalities derived from stability conditions, and both theoretical predictions and previous numerical investigations suggest that these inequalities are saturated. Systems at the jamming point are thus only marginally stable. Despite the key physical role played by these exponents, their systematic evaluation has yet to be attempted. Here, we carefully test their value by analyzing the finite-size scaling of the distributions of $f$ and $h$ for various particle-based models for jamming. Both dimension and the direction of approach to the jamming point are also considered. We show that, in all models, finite-size effects are much more pronounced in the distribution of $h$ than in that of $f$. We thus conclude that gaps are correlated over considerably longer scales than forces. Additionally, remarkable agreement with MF predictions is obtained in all but one model, namely near-crystalline packings. Our results thus help to better delineate the domain of the jamming universality class. We furthermore uncover a secondary linear regime in the distribution tails of both $f$ and $h$. This surprisingly robust feature is understood to follow from the (near) isostaticity of our configurations.

We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range $[0,2\pi ]$, which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an $n$-valley dark soliton could be in the range $[0,n\pi ]$, supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.

We consider a quantum two-level system in bichromatic classical time-periodic fields, the frequency of one of which far exceeds that of the other. Based on systematic separation of timescales and averaging over the fast motion a reduced quantum dynamics in the form of a nonlinear forced Mathieu equation is derived to identify the stable oscillatory resonance zones intercepted by unstable zones in the frequency-amplitude plot. We show how this forcing of the dressed two-level system may generate the subharmonics and superharmonics of the weak field in the stable region, which can be amplified by optimization of the strength of the high frequency field. We have carried out detailed numerical simulations of the driven quantum dynamics to corroborate the theoretical analysis.

To understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time linear dynamics. However, continuous-time linear dynamics is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modeling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, the energy costs needed for controlling systems with and without conformity are compared, and it was found that controlling networked systems with conformity features always requires less control energy. Finally, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since the conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward toward developing realistic control of complex social systems.

In large-scale brain network dynamics, brain nodes switching between modules has been found to correlate with cognition. However, how the brain nodes engage in this kind of reorganization of modules is unclear. Based on a functional magnetic resonance imaging dataset, we construct dynamic brain functional networks and investigate nodal module temporal dynamic behavior by applying the multilayer network analysis approach. We reveal three cohesive communities that are groups of brain nodes linked in the same community during brain module dynamic reorganization. We show that the cohesive communities have higher clustering coefficients and lower characteristic path lengths than the controlled community, indicating cohesive communities are the parts of brain networks with high information processing efficiency. The smaller sample entropy of functional connectivity in cohesive communities also proves their property of being more “static” compared with the controlled community in brain dynamics. Specifically, compared with the controlled community, the functional connectivity of cohesive communities is restricted strictly by structure connectivity and shows more similarity to structure connectivity. More importantly, we find that the cohesive communities are stable not only in the resting state but also when processing cognitive tasks. Our results not only show that cohesive communities may be the fundamental community organization to support brain network dynamics but also provide insights into the intrinsic structural relationship between the resting state and task states of the brain.

Understanding how genes in a single cell respond to dynamically changing signals has been a central question in stochastic gene transcription research. Recent studies have generated massive steady-state or snapshot mRNA distribution data of individual cells, and inferred a large spectrum of kinetic transcription parameters under varying conditions. However, there have been few algorithms to convert these static data into the temporal variation of kinetic rates. Real-time imaging has been developed to monitor stochastic transcription processes at the single-cell level, but the immense technicality has prevented its application to most endogenous loci in mammalian cells. In this article, we introduced a stochastic gene transcription model with variable kinetic rates induced by unstable cellular conditions. We approximated the transcription dynamics using easily obtained steady-state formulas in the model. We tested the approximation against experimental data in both prokaryotic and eukaryotic cells and further solidified the conditions that guarantee the robustness of the method. The method can be easily implemented to provide convenient tools for quantifying dynamic kinetics and mechanisms underlying the widespread static transcription data, and may shed a light on circumventing the limitation of current bursting data on transcriptional real-time imaging.

In a recent paper [S. Ghosh, Phys. Rev. E 103, 023205 (2021)], the transport properties of the two-dimensional weakly nonlinear quasilongitudinal dust lattice mode were investigated in a highly viscous, strongly coupled, and weakly ionized plasma. Based on the computational results, the author predicted strong viscosity induced Shilnikov homoclinic chaos. In this Comment, it is shown that the dynamical system presented in the paper is inconsistent and incorrect because of an error in the expression of $\epsilon$. As a result, period-2, period-4, chaotic and homoclinic chaotic phenomena do not exist, which were observed in the paper.

We study the defect texture in symmetric and asymmetric states of a nematic-liquid-crystal shell with conic and planar degenerate surface anchorings on the inner and outer spherical boundaries, respectively. To achieve the equilibrium nematic orientation, we numerically minimize the Landau–de Gennes free energy by employing surface potentials on the shell walls. The symmetric nematic shells energetically have stable configurations independent of thickness. In thick shells, the director field satisfies bipolar and hexadecapolar configurations between boundaries. In thin shells, the boojums transform into two stable disclination curves.

Using the field-theoretic renormalization group approach and the operator product expansion technique in the second order of the corresponding perturbative expansion, the influence of finite-time correlations of the turbulent velocity field on the scaling properties of the magnetic field correlation functions as well as on the anisotropy persistence deep inside the inertial range are investigated in the framework of the generalized Kazantsev-Kraichnan model of kinematic magnetohydrodynamic turbulence. Explicit two-loop expressions for the scaling exponents of the single-time two-point correlation functions of the magnetic field are derived and it is shown that the presence of the finite-time velocity correlations has a nontrivial impact on their inertial-range behavior and can lead, in general, to significantly more pronounced anomalous scaling of the magnetic field correlation functions in comparison to the rapid-change limit of the model, especially for the most interesting three-dimensional case. Moreover, by analyzing the asymptotic behavior of appropriate dimensionless ratios of the magnetic field correlation functions, it is also shown that the presence of finite-time correlations of the turbulent velocity field has a strong impact on the large-scale anisotropy persistence deep inside the inertial interval. Namely, it leads to a significant enhancement of the anisotropy persistence, again, especially in three spatial dimensions.

The behavior of partially ionized hot compressed matter is critical to the study of planetary interiors as well as nuclear fusion studies. A recent quantum study of carbon in the 10–70 Gbar range and at a temperature of 100 eV used $N$-atom density functional theory (DFT) with $N\sim 32–64$ and molecular dynamics (MD). This involves band-structure-type electronic calculations and averaging over many MD-generated ion configurations. The calculated average number of free electrons per ion, viz., $\overline{Z}$, was systematically higher than from a standard average-atom quantum calculation. To clarify this offset, we examine the effect of the self-interaction error in such estimates and the possibility of carbon being in a granular plasma state containing Coulomb crystals with a magic number. The electrical conductivity, pressure, and compressibility of the carbon system are examined. The very low conductivity and the high-$\overline{Z}$ results of DFT MD point to the existence of carbon in a complex, nonuniform, low-conducting dispersed phase, possibly containing magic-number Coulomb crystals. The neutral pseudoatom estimate of $\overline{Z}$, conductivity, compressibility, and pressure reported here pertain to the uniform liquid.

We mimic random nanowire networks by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. The number density (the number of objects per unit area of the surface) of these sticks is supposed to exceed the percolation threshold, i.e., the system under consideration is a conductor. To identify any current-carrying part (the backbone) of the percolation cluster, we have proposed and implemented a modification of the well-known wall follower algorithm—one type of maze solving algorithm. The advantage of the modified algorithm is its identification of the whole backbone without visiting all the edges. The complexity of the algorithm depends significantly on the structure of the graph and varies from $O\left(\sqrt{N_{\text{V}}}\right)$ to $\mathrm{\Theta }\left(N_{\text{V}}\right)$. The algorithm has been applied to backbone identification in networks with different number densities of conducting sticks. We have found that (i) for number densities of sticks above the percolation threshold, the strength of the percolation cluster quickly approaches unity as the number density of the sticks increases; (ii) simultaneously, the percolation cluster becomes identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of degree 1. This behavior is consistent with the presented analytical evaluations.