We extend the well-known static duality [M. Girardeau, J. Math. Phys. 1, 516 (1960); T. Cheon and T. Shigehara, Phys. Rev. Lett. 82, 2536 (1999)] between one-dimensional (1D) bosons and 1D fermions to the dynamical version. By utilizing this dynamical duality, we find the duality of nonequilibrium work distributions between interacting 1D bosonic (Lieb-Liniger model) and 1D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau gas is identical to that of 1D noninteracting fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1D noninteracting distinguishable particles, although their elementary excitations (quasiparticles) obey different statistics, e.g., the Bose-Einstein, the Fermi-Dirac, and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.

Driven particles in the presence of crowded environment, obstacles, or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. Based on the empirical studies of conserved lattice gas model, two species exclusion model and other interacting particle systems we propose a new mechanism for complex many-particle systems where slowing down of certain non-driven degrees of freedom by the external field can give rise to NDM. To prove that the slowing down of the non-driven degrees is indeed the underlying cause, we consider several driven diffusive systems including two species exclusion models, misanthrope process, and show from the exact steady state results that NDM indeed appears when some non-driven modes are slowed down deliberately. For clarity, we also provide a simple pedagogical example of two interacting random walkers on a ring which conforms to the proposed scenario.

We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.

We introduce and study a one dimensional model of classical planar spins interacting self-consistently through magnetic field. The spins and the magnetic field evolve in time according to the Hamiltonian dynamics which mimics that of a free electron laser. We show that by rescaling the energy due to magnetic field inhomogeneity, in equilibrium, this system can be mapped onto a model very similar to the paradigmatic globally coupled Hamiltonian mean-field (HMF) model. The system exhibits a continuous equilibrium phase transition from paramagnetic to ferromagnetic phase, however unlike HMF, we do not see any magnetized quasistationary states.

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one-dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed.

This paper reveals the effect of fractional Gaussian noise with Hurst exponent $H\in (1/2,1)$ on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent $H\in (1/2,1)$ could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

Complex networks are often used to represent systems that are not static but grow with time: People make new friendships, new papers are published and refer to the existing ones, and so forth. To assess the statistical significance of measurements made on such networks, we propose a randomization methodology—a time-respecting null model—that preserves both the network's degree sequence and the time evolution of individual nodes' degree values. By preserving the temporal linking patterns of the analyzed system, the proposed model is able to factor out the effect of the system's temporal patterns on its structure. We apply the model to the citation network of Physical Review scholarly papers and the citation network of US movies. The model reveals that the two data sets are strikingly different with respect to their degree-degree correlations, and we discuss the important implications of this finding on the information provided by paradigmatic node centrality metrics such as indegree and Google's PageRank. The randomization methodology proposed here can be used to assess the significance of any structural property in growing networks, which could bring new insights into the problems where null models play a critical role, such as the detection of communities and network motifs.

Measurement of the lifetime of attachments formed by a single microtubule (MT) with a single kinetochore (kt) in vitro under force-clamp conditions had earlier revealed a catch-bond-like behavior. In the past, the physical origin of this apparently counterintuitive phenomenon was traced to the nature of the force dependence of the (de)polymerization kinetics of the MTs. Here, first the same model MT-kt attachment is subjected to external tension that increases linearly with time until rupture occurs. In our force-ramp experiments in silico, the model displays the well known “mechanical signatures” of a catch bond probed by molecular force spectroscopy. Exploiting this evidence, we have further strengthened the analogy between MT-kt attachments and common ligand-receptor bonds in spite of the crucial differences in their underlying physical mechanisms. We then extend the formalism to model the stochastic kinetics of an attachment formed by a bundle of multiple parallel microtubules with a single kt considering the effect of rebinding under force-clamp and force-ramp conditions. From numerical studies of the model we predict the trends of variation of the mean lifetime and mean rupture force with the increasing number of MTs in the bundle. Both the mean lifetime and the mean rupture force display nontrivial nonlinear dependence on the maximum number of MTs that can attach simultaneously to the same kt.

The origin of multicellularity in metazoa is one of the fundamental questions of evolutionary biology. We have modeled the generic behaviors of gene regulatory networks in isogenic cells as stochastic nonlinear dynamical systems—coupled Boolean networks with perturbation. Model simulations under a variety of dynamical regimes suggest that the central characteristic of multicellularity, permanent spatial differentiation (diversification), indeed can arise. Additionally, we observe that diversification is more likely to occur near the critical regime of Lyapunov stability.

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the $D=2.33$ fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale. Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conventional quantum particles. This causes unusual phase-space dynamics that is typically not captured by the WKE. We demonstrate how to correctly model this dynamics with the WME instead. Specifically, we report full-wave phase-space simulations of the zonal-flow formation (zonostrophic instability), deterioration (tertiary instability), and the so-called predator-prey oscillations. We also show how the WME facilitates analysis of these phenomena, namely, (i) we show that full-wave effects critically affect the zonostrophic instability, particularly its nonlinear stage and saturation; (ii) we derive the tertiary-instability growth rate; and (iii) we demonstrate that, with full-wave effects retained, the predator-prey oscillations do not require zonal-flow collisional damping, contrary to previous studies. We also show how the famous Rayleigh-Kuo criterion, which has been missing in wave-kinetic theories of drift-wave turbulence, emerges from the WME.

The need of small integration time steps ($\sim 1$ fs) in conventional molecular dynamics simulations is an important issue that inhibits the study of physical, chemical, and biological systems in real timescales. Additionally, to simulate those systems in contact with a thermal bath, thermostating techniques are usually applied. In this work, we generalize the Green's function molecular dynamics technique to allow simulations within the canonical ensemble. By applying this technique to one-dimensional systems, we were able to correctly describe important thermodynamic properties such as the temperature fluctuations, the temperature distribution, and the velocity autocorrelation function. We show that the proposed technique also allows the use of time steps one order of magnitude larger than those typically used in conventional molecular dynamics simulations. We expect that this technique can be used in long-timescale molecular dynamics simulations.

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade $p_f$ as a function of the strength of the initial attack, measured by the fraction of nodes $p$ that survive the initial attack for different values of tolerance $\alpha$ in random regular and Erdös-Renyi graphs. We find the existence of a first-order phase-transition line $p_t\left(\alpha \right)$ on a $p-\alpha$ plane, such that if $p<p_t$, the cascade of failures leads to a very small fraction of survived nodes $p_f$ and the giant component of the network disappears, while for $p>p_t, p_f$ is large and the giant component of the network is still present. Exactly at $p_t$, the function $p_f\left(p\right)$ undergoes a first-order discontinuity. We find that the line $p_t\left(\alpha \right)$ ends at a critical point $(p_c,{\alpha }_c)$, in which the cascading failures are replaced by a second-order percolation transition. We find analytically the average betweenness of nodes with different degrees before and after the initial attack, we investigate their roles in the cascading failures, and we find a lower bound for $p_t\left(\alpha \right)$. We also study the difference between localized and random attacks.

Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form, and linear stability of frequency synchronization in such oscillator networks. The model takes into account a broad class of heterogeneous connection structures and identifies a functional form as well as basic properties that synchronized regimes possess classwide. The framework also captures synchronized regimes with large phase differences that commonly appear just above the critical threshold. Additionally, the accuracy of mean-field assumptions can be gauged internally through two model quantities. With our framework, the impact of local grid structure on frequency synchronization can be systematically explored.

This paper presents an approach to solving the phase problem in nuclear magnetic resonance (NMR) diffusion pore imaging, a method that allows imaging the shape of arbitrary closed pores filled with an NMR-detectable medium for investigation of the microstructure of biological tissue and porous materials. Classical $q$-space imaging composed of two short diffusion-encoding gradient pulses yields, analogously to diffraction experiments, the modulus squared of the Fourier transform of the pore image which entails an inversion problem: An unambiguous reconstruction of the pore image requires both magnitude and phase. Here the phase information is recovered from the Fourier modulus by applying a phase retrieval algorithm. This allows omitting experimentally challenging phase measurements using specialized temporal gradient profiles. A combination of the hybrid input-output algorithm and the error reduction algorithm was used with dynamically adapting support (shrinkwrap extension). No a priori knowledge on the pore shape was fed to the algorithm except for a finite pore extent. The phase retrieval approach proved successful for simulated data with and without noise and was validated in phantom experiments with well-defined pores using hyperpolarized xenon gas.

The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied. It is found that the properties of the two species' isoclines determine the interaction of species, leading to six regimes in the phase diagram of interspecies interaction; i.e., there are six different interspecific relationships described by the LV model. Four regimes allow for nontrivial species coexistence, among which it is found that three of them are stable, namely, weak competition, mutualism, and predator-prey scenarios can lead to win-win coexistence situations. The Lyapunov function for general nontrivial two-species coexistence is also constructed. Furthermore, in the presence of spatial diffusion of the species, the dynamics can lead to steady wavefront propagation and can alter the population map. Propagating wavefront solutions in one dimension are investigated analytically and by numerical solutions. The steady wavefront speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. In addition to the inter- and intraspecific interaction parameters, the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. In some regimes, both species can copropagate with the same wave speeds in a finite range of parameters. Our results are further discussed in the light of possible biological relevance and ecological implications.