Recently, a rigorous yet concise formula was derived to evaluate information flow, and hence the causality in a quantitative sense, between time series. To assess the importance of a resulting causality, it needs to be normalized. The normalization is achieved through distinguishing a Lyapunov exponent-like, one-dimensional phase-space stretching rate and a noise-to-signal ratio from the rate of information flow in the balance of the marginal entropy evolution of the flow recipient. It is verified with autoregressive models and applied to a real financial analysis problem. An unusually strong one-way causality is identified from IBM (International Business Machines Corporation) to GE (General Electric Company) in their early era, revealing to us an old story, which has almost faded into oblivion, about “Seven Dwarfs” competing with a giant for the mainframe computer market.

We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance $\eta$. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and Löwen [Phys. Rev. Lett. 91, 146101 (2003)], exhibits five different staggered phases as $\eta$ varies from 0 to intermediate values. We present a lattice summation method using the generalized Misra functions which permits us to calculate the energy per particle of the phases with a precision much higher than usual in computer simulations. This allows us to address some tiny details of the phase diagram. Going from the hexagonal phase I to phase II is shown to occur at $\eta =0$. All second-order phase transitions are proved to be of mean-field type. We also derive the asymptotic shape of critical lines close to the Coulomb and hard-spheres limits. In and close to the hard-spheres limit, the dependence of the internal parameters of the present phases on $\eta$ is determined exactly.

Gene expression is a stochastic process that affects cellular and population fitness. Noise in gene expression can enhance fitness by increasing cell to cell variability as well as the time cells spend in favorable expression states. Using a stochastic model of gene expression together with a fitness function that incorporates the costs and benefits of gene expression in a stressful environment, we show that the fitness landscape is shaped by gene expression noise in more complex ways than previously anticipated. We find that mutations modulating the properties of expression noise enable cell populations to optimize their position on the fitness landscape. Additionally, we find that low levels of expression noise evolve under conditions where the fitness benefits of expression exceed the fitness costs, and that high levels of expression noise evolve when the expression costs exceed the fitness benefits. The results presented in this study expand our understanding of the interplay between stochastic gene expression and fitness in selective environments.

We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of $N$ two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.

Molecular dynamics simulations are conducted to study the flow behavior of CsF solutions in nanochannels under external electric fields $E$. It is found that the channel surface energy greatly affects the flow behavior. In channels of high surface energy, water molecules, on average, move in the same direction as that of the electric field regardless of the strength of $E$. In low surface energy channels, however, water transports in the opposite direction to the electric field at weak $E$ and the flow direction is changed when $E$ becomes sufficiently large. The direction change of water flow is attributed to the coupled effects of different water-ion interactions, inhomogeneous water viscosity, and ion distribution changes caused by the electric field. The flow direction change observed in this work may be employed for flow control in complex micro- or nanofluidic systems.

Magnesium oxide has been experimentally and computationally investigated in the warm-dense solid and liquid ranges from 200 GPa to 1 TPa along the principal Hugoniot. The linear approximation between shock velocity and particle velocity is validated up to a shock velocity of 15 km/s from the experimental data, this suggesting that the MgO B1 structure is stable up to the corresponding shock pressure of $\sim 350$ GPa. Moreover, our Hugoniot data, combined with ab initio simulations, show two crossovers between MgO Hugoniot and the extrapolation of the linear approximation line, occurring at a shock pressures of approximately 350 and 650 GPa, with shock temperatures of 8000 and 14 000 K, respectively. These crossover regions are consistent with the solid-solid (B1-B2) and the solid-liquid (B2-melt) phase boundaries predicted by the ab initio calculations.

Distribution functions for systems in nonequilibrium steady states are usually determined through detailed experiments, both in numerical and real-life settings in the laboratory. However, for a protocol-driven distribution function, it is usually prohibitive to perform such detailed experiments for the entire range of the protocol. In this article we show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs to perform only a few detailed experiments to obtain the nonequilibrium distribution function for the entire gamut of nonlinearity. We achieve this by maximizing the relative entropy functional (MaxRent) subject to constraints supplied by the problem definition and new measurements. MaxRent is found to be superior to the principle of maximum entropy (MaxEnt), which maximizes Shannon's informational entropy for estimating distributions but lacks the ability to incorporate additional prior information. The MaxRent principle is illustrated using a toy model of ${\varphi }^4$ thermal conduction consisting of a single lattice point. An external protocol controlled position-dependent temperature field drives the system out of equilibrium. Two different thermostatting schemes are employed: the Hoover-Holian deterministic thermostat (which produces multifractal dynamics under strong nonlinearity) and the Langevin stochastic thermostat (which produces phase-space-filling dynamics). Out of the 80 possible states produced by the protocol, we assume that four states are known to us in detail, one of which is used as input into MaxRent at a time. We find that MaxRent approximates the phase-space density functions for every value of the protocol, even when they are far from the known distribution. MaxEnt, however, is unable to capture the fine details of the phase-space distribution functions. We expect this method to be useful in other external protocol-driven nonequilibrium cases as well, making it unnecessary to perform detailed experiments for all values of the protocol when one wishes to obtain approximate distributions.

We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of the intrinsic frequencies of oscillators. For a population of size $N$, we study two ways of sampling the intrinsic frequencies according to the same given unimodal distribution $g\left(\omega \right)$. In the “random” case, frequencies are generated independently in accordance with $g\left(\omega \right)$, which gives rise to oscillator number fluctuation within any given frequency interval. In the “regular” case, the $N$ frequencies are generated in a deterministic manner that minimizes the oscillator number fluctuations, leading to quasiuniformly spaced frequencies in the population. We find that the two samplings yield substantially different finite-size properties with clearly distinct scaling exponents. Moreover, the hyperscaling relation between the order parameter and its fluctuations is valid in the regular case, but it is violated in the random case. In this last case, a self-consistent mean-field theory that completely ignores dynamic fluctuations correctly predicts the FSS exponent of the order parameter but not its critical amplitude.

We propose a model for increasing liquid saturation in a granular packing, which can account for liquid redistribution at saturation levels beyond the well-studied capillary bridge regime. The model is capable of resolving and combining capillary bridges, menisci, and fully saturated pores to form local liquid clusters of any shape. They can exchange volume due to the local Laplace pressure gradient via a liquid film on the surfaces of grains. Local instabilities such as Haines jumps trigger the discontinuous evolution of the liquid front. The applicability of the model is demonstrated and compared to benchmark experiments on the level of individual liquid structures as well as on larger systems.

Gene expression is an inherently stochastic process that depends on the structure of the biochemical regulatory network in which the gene is embedded. Here we study the dynamical consequences of the interplay between stochastic gene switching and the widespread negative feedback regulatory loop in a simple model of a biochemical regulatory network. Using a simplified hybrid simulation approach, in which only the gene activation is modeled stochastically, we find that stochasticity in gene switching by itself can induce pulses in the system, providing also analytical insights into their origin. Furthermore, we find that this simple network is able to reproduce both exponential and peaked distributions of gene active and inactive times similar to those that have been observed experimentally. This simplified hybrid simulation approach also allows us to link these patterns to the dynamics of the system for each gene state.

While the wing kinematics of many flapping insects have been well characterized, understanding the underlying sensory, neural, and physiological mechanisms that determine these kinematics is still a challenge. Two main difficulties in understanding the physiological mechanisms arise from the complexity of the interaction between a flapping wing and its own unsteady flow, as well as the intricate mechanics of the insect wing hinge, which is among the most complicated joints in the animal kingdom. These difficulties call for the application of reduced-order approaches. Here this strategy is used to model the torques exerted by the wing hinge along the wing-pitch axis of maneuvering fruit flies as a damped torsional spring with elastic and damping coefficients as well as a rest angle. Furthermore, we model the air flows using simplified quasistatic aerodynamics. Our findings suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters. The damped torsional-spring model explains the changes measured in wing-pitch kinematics during roll correction maneuvers through modulation of the spring damping and elastic coefficients. These results, in conjunction with the previous literature, indicate that flies can accurately control their wing-pitch kinematics on a sub-wing-beat time scale by modulating all three effective spring parameters on longer time scales.

The bifurcation sets of symmetric and asymmetric periodically driven oscillators are investigated and classified by means of winding numbers. It is shown that periodic windows within chaotic regions are forming winding-number sequences on different levels. These sequences can be described by a simple formula that makes it possible to predict winding numbers at bifurcation points. Symmetric and asymmetric systems follow similar rules for the development of winding numbers within different sequences and these sequences can be combined into a single general rule. The role of the two distinct period-doubling cascades is investigated in the light of the winding-number sequences discovered. Examples are taken from the double-well Duffing oscillator, a special two-parameter Duffing oscillator, and a bubble oscillator.

Systems of particles interacting with “stealthy” pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like “pseudo” disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperature limit. Our techniques may be applied to sample the zero-temperature limit of the canonical ensemble of other potentials with highly degenerate ground states.

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in $d$-dimensional Euclidean space ${\mathbb{R}}^d$. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.

We construct a one-dimensional totally asymmetric simple exclusion process (TASEP) on a ring with two segments having unequal hopping rates, coupled to particle nonconserving Langmuir kinetics (LK) characterized by equal attachment and detachment rates. In the steady state, in the limit of competing LK and TASEP, the model is always found in states of phase coexistence. We uncover a nonequilibrium phase transition between a three-phase and a two-phase coexistence in the faster segment, controlled by the underlying inhomogeneity configurations and LK. The model is always found to be half-filled on average in the steady state, regardless of the hopping rates and the attachment-detachment rate.

We investigate the development of electro-osmotic (Teorell) oscillations at a weakly charged microporous membrane without a preimposed transmembrane electrolyte concentration drop. This drop, necessary for the occurrence of oscillations, develops spontaneously as a result of concentration polarization in the solution layers adjacent to the membrane. A three-layer model comprising a membrane flanked by two diffusion layers is proposed and analyzed for galvano- and potentiostatic regimes of operation.

In medical imaging and porous media research, NMR diffusion measurements are extensively used to investigate the structure of diffusion restrictions such as cell membranes. Recently, several methods have been proposed to unambiguously determine the shape of arbitrary closed pores or cells filled with an NMR-visible medium by diffusion experiments. The first approach uses a combination of a long and a short diffusion-weighting gradient pulse, while the other techniques employ short gradient pulses only. While the eventual aim of these methods is to determine pore-size and shape distributions, the focus has been so far on identical pores. Thus, the aim of this work is to investigate the ability of these different methods to resolve pore-size and orientation distributions. Simulations were performed comparing the various pore imaging techniques employing different distributions of pore size and orientation and varying timing parameters. The long-narrow gradient profile is most advantageous to investigate pore distributions, because average pore images can be directly obtained. The short-gradient methods suppress larger pores or induce a considerable blurring. Moreover, pore-shape-specific artifacts occur; for example, the central part of a distribution of cylinders may be largely underestimated. Depending on the actual pore distribution, short-gradient methods may nonetheless yield good approximations of the average pore shape. Furthermore, the application of short-gradient methods can be advantageous to differentiate whether pore-size distributions or intensity distributions, e.g., due to surface relaxation, are predominant.

Toroid formation is an important mechanism for DNA condensation in cells. The length change during DNA condensation was investigated in previous single-molecule experiments. However, DNA twist is key to understanding the topological kinetics of DNA condensation. In this study, DNA twist as well as DNA length was traced during the DNA condensation by the freely orbiting magnetic tweezers and the tilted magnetic tweezers combined with Brownian dynamics simulations. The experimental results disclose the complex relationship between DNA extension and backbone rotation. Brownian dynamics simulations show that the toroid formation follows a wiggling pathway which leads to the complex DNA backbone rotation as revealed in our experiments. These findings provide the complete description of multivalent cation-dependent DNA toroid formation under tension.

While several in vitro experiments on viral genome release have specifically studied the effects of external osmotic pressure and of the presence of polyvalent cations on the ejection of DNA from bacteriophages, few have systematically investigated how the extent of ejection is controlled by a combination of these effects. In this work we quantify the effect of osmotic pressure on the extent of DNA ejection from bacteriophage lambda as a function of polyvalent cation concentration (in particular, the tetravalent polyamine spermine). We find that the pressure required to completely inhibit ejection decreases from 38 to 17 atm as the spermine concentration is increased from 0 to 1.5 mM. Further, incubation of the phage particles in spermine concentrations as low as 0.15 mM—the threshold for DNA condensation in bulk solution—is sufficient to significantly limit the extent of ejection in the absence of osmolyte; for spermine concentrations below this threshold, the ejection is complete. In accord with recent investigations on the packaging of DNA in the presence of a condensing agent, we observe that the self-attraction induced by the polyvalent cation affects the ordering of the genome, causing it to get stuck in a broad range of nonequilibrated structures.

We propose a reaction-advection-diffusion model of epidermis consisting of two variables, the degree of differentiation and the calcium ion concentration, where calcium ions enhance differentiation. By analytically and numerically investigating this system, we show that a calcium localization layer formed beneath the stratum corneum helps reduce spatiotemporal fluctuations of the structure of the stratum corneum. In particular, spatially or temporally small-scale fluctuations in the lower structure are suppressed and do not affect the upper structure, due to acceleration of differentiation by calcium ions. Analytical expressions for the reduction rate of fluctuation amplitudes are shown.