The phase diagram of the ground states of DNA in a bad solvent is studied for a semiflexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter $x$ and effective self-attraction promoting compaction. $x=1$ corresponds to the wormlike chain model. Surprisingly, the phase diagram as well as the transition lines between the ground states are found to be a function of $x$. The model provides a simple explanation for the results of prior experimental and computational studies and makes predictions for the specific geometries of the ground states. The results underscore the impact of the form of the microscopic bending energy at macroscopic observable scales.

We present a lattice Boltzmann model (LBM) that covers the entire range of fluid flows, from low Mach weakly compressible to transonic and supersonic flows. One of the most restrictive limitations of the lattice Boltzmann method, the low Mach number limit, is overcome here by three fundamental changes to the LBM scheme: use of an appropriately chosen multispeed lattice, accurate evaluation of the equilibrium, and the entropic relaxation for the collision. The range of applications is demonstrated through the simulation of a bow shock in front of an airfoil and the simulation of decaying compressible turbulence with shocklets.

We derive the quantum Langevin equation (QLE) for a harmonically single trapped cold atom subjected to artificial non-Abelian gauge potentials and linearly coupled to a heat bath. The independent-oscillator (IO) and the momentum-momenta coupling models are studied. In each case, the non-Abelian effect on the QLE is pointed out for a $\text{U}\left(2\right)$ gauge transformation. For the IO model, only the generalized Lorentz force is modified by the appearance of an additive term. For the momentum-momenta coupling model, the generalized Lorentz force as well as the friction force are subjected to modifications. The dependence of the system on the magnetic field is explicit even if the gauge potential is uniform in space.

Thermal fluctuations can play an important role in the buckling of elastic objects at small scales, such as polymers or nanotubes. In this paper, we study the finite-temperature buckling transition of an extensible rod by analyzing fluctuation corrections to the elasticity of the rod. We find that, in both two and three dimensions, thermal fluctuations delay the buckling transition, and near the transition, there is a critical regime in which fluctuations are prominent and make a contribution to the effective force that is of order $\sqrt{T}$. We verify our theoretical prediction of the phase diagram with Monte Carlo simulations.

Using the Monte Carlo simulation, we study the percolation and jamming of oriented linear $k$-mers on a square lattice that contains defects. The point defects with a concentration $d$ are placed randomly and uniformly on the substrate before deposition of the $k$-mers. The general case of unequal probabilities for orientation of depositing of $k$-mers along different directions of the lattice is analyzed. Two different relaxation models of deposition that preserve the predetermined order parameter $s$ are used. In the relaxation random sequential adsorption (RRSA) model, the deposition of $k$-mers is distributed over different sites on the substrate. In the single-cluster relaxation (RSC) model, the single cluster grows by the random accumulation of $k$-mers on the boundary of the cluster (Eden-like model). For both models, a suppression of growth of the infinite (percolation) cluster at some critical concentration of defects $d_c$ is observed. In the zero-defect lattices, the jamming concentration $p_j$ (RRSA model) and the density of single clusters $p_s$ (RSC model) decrease with increasing length $k$-mers and with a decrease in the order parameter. For the RRSA model, the value of $d_c$ decreases for short $k$-mers $\left(k<16\right)$ as the value of $s$ increases. For $k=16$ and 32, the value of $d_c$ is almost independent of $s$. Moreover, for short $k$-mers, the percolation threshold is almost insensitive to the defect concentration for all values of $s$. For the RSC model, the growth of clusters with ellipselike shapes is observed for nonzero values of $s$. The density of the clusters $p_s$ at the critical concentration of defects $d_c$ depends in a complex manner on the values of $s$ and $k$. An interesting finding for disordered systems $(s=0)$ is that the value of $p_s$ tends towards zero in the limits of the very long $k$-mers, $k\to \infty$, and very small critical concentrations $d_c\to 0$. In this case, the introduction of defects results in a suppression of $k$-mer stacking and in the formation of empty or loose clusters with very low density. On the other hand, denser clusters are formed for ordered systems with $p_s\approx 0.065$ at $s=0.5$ and $p_s\approx 0.38$ at $s=1.0$.

This paper presents a theoretical framework for analyzing the quantum fluctuation properties of a quantum spin chain subject to a quantum phase transition. We can quantify the fluctuation properties by examining the correlation between the fluctuations of two neighboring spins subject to the quantum uncertainty. To do this, we first compute the reduced density matrix ρ of the spin pair from the ground state |Ψ⟩ of a spin chain, and then identify the quantum correlation part ${\rho }_q$ embedded in ρ. If the spin chain is translationally symmetric and characterized by a nearest-neighbor two-body spin interaction, we can determine uniquely the form of ${\rho }_q$ as $W|\mathrm{\Phi }\rangle \langle \mathrm{\Phi }|$ with the weight $W$ $\le 1$, and quantify the fluctuation properties using the two-spin entangled state $|\mathrm{\Phi }\rangle$. We demonstrate the framework for a transverse-field quantum Ising spin chain and indicate its validity for more general spin chain models.

The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases, which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations—often referred to as the blockade radius—is not a static but rather a dynamic quantity.

Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped two-dimensional system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single-particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.

We show the effects of simulated supersonic granular flow made up of smooth particles passing over two prototypical bodies: a wedge and a disk. We describe a way of computationally identifying shock wave locations in granular flows and tabulate the shock wave locations for flow over wedges and disks. We quantify the shock structure in terms of oblique shock angle for wedge impediments and shock standoff distance for disk impediments. We vary granular flow parameters including upstream volume fraction, average upstream velocity, granular temperature, and the collision coefficient of restitution. Both wedges and disks have been used in the aerospace community as prototypical impediments to flowing air in order to investigate the fundamentally different shock structures emanating from sharp and blunt bodies, and we present these results in order to increase the understanding of the fundamental behavior of supersonic granular flow.

Irreversible one-dimensional (1D) epitaxial growth at small coverages via the recently suggested two-step growth protocol [Tokar and Dreyssé, Surf. Sci. 637-638, 116 (2015)] has been studied with the use of the kinetic Monte Carlo and the rate-equation techniques. It has been found that similar to the two-dimensional (2D) case the island capture zones could be accurately approximated with the Gamma probability distribution (GD). Coverage independence of the average island sizes grown at the first step that was also found in two dimensions was observed. In contrast to 2D case, the shape parameter of the GD was also found to be coverage-independent. Using these two constants as the input, an analytical approach that allowed for the description of the commonly studied statistical distributions to the accuracy of about 2% has been developed. Furthermore, it was established that the distributions of the island sizes and the interisland gaps grown via the two-step protocol were about 50% narrower than in the case of nucleation on random defects, which can be of practical importance. Equivalence between the GD shape of the island size distribution in the scaling regime and the linear dependence of the capture numbers on the island size in the rate-equation approach has been proved.

We consider the interaction between nematic liquid crystals (NLCs) and polymer substrates. Such substrates can interact with NLCs, exhibiting a phenomenon known as director gliding: the preferred orientation of the NLC molecules at the interface changes on time scales that are slow relative to the elastic relaxation time scale of the NLC. We present two models for gliding, inspired by experiments that investigate the interaction between the NLC and a polymer substrate. These models, though simple, lead to nontrivial results, including loss of bistability under gliding. Perhaps surprisingly, we find that externally imposed switching between the steady states of a bistable system may reverse the effect of gliding, preventing loss of bistability if switching is sufficiently frequent. Our findings may be of relevance to a variety of technological applications involving liquid crystal devices, and particularly to a new generation of flexible liquid crystal displays that implement polymeric substrates.

In the present paper, we have studied dynamics and relaxation of the charge carriers in polymethylmethacrylate-lithium bis(trifluoromethane sulfonyl)imide polymer electrolytes embedded with 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide ionic liquid. We have analyzed the frequency dependent conductivity spectra using the random free-energy barrier model coupled with the contribution of electrode polarization in the low frequency region. The temperature dependence of ionic conductivity, and relaxation time obtained from the analysis of the spectra exhibits Vogel-Tammann-Fulcher type behavior. The Barton-Nakajima-Namikawa relation is consistent with the results obtained from the random free-energy barrier model. The scaling of ac conductivity spectra has been performed to understand the effect of temperature as well as the composition on the relaxation mechanism. The analysis of the ac conductivity also clearly indicates the existence of a nearly constant loss phenomenon at low temperatures or at high frequencies.

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

We study the performance of the euro–Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Target zones and exchange rate dynamics, Q. J. Econ. 106, 669 (1991)]. We present direct quantitative empirical evidence that Krugman's theoretical model provides an accurate description of the euro–Swiss franc target zone. Motivated by the insights from the economic model, we revise the initial economics-physics analogy and show that, within the context of hindered diffusion, the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.

Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer aimed at decompositions of predictive information about a target variable, while excluding effects of common drivers and indirect influences. While common drivers clearly constitute a spurious causality, the aim of the present article is to develop measures quantifying different notions of the strength of information transfer along indirect causal paths, based on first reconstructing the multivariate causal network. Another class of novel measures quantifies to what extent different intermediate processes on causal paths contribute to an interaction mechanism to determine pathways of causal information transfer. The proposed framework complements predictive decomposition schemes by focusing more on the interaction mechanism between multiple processes. A rigorous mathematical framework allows for a clear information-theoretic interpretation that can also be related to the underlying dynamics as proven for certain classes of processes. Generally, however, estimates of information transfer remain hard to interpret for nonlinearly intertwined complex systems. But if experiments or mathematical models are not available, then measuring pathways of information transfer within the causal dependency structure allows at least for an abstraction of the dynamics. The measures are illustrated on a climatological example to disentangle pathways of atmospheric flow over Europe.

When an integrable classical system is perturbed, nonlinear resonances are born, grow, and eventually disappear due to chaos. In this paper the quantum manifestations of such a transition are studied in the standard map. We show that nonlinear resonances act as a perturbation that break eigenphase degeneracies for unperturbed states with quantum numbers that differ in a multiple of the order of the resonance. We show that the eigenphase splittings are well described by a semiclassical expression based on an integrable approximation of the Hamiltonian in the vicinity of the resonance. The morphology in phase space of these states is also studied. We show that the nonlinear resonance imprints a systematic influence in their localization properties

Chimera states are complex spatiotemporal patterns in networks of identical oscillators, characterized by the coexistence of synchronized and desynchronized dynamics. Here we propose to extend the phenomenon of chimera states to the quantum regime, and uncover intriguing quantum signatures of these states. We calculate the quantum fluctuations about semiclassical trajectories and demonstrate that chimera states in the quantum regime can be characterized by bosonic squeezing, weighted quantum correlations, and measures of mutual information. Our findings reveal the relation of chimera states to quantum information theory, and give promising directions for experimental realization of chimera states in quantum systems.

The ubiquity of power-law relations in empirical data displays physicists' love of simple laws and uncovering common causes among seemingly unrelated phenomena. However, many reported power laws lack statistical support and mechanistic backings, not to mention discrepancies with real data are often explained away as corrections due to finite size or other variables. We propose a simple experiment and rigorous statistical procedures to look into these issues. Making use of the fact that the occurrence rate and pulse intensity of crumple sound obey a power law with an exponent that varies with material, we simulate a complex system with two driving mechanisms by crumpling two different sheets together. The probability function of the crumple sound is found to transit from two power-law terms to a bona fide power law as compaction increases. In addition to showing the vicinity of these two distributions in the phase space, this observation nicely demonstrates the effect of interactions to bring about a subtle change in macroscopic behavior and more information may be retrieved if the data are subject to sorting. Our analyses are based on the Akaike information criterion that is a direct measurement of information loss and emphasizes the need to strike a balance between model simplicity and goodness of fit. As a show of force, the Akaike information criterion also found the Gutenberg-Richter law for earthquakes and the scale-free model for a brain functional network, a two-dimensional sandpile, and solar flare intensity to suffer an excessive loss of information. They resemble more the crumpled-together ball at low compactions in that there appear to be two driving mechanisms that take turns occurring.

The refined similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermittent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number $R_{\lambda }\sim 650$, on a periodic box of ${4096}^3$ grid points to test the hypotheses using three-dimensional averages. In particular, we study the small-scale properties of the stochastic variable $V=\mathrm{\Delta }u\left(r\right)/{\left(r{\epsilon }_r\right)}^{1/3}$, where $\mathrm{\Delta }u\left(r\right)$ is the longitudinal velocity increment and ${\epsilon }_r$ is the dissipation rate averaged over a three-dimensional volume of linear size $r$. We show that $V$ is universal in the inertial subrange. In the dissipation range, the statistics of $V$ are shown to depend solely on a local Reynolds number.

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.