Many intramolecular electron transfer (ET) reactions in biology are mediated by metal centers in proteins. This process is commonly described by a model of diffusive hopping according to the semiclassical theories of Marcus and Hopfield. However, recent studies have raised the possibility that nontrivial quantum mechanical effects play a functioning role in certain biomolecular processes. Here, we investigate the potential effects of quantum coherence in biological ET by extending the semiclassical model to allow for the possibility of quantum coherent phenomena using a quantum master equation based on the Holstein Hamiltonian. We test the model on the structurally defined chain of seven iron-sulfur clusters in nicotinamide adenine dinucleotide plus hydrogen:ubiquinone oxidoreductase (complex I), a crucial respiratory enzyme and one of the longest chains of metal centers in biology. Using experimental parameters where possible, we find that, in limited circumstances, a small quantum mechanical contribution can provide a marked increase in the ET rate above the semiclassical diffusive-hopping rate. Under typical biological conditions, our model reduces to well-known diffusive behavior.

We take a single-level quantum dot embedded between two metallic leads at different temperatures and chemical potentials which works as a heat engine. Two optimization criteria were used and their corresponding optimized efficiencies, powers, and periods evaluated. A comparison between similar quantities of the two optimization criteria reveals mixed advantages and disadvantages. We quantify the engine's overall performance by suggesting a figure of merit that takes into account the contribution of each of the three quantities. Based on the proposed figure of merit, one of the optimization criterion presents a clear advantage. This same criterion is found to be invariably advantageous when applied to three other representative models.

Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers.

A method is proposed for determining dynamical and observational noise parameters in state and parameter identification from time series using Kalman filters. The noise covariances are estimated in a secondary optimization by maximizing the predictive likelihood of the data. The approach is based on internal consistency; for the correct noise parameters, the uncertainty projected by the Kalman filter matches the actual predictive uncertainty. The method is able to disentangle dynamical and observational noise. The algorithm is demonstrated for the linear, extended, and unscented Kalman filters using an Ornstein-Uhlenbeck process, the noise-driven Lorenz system, and van der Pol oscillator as well as a paleoclimatic ice-core record as examples. The approach is also applicable to the ensemble Kalman filter and can be readily extended to non-Gaussian estimation frameworks such as Gaussian-sum filters and particle filters.

Numerical simulations of bubble pulsation and sonoluminescence (SL) have been performed for helium or xenon bubbles in mercury and water under the experimental conditions of Futakawa et al. [M. Futakawa, T. Naoe, and M. Kawai, in Nonlinear Acoustics—Fundamentals and Applications: 18th International Symposium on Nonlinear Acoustics (ISNA 18), AIP Conf. Proc. No. 1022, edited by B. O. Enflo, C. M. Hedberg, and L. Kari (AIP, New York, 2008), p. 197]. The results of the numerical simulations have revealed that the bubble expansion is much larger in water than in mercury mainly because the density of water is one order of magnitude smaller than that of mercury. The SL intensity is higher in water than that in mercury although the maximum bubble temperature is lower. This is caused by the much larger amount of vapor inside a bubble as the saturated vapor pressure of water is four orders of magnitude larger than that of mercury at room temperature. The SL intensity from xenon is much larger than that from helium due both to lower ionization potential and higher bubble temperature due to lower thermal conductivity. The instantaneous SL power may be as large as 200 W from xenon in water. The maximum temperature inside a xenon bubble in mercury may be as high as about 80 000 K. It is suggested that the maximum pressure in mercury due to shock waves emitted from bubbles increases as the SL intensity increases, although they are not simply correlated in water because the amount of water vapor trapped inside a bubble influences the SL intensity in a complex way.

The average-atom model is applied to study Thomson scattering of x-rays from warm dense matter with emphasis on scattering by bound electrons. Parameters needed to evaluate the dynamic structure function (chemical potential, average ionic charge, free electron density, bound and continuum wave functions, and occupation numbers) are obtained from the average-atom model. The resulting analysis provides a relatively simple diagnostic for use in connection with x-ray scattering measurements. Applications are given to dense hydrogen, beryllium, aluminum, and titanium plasmas. In the case of titanium, bound states are predicted to modify the spectrum significantly.

We introduce a discrete linear lossy system with an embedded “hot spot” (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective excitation of particular cores is possible. Localized modes pinned to the HS are constructed in an implicit analytical form, and their stability is investigated numerically. Stability regions for the modes are obtained in the parameter space of the linear gain and cubic gain or loss. An essential result is that the interaction of the unsaturated cubic gain and self-defocusing nonlinearity can produce stable modes, although they may be destabilized by finite-amplitude perturbations. On the other hand, the interplay of the cubic loss and self-defocusing gives rise to a bistability.

Berezhkovskii and co-workers introduced the concept of local accumulation time as a finite measure of the time required for the transient solution of a reaction-diffusion equation to effectively reach steady state [Biophys J. 99, L59 (2010); Phys. Rev. E 83, 051906 (2011)]. Berezhkovskii's approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb [IMA J. Appl. Math. 47, 193 (1991)]. Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time, the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one-dimensional linear advection-diffusion-reaction partial differential equation (PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random-walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.

We study information geometry of the Dicke model, in the thermodynamic limit. The scalar curvature $R$ of the Riemannian metric tensor induced on the parameter space of the model is calculated. We analyze this both with and without the rotating wave approximation, and show that the parameter manifold is smooth even at the phase transition, and that the scalar curvature is continuous across the phase boundary.

We study heat conduction in a billiard channel formed by two sinusoidal walls and the diffusion of particles in the corresponding channel of infinite length; the latter system has an infinite horizon, i.e., a particle can travel an arbitrary distance without colliding with the rippled walls. For small ripple amplitudes, the dynamics of the heat carriers is regular and analytical results for the temperature profile and heat flux are obtained using an effective potential. The study also proposes a formula for the temperature profile that is valid for any ripple amplitude. When the dynamics is regular, ballistic conductance and ballistic diffusion are present. The Poincaré plots of the associated dynamical system (the infinitely long channel) exhibit the generic transition to chaos as ripple amplitude is increased. When no Kolmogorov-Arnold-Moser (KAM) curves are present to forbid the connection of all chaotic regions, the mean square displacement grows asymptotically with time $t$ as $t\text{ln}\left(t\right)$.

Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This $U$ shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a $U$ shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated.

Critical behavior of soft repulsive particles after quench of temperature near the jamming transition is numerically investigated. It is found that the plateau of the mean-square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.

By performing Monte Carlo sampling of $N$-steps self-avoiding polygons embedded on different Bravais lattices we explore the robustness of universality in the entropic, metric, and geometrical properties of knotted polymer rings. In particular, by simulating polygons with $N$ up to ${10}^5$ we furnish a sharp estimate of the asymptotic values of the knot probability ratios and show their independence on the lattice type. This universal feature was previously suggested, although with different estimates of the asymptotic values. In addition, we show that the scaling behavior of the mean-squared radius of gyration of polygons depends on their knot type only through its correction to scaling. Finally, as a measure of the geometrical self-entanglement of the self-avoiding polygons we consider the standard deviation of the writhe distribution and estimate its power-law behavior in the large $N$ limit. The estimates of the power exponent do depend neither on the lattice nor on the knot type, strongly supporting an extension of the universality property to some features of the geometrical entanglement.

We demonstrate using neutron reflectometry that the internal interfaces in a trilayer system of two identical thick polystyrene layers sandwiching a much thinner (deuterated) poly(methyl methacrylate) layer 15 nm thick (viscosity matched with the polystyrene layers) increase in roughness at the same rate. When the lower polystyrene layer is replaced with a layer of the same polymer of much greater molecular mass, two different growths of the interfaces are observed. From the growth of the interface for this asymmetric case in the solid regime using the theoretical prediction of the spinodal instability including slippage at the interface, a value of the Hamaker constant of the system has been extracted in agreement with the calculated value. For the symmetric case the rise time of the instability is much faster.

The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semiannealed approximation to study the stability properties of random Boolean networks in multiplex (multilayered) graphs. Our main finding is that the multilevel structure provides a mechanism for the stabilization of the dynamics of the whole system even when individual layers work on the chaotic regime, therefore identifying new ways of feedback between the structure and the dynamics of these systems. Our results point out the need for a conceptual transition from the physics of single-layered networks to the physics of multiplex networks. Finally, the fact that the coupling modifies the phase diagram and the critical conditions of the isolated layers suggests that interdependency can be used as a control mechanism.

The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small velocities uniform acceleration takes place, and at a later stage fluctuations of the potential are encountered, resulting in a regime of anomalous diffusion. This regime was studied in the framework of the Fokker-Planck approximation. The diffusion coefficient in velocity was expressed in terms of the average power spectral density, which is the Fourier transform of the potential correlation function. This enabled to establish a scaling form for the Fokker-Planck equation and to compute the large and small velocity limits of the diffusion coefficient. A classification of the random potentials into universality classes, characterized by the form of the diffusion coefficient in the limit of large and small velocity, was performed. It was shown that one-dimensional systems exhibit a large variety of universality classes, contrary to systems in higher dimensions, where only one universality class is possible. The relation to Chirikov resonances, which are central in the theory of chaos, was demonstrated. The general theory was applied and numerically tested for specific physically relevant examples.

We study the transport of energy in a finite linear harmonic chain by solving the Heisenberg equation of motion, as well as by using nonequilibrium Green's functions to verify our results. The initial state of the system consists of two separate and finite linear chains that are in their respective equilibriums at different temperatures. The chains are then abruptly attached to form a composite chain. The time evolution of the current from just after switch-on to the transient regime and then to later times is determined numerically. We expect the current to approach a steady-state value at later times. Surprisingly, this is possible only if a nonzero quadratic on-site pinning potential is applied to each particle in the chain. If there is no on-site potential a recurrent phenomenon appears when the time scale is longer than the traveling time of sound to make a round trip from the midpoint to a chain edge and then back. Analytic expressions for the transient and steady-state currents are derived to further elucidate the role of the on-site potential.

Intuitively, lower target densities and lower detection capabilities should demand more sophisticated search strategies for a random search reasonable outcome. In contrast, when targets are easily found, a simple Brownian random walk strategy is enough. But where is the threshold between these two scenarios and when is optimization really necessary? We address this considering the interplay between two essential scales in random search, the average distance between neighbor targets $l_0$ and the detection capability $r_v$. In the limit cases the ratio $\beta =r_v/l_0$ suffices to characterize the problem. For low (high) $\beta$ a superdiffusive behavior is (is not) crucial for the process optimization. However, there is a crossover range, which is a nontrivial function of $r_v$ and $l_0$, separating the two regimes. We analyze this intermediate region, common in nature, and discuss the often overlooked important trade between resources availability and the searcher location power. Our results highlight contexts where efficient random search is a key factor for survival, such as in animal foraging.

We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of the hydrodynamic fields are obtained from the microscopic dynamics. This analysis yields a fluctuating balance equation for the local energy density at the mesoscopic level, characterized by two terms: (i) a diffusive term, with a current that fluctuates around its average behavior given by nonlinear Fourier's law, and (ii) a dissipation term which is a general function of the local energy density. The quasielasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation in the macroscopic limit, implies a noiseless dissipation term in the balance equation, so dissipation fluctuations are enslaved to those of the density field. The microscopic complexity is thus condensed in just three transport coefficients—the diffusivity, the mobility, and a new dissipation coefficient—which are explicitly calculated within a local equilibrium approximation. Interestingly, the diffusivity and mobility coefficients obey an Einstein relation despite the fully nonequilibrium character of the problem. The general theory here presented is applied to a particular albeit broad family of systems, the simplest nonlinear dissipative variant of the so-called KMP model for heat transport. The theoretical predictions are compared to extensive numerical simulations, and an excellent agreement is found.

We study a system of particles with nearest- and next-nearest-neighbor exclusion on the square lattice (hard squares). This system undergoes a transition from a fluid phase at low density to a columnar-ordered phase at high density. We develop a systematic high-activity perturbation expansion for the free energy per site about a state with perfect columnar order. We show that the different terms of the series can be regrouped to get a Mayer-like series for a polydisperse system of interacting vertical rods in which the $n$th term is of order $z^{-(n+1)/2}$, where $z$ is the fugacity associated with each particle. We sum this series to get the exact expansion to order $1/z^{3/2}$.