We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize the deviation from the internal equilibrium situation. Using a power-law force autocorrelation function, the mean-square displacement and the velocity autocorrelation function are analytically obtained in terms of Mittag-Leffler functions. In this case, we show that the present model exhibits a superdiffusive regime as a consequence of the competition between passive and active processes.

During collective locomotion, beating flagella of spermatozoa interact hydrodynamically and are observed experimentally to synchronize. G. I. Taylor used a small-amplitude two-dimensional sheet model to show that the rate at which swimmers do work against the fluid is minimal for in-phase beating. We use a semianalytical approach based on hydrodynamic reflections to extend these results to the small-amplitude three-dimensional beating of infinite flagellar filaments. We first consider a configuration of two parallel filaments. In the case where the beating of both flagella occurs in the same plane as that defined by their axis, in-phase beating is found to lead to an overall minimum of energy dissipation, while opposite-phase leads to a maximum. If we allow the orientation of the beating planes to vary, we find that the minimum of energy dissipation is obtained for either the in-phase or opposite-phase conformation, in a manner that depends on the flagella orientation and their relative distance. We further characterize numerically the set of optimal relative orientations. Quantitatively analogous results are obtained using a simple model based on the beating of two spheres interacting hydrodynamically in the far field. Exploiting the linearity of Stokes equation, we then extend our results to the case of three beating flagella in an aligned and triangular conformation. Consistent with Taylor’s two-dimensional work, our results suggest that, from a hydrodynamic standpoint, it is more energetically favorable for spermatozoa with three-dimensional flagella to swim close to each other and with synchronized, parallel, in-phase beating.

The metal-reducing bacterium Geobacter sulfurreducens produces conductive protein appendages known as “pilus nanowires” to transfer electrons to metal oxides and to other cells. These processes can be harnessed for the bioremediation of toxic metals and the generation of electricity in bioelectrochemical cells. Key to these applications is a detailed understanding of how these nanostructures conduct electrons. However, to the best of our knowledge, their mechanism of electron transport is not known. We used the capability of scanning tunneling microscopy (STM) to probe conductive materials with higher spatial resolution than other scanning probe methods to gain insights into the transversal electronic behavior of native, cell-anchored pili. Despite the presence of insulating cellular components, the STM topography resolved electronic molecular substructures with periodicities similar to those reported for the pilus shaft. STM spectroscopy revealed electronic states near the Fermi level, consistent with a conducting material, but did not reveal electronic states expected for cytochromes. Furthermore, the transversal conductance was asymmetric, as previously reported for assemblies of helical peptides. Our results thus indicate that the Geobacter pilus shaft has an intrinsic electronic structure that could play a role in charge transport.

We consider chains of rotors subjected to both thermal and mechanical forcings in a nonequilibrium steady state. Unusual nonlinear profiles of temperature and velocities are observed in the system. In particular, the temperature is maximal in the center, which is an indication of the nonlocal behavior of the system. Despite this uncommon behavior, local equilibrium holds for long enough chains. Our numerical results also show that when the mechanical forcing is strong enough, the energy current can be increased by an inverse temperature gradient. This counterintuitive result again reveals the complexity of nonequilibrium states.

The estimation of causal relationships from time series data is an important factor in predicting or regulating control in various fields. Usually, when estimating causal relationships, either a causality or a correlation measure is used. However, many studies fail to adequately consider qualitative differences and relations between these measures when applied to time series. In this paper, we present a unified formulation of the causality measure based on information theory as well as relationships and disparities between correlation and causality measures. An advantage of our approach is that the formulated causality measure can extract linear subspaces with strong causal relationships. A significant contribution is the verification that time-delayed mutual information (TDMI) is not appropriate for nonindependent and identically distributed (non-i.i.d.) time series, which is done by demonstrating the behavior of projection vectors in an experiment with synthetic data.

The measurement of thermal fluctuations provides information about the microscopic state of a thermodynamic system and can be used in order to extract work from a single heat bath in a suitable cyclic process. We present a minimal framework for the modeling of a measurement device and we propose a protocol for the measurement of thermal fluctuations. In this framework, the measurement of thermal fluctuations naturally leads to the dissipation of work. We illustrate this framework on a simple two states system inspired by the Szilard's information engine.

We consider a nanodimer in solution with asymmetric thermal properties that shows self-propelled motion. One monomer of the nanodimer can be heated to a fixed temperature producing a radially symmetric temperature gradient. The thermophoretic properties of the second monomer produce then a propulsion against or toward the heated particle, such that the nanodimer becomes a puller or pusher nanoswimmer. We combine our simulation measurements with a theoretical analysis that satisfactorily characterizes the self-propelled velocity with the temperature gradient, and the thermophoretic properties of the bead.

Suitably designed optical fibers are shown to offer a powerful tool for functional brain mapping, facilitating the detection of Cherenkov radiation generated by relativistic positrons from positron-emitting radionuclides. Fiber probes support a low-loss delivery of the high-intensity short-wavelength part of the Cherenkov spectrum, which is strongly absorbed by biotissues, and lower the threshold positron energy ε required for Cherenkov radiation relative to ε values typical of biotissues, thus enhancing the conversion of positron energy into Cherenkov radiation.

The interaction between surface patches of proteins with different surface properties has a vital role to play driving conformational changes in proteins in different salt solutions. We demonstrate the existence of ion-specific attractive double-layer forces between neutral hydrophobic and hydrophilic surfaces in the presence of certain salt solutions. This is performed by solving a generalized Poisson-Boltzmann equation for two unequal surfaces. In the calculations, we utilize parametrized ion-surface potentials and dielectric-constant profiles deduced from recent non-primitive-model molecular dynamics simulations that partially account for molecular structure and hydration effects.

The description of the fibrillogenesis pathway and the identification of “on-pathway” or “off-pathway” intermediates are key issues in amyloid research as they are concerned with the mechanism for onset of certain diseases and with therapeutic treatments. Recent results on the fibril formation process revealed an unexpected complexity both in the number and in the types of species involved, but the early aggregation events are still largely unknown, mainly because of their experimental inaccessibility. To provide information on the early stage events of self-assembly of an amyloidogenic protein, during the so-called lag phase, stopped-flow time-resolved small angle x-ray scattering (SAXS) experiments were performed. Using a global fitting analysis, the structural and aggregation properties of the apomyoglobin W7FW14F mutant, which is monomeric and partly folded at acidic pH but forms amyloid fibrils after neutralization, were derived from the first few milliseconds onward. SAXS data indicated that the first aggregates appear in less than 20 ms after the pH jump to neutrality and further revealed the simultaneous presence of diverse species. In particular, worm-like unstructured monomers, very large assemblies, and elongated particles were detected, and their structural features and relative concentrations were derived as a function of time on the basis of our model. The final results show that, during the lag phase, early assembling occurs due to the presence of transient monomeric species very prone to association and through successive competing aggregation and rearrangement processes leading to coexisting on-pathway and off-pathway transient species.

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble.

A recent experimental study [Traulsen et al., Proc. Natl. Acad. Sci. 107, 2962 (2010)] shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy, which is equivalent to inertia. However, it remains largely unclear how such a predisposed inertia affects $2\times 2$ games in a well-mixed population of finite size. To address this issue, the “inertia bonus” (strategy switching cost) is added to the learner payoff in the Fermi process. We find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes, with each covering seven regions in the plane spanned by two inertia parameters. We also obtain the extended “1/3” rule with inertia and the speed criterion with inertia; these two findings hold for a population above two. We illustrate the above results in the framework of the Prisoner's Dilemma game. As inertia varies, two intriguing stationary distributions emerge: the probability of coexistence state is maximized, or those of two full states are simultaneously peaked. Our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and, in particular, the evolution of cooperation.

We experimentally demonstrate the use of continuous, time-delayed, feedback stimulation for controlling the synchronization of neuron action potentials. Phase-based models were experimentally constructed from a single synaptically isolated cultured hippocampal neuron. These models were used to determine the stimulation parameters necessary to produce the desired synchronization behavior in the action potentials of a pair of neurons coupled through a global time-delayed interaction. Measurements made using a dynamic clamp system confirm the generation of the synchronized states predicted by the experimentally constructed phase model. This model was then utilized to extrapolate the feedback stimulation parameters necessary to disrupt the action potential synchronization of a large population of globally interacting neurons.

Over the last few years, significant efforts have been devoted to exploring the capabilities of carbon based structures for gas separation and filtration. In the present study the layering behavior of carbon dioxide transported through carbon nanoscrolls is examined through molecular dynamics simulations. The layering arrangements are investigated for carbon nanoscrolls with intralayer distances spanning from 4.2 to 8.3 Å at temperature of 300 K and pressures ranging from 5 to 20 bars. Characteristic layering structures are developed around the internal and external surfaces of the nanoscroll for all the examined cases. It is shown that the number of layers, their relative strength, and the starting point of bifurcation phenomena vary as a function of the nanoscrolls’ intralayer distance, scroll's core radius, CO${}_2$ density, and gas structure interactions. It is also shown that the number of carbon dioxide molecules adsorbed per scroll's carbon particles is a function of the scroll's surface-to-volume ratio and is maximized under certain structural configurations.

The effects of dust charge variations on low-frequency wave modulations in an electronegative dusty plasma are investigated. The dynamics of the modulated wave is governed by a nonlinear Schrödinger equation with a dissipative term. The dissipation arises due to the nonsteady (nonadiabatic) dust charge variations. Theoretical and numerical investigations predict the formation of dissipative bright (envelope) and dark solitons. The nonsteady charge-variation-induced dissipation reduces the modulational instability growth rate and introduces a characteristic time scale to observe bright solitons. Results are discussed in the context of electronegative dusty plasma experiments.

The continuous-time random walk (CTRW) is a model of anomalous subdiffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, $\psi \left(\tau \right)\sim {\tau }^{-(1+\alpha )}$, leads to subdiffusion ($\langle x^2\rangle \sim t^{\alpha }$) for $0<\alpha <1$. In closed systems, the long stagnation periods cause time averages to divert from the corresponding ensemble averages, which is a manifestation of weak ergodicity breaking. The time average of a general observable $\overline{U}\left(t\right)=\frac{1}{t}{\int }_0^{t}U\left[x\left(\tau \right)\right]d\tau$ is a functional of the path and is described by the well-known Feynman-Kac equation if the motion is Brownian. Here, we derive forward and backward fractional Feynman-Kac equations for functionals of CTRW in a binding potential. We use our equations to study two specific time averages: the fraction of time spent by a particle in half-box, and the time average of the particle's position in a harmonic field. In both cases, we obtain the probability density function of the time averages for $t\to \infty$ and the first two moments. Our results show that both the occupation fraction and the time-averaged position are random variables even for long times, except for $\alpha =1$, when they are identical to their ensemble averages. Using our fractional Feynman-Kac equation, we also study the dynamics leading to weak ergodicity breaking, namely the convergence of the fluctuations to their asymptotic values.

We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand-canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region, the force decays exponentially fast when distance $D$ between the walls tends to infinity. When the Bose-Einstein condensation point is approached, the decay length in the exponential law diverges with critical exponent ${\nu }_{IMP}=1$, which differs from the perfect gas case where ${\nu }_P=1/2$. In the two-phase region, the Casimir force is long range and decays following the power law $D^{-3}$, with the same amplitude as in the perfect gas.

We investigate the properties of the nonequilibrium steady state for the stochastic system driven by a nonlinear drift force and influenced by noises that are not identically and independently distributed. The nonequilibrium steady state (NESS) current results from a residual part of the drift force that is not canceled by the diffusive action of noises. From our previous study for the linear drift force, the NESS current was found to circulate on the equiprobability surface with the maximum at a stable fixed point of the drift force. For the nonlinear drift force, we use the perturbation theory with respect to the cubic and quartic coefficients of the drift force. We find an interesting potential landscape picture where the probability maximum shifts from the fixed point of the drift force and, furthermore, the NESS current has a nontrivial circulation that flows off the equiprobability surface and has various centers not located at the probability maximum. The theoretical result is well confirmed by the computer simulation.

The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model.

We reexamine the convolution approximation commonly used in the mode-coupling theory (MCT) of nonergodic states of classical fluids. This approximation concerns the static correlation functions used as input in the MCT treatment of the dynamics. Besides the hard-sphere model, we consider interaction potentials that present a short-range tail, either attractive or repulsive, beyond the hard core. By using accurate static correlation functions obtained from the fundamental measures functional for hard spheres, we show that the role of three-body direct correlations can be more significant than what is inferred from previous simple ansatzs for pure hard spheres. This may in particular impact the location of the glass transition line and the nonergodicity parameter.