In the past, the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper, we aim at characterizing the properties of diffusion-limited reactions both in their steady states and out of stationarity. Many reaction-diffusion systems have the peculiarity that microscopic reversibility is broken such that their transient behavior cannot be investigated through the study of most of the observables discussed in the literature. For this reason, we analyze the transient properties of reaction-diffusion systems through a specific work observable that remains well defined even in the absence of microscopic reversibility and that obeys an exact detailed fluctuation relation in cases where detailed balance is fulfilled. We thereby drive the systems out of their nonequilibrium steady states through time-dependent reaction rates. Using a numerical exact method and computer simulations, we analyze fluctuation ratios of the probability distributions obtained during the forward and reversed processes. We show that the underlying microscopic dynamics gives rise to peculiarities in the configuration-space trajectories, thereby, yielding prominent features in the fluctuation ratios.

We explore heat transfer in molecular junctions between two leads in the absence of a finite net thermal bias. The application of an unbiased time-periodic temperature modulation of the leads entails a dynamical breaking of reflection symmetry, such that a directed heat current may emerge (ratchet effect). In particular, we consider two cases of adiabatically slow driving, namely, (i) periodic temperature modulation of only one lead and (ii) temperature modulation of both leads with an ac driving that contains a second harmonic, thus, generating harmonic mixing. Both scenarios yield sizable directed heat currents, which should be detectable with present techniques. Adding a static thermal bias allows one to compute the heat current-thermal load characteristics, which includes the ratchet effect of negative thermal bias with positive-valued heat flow against the thermal bias, up to the thermal stop load. The ratchet heat flow in turn generates also an electric current. An applied electric stop voltage, yielding effective zero electric current flow, then mimics a solely heat-ratchet-induced thermopower (“ratchet Seebeck effect”), although no net thermal bias is acting. Moreover, we find that the relative phase between the two harmonics in scenario (ii) enables steering the net heat current into a direction of choice.

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian core model possesses unexplored symmetries, and they have implications for a broad range of soft-core potentials.

Rosenfeld [Phys. Rev. A 15, 2545 (1977)] originally noticed that casting the transport coefficients of simple monatomic equilibrium fluids in a specific dimensionless form makes them approximately single-valued functions of excess entropy. This observation has predictive value because, while the transport coefficients of dense fluids can be difficult to estimate from first principles, the excess entropy can often be accurately predicted from liquid-state theory. In this work, we use molecular simulations to investigate whether Rosenfeld’s observation is a special case of a more general scaling law relating the tracer diffusivities of particles in mixtures to the excess entropy. Specifically, we study the tracer diffusivities, static structure, and thermodynamic properties of a variety of one- and two-component model fluid systems with either additive or nonadditive interactions of the hard-sphere or Gaussian-core form. The results of the simulations demonstrate that the effects of mixture concentration and composition, particle-size asymmetry and additivity, and strength of the interparticle interactions in these fluids are consistent with an empirical scaling law relating the excess entropy to a dimensionless (generalized Rosenfeld) form of tracer diffusivity, which we introduce here. The dimensionless form of the tracer diffusivity follows from knowledge of the intermolecular potential and the transport/thermodynamic behavior of fluids in the dilute limit. The generalized Rosenfeld scaling requires less information and provides more accurate predictions than either Enskog theory or scalings based on the pair-correlation contribution to the excess entropy. As we show, however, it also suffers from some limitations especially for systems that exhibit significant decoupling of individual component tracer diffusivities.

We used video microscopy and particle tracking to study the dynamics of confined hard-sphere suspensions. Our fluids consisted of $1.1\text{−}\mu \text{m}$-diameter silica spheres suspended at volume fractions of 0.33–0.42 in water-dimethyl sulfoxide. Suspensions were confined in a quasiparallel geometry between two glass surfaces: a millimeter-sized rough sphere and a smooth flat wall. First, as the separation distance $\left(H\right)$ is decreased from 18 to 1 particle diameter, a transition takes place from a subdiffusive behavior (as in bulk) at large $H$, to completely caged particle dynamics at small $H$. These changes are accompanied by a strong decrease in the amplitude of the mean-square displacement (MSD) in the horizontal plane parallel to the confining surfaces. In contrast, the global volume fraction essentially remains constant when $H$ is decreased. Second, measuring the MSD as a function of distance from the confining walls, we found that the MSD is not spatially uniform but smaller close to the walls. This effect is the strongest near the smooth wall where layering takes place. Although confinement also induces local variations in volume fraction, the spatial variations in MSD can be attributed only partially to this effect. The changes in MSD are predominantly a direct effect of the confining surfaces. Hence, both the wall roughness and the separation distance $\left(H\right)$ influence the dynamics in confined geometries.

Setae of the polychaete worm Pherusa exhibit remarkably strong photonic effects, which arise from their two-dimensional-periodic internal structure of hexagonally packed cylindrical channels. The hexagonal order is limited to monocrystalline domains of different orientation, which results in an overall polycrystalline effect. A detailed experimental and theoretical investigation of this structure reveals that the internal photonic structure is carefully tuned with respect to its lattice constant in order to provide an optical response coinciding with the visible wavelength rage. A further optimization is observed for the packing fraction of cylindrical channels in order to maximize the width of photonic band gaps, and hence the reflectance of incident visible light.

Coiled-coil domains within and between proteins play important structural roles in biology. They consist of two or more $\alpha$ helices that form a superhelical structure due to packing of the hydrophobic residues that pattern each helix. A recent continuum model showed that the correspondence between the chirality of the pack to that of the underlying hydrophobic pattern comes about because of the internal deformation energy associated with each helix in forming the superhelix. We have developed a coarse-grained atomistic model for coiled coils that includes the competition between the hydrophobic energy that drives folding and the cost due to deforming each helix. The model exhibits a structural transition from a non-coiled-coil to coiled-coil state as the contribution from the deformation energy changes. Our model is able to reproduce naturally occurring coiled coils and essential features seen in unzipping experiments. We explore the force-extension properties of these model coiled coils as a function helix length and find that shorter coils unfold at lower force than longer ones with the required unfolding force eventually becoming length independent.

We point out that the disagreement between the paper by Neukirch and Starostin [S. Neukirch and E. L. Starostin, Phys. Rev. E 78, 041912 (2008)] and ours [J. Samuel, S. Sinha, and A. Ghosh, J. Phys.: Condens. Matter 18, S253 (2006)] is only apparent and stems from a difference in approach. Neukirch and Starostin are concerned with classical elasticity and individual curves while we focus on statistical averages over curves.

We persist in considering that, for a wide range of (experimentally available) forces and torques, evaluating the writhe of a DNA molecule in magnetic tweezers experiments should not be done with Fuller’s formula. We propose a tentative plot of the limit of applicability of Fuller’s formula in the (force, torque) plane.

To shed light on how biological and technological systems can establish or maintain a synchronous functioning, we address the problem of how to engineer an external pinning action on a network of dynamical units. In particular, we study the regulation of a network toward a synchronized behavior by means of a bidirectional interaction with an external node that leaves unchanged its inner parameters and architecture. We demonstrate that there are two classes of networks susceptible of being regulated into a synchronous motion and provide a simple method, for each one of them, to properly design a pinning sequence to achieve regulation. We also discuss how the obtained sequence can be compared with a topological ranking of the network nodes.

Networks of selectively neutral genotypes underlie the evolution of populations of replicators in constant environments. Previous theoretical analysis predicted that such populations will evolve toward highly connected regions of the genome space. We first study the evolution of populations of replicators on simple networks and quantify how the transient time to equilibrium depends on the initial distribution of sequences on the neutral network, on the topological properties of the latter, and on the mutation rate. Second, network neutrality is broken through the introduction of an energy for each sequence. This allows to study the competition between two features (neutrality and energetic stability) relevant for survival and subjected to different selective pressures. In cases where the two features are negatively correlated, the population experiences sudden migrations in the genome space for values of the relevant parameters that we calculate. The numerical study of larger networks indicates that the qualitative behavior to be expected in more realistic cases is already seen in representative examples of small networks.

Not all tangent space directions play equivalent roles in the local chaotic motions of classical Hamiltonian many-body systems. These directions are numerically represented by basis sets of mutually orthogonal Gram-Schmidt vectors, whose statistical properties may depend on the chosen phase space-time domain of a trajectory. We examine the degree of stability and localization of Gram-Schmidt vector sets simulated with trajectories of a model three-atom Lennard-Jones cluster. Distributions of finite-time Lyapunov exponent and inverse participation ratio spectra formed from short-time histories reveal that ergodicity begins to emerge on different time scales for trajectories spanning different phase-space regions, in a narrow range of total energy and history length. Over a range of history lengths, the most localized directions were typically the most unstable and corresponded to atomic configurations near potential landscape saddles.

We study the steady dynamics of an exothermic Fisher-Kolmogorov-Petrovsky-Piskunov chemical wave front traveling in a one-dimensional van der Waals fluid. The propagating wave is initiated by a nonuniformity in reactant concentration contrary to usual combustion ignition processes. The heat release and activation energy of the reaction play the role of control parameters. We recently proved that the propagation of an exothermic chemical wave front in a perfect gas displays a forbidden interval of stationary wave front speeds [G. Dumazer, M. Leda, B. Nowakowski, and A. Lemarchand, Phys. Rev. E 78, 016309 (2008)]. We examine how this result is modified for nonideal fluids and determine the effect of the van der Waals parameters and fluid density on the bifurcation between diffusion flames and Chapman-Jouguet detonation waves as heat release increases. Analytical predictions are confirmed by the numerical solution of the hydrodynamic equations including reaction kinetics.

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean-field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained by correcting the hypernetted chain approximation with a representation for the associated bridge functions.

The non-Newtonian behavior of a monodisperse concentrated dispersion of spherical particles was investigated using a direct numerical simulation method, which takes into account hydrodynamic interactions and thermal fluctuations accurately. Simulations were performed under steady shear flow with periodic boundary conditions in the three directions. The apparent shear viscosity of the dispersions was calculated at volume fractions ranging from 0.31 to 0.56. Shear-thinning behavior was clearly observed at high volume fractions. The low- and high-limiting viscosities were then estimated from the apparent viscosity by fitting these data into a semiempirical formula. Furthermore, the short-time motions were examined for Brownian particles fluctuating in concentrated dispersions, for which the fluid inertia plays an important role. The mean square displacement was monitored in the vorticity direction at several different Peclet numbers and volume fractions so that the particle diffusion coefficient is determined from the long-time behavior of the mean square displacement. Finally, the relationship between the non-Newtonian viscosity of the dispersions and the structural relaxation of the dispersed Brownian particles is examined.

In this work, we will study the relative contribution of each of the two dissipative channels of the Eriksen, Leslie, and Parodi (ELP) approach to the observed values of the Miesowicz viscosity coefficients of the nematic liquid crystals. According to the fundamental equation of the liquid crystal’s viscosity dissipative process, $T\dot{S}=-\int d^{3}r\left\{{\sigma }_{ij}{A}_{ij}+\vec{h}\cdot \vec{N}\right\}$, there are two channels by which the nematic viscous dissipation can occur: or it occurs by means of a shear flow configuration, where $A_{ij}$ is the characterizing term, or it occurs by means of a rotational configuration, where $\vec{N}$ is the characterizing term (these parameters will be defined in the paper). It will be also shown that this relative contribution can be measured by a simple relationship connecting the Miesowicz coefficients, which exhibits a quasitemperature independent behavior, suggesting that it is nearly constant through the entire domain of the nematic phase.

Recent studies attracted the attention on the inherent-structure-landscape (ISL) approach as a reduced description of proteins allowing to map their full thermodynamic properties. However, the analysis has been so far limited to a single topology of a two-state folding protein, and the simplifying assumptions of the method have not been examined. In this work, we construct the thermodynamics of four two-state folding proteins of different sizes and secondary structure by molecular dynamics (MD) simulations using the ISL method and critically examine possible limitations of the method. Our results show that the ISL approach correctly describes the thermodynamics function, such as the specific heat, on a qualitative level. Using both analytical and numerical methods, we show that some quantitative limitations cannot be overcome with enhanced sampling or the inclusion of harmonic corrections.

We use molecular dynamics to study the nucleation of cracks in a two-dimensional material without pre-existing cracks. We study models with zero and nonzero shear moduli. In both situations, the time required for crack formation obeys an Arrhenius law, from which the energy barrier and prefactor are extracted for different system sizes. For large systems, the characteristic time of rupture is found to decrease with system size, in agreement with classical Weibull theory. In the case of zero shear modulus, the energy opposing rupture is identified with the breakage of a single atomic bond. In the case of nonzero shear modulus, thermally activated fracture can only be studied within a reasonable time at very high strains. In this case, the energy barrier is much higher compared to the zero shear modulus case. This barrier is understood within adiabatic simulations.

This paper proposes a routing strategy for network systems based on the local information of “pheromone.” The overall traffic capacity of a network system can be evaluated by the critical packet generating rate $R_c$. Under this critical generating rate, the total packet number in the system first increases and then decreases to reach a balance state. The system behaves differently from that with a local routing strategy based on the node degree or shortest path routing strategy. Moreover, the pheromone routing strategy performs much better than the local routing strategy, which is demonstrated by a larger value of the critical generating rate. This protocol can be an alternation for superlarge networks, in which the global topology may not be available.

Stable domain walls which are realized by a defect between oppositely traveling spiral waves in a pattern-forming hydrodynamic system, i.e., Taylor-Couette flow, are studied numerically as well as experimentally. A nonlinear mode coupling resulting from the nonlinearities in the underlying momentum balance is found to be essential for the stability of the defects. These nonlinearly driven defects separate spiral domains and act either as a phase generating or annihilating defect. Specific phase differences of either 0 or $\pi$ between the participating traveling waves are a characteristic feature of this defect. The influence of a symmetry breaking externally imposed flow on the spiral domains and the defects is studied. The numerical and experimental results are in excellent agreement.