Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on this problem, shedding light on, e.g., the physics behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions, and new symmetries. This makes the understanding of the properties of these optimal paths a central issue. Here we derive a fundamental relation which strongly constrains the architecture of these optimal paths for general $d$-dimensional nonequilibrium diffusive systems, and implies a nontrivial structure for the dominant current vector fields. Interestingly, this general relation (which encompasses and explains previous results) makes manifest the spatiotemporal nonlocality of the current statistics and the associated optimal trajectories.

We develop a theory to describe solid-solid phase transitions. The density functional formalism of classical statistical mechanics is used to find an exact expression for the difference in the grand thermodynamic potentials of the two coexisting phases. The expression involves both the symmetry conserving and the symmetry broken parts of the direct pair correlation function. The theory is used to calculate phase diagram of systems of soft spheres interacting via inverse power potentials $u\left(r\right)=\epsilon {\left(\sigma /r\right)}^n$, where parameter $n$ measures softness of the potential. We find that for $1/n<0.154$ systems freeze into the face centered cubic (fcc) structure while for $1/n\ge 0.154$ the body-centred-cubic (bcc) structure is preferred. The bcc structure transforms into the fcc structure upon increasing the density. The calculated phase diagram is in good agreement with the one found from molecular simulations.

A diffusive lattice gas is characterized by the diffusion coefficient depending only on the density. The Green-Kubo formula for diffusivity can be represented as a variational formula, but even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient can be computed only in the exceptional situation when the lattice gas is gradient. In the general case, minimization over an infinite-dimensional space is required. We propose an approximation scheme based on minimizing over finite-dimensional subspaces of functions. The procedure is demonstrated for one-dimensional generalized exclusion processes in which each site can accommodate at most two particles. Our analytical predictions provide upper bounds for the diffusivity that are very close to simulation results throughout the entire density range. We also analyze nonequilibrium density profiles for finite chains coupled to reservoirs. The predictions for the profiles are in excellent agreement with simulations.

Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between otherwise common inputs are unavoidable. Since common inputs can be a source of correlation between the elements of multi-unit dynamical systems, regardless of whether these elements are directly connected with one another or not, it is of importance to understand their impact on synchronization. As a canonical model that is representative for a variety of different dynamical systems, we study limit-cycle oscillators that are driven by stochastic time-shifted common inputs. We show that if the oscillators are coupled, time shifts in stochastic common inputs do not simply shift the distribution of the phase differences, but rather the distribution actually changes as a result. The best synchronization is therefore achieved at a precise intermediate value of the time shift, which is due to a resonance-like effect with the most probable phase difference that is determined by the deterministic dynamics.

We present a numerical study of the cubic-quintic nonlinear Schrödinger equation in two transverse dimensions, relevant for the propagation of light in certain exotic media. A well-known feature of the model is the existence of flat-top bright solitons of fixed intensity, whose dynamics resembles the physics of a liquid. They support traveling wave solutions, consisting of rarefaction pulses and vortex-antivortex pairs. In this work, we demonstrate how the vortex-antivortex pairs can be generated in bright soliton collisions displaying destructive interference followed by a snake instability. We then discuss the collisional dynamics of the dark excitations for different initial conditions. We describe a number of distinct phenomena including vortex exchange modes, quasielastic flyby scattering, solitonlike crossing, fully inelastic collisions, and rarefaction pulse merging.

The redistribution of electrical currents in resistor networks after single-bond failures is analyzed in terms of current-redistribution factors that are shown to depend only on the topology of the network and on the values of the bond resistances. We investigate the properties of these current-redistribution factors for regular network topologies (e.g., $d$-dimensional hypercubic lattices) as well as for small-world networks. In particular, we find that the statistics of the current redistribution factors exhibits a fat-tail behavior, which reflects the long-range nature of the current redistribution as determined by Kirchhoff's circuit laws.

The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing ${10}^6$ time series of videos' views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat's law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with Lévy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models.

We examine high-resolution urban infrastructure data using every pipe for the water distribution network (WDN) and sanitary sewer network (SSN) in a large Asian city (≈4 million residents) to explore the structure as well as the spatial and temporal evolution of these infrastructure networks. Network data were spatially disaggregated into multiple subnets to examine intracity topological differences for functional zones of the WDN and SSN, and time-stamped SSN data were examined to understand network evolution over several decades as the city expanded. Graphs were generated using a dual-mapping technique (Hierarchical Intersection Continuity Negotiation), which emphasizes the functional attributes of these networks. Network graphs for WDNs and SSNs are characterized by several network topological metrics, and a double Pareto (power-law) model approximates the node-degree distributions of both water infrastructure networks (WDN and SSN), across spatial and hierarchical scales relevant to urban settings, and throughout their temporal evolution over several decades. These results indicate that generic mechanisms govern the networks’ evolution, similar to those of scale-free networks found in nature. Deviations from the general topological patterns are indicative of (1) incomplete establishment of network hierarchies and functional network evolution, (2) capacity for growth (expansion) or densification (e.g., in-fill), and (3) likely network vulnerabilities. We discuss the implications of our findings for the (re-)design of urban infrastructure networks to enhance their resilience to external and internal threats.

We propose to combine a mean-field approach with all-atom molecular dynamics (MD) into a multistage algorithm that can model protein folding and dynamics over very long time periods yet with atomic-level precision. As an example, we investigate an isolated monomeric Myc oncoprotein that has been implicated in carcinomas including those in colon, breast, and lungs. Under physiological conditions a monomeric Myc is presumed to be an example of intrinsically disordered proteins that pose a serious challenge to existing modeling techniques. We argue that a room-temperature monomeric Myc is in a dynamical state, it oscillates between different conformations that we identify. For this we adopt the $\mathrm{C}\alpha$ backbone of Myc in a crystallographic heteromer as an initial ansatz for the monomeric structure. We construct a multisoliton of the pertinent Landau free energy to describe the $\mathrm{C}\alpha$ profile with ultrahigh precision. We use Glauber dynamics to resolve how the multisoliton responds to repeated increases and decreases in ambient temperature. We confirm that the initial structure is unstable in isolation. We reveal a highly degenerate ground-state landscape, an attractive set towards which Glauber dynamics converges in the limit of vanishing ambient temperature. We analyze the thermal stability of this Glauber attractor using room-temperature molecular dynamics. We identify and scrutinize a particularly stable subset in which the two helical segments of the original multisoliton align in parallel next to each other. During the MD time evolution of a representative structure from this subset, we observe intermittent quasiparticle oscillations along the C-terminal $\alpha$ helix, some of which resemble a translating Davydov's Amide-I soliton. We propose that the presence of oscillatory motion is in line with the expected intrinsically disordered character of Myc.

The influence of a plane boundary on low-Reynolds-number swimmers has frequently been studied using image systems for flow singularities. However, the boundary effect can also be expressed using a boundary integral representation over the traction on the boundary. We show that examining the traction pattern on the boundary caused by a swimmer can yield physical insights into determining when far-field multipole models are accurate. We investigate the swimming velocities and the traction of a three-sphere swimmer initially placed parallel to an infinite planar wall. In the far field, the instantaneous effect of the wall on the swimmer is well approximated by that of a multipole expansion consisting of a force dipole and a force quadrupole. On the other hand, the swimmer close to the wall must be described by a system of singularities reflecting its internal structure. We show that these limits and the transition between them can be independently identified by examining the traction pattern on the wall, either using a quantitative correlation coefficient or by visual inspection. Last, we find that for nonconstant propulsion, correlations between swimming stroke motions and internal positions are important and not captured by time-averaged traction on the wall, indicating that care must be taken when applying multipole expansions to study boundary effects in cases of nonconstant propulsion.

Nonequilibrium drivings applied in molecular dynamics (MD) simulations can efficiently extend the visiting range of protein conformations, but might compel systems to go far away from equilibrium and thus mainly explore irrelevant conformations. Here we propose a general method, called adaptive nonequilibrium simulation (ANES), to automatically adjust the external driving on the fly, based on the feedback of the short-time average response of system. Thus, the ANES approximately keeps the local equilibrium but efficiently accelerates the global motion. We illustrate the capability of the ANES in highly efficiently exploring metastable conformations in the deca-alanine peptide and find that the $0.2-\mu \mathrm{s}$ ANES approximately captures the important states and folding and unfolding pathways in the HP35 solution by comparing with the result of the recent $398-\mu \mathrm{s}$ equilibrium MD simulation on Anton [S. Piana et al., Proc. Natl. Acad. Sci. USA 109, 17845 (2012)].

We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size $L$ like $\sim Llnln\left(L\right)$. In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a $\delta$ peak in the thermodynamic limit $L\to \infty$. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.

The phenomenon of chaotic scattering is very relevant in different fields of science and engineering. It has been mainly studied in the context of Newtonian mechanics, where the velocities of the particles are low in comparison with the speed of light. Here, we analyze global properties such as the escape time distribution and the decay law of the Hénon-Heiles system in the context of special relativity. Our results show that the average escape time decreases with increasing values of the relativistic factor $\beta$. As a matter of fact, we have found a crossover point for which the KAM islands in the phase space are destroyed when $\beta \simeq 0.4$. On the other hand, the study of the survival probability of particles in the scattering region shows an algebraic decay for values of $\beta \le 0.4$, and this law becomes exponential for $\beta >0.4$. Surprisingly, a scaling law between the exponent of the decay law and the $\beta$ factor is uncovered where a quadratic fitting between them is found. The results of our numerical simulations agree faithfully with our qualitative arguments. We expect this work to be useful for a better understanding of both chaotic and relativistic systems.

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the “resonant” case, when the free rotation period is commensurate to $2\pi$, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

Bacterial migration through confined spaces is critical for several phenomena, such as biofilm formation, bacterial transport in soils, and bacterial therapy against cancer. In the present work, E. coli (strain K12-MG1655 WT) motility was characterized by recording and analyzing individual bacterium trajectories in a simulated quasi-two-dimensional porous medium. The porous medium was simulated by enclosing, between slide and cover slip, a bacterial-culture sample mixed with uniform 2.98-$\mu \text{m}$-diameter spherical latex particles. The porosity of the medium was controlled by changing the latex particle concentration. By statistically analyzing several trajectory parameters (instantaneous velocity, turn angle, mean squared displacement, etc.), and contrasting with the results of a random-walk model developed ad hoc, we were able to quantify the effects that different obstacle concentrations have upon bacterial motility.

Here we report how interference and scattering-enhanced absorption act together to produce the golden wing patches of the burnished brass moth. The key mechanism is scattering on rough internal surfaces of the wing scales, accompanied by a large increase of absorption in the UV-blue spectral range. Unscattered light interferes and efficiently reflects from the multilayer composed of the scales and the wing membranes. The resulting spectrum is remarkably similar to the spectrum of metallic gold. Subwavelength morphology and spectral and absorptive properties of the wings are described. Theories of subwavelength surface scattering and local intensity enhancement are used to quantitatively explain the observed reflectance spectrum.

In this paper, we investigate the properties of aggregation transitions in the context of generic coarse-grained homopolymer systems. By means of parallel replica-exchange Monte Carlo methods, we perform extensive simulations of systems consisting of up to 20 individual oligomer chains with five monomers each. Using the tools of the versatile microcanonical inflection-point analysis, we show that the aggregation transition is a first-order process consisting of a sequence of subtransitions between intermediate structural phases. We unravel the properties of these intermediate phases by collecting and analyzing their individual contributions towards the density of states of the system. The central theme of this systematic study revolves around translational entropy and its role in the striking phenomena of missing intermediate phases. We conclude with a brief discussion of the scaling properties of the transition temperature and the latent heat.

We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at a low Reynolds number and subject to a magnetic field. Its corresponding mean-square displacement, showing the effect of a particles's shape, activity, and magnetic field on the microswimmer's diffusion, is analytically obtained. Comparison between analytical and computational results shows good agreement. In addition, the effect of self-propulsion on the transition time from anisotropic to isotropic diffusion of the ellipse is investigated.

The usual viscous fingering instability arises when a fluid displaces another of higher viscosity in a flat Hele-Shaw cell, under sufficiently large capillary number conditions. In this traditional framing, the reverse flow case (more viscous fluid displacing a less viscous one) and the viscosity-matched situation (fluids of equal viscosities) are stable. We revisit this classical fluid dynamic problem, now considering flow in a nonflat Hele-Shaw cell. For a specific nonflat environment, we show that both the reverse and the viscosity-matched flows can become unstable, even at low capillary number. This peculiar fluid fingering instability is driven by the combined action of capillary effects and geometric properties of the nonflat Hele-Shaw cell. Our theoretical results indicate that the Hele-Shaw cell geometry significantly impacts the linear stability and nonlinear pattern-forming dynamics of the system. This suggests that the geometry of the medium plays an important role in favoring the occurrence of fingering patterns in nonflat, confined fluid flows.