In the study of networked systems, a method that can extract information about how the individual nodes are connected with one another would be valuable. In this paper, we present a method that can yield such information of network connectivity using measurements of the dynamics of the nodes as the only input data. Our method is built upon a noise-induced relation between the Laplacian matrix of the network and the dynamical covariance matrix of the nodes, and applies to networked dynamical systems in which the coupling between nodes is uniform and bidirectional. Using examples of different networks and dynamics, we demonstrate that the method can give accurate connectivity information for a wide range of noise amplitude and coupling strength. Moreover, we can calculate a parameter $\Delta$ using again only the input of time-series data, and assess the accuracy of the extracted connectivity information based on the value of $\Delta$.

We study magnetic artificial flagella whose swimming speed and direction can be controlled using light and magnetic field as external triggers. The dependence of the swimming velocity on the system parameters (e.g., length, stiffness, fluid viscosity, and magnetic field) is explored using a computational framework in which the magnetostatic, fluid dynamic, and solid mechanics equations are solved simultaneously. A dimensionless analysis is carried out to obtain an optimal combination of system parameters for which the swimming velocity is maximal. The swimming direction reversal is addressed by incorporating photoresponsive materials, which in the photoactuated state can mimic natural mastigonemes.

The modulational instability (MI) phenomenon in the nonlinear Schrödinger equation (NLSE) extended by two different nonlinear dispersion terms and the gradient term is investigated. We find that the possibility of instability of plane waves depends on the sign of the nonlinear dispersion parameters with regard to the linear dispersion coefficient. In contrast to the basic NLSE, the system may exhibit instability in the defocusing media for amplitude exceeding a critical value depending on the magnitude of the nonlinear dispersion. An additional feature, namely the higher order or the infinite gain band, absent in the NLSE case, may appear and in which MI induces the birth of the nonlinear localized wave (NLW) of different carrier wave numbers. The result of the qualitative investigations of the system's dynamics indicates the existence of the NLW, such as peak, bright, dark, and compact dark solitary waves which can be well predicted by the MI criteria. In addition the nonlinear dispersion induces the existence of a pair of bright-dark solitary waves which is usually exhibited by the coupled NLSEs only, and the pairs of peak-dark and compact dark-bright solitary waves.

Nematic elastomers contract along their director when heated or illuminated (in the case of photoelastomers). We present a conceptual design for an elastomer-based engine to extract mechanical work from heat or light. The material parameters and the geometry of such an engine are explored, and it is shown that its efficiency can go up to 20%.

We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time-dependent control parameter, the environment is modeled by $N$-independent harmonic oscillators with arbitrary frequencies, and the system-environment coupling is bilinear and not necessarily weak. The initial conditions of the combined system and environment are sampled from a microcanonical distribution and the system is driven out of equilibrium by changing the control parameter according to a prescribed protocol. In the limit of infinitely large environment, i.e., $N\to \infty$, we recover the nonequilibrium work relation and Crooks's fluctuation relation. Moreover, the microcanonical Crooks relation is verified for finite environments. Finally, we show the equivalence of multitime correlation functions of the system in the infinite environment limit for canonical and microcanonical ensembles.

We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse. Furthermore, the conditions under which the resulting system emerges as a fractal are found, the fractal dimension of the system is given, and the relationship between this fractal dimension and a conserved quantity is pointed out.

We study the nonequilibrium critical point of the zero-temperature random-field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random-field Ising model belong to the same universality class. The physics of this curious result is not fully understood.

This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This “pseudohomogeneous” property makes explicit that—and in which sense—such a system has a hidden scale invariance. The second part of the paper gives a potential-energy formulation of the quasiuniversality of monatomic Roskilde-simple liquids, which was recently rationalized in terms of the existence of a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106 (2013)]. The new formulation involves a quasiuniversal reduced-coordinate potential-energy function. A few consequences of this are discussed.

During polymer translocation driven by, e.g., voltage drop across a nanopore, the segments in the cis side are incessantly pulled into the pore, which are then pushed out of it into the trans side. This pulling and pushing of polymer segments are described in the continuum level by nonlinear transport processes known, respectively, as fast and slow diffusions. By matching solutions of both sides through the mass conservation across the pore, we provide a physical basis for the cis and trans dynamical asymmetry, a feature repeatedly reported in recent numerical simulations. We then predict how the total driving force is dynamically allocated between cis (pulling) and trans (pushing) sides, demonstrating that the trans-side event adds a weak finite-chain length effect to the dynamical scaling.

Radiation of energy by large-amplitude leaky Rayleigh waves is regarded as one of the key physical mechanisms regulating the actuation and manipulation of droplets in surface acoustic wave (SAW) microfluidic devices. The interaction between a SAW and a droplet is highly complex and is presently the subject of extensive research. This paper investigates the existence of an additional interaction mechanism based on the propagation of quasi-Stoneley waves inside sessile droplets deposited on a solid substrate. In contrast with the leaky Rayleigh wave, the energy of the Stoneley wave is confined within a thin fluid layer in contact with the substrate. The hypothesis is confirmed by three-dimensional finite element simulations and ultrasonic scattering experiments measuring the reflection of Rayleigh waves from droplets of different diameters. Moreover, real-time monitoring of the droplet evaporation process reveals a clear correlation between the droplet contact angle and the spectral information of the reflected Rayleigh signal, thus paving the way for ultrasonic measurements of surface tension.

We study the coupled dynamics of two closely spaced micron or nanoscale elastic objects immersed in a viscous fluid. The dynamics of the elastic objects are coupled through the motion of the surrounding viscous fluid. We consider two cases: (i) one object is driven externally by an imposed harmonic actuation force and the second object is passive and (ii) both objects are driven by a Brownian force to yield stochastic dynamics. Using a harmonic oscillator approximation for the elastic objects and the unsteady Stokes equations to describe the fluid dynamics, we develop analytical expressions for the amplitude and phase of the displacement of the oscillating objects. For the case of an imposed actuation we use an impulse in force to determine the resulting dynamics over all frequencies. For the Brownian-driven objects the stochastic dynamics are found using the fluctuation-dissipation theorem. We validate our theoretical expressions by comparison with results from finite-element numerical simulations of the complete fluid-solid interaction problem. Our results yield interesting features in the amplitude and phase of the displacement of the elastic objects due to the fluid motion. We find that the dynamics depend on the separation of the objects, a measure of the mass loading due to the fluid, and the frequency parameter which acts as a frequency-based Reynolds number. Our results are valid over the range of parameters typical of micron and nanoscale elastic objects in fluid. The range of dynamics found can be understood in terms of the interplay between the viscous and potential components of the fluid flow field described by the unsteady Stokes equation for an oscillating cylinder. For small values of the frequency parameter, typical of nanoscale elastic objects, the dynamics are overdamped due to the dominance of viscous forces over inertial forces. For moderate and large values of the frequency parameter, typical of micron-scale elastic objects, we find that the dynamics of the fluid-coupled objects exhibits an interesting mode splitting to yield a bimodal signature in the amplitude-frequency plots. We find that the mode splitting can be described using a normal mode analysis containing only potential fluid interactions between the cylinders.

We investigate how nonspecific interactions and unbinding-rebinding events give rise to a length- and conformation-dependent enhancement of the “macroscopic” dissociation time of proteins from a DNA, or in general for the release of ligands initially bound to a long polymer. By numerically simulating the release of ligands from polymers of different conformations, we show that the total dissociation time increases logarithmically with polymer length for an extended conformation, and as a power law for self-avoiding and compact conformations. For the latter two cases, the presence of self-avoidance acting between the diffusing ligands affects the power-law exponents. Our results are important in relating kinetic measurements of protein on- and off-rates for large DNAs to equilibrium affinities for a single binding site.

The local thermodynamics of a system with long-range interactions in $d$ dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

We investigate the influence of the shape of a particle on the structure of the jamming phase diagram of wet granular materials. We compute the jamming phase diagram of wet dimers (two fused disks) and compare it with that of the wet disks. Amplitude of the external force at solidification, i.e., the jamming force $F_s$, is computed as a function of the packing fraction $\varphi$, the capillary bridge energy $\varepsilon$, and the aspect ratio of dimers $\alpha$. Based on data collapse, an equation for amplitude of the external force at solidification $F_s(\varphi ,\varepsilon ,\alpha )$ is derived. $F_s$ has scaling and logarithmic relations with $\varphi$ and $\varepsilon$, respectively, exactly the same type reported for wet disks earlier. Interestingly, $F_s$ does not depend on the aspect ratio of dimers $\alpha$. The only difference is that wet dimers are found to be more stiffer than wet disks. However, the similarities of the equations describing $F_s(\varphi ,\varepsilon ,\alpha )$ of wet dimers and disks imply that there exists, yet unknown, universal aspects of mechanical response of wet granular materials to the external forces, independent from the particle shape. In addition, we study local orientation of particles and its statistical properties.

Inverse statistical-mechanical methods have recently been employed to design optimized short-range radial (isotropic) pair potentials that robustly produce novel targeted classical ground-state many-particle configurations. The target structures considered in those studies were low-coordinated crystals with a high degree of symmetry. In this paper, we further test the fundamental limitations of radial pair potentials by targeting crystal structures with appreciably less symmetry, including those in which the particles have different local structural environments. These challenging target configurations demanded that we modify previous inverse optimization techniques. In particular, we first find local minima of a candidate enthalpy surface and determine the enthalpy difference $\Delta H$ between such inherent structures and the target structure. Then we determine the lowest positive eigenvalue ${\lambda }_0$ of the Hessian matrix of the enthalpy surface at the target configuration. Finally, we maximize ${\lambda }_0\Delta H$ so that the target structure is both locally stable and globally stable with respect to the inherent structures. Using this modified optimization technique, we have designed short-range radial pair potentials that stabilize the two-dimensional kagome crystal, the rectangular kagome crystal, and rectangular lattices, as well as the three-dimensional structure of the CaF${}_2$ crystal inhabited by a single-particle species. We verify our results by cooling liquid configurations to absolute zero temperature via simulated annealing and ensuring that such states have stable phonon spectra. Except for the rectangular kagome structure, all of the target structures can be stabilized with monotonic repulsive potentials. Our work demonstrates that single-component systems with short-range radial pair potentials can counterintuitively self-assemble into crystal ground states with low symmetry and different local structural environments. Finally, we present general principles that offer guidance in determining whether certain target structures can be achieved as ground states by radial pair potentials.

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients ($B_2$ and $B_3$) are evaluated as functions of the dipolar coupling constant $\lambda$, and the Langevin parameter $\alpha$. The formula for $B_3$ for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing $\lambda$ and $\alpha$ are examined. Very good agreement between theory and computation is demonstrated for the realistic values $\lambda \le 2$. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.

This work is devoted to the calculation of transport coefficients for He${}_2$${}^{+}$ ions in gaseous He at intermediate reduced electric fields. These swarm data are of great interest for a better understanding of the mechanisms of formation and propagation of the fast plasma bullets or ionization waves observed in dielectric barrier plasma jet devices. For transport data, the collision cross sections required are determined from several theoretical methods based on quantum, semiclassical, and hybrid approaches and a diatomics-in-molecules model for the potential energy surfaces of He${}_3$${}^{+}$. The corresponding collision cross sections are then used in an optimized Monte Carlo code to calculate the ion transport coefficients over a wide range of reduced electric fields extending over the experimental range. Calculated transport coefficients are compared with available experimental data at low electric fields. Moreover, an extrapolation method is used in order to determine the reduced mobility for stronger fields. A critical discussion has been performed on the pertinence and the reliability of these different methods of determination of collision cross sections needed for the calculation of ion transport data. Such ion data will be used in electrohydrodynamic and chemical kinetic models of the low-temperature plasma jet to quantify and to tune the active species production for a better use in biomedical applications.

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the nonchaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.