A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to regular polygons, and the isoperimetric ratio. The map serves as a low-dimensional signature of the fracture network and is visually presented as a pair of three-dimensional graphs. A systematic study is made of a wide collection of real crack networks for various materials, collected from different sources. To identify the characteristics of the real materials, several well-known mathematical models of convex polygonal networks are presented and worked out. These geometric models may correspond to different physical fracturing processes. The proposed map is shown to be discriminative, and the points corresponding to materials of similar properties are found to form closely spaced groups in the parameter space. Results for the real and simulated systems are compared in an attempt to identify crack networks of unknown materials.

Transition rates among different states in a system of noninteracting quantum particles in contact with a heat reservoir include the factor $1\mp {\overline{n}}_i$, with a minus sign for fermions and a plus sign for bosons, where ${\overline{n}}_i$ is the average occupation number of the final state. It is shown that this factor can be related to the difference of the chemical potential from that of an ideal classical mixture; this difference is formally equivalent to the excess chemical potential in a classical system of interacting particles. Using this analogy, Widom's insertion formula is used in the calculation of transition rates. The result allows an alternative derivation of quantum statistics from the condition that transition rates depend only on the number of particles in the target energy level. Instead, if transition rates depend on the particle number only in the origin level, the statistics of ewkons is obtained; this is an exotic statistics that can be applied to the description of dark energy.

We address the problem of evaluating the transfer entropy (TE) produced by biochemical reactions from experimentally measured data. Although these reactions are generally nonlinear and nonstationary processes making it challenging to achieve accurate modeling, Gaussian approximation can facilitate the TE assessment only by estimating covariance matrices using multiple data obtained from simultaneously measured time series representing the activation levels of biomolecules such as proteins. Nevertheless, the nonstationary nature of biochemical signals makes it difficult to theoretically assess the sampling distributions of TE, which are necessary for evaluating the statistical confidence and significance of the data-driven estimates. We resolve this difficulty by computationally assessing the sampling distributions using techniques from computational statistics. The computational methods are tested by using them in analyzing data generated from a theoretically tractable time-varying signal model, which leads to the development of a method to screen only statistically significant estimates. The usefulness of the developed method is examined by applying it to real biological data experimentally measured from the ERBB-RAS-MAPK system that superintends diverse cell fate decisions. A comparison between cells containing wild-type and mutant proteins exhibits a distinct difference in the time evolution of TE while any apparent difference is hardly found in average profiles of the raw signals. Such a comparison may help in unveiling important pathways of biochemical reactions.

Molecular dynamics simulations were employed to investigate the impact of interactions between dendritic polyeclectrolytes and amphiphilic surfactants on the supramolecular complex formation. We recognize two crucial parameters that govern association of surfactants within dendrimers: surfactant hydrophobicity, ${\epsilon }^{*}$, and dendrimer generation, $G$. We find that depending on the values of ${\epsilon }^{*}$ and $G$ encapsulation of surfactants by dendrimers is either noncooperative or cooperative. The noncooperative binding is characterized by absorption of surfactants as unimers, whereas in cooperative binding absorption of unimers is followed by aggregate formation through hydrophobic attractions between the surfactant tails. Our results provide guidelines for controlled encapsulation of guest molecules in dendrimer-based guest-host complexes.

We study the influence of arm architecture on the conformational properties of hybrid star-shaped macromolecules called rosette polymers containing linear and ring grafts connected to a central branching point in a good solvent regime. We utilize analytical methods and molecular dynamics simulations to determine the estimates for the relative size ratios of these polymers with respect to linear chains and starlike polymers composed of the same number of solely linear arms and equal molecular weights. The results of numerical simulations corroborate our theoretical prediction that rosette polymers undergo conformational compactification with increasing functionality of grafted rings. Our results quantitatively describe the impact of the complex architecture of the molecules with excluded volume on their effective size measures.

We study the role of phase change and thermal noise in particle transport in turbulent flows. We employ a toy model to extract the main physics: Condensing droplets are modelled as heavy particles which grow in size, the ambient flow is modelled as a two-dimensional Taylor-Green flow consisting of an array of vortices delineated by separatrices, and thermal noise are modelled as uncorrelated Gaussian white noise. In general, heavy inertial particles are centrifuged out of regions of high vorticity and into regions of high strain. In cellular flows, we find, in agreement with earlier results, that droplets with Stokes numbers smaller than a critical value, $\mathrm{St}<{\mathrm{St}}_{\mathrm{cr}}$, remain trapped in the vortices in which they are initialized, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the Péclet number Pe characterizing the amplitude of thermal noise and the condensation rate $\mathrm{\Pi }$ to study their effects on the critical Stokes number for droplet trapping, as well as on the final states of motion of the droplets. We find that the imposition of thermal noise, or of a finite condensation rate, allows droplets of $\mathrm{St}<{\mathrm{St}}_{\mathrm{cr}}$ to leave their initial vortices. We find that the effects of thermal noise become negligible for growing droplets and that growing droplets achieve ballistic motion when their Stokes numbers become $\mathcal{O}\left(1\right)$. We also find an intermediate regime prior to attaining the ballistic state, in which droplets move diffusively away from their initial vortices in the presence of thermal noise.

Reynolds and dispersive shear stresses in turbulent flow over spanwise-aligned square bars in an open channel flow are examined. Results of large-eddy simulation of flow over two different bar spacings corresponding to transitional and $k$-type (reattaching flow) roughness are analyzed. The Reynolds shear stress contribution to the momentum loss (or the friction factor, respectively) is greater than the dispersive shear stress contribution. By increasing the bars spacing, however, the contribution of the dispersive shear stress increases while the Reynolds shear stress contribution decreases, which is due to a standing wave at the water surface in the flow over $k$-type roughness which results in significant spatial variations in the time-averaged velocities. Strong sweep events take place and contribute to the friction coefficient. Investigating the dynamics of the flow reveals that there is momentum source below the crest of the bars and momentum sink above them, leading to acceleration or deceleration of flow, respectively. The contribution of dispersive shear stress is significant only in the deceleration of the flow near the crest of the bars and in the acceleration of the flow under the water surface. Quantification of the three components of total kinetic energy, i.e. mean, turbulent, and wake kinetic energy, reveals that the largest contribution is that of the mean flow in both geometries. By increasing the bar spacing, the contributions of turbulent and wake kinetic energy, which are localized at the bar height, increase, while the kinetic energy of the mean flow decreases.

We study particle trapping driven by the axial primary radiation force (A-PRF) in shaped traps exposed to standing bulk acoustic waves (S-BAW) using numerical simulations and experiments. The utilization of the stronger A-PRF as the main retention force is a consequence of standing-wave formation along the flow direction, instead of the orthogonal direction as in the case of traditionally used lateral-PRF S-BAW trapping setups. The study of particle dynamics reveals that the competition between A-PRF and viscous drag force governs particle trajectory. The ratio of the acoustic energy to the viscous work $\left(\beta \right)$ provides a general criterion for particle trapping at a distinctive off-node site that is spatially controllable. Particles get trapped for $\beta \ge {\beta }_{\mathrm{cr}}$ at some distance away from the nodal plane and the distance varies as ${\beta }^{-c} \left(c=0.6–1.0\right)$. The use of A-PRF as the retention force could potentially allow traditional S-BAW trapping systems to envisage high-throughput advancements surpassing the current standards in cell-handling unit operations.

Modern equations of state for real nonspherical molecules are often based on Wertheim's first-order thermodynamic perturbation theory (TPT1). A major drawback of TPT1 is that it assumes tangentially bonded spheres. In this work, we develop a Helmholtz energy functional for systems comprising hard heterosegmented chains with arbitrary bond lengths. This is achieved by using hard-sphere fragments (i.e., hard spheres with spherical caps removed at the intersection to their neighbors) as monomers as opposed to full hard spheres. The model is written as a Helmholtz energy functional for inhomogeneous systems and the equation of state for a homogeneous system is determined as a special case. We thereby obtain an equation of state that can be used as a reference to develop statistical associating fluid theory models that more accurately describe the thermodynamic properties of nonspherical molecules. The model is validated against molecular simulation results of bulk pressures and density profiles in slit pores. For the bulk pressures, we show that the equation of state is in excellent agreement with results from molecular simulation for dimers, trimers, and chains of up to 20 segments. The density profiles of individual segments of the chains are regarded in slit pores. Some deviations of the theory from results of molecular simulations are observed for strongly fused chains. Overall, however, good agreement is found for inhomogeneous systems.

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often observed to be non-Markovian, and the dynamics of their links are often correlated. Hence, to accurately model these networks, predict their evolution, and understand how information and other relevant quantities propagate over them, the inclusion of both memory and dynamical dependencies between links is key. In this article we introduce a general class of models of temporal networks based on discrete autoregressive processes for link dynamics. As a concrete and useful case study, we then concentrate on a specific model within this class, which allows to generate temporal networks with a specified underlying structural backbone, and with precise control over the dynamical dependencies between links and the strength and length of their memories. In this network model the presence of each link is influenced not only by its past activity, but also by the past activities of other links, as specified by a coupling matrix, which directly controls the causal relations, and hence the correlations, among links. We propose a maximum likelihood method for estimating the model's parameters from data, showing how the model allows a more realistic description of real-world temporal networks and also to predict their evolution. Due to the flexibility of maximum likelihood inference, we illustrate how to deal with heterogeneity and time-varying patterns, possibly including also nonstationary network dynamics. We then use our network model to investigate the role that, both the features of memory and the type of correlations in the dynamics of links have on the properties of processes occurring over a temporal network. Namely, we study the speed of a spreading process, as measured by the time it takes for diffusion to reach equilibrium. Through both numerical simulations and analytical results, we are able to separate the roles of autocorrelations and neighborhood correlations in link dynamics, showing that not only is the speed of diffusion nonmonotonically dependent on the memory length, but also that correlations among neighboring links help to speed up the spreading process, while autocorrelations slow it back down. Our results have implications in the study of opinion formation, the modeling of social networks, and the spreading of epidemics through mobile populations.

Contact inhibition limits migration and proliferation of cells in cell colonies. We consider a multiphase field model to investigate the growth dynamics of a cell colony, composed of proliferating cells. The model takes into account the mechanism of contact inhibition of proliferation by local mechanical interactions. We compare nonmigrating and migrating cells, in order to provide a quantitative characterization of the dynamics and analyze the velocity of the colony boundary for both cases. Additionally, we measure single cell velocities, number of neighbor distributions, as well as the influence of stress and age on positions of the cells and with respect to each other.

This is the first of a pair of articles that present the theory of kinetic and transport phenomena in micelle-forming surfactant solutions in a form that facilitates discussion of large deviations from equilibrium. Our goal is to construct approximate but robust reduced models for both homogeneous and inhomogeneous systems as differential equations for unimer concentration $c_1$, micelle number concentration $c_{\mathrm{m}}$, average micelle aggregation number $q$ and (optionally) aggregation number variance ${\sigma }_{\mathrm{m}}^2$. This first article discusses kinetics in homogeneous solutions. We focus particularly on developing models that can describe both weakly perturbed states and states in which $c_1$ is suppressed significantly below the critical micelle concentration, which leads to rapid shrinkage and dissociation of any remaining micelles. This focus is motivated by the strong local suppression of $c_1$ that is predicted to occur near interfaces during some adsorption processes that are considered in the second article. Toward this end, we develop a general nonlinear theory of fast stepwise processes for systems that may be subjected to large changes in $q$ and $c_1$. This is combined with the existing nonlinear theory of slow association and dissociation processes to construct a general model for systems governed by stepwise reaction kinetics. We also consider situations in which the slow process of micelle creation and destruction instead occurs primarily by micelle fission and fusion, and analyze the dependencies of micelle lifetime and the slow relaxation time upon surfactant concentration in systems controlled by either association-dissociation or fission-fusion mechanisms.

We discuss diffusion in micellar surfactant solutions in a form appropriate for analyzing experiments that involve large deviations from equilibrium. A general nonlinear dynamical model for inhomogeneous systems is developed that describes the effects of diffusion and micelle kinetics as a set of coupled partial differential equations for unimer concentration, micelle number concentration, average micelle aggregation number, and, optionally, the variance of the micelle aggregation number. More specialized models are developed to describe slow dynamics in situations in which the system stays in a state of partial local equilibrium or full local equilibrium. As an illustrative example of a nonlinear transport phenomenon, we discuss a simple model of diffusion from an initially homogeneous micellar solution to a rapidly created absorbing interface with fast unimer adsorption.

Experiments of periodically sheared colloidal suspensions or soft amorphous solids display a transition from reversible to irreversible particle motion that, when analyzed stroboscopically in time, is interpreted as an absorbing phase transition with infinitely many absorbing states. In these systems, interactions mediated by hydrodynamics or elasticity are present, causing passive regions to be affected by nearby active ones. We show that mediated interactions induce a universality class of absorbing phase transitions distinct from conserved directed percolation, and we obtain the corresponding critical exponents. We do so with large-scale numerical simulations of a minimal model for the stroboscopic dynamics of sheared soft materials and we derive the minimal field theoretical description.

In semisupervised community detection, the membership of a set of revealed nodes is known in addition to the graph structure and can be leveraged to achieve better inference accuracies. While previous works investigated the case where the revealed nodes are selected at random, this paper focuses on correlated subsets leading to atypically high accuracies. In the framework of the dense stochastic block model, we employ statistical physics methods to derive a large deviation analysis of the number of these rare subsets, as characterized by their free energy. We find theoretical evidence of a nonmonotonic relationship between reconstruction accuracy and the free energy associated to the posterior measure of the inference problem. We further discuss possible implications for active learning applications in community detection.

We investigate the first passage properties of a Brownian particle diffusing freely inside a $d$-dimensional sphere with absorbing spherical surface subject to stochastic resetting. We derive the mean time to absorption (MTA) as functions of resetting rate $\gamma$ and initial distance $r$ of the particle to the center of the sphere. We find that when $r>r_c$ there exists a nonzero optimal resetting rate ${\gamma }_{\mathrm{opt}}$ at which the MTA is a minimum, where $r_c=\sqrt{d/\left(d+4\right)}R$ and $R$ is the radius of the sphere. As $r$ increases, ${\gamma }_{\mathrm{opt}}$ exhibits a continuous transition from zero to nonzero at $r=r_c$. Furthermore, we consider that the particle lies between two two-dimensional or three-dimensional concentric spheres with absorbing boundaries, and obtain the domain in which resetting expedites the MTA, which is $(R_1,r_{c_1})\cup (r_{c_2},R_2)$, with $R_1$ and $R_2$ being the radii of inner and outer spheres, respectively. Interestingly, when $R_1/R_2$ is less than a critical value, ${\gamma }_{\mathrm{opt}}$ exhibits a discontinuous transition at $r=r_{c_1}$; otherwise, such a transition is continuous. However, at $r=r_{c_2}$ the transition is always continuous.

Using external illumination cues, we induce the formation and dissolution of laboratory swarms of the nonbiting midge Chironomus riparius and study their behavior during these transient processes. In general, swarm formation is slower than swarm dissolution. We find that the swarm property that appears most rapidly during formation and disappears most rapidly during dissolution is an emergent mean radial acceleration pointing toward the center of the swarm. Our results strengthen the conjecture that this central effective force may be used as an indicator to distinguish when the midges are swarming from when they are not.

The current filamentation instability, which generically arises in the counterstreaming of plasma flows, is known for its ability to convert the free energy associated with anisotropic momentum distributions into kinetic-scale magnetic fields. The saturation of this instability has been extensively studied in symmetric configurations where the interpenetrating plasmas share the same properties (velocity, density, temperature). In many physical settings, however, the most common configuration is that of asymmetric plasma flows. For instance, the precursor of relativistic collisionless shock waves involves a hot, dilute beam of accelerated particles reflected at the shock front and a cold, dense inflowing background plasma. To determine the appropriate criterion for saturation in this case, we have performed large-scale two-dimensional particle-in-cell simulations of counterstreaming electron-positron pair and electron-ion plasmas. We show that, in interpenetrating pair plasmas, the relevant criterion is that of magnetic trapping as applied to the component (beam or plasma) that carries the larger inertia of the two; namely, the instability growth suddenly slows down once the quiver frequency of those particles equals or exceeds the instability growth rate. We present theoretical approximations for the saturation level. These findings remain valid for electron-ion plasmas provided that electrons and ions are close to equipartition in the plasma flow of larger inertia. Our results can be directly applied to the physics of relativistic, weakly magnetized shock waves, but they can also be generalized to other cases of study.

We elucidate the nature of universal scaling in a class of quenched disordered driven models. In particular, we explore the intriguing possibility of whether coupling with quenched disorders can lead to continuously varying universality classes. We examine this question in the context of the Kardar-Parisi-Zhang (KPZ) equation, with and without a conservation law, coupled with quenched disorders having distributions with pertinent structures. We show that when the disorder is relevant in the renormalization group sense, the scaling exponents can depend continuously on a dimensionless parameter that defines the disorder distribution. This result is generic and holds for quenched disorders with or without spatially long-ranged correlations, as long as the disorder remains a “relevant perturbation” on the pure system in the renormalization group sense and a dimensionless parameter naturally exists in its distribution. We speculate on its implications for generic driven systems with quenched disorders, and we compare and contrast with the scaling displayed in the presence of annealed disorders.