We present a simple and microscopic physical model that breaks the ergodicity. Our model consists of coupled classical harmonic oscillators, and the motion of the tagged particle obeys the generalized Langevin equation satisfying the second fluctuation dissipation theorem. It is found that although the nonergodicity strength, which is expected to detect the ergodicity breaking, for this model vanishes, the velocity autocorrelation function of the tagged particle asymptotically oscillates. We analyze the model by using the molecular dynamics and the exact diagonalization as well as the rigorous mapping to the generalized Langevin equation. Our analysis reveals that the asymptotic oscillation is caused by a localized mode with an isolated frequency from the continuous phonon spectrum.

The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis and bistability are also present if the frequency distribution of a single network is bimodal. In this study, we are interested in the interplay of these two configurations and analyze the Kuramoto model with compact bimodal frequency distributions in the continuum limit. As of yet, a rigorous analytic treatment has been elusive. By combining Kuramoto's self-consistency approach, Crawford's symmetry considerations, and exploiting the Ott-Antonsen ansatz applied to a family of rational distribution functions that converge towards the compact distribution, we derive a full bifurcation diagram for the system's order-parameter dynamics. We show that the route to synchronization always passes through a standing wave regime when the bimodal distribution is compounded by two unimodal distributions with compact support. This is in contrast to a possible transition across a region of bistability when the two compounding unimodal distributions have infinite support.

The existence of stable bound states of three solitons in a Bose-Einstein condensate with nonlocal interactions is demonstrated by means of the variational approach (VA) and numerical simulations. The potential of interaction between solitons derived from VA is shown to be of molecular type, i.e., attractive at long distances and repulsive at short distances. Normal modes of a three-soliton molecule are investigated by computing small amplitude oscillations of individual solitons near their equilibrium positions. Symmetric and asymmetric stretched states of the molecule are prepared and used as initial conditions in numerical simulations of the nonlocal Gross-Pitaevskii equation. As opposed to usual triatomic molecules, we find that the frequency of the asymmetric mode of a three-soliton molecule is smaller than the one of the symmetric mode. Possible experimental settings for the observation of these results are briefly discussed.

Networks are often presented as containing a “core” and a “periphery.” The existence of a core suggests that some vertices are central and form the skeleton of the network, to which all other vertices are connected. An alternative view of graphs is through communities. Multiple measures have been proposed for dense communities in graphs, the most classical being $k$-cliques, $k$-cores, and $k$-plexes, all presenting groups of tightly connected vertices. We here show that the edge number thresholds for such communities to emerge and for their percolation into a single dense connectivity component are very close, in all networks studied. These percolating cliques produce a natural core and periphery structure. This result is generic and is tested in configuration models and in real-world networks. This is also true for $k$-cores and $k$-plexes. Thus, the emergence of this connectedness among communities leading to a core is not dependent on some specific mechanism but a direct result of the natural percolation of dense communities.

Internet communication channels, e.g., Facebook, Twitter, and email, are multiplex networks that facilitate interaction and information-sharing among individuals. During brief time periods users often use a single communication channel, but then communication channel alteration (CCA) occurs. This means that we must refine our understanding of the dynamics of social contagions. We propose a non-Markovian behavior spreading model in multiplex networks that takes into account the CCA mechanism, and we develop a generalized edge-based compartmental method to describe the spreading dynamics. Through extensive numerical simulations and theoretical analyses we find that the time delays induced by CCA slow the behavior spreading but do not affect the final adoption size. We also find that the CCA suppresses behavior spreading. On two coupled random regular networks, the adoption size exhibits hybrid growth, i.e., it grows first continuously and then discontinuously with the information transmission probability. CCA in Erdős-Rényi–Scale-Free (ER-SF) multiplex networks in which two subnetworks are ER and SF introduces a crossover from continuous to hybrid growth in adoption size versus information transmission probability. Our results extend our understanding of the role of CCA in spreading dynamics and may elicit further research.

Most empirical studies of networks assume that the network data we are given represent a complete and accurate picture of the nodes and edges in the system of interest, but in real-world situations this is rarely the case. More often the data only specify the network structure imperfectly: Like data in essentially every other area of empirical science, network data are prone to measurement error and noise. At the same time, the data may be richer than simple network measurements, incorporating multiple measurements, weights, lengths, or strengths of edges, node or edge labels, or annotations of various kinds. Here we develop a general method for making estimates of network structure and properties using any form of network data, simple or complex, when the data are unreliable, and give example applications to a selection of social and biological networks.

In this paper we study the structural properties of a functional network of the human brain during the evaluation of mental tasks using the concept of betweenness centrality. We carry out the experiments involving the alternating trials of mental task evaluation with simultaneous registration of electroencephalographic (EEG) data. Using the wavelet phase coherence we reconstruct the functional multiplex network of the brain considering the different typical frequency bands of EEG activity as interconnected layers. We reveal that transition from a resting state to evaluation of a cognitive task leads to the strong outflow of shortest paths from low frequencies and strengthening of high-frequency connectivity in the brain. At the same time, we observe that mental activity shapes the shortest paths in a more uniform distribution across the brain, which implies the emergence of a more distributed functional network. Our results are in good agreement with recent studies of cognitive activity and can be implied in the design of brain-computer interfaces for the estimation of cognitive load or attention.

Transient networks composed of polymers connected by short-lived bonds are a common design theme for biological and synthetic materials. Transient bonds can provide mechanical rigidity, while still allowing for viscoelastic flows on timescales longer than the bond lifetime. In many biological polymer networks, such as the actin cytoskeleton, the short-lived bonds are formed by accessory proteins that diffuse away after unbinding. By contrast, bonds in synthetic networks, such as the pendant groups of telechelic polymers, can only rebind in the same location. Using a recently developed theoretical model of the fracturing of viscoelastic materials, we here investigate the effect of linker mobility on the bond dynamics of a network under stress. We find that although mean-field properties such as the average bond linker lifetime are barely affected by bond mobility, networks crosslinked by mobile bonds fracture more readily due to “leaking” of linkers from crack areas to less-stressed regions within the network. We propose a theoretical model to describe the redistribution of mobile linkers, which we validate by simulations. Our work offers insight into a potential tradeoff that cells face, between fracture strength versus the modularity and tight dynamic control offered by mobile linkers.

Colloidal particles, including ferrofluidic nanoparticles (NP), move in a temperature gradient due to thermodiffusion. Organic salts, which are often added to disperse the NP in aqueous solution, also move in the temperature gradient. This can have a strong influence on the behavior of the NP, which not only respond to the temperature gradient but also to the concentration gradient of the dispersive salt, an effect termed diffusiophoresis. In this work we present experimental results on thermodiffusion of iron oxide nanoparticles dispersed in aqueous solutions of organic hydroxides, which illustrate the possibility to manipulate the thermodiffusion of NP through the addition of organic salts. Our experiments investigate the temperature dependence of the particles' Soret coefficient, a recurring question on thermodiffusion of water-dispersed particles. Existing theoretical approaches are compared and we relate the Soret coefficient of the NP with two main physical parameters ruling particle motion: the NP's electrostatic potential and the Soret coefficient of the dispersing ions. These parameters are also experimentally determined. At the order of magnitude of the NP's Soret coefficient good agreement between experiments and theory is achieved by including the experimental data on the Soret coefficient of the dispersing ions and therefore the NP's displacement due to the ion concentration gradient. Taking into account the temperature dependence of such previously unknown parameters is a relevant step to describe the temperature dependence of the NP's Soret coefficient.

Superlattice formation in dried suspensions of colloidal silver nanocrystals (AgNCs) is investigated through a combination of experiment, theory, and simulation. Using microscopic and spectroscopic techniques, we explore the phase behavior of dried AgNC suspensions, and we model the system using Monte Carlo simulations of a coarse-grained model with an effective pair potential that accounts for the composition of the nanocrystal core, the stabilizing ligand shell, and entropic effects associated with unbound ligand in solution. In the absence of free ligands, the effective potential at ligand contact is purely repulsive, and we find superlattice formation at an effective AgNC volume fraction close to that anticipated for hard-sphere freezing. In the presence of free ligands, the effective potential becomes attractive, and crystallization is accompanied by phase separation and multiphase coexistence, as anticipated for colloid-polymer mixtures.

Gels are very important states of matter in our life and can be classified into three types: chemical, stable physical, and transient gels. The first two are formed by the percolation of chemical and physical bonds, respectively, and practically have an infinite lifetime, meaning that they have nonzero static shear moduli and behave as soft solids. On the other hand, the last one is formed only transiently during demixing of a dynamically asymmetric mixture composed of large (slow) and small (fast) components. It emerges as a transient percolated network of the large components, and accordingly it has a finite lifetime (or, it eventually behaves as a liquid). Although the states of chemical and physical gels are reasonably well understood, the physical understanding of transient gelation has remained very poor; for example, a mechanical boundary condition originating from transient elasticity has not been considered before. The fundamental difficulty originates from the fact that transient gelation is a dynamically evolving nonequilibrium process as a consequence of complex dynamical interplay between phase separation and mechanical relaxation (or rheology), but there is no reliable theory for the rheology of a nonequilibrium system. To overcome this difficulty and elucidate the physical essence of transient gelation, we combine experimental and theoretical approaches to study the volume-shrinking kinetics of a transient gel and compare it with that of a permanent chemical gel undergoing a volume phase transition. We reveal that the volume-shrinking behavior of a transient gel is fundamentally different from that of a chemical gel. A permanent gel has static elasticity coming from its permanent network topology. In contrast, a transient gel is formed by hierarchical structure formation (polymers $\to$ globules $\to$ percolated network) and is stabilized only by weak van der Waals bonding between globules, and thus it does not have static elasticity and its elasticity decays with time: viscoelastic relaxation. This relaxational feature leads to the switching of the relevant order parameter during phase separation in the order of scalar (composition), tensors (volume and shear deformations), and scalar (composition). Depending on the relation of the deformation rate generated by phase separation itself to the bulk and shear mechanical relaxation rates, a transient network behaves liquid-like, viscoelastic, and elastic; leading to liquid-like, ductile, and brittle fracture of the network during shrinking, respectively. We also find that the emergence of elasticity during transient gelation is the reverse of its disappearance and there is a one-to-one correspondence between them, strongly indicating the key role of viscoelastic relaxation in transient gelation. We argue that these basic features should be generic to any demixing-induced transient gels of soft matter, including polymer solutions, colloidal suspensions, emulsions, and biological solutions such as protein solutions. Our finding not only sheds new light on the physical nature of this intrinsically nonequilibrium transient state of matter but also provides the physical basis for demixing of soft- and bio-matter.

Fast-field-cycling nuclear-magnetic-resonance (FFC NMR) experimentation measures the spin-lattice relaxation rate $T_1^{-1}=R_1$ as a function of NMR frequency $f$. It is a proven technique for probing the nanoscale dynamics of ${}^1\mathrm{H}$ spins over multiple timescales. In many porous systems, fluid is confined to quasi-zero-dimensional (closed), quasi-one-dimensional (channel), or quasi-two-dimensional (planar) pores. Expressions are presented for $R_1\left(f\right)$ providing simulated dispersion curves for closed, channel, and planar pores where relaxation is associated with fluid movement relative to fixed relaxation centers in the solid. It is shown that fluid confined to nanosized (1–5 nm) spaces can be identified by submillisecond relaxation times for any geometry. The shape and magnitude of $R_1\left(f\right)$ is shown to be sensitive to pore geometry at low frequency only if relaxation is dominated by the motion of pore bulk fluid. Relaxation in most porous material is dominated by slow-moving surface fluid. Here, the pore geometry can only be distinguished if the relaxation center density is known a priori and then only at very low frequency. Systems containing mixtures of closed, channel, and planar pores of similar characteristic dimension $h$ would present as three peaks at low frequency with closed pores providing the largest $R_1$ and planar pores the smallest. Pore size and shape variability in real systems is shown to diminish the ability to distinguish the three peaks. We show that the ratio $T_1/T_2$, where $T_2$ is the spin-spin relaxation time, is a complex function of $h$, the surface diffusion time constant ${\tau }_{\ell }$, and NMR frequency for $f>1$ MHz. It is shown that measurements of $T_1/T_2$ at 20 MHz in cement paste and hydrocarbon rock capture information on both ${\tau }_{\ell }$ and $h$.

Microscale swimming may be intuited to be dominated by background flows, sweeping away any untethered bodies with the prevalent flow direction. However, it has been observed that many microswimmers utilize ambient flows as guidance cues, in some cases resulting in net motion upstream, contrary to the dominant background fluid direction and our accompanying intuition. Thus the hydrodynamic response of small-scale motile organisms requires careful analysis of the complex interaction between swimmer and environment. Here we investigate the effects of a Newtonian shear flow on monoflagellated swimmers with specified body symmetry, representing, for instance, the Leishmania mexicana promastigote, a parasitic hydrodynamic puller that inhabits the microenvironment of a sandfly vector midgut and is the cause of a major and neglected human tropical disease. We observe that a lack of symmetry-breaking cellular geometry results in the periodic tumbling of swimmers in the bulk, with the rotations exhibiting a linear response to changes in shearing rate enabling analytic approximation. In order to draw comparisons with the better-studied pushers, we additionally consider virtual Leishmania promastigotes in a confined but typical geometry, that of a no-slip planar solid boundary, and note that in general stable guided taxis is not exhibited amongst the range of observed behaviors. However, a repulsive boundary gives rise to significant continued taxis in the presence of shearing flow, a phenomenon that may be of particular pertinence to the infective lifecycle stage of such swimmers subject to the assumption of a Newtonian medium. We finally propose a viable and general in vitro method of controlling microswimmer boundary accumulation using temporally evolving background shear flows, based on the analysis of phase-averaged dynamics and verified in silico.

In this work, an improved fully implicit discrete-velocity method (DVM) is developed for flows over all Knudsen numbers. The improvements aim to overcome the drawbacks of the conventional semi-implicit DVM which performs with low accuracy and efficiency in the continuum flow regime. These defects originate from the explicit discretization of the equilibrium state in the collision term at the cell center and the ignorance of the particle collision effect in the calculation of numerical flux on the cell interface. To alleviate these drawbacks, the present method innovatively incorporates an implicit prediction step into the conventional model. In this step, the macroscopic governing equation is resolved to estimate the equilibrium state, and the local solution of the Boltzmann equation with the collision term is adopted to physically reconstruct the macroscopic numerical flux. Two major merits are brought by this strategy. On one hand, by using the predicted equilibrium state, the collision term in the discrete velocity Boltzmann equation can be discretized implicitly, which significantly improves the computational efficiency. On the other hand, the consideration of the collision effect in the physical reconstruction of the numerical flux on the cell interface benefits the solution accuracy, especially in the continuum flow regime. Meanwhile, the developed scheme well keeps the inherent simplicity of the conventional semi-implicit DVM by maintaining the basic resolving process of distribution functions. Numerical results show that in the rarefied flow regime, the improved scheme gives a similar solution as the conventional semi-implicit DVM with little extra computational efforts, while in the continuum flow regime, the present scheme shows higher efficiency and accuracy.

In this paper, a simplified multiphase lattice Boltzmann method (SMLBM) is developed for modeling incompressible multiphase flows with large density ratios and complex interfaces. SMLBM is derived from reconstructing solutions to macroscopic equations recovered from the multiphase lattice Boltzmann model through Chapman-Enskog expansion analysis and resolved in a predictor-corrector step. The Cahn-Hilliard equation is utilized as the interface tracking algorithm, the solution of which is also reconstructed within the lattice Boltzmann framework. The resultant formulation of SMLBM reflects a direct update of macroscopic variables instead of distribution functions, which could remarkably save virtual memory and facilitate implementation of physical boundary conditions. Numerical tests also indicate that our scheme could effectively simulate challenging cases with large density ratios (up to 1000) and complex interfaces, and at high Reynolds numbers.

We study the optimal performance of Carnot-like heat engines working in the low-dissipation regime using the product of the efficiency and the power output, also known as the efficient power, as our objective function. Efficient power function represents a trade-off between power and efficiency of a heat engine. We find lower and upper bounds on the efficiency in the case of extreme asymmetric dissipation when the ratio of dissipation coefficients at the cold and the hot contacts approaches, respectively, zero or infinity. In addition, we obtain the form of efficiency for the case of symmetric dissipation. We also discuss the universal features of efficiency at maximum efficient power and derive the bounds on the efficiency using a global linear-irreversible framework introduced recently by one of the authors.

We have studied the statistics of semiflexible linear polymer chains modeled by self-avoiding random walk (SAW) on the square lattice. We applied the PERM Monte Carlo simulation method to sample the polymer chain configurations for SAWs up to 2000 steps. Varying the stiffness parameter $s$ of the chain we have calculated numerically the critical exponents $\nu$ (associated with the mean squared end-to-end distance of polymer chain) and $\gamma$ (associated with the partition function of polymer chain system), as well as the growth constant $\mu$. We find a clear numerical evidence that, in the studied region of $s$, both critical exponents ($\nu$ and $\gamma$) do not depend on polymer flexibility. Besides, for moderately flexible chains, we show that the growth constant $\mu$ displays a linear dependance on the stiffness parameter $s$. We discuss and relate our findings to those obtained previously for Euclidean and fractal polymer containers.

We introduce an assisted exchange model (AEM) on a one-dimensional periodic lattice with $(K+1)$ different species of hardcore particles, where the exchange rate depends on the pair of particles which undergo exchange and their immediate left neighbor. We show that this stochastic process has a pair-factorized steady state for a broad class of exchange dynamics and calculate particle current and spatial correlations analytically for any $K>0$ using a transfer matrix formalism. Interestingly, the current in AEM exhibits density-dependent current reversal and negative differential mobility, both of which have been discussed elaborately by using a two-species exchange model which resembles the partially asymmetric conserved lattice gas model in one dimension. Moreover, the multispecies version of AEM exhibits additional features like multiple points of current reversal and an unusual response where the current-bias relation has multiple extrema.

We introduce a Gibbs Markov random field for spatial data on Cartesian grids based on the modified planar rotator (MPR) model of statistical physics. The MPR model captures spatial correlations using nearest-neighbor interactions of continuously valued spins and does not rely on Gaussian assumptions. The only model parameter is the reduced temperature, which we estimate by means of an ergodic specific energy matching principle. We propose an efficient hybrid Monte Carlo simulation algorithm that leads to fast relaxation of the MPR model and allows vectorization. Consequently, the MPR model's computational time for inference and simulation scales approximately linearly with system size. This makes it more suitable for big data sets, such as satellite and radar images, than conventional geostatistical approaches. The performance (accuracy and computational speed) of the MPR model is validated with conditional simulation of Gaussian synthetic and non-Gaussian real data (atmospheric heat release measurements and Walker-lake DEM-based concentrations) and comparisons with standard gap-filling methods.