Motivated by cancer cell capture and sorting applications, we investigate the scalar velocity field of two-dimensional (2D) laminar flows through configurations of fixed congruent circular disks with a disordered hyperuniform (HU) distribution of the disk centers. Disordered HU many-particle systems suppress large-scale density fluctuations like perfect crystals and yet possess no Bragg peaks, and are endowed with many novel physical properties. Here, we generate 2D HU configurations of congruent nonoverlapping (hard) circular disks with various packing densities via Monte Carlo simulations and obtain the corresponding scalar velocity fields of laminar flows via the lattice Boltzmann method. Using numerical spectral analysis, we find that hyperuniform configurations of the disks can lead to hyperuniform flow fields for a certain range of disk packing fraction $\varphi$ and normalized flow rate $q$ over porosity $\epsilon =1-\varphi$. The degree of hyperuniformity of the flow fields, as quantified via the spectral density value at the zero-wave-number limit, reduces as $\varphi$ and $q$ increase and eventually the fields become nonhyperuniform. The transition from HU flow fields to non-HU fields as $\varphi$ and $q$ vary is captured using a “phase diagram.” For purpose of comparison, disordered nonhyperuniform configurations of circular disks are generated via the random sequential addition process and the resulting flow field is found to be nonhyperuniform. To complement our numerical analysis, we show analytically that HU configurations of circular disks, in the dilute (low-packing-density) limit, lead to HU flow field. Our findings have implications in the design and optimization of microfluidic chips for capture and differentiation of subpopulations in circulating tumor cells.

Many problems in physics demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially collected data. Here we introduce a general methodology for the joint estimation of the static parameters and the forecasting of the state variables of nonlinear stochastic dynamical models. The proposed scheme is essentially probabilistic. It aims at recursively computing the sequence of joint posterior probability distributions of the unknown model parameters and its (time-varying) state variables conditional on the available observations. This framework combines two layers of inference: In the first layer, a grid-based scheme is used to approximate the posterior probability distribution of the fixed parameters; in the second layer, filtering (or data assimilation) techniques are employed to track and predict different conditional probability distributions of the state variables. Various types of procedures (deterministic grids, Monte Carlo, Gaussian filters, etc.) can be plugged into both layers, leading to a wealth of algorithms. For this reason, we refer to the proposed methodology as nested hybrid filtering. In this paper we specifically explore the combination of Monte Carlo and quasi–Monte Carlo (deterministic) approximations in the first layer with Gaussian filtering methods in the second layer, but other approaches fit naturally within the framework. We prove a general convergence result for a class of procedures that use sequential Monte Carlo in the first layer. Then we turn to an illustrative numerical example. In particular, we apply and compare different implementations of the methodology to the tracking of the state, and the estimation of the fixed parameters, of a stochastic two-scale Lorenz 96 system. This model is commonly used to assess data assimilation procedures in meteorology. We show estimation and forecasting results, obtained with a desktop computer, for up to 5000 dynamic state variables.

Concepts like “typicality” and the “eigenstate thermalization hypothesis” aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in which this equilibrium is approached. Our point of departure is the (evident) observation that some forms of the approach to equilibrium, such as, e.g., exponential decay of observables, are much more common than others. We suggest to trace this dominance of certain decay dynamics back to a larger stability with respect to generic Hamiltonian perturbations. A numerical study of a number of examples in which both the unperturbed Hamiltonians and the perturbations are modeled by partially random matrices is presented. We furthermore develop a simple heuristic, mathematical scheme that describes the result of the numerical investigations remarkably well. According to those investigations, the exponential decay indeed appears to be most stable. Dynamics that are in a certain sense at odds with the arrow of time are found to be very unstable.

We discuss a general useful theoretical framework to study dynamical localization in ultracold atomic systems confined in periodically shaken optical lattices. Our theory allows to understand some limitations of the usual approach concerning prototypical $\delta$-kicked systems, as well as to explain the experimental results for which finite-time effects cannot be neglected. Specifically, we predict that the strength of dynamical localization reaches a maximum as a function of the width of the pulsatile modulation, whenever its amplitude and period satisfy a given relationship. Additionally, we describe a quite simple scenario for the quantum suppression of classical diffusion, which is confirmed by extensive numerical simulations: The activation of Heisenberg's uncertainty principle giving rise to a drastic reduction of the quantum momentum dispersion if, and only if, the classical dynamics is sufficiently chaotic.

Using molecular dynamics simulation of a polymer glass model we investigate free-standing polymer films focusing on the in-plane shear modulus $\mu$, defined by means of the stress-fluctuation formula, as a function of temperature $T$, film thickness $H$ (tuned by means of the lateral box size $L$), and sampling time $\mathrm{\Delta }t$. Various observables are seen to vary linearly with $1/H$, demonstrating thus the (to leading order) linear superposition of bulk and surface properties. Confirming the time-translational invariance of our systems, $\mu \left(\mathrm{\Delta }t\right)$ is shown to be numerically equivalent to a second integral over the shear-stress relaxation modulus $G\left(t\right)$. It is thus a natural smoothing function statistically better behaved as $G\left(t\right)$. As shown from the standard deviations $\delta \mu$ and $\delta G$, this is especially important for large times and for temperatures around the glass transition. $\mu$ and $G$ are found to decrease continuously with $T$ and a jump-singularity is not observed. Using the Einstein-Helfand relation for $\mu \left(\mathrm{\Delta }t\right)$ and the successful time-temperature superposition scaling of $\mu \left(\mathrm{\Delta }t\right)$ and $G\left(t\right)$, the shear viscosity $\eta \left(T\right)$ can be estimated for a broad range of temperatures.

While perfect crystals may exhibit a purely elastic response to shear all the way to yielding, the response of amorphous solids is punctuated by plastic events. The prevalence of this plasticity depends on the number of particles $N$ of the system, with the average strain interval before the first plastic event, $\overline{\mathrm{\Delta }\gamma }$, scaling like $N^{\alpha }$ with $\alpha$ negative: larger samples are more susceptible to plasticity due to more numerous disorder-induced soft spots. In this paper we examine this scaling relation in ultrastable glasses prepared with the swap Monte Carlo algorithm, with regard to the possibility of a protocol-dependent scaling exponent, which would also imply a protocol dependence in the distribution of local yield stresses in the glass. We show that, while a superficial analysis seems to corroborate this hypothesis, this is only a preasymptotic effect and in fact our data can be well explained by a simple model wherein such protocol dependence is absent.

Under liquidlike conditions, particles are found to rearrange on multiple timescales in a two-dimensional dusty plasma experiment. Our analysis is based on survival functions, which are time-series graphs of the probability that a particle's number of nearest neighbors remains unchanged. Nondefects are found to exhibit two distinct timescales, revealed by an elbow in their survival function. Defects have survival functions that are more nearly exponential, with decay rates that offer insight at a microscopic level into the viscoelastic relaxation in a liquid.

We introduce policy-guided Monte Carlo (PGMC), a computational framework using reinforcement learning to improve Markov chain Monte Carlo (MCMC) sampling. The methodology is generally applicable, unbiased, and opens up a path to automated discovery of efficient MCMC samplers. After developing a general theory, we demonstrate some of PGMC's prospects on an Ising model on the kagome lattice, including when the model is in its computationally challenging kagome spin ice regime. Here we show that PGMC is able to automatically machine learn efficient MCMC updates without a priori knowledge of the physics at hand.

Advanced optoelectronic simulation models are needed to study and optimize emerging photonic devices such as thin-film solar cells, lasers, and light-emitting diodes (LEDs). In particular, better tools are required for self-consistent modeling of coupled electrical and optical systems. The recently introduced quantized fluctuational electrodynamics (QFED) and the associated interference-exact radiative transfer equations have been developed for this purpose, but their use is in part complicated by the need to calculate the full dyadic Green's functions. To make QFED and the underlying physical quantities more accessible for new device studies, we introduce a directly usable method where Green's functions are obtained through optical admittances. The optical admittances can be solved analytically for piecewise-homogeneous layer structures and selected graded-index profiles, and numerically for arbitrary position-dependent refractive index profiles using well-known techniques. The solutions enable direct construction of the dyadic Green's functions and all the related optical quantities. To give examples of the general applicability of the method, we calculate the local and nonlocal optical densities of states for selected devices, including GaN-based flip-chip LEDs and vertical-cavity surface-emitting lasers. Using only the rather simple framework presented in this paper, one can analyze energy transport in a wide range of planar photonic devices accurately without additional difficulties or inputs from external solvers.

We investigate the roughness properties of the three-phase contact line on random self-affine rough surfaces by means of numerical simulations in the framework of the full capillary model. In contrast to the theoretically predicted universal exponents ${\zeta }_s=1/2$ for short and ${\zeta }_l=1/3$ for long length scales determined within the assumption for weak heterogeneity, a broad range of roughness exponents have been reported in numerous experimental studies. We show that both scaling exponents depend on the surface properties as well as on the equilibrium contact angle, and that their values lie within the intervals ${\zeta }_s\in [0.75,0.9]$ and ${\zeta }_l\in [0,0.65]$. Our results explain the origin of the experimentally obtained roughness exponents and show that the assumption of randomly distributed isolated defects is insufficient when wetting on real surfaces is considered.

We investigate the influence of the range of interactions in the two-dimensional bond percolation model by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges, as expressed by the number $z$ of equivalent neighbors. We also consider the $z\to \infty$ limit, i.e., the complete graph case, where percolation bonds are allowed between each pair of sites, and the model becomes mean-field-like. All investigated models with finite $z$ are found to belong to the short-range universality class. There is no evidence of a tricritical point separating the short-range and long-range behavior, such as is known to occur for $q=3$ and $q=4$ Potts models. We determine the renormalization exponent describing a finite-range perturbation at the mean-field limit as $y_r\approx 2/3$. Its relevance confirms the continuous crossover from mean-field percolation universality to short-range percolation universality. For finite interaction ranges, we find approximate relations between the coordination numbers and the amplitudes of the leading correction terms as found in the finite-size scaling analysis.

A model is developed for anisotropies in the conductivity in monodisperse systems of uniaxially aligned cylindrical fibers. Concepts from percolation theory (specifically, a lattice approach toward describing percolation by rods with large aspect ratios) are unified with a simple picture based upon resistors combined in series and parallel to calculate the conductivities in fiber-based nanocomposites in directions that are longitudinal and transverse with respect to the axis of particle alignment. Results obtained for three different orientational distribution functions (ODFs) reveal a peak in the dependence of the longitudinal conductivity upon mean orientational order parameter ($\langle S\rangle$), qualitatively similar to findings that have been reported from computer simulations. In contrast, the transverse conductivity decreases monotonically with increasing values of $\langle S\rangle$ for each of the ODFs investigated.

In this work, we investigate solitary waves in a nonlinear two-dimensional discrete electrical lattice. It is made of several of the well-known Noguchi electrical transmission lines, that are transversely or longitudinally coupled to one another by an inductor $L_2$ or $L_1$ and a capacitor $C_2$ or $C_1$ mounted in parallel. The linear dispersion law of the network is given and the effects of the transverse coupling elements $L_2$ and $C_2$ on the allowed bandwidth frequencies are examined. Using the continuum limit approximation, we show that the dynamics of the small amplitude signals in the network can be governed by a (2+1)-dimensional generalized modified Zakharov-Kuznetsov equation. The fixed points of our model equation are examined and the bifurcations of its phase portrait are presented, as functions of the wave velocity of the signals that are to propagate in lattice. Likewise, we derive exact explicit solutions that are possible under different wave velocities and for physically realistic values of the network's parameters. These include pulse, kink, and anti-kink wave solutions and correspond to some special level curves of the first integral of the model equation. We find out that the transverse coupling parameters considerably affect the characteristics of the waves that are propagated throughout the system. Direct numerical simulations are also performed on the exact equations of the network and the results are in agreement with the analytical predictions.

An articulation point (AP) in a network is a node whose deletion would split the network component on which it resides into two or more components. APs are vulnerable spots that play an important role in network collapse processes, which may result from node failures, attacks, or epidemics. Therefore, the abundance and properties of APs affect the resilience of the network to these collapse scenarios. Here we present analytical results for the statistical properties of APs in configuration model networks. In order to quantify the abundance of APs, we calculate the probability $P(i\in \mathrm{AP})$ that a random node, $i$, in a configuration model network with a given degree distribution, $P(K=k)$, is an AP. We also obtain the conditional probability $P(i\in \mathrm{AP}|k)$ that a random node of degree $k$ is an AP and find that high-degree nodes are more likely to be APs than low-degree nodes. Using Bayes's theorem, we obtain the conditional degree distribution, $P(K=k|\mathrm{AP})$, over the set of APs and compare it to the overall degree distribution $P(K=k)$. We propose a centrality measure based on APs: Each node can be characterized by its articulation rank, $r$, which is the number of components that would be added to the network upon deletion of that node. For nodes which are not APs, the articulation rank is $r=0$, while for APs it satisfies $r\ge 1$. We obtain a closed-form analytical expression for the distribution of articulation ranks, $P(R=r)$. Configuration model networks often exhibit a coexistence between a giant component and finite components. While the giant component is extensive in the network size and exhibits cycles, the finite components are nonextensive tree structures. To examine the distinct properties of APs on the giant and on the finite components, we calculate the probabilities presented above separately for the giant and the finite components. We apply these results to ensembles of configuration model networks with degree distributions that follow a Poisson distribution (Erdős-Rényi networks), an exponential distribution of the form $P(K=k)\sim e^{-\alpha k}$, and a power-law distribution of the form $P(K=k)\sim k^{-\gamma }$ (scale-free networks), where $k\ge k_{\min }=1$. The implications of these results are discussed in the context of common attack scenarios and network dismantling processes.

A pivotal idea in network science, marketing research, and innovation diffusion theories is that a small group of nodes—called influencers—have the largest impact on social contagion and epidemic processes in networks. Despite the long-standing interest in the influencers identification problem in socioeconomic and biological networks, there is not yet agreement on which is the best identification strategy. State-of-the-art strategies are typically based either on heuristic centrality measures or on analytic arguments that only hold for specific network topologies or peculiar dynamical regimes. Here, we leverage the recently introduced random-walk effective distance—a topological metric that estimates almost perfectly the arrival time of diffusive spreading processes on networks—to introduce a centrality metric which quantifies how close a node is to the other nodes. We show that the new centrality metric significantly outperforms state-of-the-art metrics in detecting the influencers for global contagion processes. Our findings reveal the essential role of the network effective distance for the influencers identification and lead us closer to the optimal solution of the problem.

Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently, mainly thanks to the development of multiplex and time-varying networks. However, these two advancements have progressed almost in parallel with very little overlap. Thus, the interplay between multiplexity and the temporal nature of connectivity patterns is poorly understood. Here, we aim to tackle this limitation by introducing a time-varying model of multiplex networks. We are interested in characterizing how these two properties affect contagion processes. To this end, we study susceptible-infected-susceptible epidemic models unfolding at comparable timescale with respect to the evolution of the multiplex network. We study both analytically and numerically the epidemic threshold as a function of the multiplexity and the features of each layer. We found that higher values of multiplexity significantly reduce the epidemic threshold especially when the temporal activation patterns of nodes present on multiple layers are positively correlated. Furthermore, when the average connectivity across layers is very different, the contagion dynamics is driven by the features of the more densely connected layer. Here, the epidemic threshold is equivalent to that of a single layered graph and the impact of the disease, in the layer driving the contagion, is independent of the multiplexity. However, this is not the case in the other layers where the spreading dynamics is sharply influenced by it. The results presented provide another step towards the characterization of the properties of real networks and their effects on contagion phenomena.

This paper reports the force spectroscopy analysis of a polymer that translocates from one side of a membrane to the other side through an extended pore, pulled by a cantilever that moves with constant velocity against the damping and the potential barrier generated by the reaction of the membrane walls. The polymer is modeled as a beads-springs chain with both excluded volume and bending contributions and moves in a stochastic three-dimensional environment described by a Langevin dynamics at fixed temperature. The force trajectories recorded at different velocities reveal two exponential regimes: The force increases when the first part of the chain enters the pore and then decreases when the first monomer reaches the trans region. The spectroscopy analysis of the force values permit the estimation of the limit force to allow the translocation, related to the free-energy barrier. The stall force to maintain the polymer fixed has been also calculated independently, and its value confirms the force spectroscopy outcomes.

Measuring the effective charge of a molecule inside a conducting fluid is difficult. One of the commonly used techniques is electrophoresis in centimeter-sized gels. Here we implemented a miniaturized, electrophoresis-based method on the microscale using an optically driven photodissociation reaction. Inside a focused laser beam, oppositely charged species of different size are created which diffuse out of the beam with different velocities. This creates a local electrical field which moves charged biomolecules via electrophoresis in the diffusion-dominated regime of low Peclet numbers (Pe < 1). The steady state fluorescence in the center is used to determine the effective biomolecule charge even for large molecules with charge-independent electrophoretic mobilities. We tested the mechanism for DNA and proteins and used two different photochemical reactions to generate inward or outward pointing electrical fields. A master curve described the proton transfer from the photodissociation reaction to the buffer. The full mechanistic understanding offers many possibilities for the all-optical manipulation of molecules.

We consider a class of systems where $N$ identical particles with positions ${\mathbf{q}}_1,...,{\mathbf{q}}_N$ and momenta ${\mathbf{p}}_1,...,{\mathbf{p}}_N$ are enclosed in a box of size $L$ and exhibit the scaling $\mathcal{U}(L{\mathbf{r}}_1,...,L{\mathbf{r}}_N)=\alpha \left(L\right)\mathcal{U}({\mathbf{r}}_1,...,{\mathbf{r}}_N)$ for the associated potential energy function $\mathcal{U}({\mathbf{q}}_1,...,{\mathbf{q}}_N)$. For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box.

Recently, Krüger and Vlugt [Phys. Rev. E 97, 051301(R) (2018)] have proposed a method to approximate an improper integral ${\int }_0^{\infty }drF\left(r\right)$, where $F\left(r\right)$ is a given oscillatory function, by a finite-range integral ${\int }_0^{L}drF\left(r\right)W(r/L)$ with an appropriate weight function $W\left(x\right)$. The method is extended here to an arbitrary (embedding) dimensionality $d$. A study of three-dimensional Kirkwood-Buff integrals, where $F\left(r\right)=4\pi r^{2}h\left(r\right)$, and static structure factors, where $F\left(r\right)=(4\pi /q)rsin\left(qr\right)h\left(r\right)$, $h\left(r\right)$ being the pair correlation function, shows that, in general, a choice $d\ne 3$ (e.g., $d=7$) for the embedding dimensionality may significantly reduce the error of the approximation ${\int }_0^{\infty }drF\left(r\right)\simeq {\int }_0^{L}drF\left(r\right)W(r/L)$.