We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several nontypical phenomena. In two layers, the giant component emerges with a continuous phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent $\gamma$, the discontinuity vanishes but at $\gamma =1.5$ in three layers, more generally at $\gamma =1+1/(M-1)$ in $M$ layers.

We present a new study on the interaction of the DNA molecule with the surfactant dodecyltrimethylammonium bromide (DTAB), performed mainly with optical tweezers. Single-molecule force spectroscopy experiments performed in the low-force entropic regime allowed a robust characterization of the DNA-DTAB interaction, unveiling how the surfactant changes the mechanical properties of the biopolymer, the binding parameters, and the competition of the two mechanisms involved in the interaction: electrostatic attraction between the cationic surfactant heads and the negative phosphate backbone of the DNA and hydrophobic interactions between the tails of the bound DTAB molecules, which can result in DNA compaction in solution depending on the quantity of bound surfactant. Finally, force clamp experiments with magnetic tweezers and gel electrophoresis assays confirm that DTAB compacts DNA depending not only on the surfactant concentration but also on the conformation of the biopolymer in solution. The present study provides new insights on general aspects of the DNA-surfactant complexes formation, contributing to the fundamental knowledge of the physics of such interactions.

Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean-square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e., random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.

A theoretical study on the electrophoresis of a soft particle is made by taking into account the ion steric interactions and ion partitioning effects under a thin Debye layer consideration with negligible surface conduction. Objective of this study is to provide a simple expression for the mobility of a soft particle which accounts for the finite-ion-size effect and the ion partitioning arise due to the Born energy difference between two media. The Donnan potential in the soft layer is determined by considering the ion steric interactions and the ion partitioning effect. The volume exclusion due to the finite ion size is considered by the Carnahan-Starling equation and the ion partitioning is accounted through the difference in Born energy. The modified Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations are considered to determine the mobility. A closed-form expression for the electrophoretic mobility is obtained, which reduces to several existing expressions for mobility under various limiting cases.

This work generalizes the granular integration through transients formalism introduced by Kranz et al. [Phys. Rev. Lett. 121, 148002 (2018)] to the determination of the pressure. We focus on the Bagnold regime and provide theoretical support to the empirical $\mu \left(\mathcal{I}\right)$ rheology laws that have been successfully applied in many granular flow problems. In particular, we confirm that the interparticle friction is irrelevant in the regime where the $\mu \left(\mathcal{I}\right)$ laws apply.

Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the properties of disordered quantum systems as a function of the system size. We implement a scalable convolutional network that can address arbitrary system sizes. This network is compared with a recently introduced extensive convolutional architecture [Mills et al., Chem. Sci. 10, 4129 (2019)] and with conventional dense networks with all-to-all connectivity. The networks are trained to predict the exact ground-state energies of various disordered systems, namely, a continuous-space single-particle Hamiltonian for cold-atoms in speckle disorder, and different setups of a quantum Ising chain with random couplings, including one with only short-range interactions and one augmented with a long-range term. In all testbeds we consider, the scalable network retains high accuracy as the system size increases. Furthermore, we demonstrate that the network scalability enables a transfer-learning protocol, whereby a pretraining performed on small systems drastically accelerates the learning of large-system properties, allowing reaching high accuracy with small training sets. In fact, with the scalable network one can even extrapolate to sizes larger than those included in the training set, accurately reproducing the results of state-of-the-art quantum Monte Carlo simulations.

Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch-angle scattering. This approach is frequently used in particle-based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a structure-preserving numerical algorithm for the Langevin equation for pitch-angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method. The numerical scheme is benchmarked by simulating the pitch-angle scattering of a particle beam and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long-time accuracy of the proposed algorithm.

Collective chemotaxis plays a key role in the navigation of cell clusters in, e.g., embryogenesis and cancer metastasis. Using the active nematic continuum equations, coupled to a chemical field that regulates activity, we demonstrate and explain a physical mechanism that results in collective chemotaxis. The activity naturally leads to cell polarization at the cluster interface which induces outward flows. The chemical gradient then breaks the symmetry of the flow field, leading to a net motion. The velocity is independent of the cluster size, in agreement with experiment.

Electrostatic interactions between point charges embedded into interfaces separating dielectric media are omnipresent in soft matter systems and often control their stability. Such interactions are typically complicated and do not resemble their bulk counterparts. For instance, the electrostatic potential of a point charge at an air-water interface falls off as $r^{-3}$, where $r$ is the distance from the charge, exhibiting a dipolar behavior. This behavior is often assumed to be generic, and is widely referred to when interpreting experimental results. Here we explicitly calculate the in-plane potential of a point charge at an interface between two electrolyte solutions with different, finite dielectric permittivities and Debye screening lengths, such as oil and water. We show that the asymptotic behavior of this potential is neither a dipole, which characterizes the potential at air-water interfaces, nor a screened monopole, which describes the bulk behavior in a single electrolyte solution. By considering the same problem in arbitrary dimensions, we find that the physics behind this difference can be traced to the asymmetric propagation of the interaction in the two media. Our results should be relevant to understand the effective potential acting between interfacial proteins in biofilms, and the self-assembly of charged colloids at droplet surfaces in oil-water emulsions.

For the statistics of currents in quantum transport, microreversibility is shown to provide a way to obtain the statistical cumulants at the order $n+1$ from the measurement of the cumulants at the order $n$ or lower. This fundamental result is based on relations generalizing the fluctuation-dissipation theorem and the Onsager-Casimir reciprocal relations from linear toward nonlinear transport properties, as a consequence of the time-reversal symmetry of the underlying microscopic Hamiltonian dynamics. The method is demonstrated in detail in the case of multiterminal Aharonov-Bohm rings. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is obtained from the scattering matrix of these circuits. The time-reversal symmetry relations are explicitly shown to express the cumulants at equilibrium up to the fourth order in terms of lower-order cumulants and their nonequilibrium responses in the presence of an external magnetic field.

In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian process with transition probabilities between nodes expressed in terms of powers of the Laplacian matrix. We analyze the elements of the transition matrices and their respective eigenvalues and eigenvectors, the mean first passage times and global times to characterize the random walk strategies. We apply this approach to the study of particular local and nonlocal ergodic random walks on different directed networks; we explore circulant networks, the biased transport on rings and the dynamics on random networks. We study the efficiency of a fractional random walker with bias on these structures. Effects of ergodicity loss which occur when a directed network is not any more strongly connected are also discussed.

A quantum Otto engine using two-interacting spins as its working medium is analyzed within framework of stochastic thermodynamics. The time-dependent power fluctuations and average power are explicitly derived for a complete cycle of engine operation. We find that the efficiency and power fluctuations are affected significantly by interparticle interactions, but both of them become interaction-independent under maximal power via optimizing the external control parameter. The behavior of the efficiency at maximum power is further explained by analyzing the optimal protocol of the engine.

The $q$-voter model with independence is investigated on multiplex networks with full overlap of nodes in the layers. The layers are various complex networks corresponding to different levels of social influence. Detailed studies are performed for the model on multiplex networks with two layers with identical degree distributions, obeying the LOCAL&AND and GLOBAL&AND spin update rules differing by the way in which the $q$-lobbies of neighbors within different layers exert their joint influence on the opinion of a given agent. Homogeneous pair approximation is derived for a general case of a two-state spin model on a multiplex network and its predictions are compared with results of mean-field approximation and Monte Carlo simulations of the above-mentioned $q$-voter model with independence for a broad range of parameters. As the parameter controlling the level of agents' independence is changed ferromagnetic phase transition occurs which can be first- or second-order, depending on the size of the lobby $q$. Details of this transition, e.g., position of the critical points, critical exponents and the width of the possible hysteresis loop, depend on the topology and other features of the layers, in particular on the mean degree of nodes in the layers which is directly predicted by the homogeneous pair approximation. If the mean degree of nodes is substantially larger than the size of the $q$-lobby good agreement is obtained between numerical results and theoretical predictions based on the homogeneous pair approximation concerning the order and details of the ferromagnetic transition. In the case of the model on multiplex networks with layers in the form of homogeneous Erdős-Rényi and random regular graphs as well as weakly heterogeneous scale-free networks this agreement is quantitative, while in the case of layers in the form of strongly heterogeneous scale-free networks it is only qualitative. If the mean degree of nodes is small and comparable with $q$ predictions of the homogeneous pair approximation are in general even qualitatively wrong.

We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA.

The lateral migration of a two-dimensional (2D) viscous ferrofluid droplet in a plane Poiseuille flow under a uniform magnetic field is studied numerically by using the level set method. Focusing on low droplet Reynolds number flows (${\text{Re}}_d\le 0.05$), several numerical simulations are carried out to analyze the effects of magnetic field direction and strength, droplet size, and viscosity ratio on the lateral migration behavior of the droplet. The results indicate that the magnetic field direction plays a pivotal role in the trajectory of lateral migration of the droplet and the final equilibrium position in the channel. When the magnetic field is parallel to the channel, i.e., $\alpha =0^{\circ }$ (the direction of magnetic field), the droplet is found to settle closer to the wall with an increase in magnetic Bond number ${\text{Bo}}_m$, while at $\alpha ={45}^{\circ }$, the droplet settles closer to the channel center. Varying the initial droplet sizes at a fixed magnetic Bond number ${\text{Bo}}_m$ and viscosity ratio $\lambda$ results in different final equilibrium positions within the channel. Additionally, the effect of different viscosity ratios on the migration behavior of the droplet is examined at variable magnetic Bond numbers ${\text{Bo}}_m$. At $\alpha ={45}^{\circ }$, a critical steady state of deformation is found for $\lambda =0.5$ and 1 where the droplet changes its migration direction and shifts toward the center of the channel, while at $\lambda =0.05$, the droplet crosses the center. At $\alpha ={90}^{\circ }$, the droplet is found to settle exactly at the center of the flow domain irrespective of different magnetic Bond numbers, droplet sizes, and viscosity ratios.

Subject to an applied electric field, soft dielectrics with intrinsic low moduli can easily achieve a large deformation through the so-called electrostatic Maxwell stress. Meanwhile, the highly nonlinear electromechanical coupling between the mechanical and electric loads in soft dielectrics gives a variety of failure modes, especially pull-in instability. These failure modes make the application of soft dielectrics highly limited. In this paper, we investigate the large deformation, pull-in instability, and electroactuation of a graded circular dielectric plate subject to the in-plane mechanical load and the applied electric load in the thickness direction. The results obtained herein cover, as special cases, the electromechanical behaviors of homogeneous dielectrics. There is a universal physical intuition that stiffer dielectrics can sustain higher electromechanical loads for pull-in instability but achieve less deformation, and vice versa. We show this physical intuition theoretically in different homogeneous dielectrics and graded dielectrics. Interestingly, we find that the ability to sustain a high electric field or a large deformation in a stiff or soft homogeneous circular dielectric plate can be achieved by just using a graded circular dielectric plate. We only have to partly change the modulus of a circular plate, with a stiff or soft outer region. The change makes the same electromechanical behavior as that of a homogeneous dielectric, even increases the maximum electroactuation stretch from 1.26 to 1.5. This sheds light on the effects of the material inhomogeneity on the design of advanced dielectric devices including actuators and energy harvestors.

Rupture of a liquid bridge is a complex dynamic process, which has attracted much attention over several decades. We numerically investigated the effects of the thermal fluctuations on the rupture process of liquid bridges by using a particle-based method know as many-body dissipative particle dynamics. After providing a comparison of growth rate with the classical linear stability theory, the complete process of thinning liquid bridges is captured. The transitions among the inertial regime (I), the viscous regime (V), and the viscous-inertial regime (VI) with different liquid properties are found in agreement with previous work. A detailed description of the thermal fluctuation regime (TF) and another regime, named the breakup regime, are proposed in the present study. The full trajectories of thinning liquid bridges are summarized as $\mathrm{I}\to \mathrm{V}\to \mathrm{VI}\to \mathrm{TF}\to$ breakup for low-Oh liquids and $\mathrm{V}\to \mathrm{I}\to$ Intermediate $\to \mathrm{V}\to \mathrm{VI}\to \mathrm{TF}\to$ breakup for high-Oh liquids, respectively. Moreover, the effects of the thermal fluctuations on the formation of satellite drops are also investigated. The distance between the peaks of axial velocity is believed to play an important role in forming satellite drops. The strong thermal fluctuations smooth the distribution of axial velocity and change the liquid bridge shape into a double cone without generating satellite drops for low-Oh liquids, while for high-Oh liquids, this distance is extended and a large satellite drop is formed after the breakup of the liquid filament occurs on both ends, which might be due to strong thermal fluctuations. This work can provide insights on the rupture mechanism of liquid bridges and be helpful for designing superfine nanoprinting.

Evolution of waves and hydrodynamic instabilities of a thin viscoelastic fluid film flowing down an inclined wavy bottom of moderate steepness have been analyzed analytically and numerically. The classical long-wave expansion method has been used to formulate a nonlinear evolution equation for the development of the free surface. A normal-mode approach has been adopted to discuss the linear stability analysis from the viewpoint of the spatial and temporal study. The method of multiple scales is used to derive a Ginzburg-Landau-type nonlinear equation for studying the weakly nonlinear stability solutions. Two significant wave families, viz., ${\gamma }_1$ and ${\gamma }_2$, are found and discussed in detail along with the traveling wave solution of the evolution system. A time-dependent numerical study is performed with Scikit-FDif. The entire investigation is conducted primarily for a general periodic bottom, and the detailed results of a particular case study of sinusoidal topography are then discussed. The case study reveals that the bottom steepness $\zeta$ plays a dual role in the linear regime. Increasing $\zeta$ has a stabilizing effect in the uphill region, and the opposite occurs in the downhill region. While the viscoelastic parameter $\mathrm{\Gamma }$ has a destabilizing effect throughout the domain in both the linear and the nonlinear regime. Both supercritical and subcritical solutions are possible through a weakly nonlinear analysis. It is interesting to note that the unconditional zone decreases and the explosive zone increases in the downhill region rather than the uphill region for a fixed $\mathrm{\Gamma }$ and $\zeta$. The same phenomena occur in a particular region if we increase $\mathrm{\Gamma }$ and keep $\zeta$ fixed. The traveling wave solution reveals the fact that to get the ${\gamma }_1$ family of waves we need to increase the Reynolds number a bit more than the value at which the ${\gamma }_2$ family of waves is found. The spatiotemporal evolution of the nonlinear surface equation indicates that different kinds of finite-amplitude permanent waves exist.

We explore the consequences of periodically modulating a quantum two-level system (TLS) with an asymmetric pulse when the system is in contact with thermal baths. By adopting the Floquet-Lindblad formalism for our analysis, we find that the unequal “up” and “down” time duration of the pulse has two main ramifications. First, the energy gap of the multiple sidebands or photon sectors created as a result of the periodic modulation are renormalized by a term which is dependent on both the modulation strength as well as the fraction of up (or down) time duration. Second, the weights of the different sidebands are no longer symmetrically distributed about the central band or zero photon sector. We illustrate the advantages of these findings in the context of applications in quantum thermal machines and thermometry. For a thermal machine constructed by coupling the TLS to two thermal baths, we demonstrate that the asymmetric pulse provides an extra degree of control over the mode of operation of the thermal machine. Further, by appropriately tuning the weight of the subbands, we also show that an asymmetric pulse may provide superior optimality in a recently proposed protocol for quantum thermometry, where dynamical control has been shown to enhance the precision of measurement.

We address the question of why larger, high-symmetry crystals are mostly weak, ductile, and statistically subcritical, while smaller crystals with the same symmetry are strong, brittle and supercritical. We link it to another question of why intermittent elasto-plastic deformation of submicron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, submicron crystals undergo a crossover from spin-glass marginality to criticality characterizing the second order brittle-to-ductile (BD) transition. We argue that this crossover is behind the nonuniversality of scaling exponents observed in physical and numerical experiments. The nonuniversality emerges only if the quenched disorder is elastically incompatible, and it disappears if the disorder is compatible.