This paper investigates adversarial attacks conducted to distort voter model dynamics in complex networks. Specifically, a simple adversarial attack method is proposed to hold the state of opinions of an individual closer to the target state in the voter model dynamics. This indicates that even when one opinion is the majority the vote outcome can be inverted (i.e., the outcome can lean toward the other opinion) by adding extremely small (hard-to-detect) perturbations strategically generated in social networks. Adversarial attacks are relatively more effective in complex (large and dense) networks. These results indicate that opinion dynamics can be unknowingly distorted.

Quantitative research of interdisciplinary fields, including biological and social systems, has attracted great attention in recent years. Complex networks are popular and important tools for the investigations. Explosively increasing data are created by practical networks, from which useful information about dynamic networks can be extracted. From data to network structure, i.e., network reconstruction, is a crucial task. There are many difficulties in fulfilling network reconstruction, including data shortage (existence of hidden nodes) and time delay for signal propagation between adjacent nodes. In this paper a deep network reconstruction method is proposed, which can work in the conditions that even only two nodes (say $A$ and $B$) are perceptible and all other network nodes are hidden. With a well-designed stochastic driving on node $A$, this method can reconstruct multiple interaction paths from $A$ to $B$ based on measured data. The distance, effective intensity, and transmission time delay of each path can be inferred accurately.

The mechanics and statistical mechanics of a suspension of active particles are determined by the traction (force per unit area) on their surfaces. Here we present an exact solution of the direct boundary integral equation for the traction on a spherical active particle in an imposed slow viscous flow. Both single- and double-layer integral operators can be simultaneously diagonalized in a basis of irreducible tensorial spherical harmonics and the solution, thus, can be presented as an infinite number of linear relations between the harmonic coefficients of the traction and the velocity at the boundary of the particle. These generalize Stokes laws for the force and torque. Using these relations we obtain simple expressions for physically relevant quantities such as the symmetric-irreducible dipole acting on, or the power dissipated by, an active particle in an arbitrary imposed flow. We further present an explicit expression for the variance of the Brownian contributions to the traction on an active colloid in a thermally fluctuating fluid.

Particles-on-demand formulation of kinetic theory [B. Dorschner, F. Bösch and I. V. Karlin, Phys. Rev. Lett. 121, 130602 (2018)] is used to simulate a variety of compressible flows with strong discontinuities in density, pressure, and velocity. Two modifications are applied to the original formulation of the particles-on-demand method. First, a regularization by Grad's projection of particles populations is combined with the reference frame transformations in order to enhance stability and accuracy. Second, a finite-volume scheme is implemented which allows tight control of mass, momentum, and energy conservation. The proposed model is validated with an array of challenging one- and two-dimensional benchmarks of compressible flows, including hypersonic and near-vacuum situations, Richtmyer-Meshkov instability, double Mach reflection, and astrophysical jet. Excellent performance of the modified particles-on-demand method is demonstrated beyond the limitations of other lattice Boltzmann-like approaches to compressible flows.

Simulations of protein folding and protein association happen on timescales that are orders of magnitude larger than what can typically be covered in all-atom molecular dynamics simulations. Use of low-resolution models alleviates this problem but may reduce the accuracy of the simulations. We introduce a replica-exchange-based multiscale sampling technique that combines the faster sampling in coarse-grained simulations with the potentially higher accuracy of all-atom simulations. After testing the efficiency of our Resolution Exchange with Tunneling (ResET) in simulations of the Trp-cage protein, an often used model to evaluate sampling techniques in protein simulations, we use our approach to compare the landscape of wild-type and A2T mutant $\mathrm{A}{\beta }_{1-42}$ peptides. Our results suggest a mechanism by that the mutation of a small hydrophobic alanine (A) into a bulky polar threonine (T) may interfere with the self-assembly of $\mathrm{A}\beta$ fibrils.

In living and engineered systems of active particles, self-propulsion induces an unjamming transition from a solid to a fluid phase and phase separation between a gas and a liquidlike phase. We demonstrate an interplay between these two nonequilibrium transitions in systems of persistent active particles. The coexistence and jamming lines in the activity-density plane meet at the jamming transition point in the limit of hard particles or zero activity. This interplay induces an anomalous dynamic in the liquid phase and hysteresis at the active jamming transition.

We provide highly accurate equation-of-state data for the isotropic phase of hard lenses obtained by means of cluster Monte Carlo simulations. This data is analyzed using a virial approach considering coefficients up to the order eight and Carnahan-Starling type closure relations for the virial series. The comparison with previously investigated systems consisting of hard, oblate ellipsoids of revolution allows insights into the detailed influence of the particle geometry. We propose a generalized Carnahan-Starling approach as a heuristic equation of state for the isotropic phase of hard lenses that in first approximation shows the same dependence on the excess part of the excluded volume as identified for oblate, hard lenses of revolution.

We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the backdrop of the critical collapse driven by the cubic self-attraction with strength $g$. The TEM scheme may be implemented, as spatially or temporally periodic modulations, in optics or BEC, respectively. The consideration is carried out by dint of numerical simulations and variational approximation (VA). In terms of the VA, the dynamics amounts to a nonlinear Ermakov equation, which, in turn, is tantamount to a linear Mathieu equation. Stability boundaries are found as functions of $g$ and parameters of the periodic modulation of the trapping potential. Below the usual collapse threshold, which is known, in the numerical form, as $g<g_c^{\left(\mathrm{num}\right)}\approx 5.85$ (in the standard notation), the stability is limited by the onset of the parametric resonance. This stability limit, including the setup with the self-repulsive sign of the cubic term ($g<0$), is accurately predicted by the VA. At $g>g_c^{\left(\mathrm{num}\right)}$, the collapse threshold is found with the help of full numerical simulations. The relative increase of $g_c$ above $g_c^{\left(\mathrm{num}\right)}$ is $\approx 1.5\%$. It is a meaningful result, even if its size is small, because the collapse threshold is a universal constant which is difficult to change.

A new scheme is investigated for evaluating the temperature dependence and dispersion relation of the Kerr constant ($K$) of an optically isotropic medium in isotropic and blue phases (BPs) liquid crystals. The scheme employs the measurement of the component of the transmitted light intensity of double modulated frequency using the modified in-plane-switching cell geometry (based on metallic film electrodes). It overcomes to a large extent the problem of a nonuniform electric field, employs relatively small driving voltages, and allows $K$ to be measured directly. It is shown that the dispersion relation based on the single-band birefringence model describes well both blue and isotropic liquid crystal phases. It is found that the experimental data indicate that the temperature-dependent coefficients in this relation have a simple linear form in the isotropic phase, which allows a general model for the temperature and wavelength dependence of the Kerr constant in the isotropic liquid crystal phase to be formulated. In the BPs the temperature dependence of the experimental data deviate from the simple linear trend, but follow well an inverse exponential form.

We report on phase transitions between isotropic and nematic liquid crystal phases in nonequilibrium systems (NESs). ac field-driven electroconvection (EC) provides an NES, which can be well controlled by the voltage $V$ and frequency $f$; it arises electrohydrodynamically at a threshold voltage $V_{\mathrm{c}}$. In continuous cooling and heating processes with various rates $R$, the critical temperature $T_{\mathrm{c}}$ was determined at a critical time $t_{\mathrm{c}}$ for phase transitions. Moreover, the morphological and dynamical features in the phase transitions were examined using an electro-optical image processing method. In comparison with an equilibrium system ($V=0$), two typical turbulent ECs (i.e., NESs), which are called dynamic scattering mode 1 (DSM1 for $V>V_{\mathrm{c}}$) and DSM2 (for $V\gg V_{\mathrm{c}}$), were examined to understand the nonequilibrium phase transitions. In particular, our results show that in high voltage-induced turbulence (i.e., DSM2), $T_{\mathrm{c}}$ can be determined effectively without considering $R$; this provides a possibility for a material technology application in nonequilibrium-based circumstances.

The advection and mixing of a scalar quantity by fluid flow is an important problem in engineering and natural sciences. The statistics of the passive scalar exhibit complex behavior even in the presence of a Gaussian velocity field. This paper is concerned with two Lagrangian turbulence models that are based on the recent fluid deformation model, but adding a passive scalar field with uniform mean gradient. For a range of Reynolds numbers, these models can reproduce the statistics of passive scalar turbulence. For these models, we demonstrate how events of extreme passive scalar gradients can be recovered by computing the instanton, i.e., the saddle-point configuration of the associated stochastic field theory. It allows us to both reproduce the heavy-tailed statistics associated with passive scalar turbulence, and recover the most likely mechanism leading to such extreme events. We further demonstrate that events of large negative strain in these models undergo spontaneous symmetry breaking.

It has been shown recently that the optimal fluctuation method—essentially geometrical optics—provides a valuable insight into large deviations of Brownian motion. Here we extend the geometrical optics formalism to two-sided, $-\infty <t<\infty$, fractional Brownian motion (fBm) on the line, which is “pushed” to a large deviation regime by imposed constraints. We test the formalism on three examples where exact solutions are available: the two- and three-point probability distributions of the fBm and the distribution of the area under the fBm on a specified time interval. Then we apply the formalism to several previously unsolved problems by evaluating large-deviation tails of the following distributions: (i) of the first-passage time, (ii) of the maximum of, and (iii) of the area under, fractional Brownian bridge and fractional Brownian excursion, and (iv) of the first-passage area distribution of the fBm. An intrinsic part of a geometrical optics calculation is determination of the optimal path—the most likely realization of the process which dominates the probability distribution of the conditioned process. Due to the non-Markovian nature of the fBm, the optimal paths of a fBm, subject to constraints on a finite interval $0<t\le T$, involve both the past $-\infty <t<0$ and the future $T<t<\infty$.

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. Further, we also compare the stochastic bridges we produce to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the generated paths, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that the method can also be used to judge the accuracy of the WKB approximation at finite levels of noise.

The latest advances of statistical physics have shown remarkable performance of machine learning in identifying phase transitions. In this paper, we apply domain adversarial neural network (DANN) based on transfer learning to studying nonequilibrium and equilibrium phase transition models, which are percolation model and directed percolation (DP) model, respectively. With the DANN, only a small fraction of input configurations (two-dimensional images) needs to be labeled, which is automatically chosen, to capture the critical point. To learn the DP model, the method is refined by an iterative procedure in determining the critical point, which is a prerequisite for the data collapse in calculating the critical exponent ${\nu }_{\perp }$. We then apply the DANN to a two-dimensional site percolation with configurations filtered to include only the largest cluster which may contain the information related to the order parameter. The DANN learning of both models yields reliable results which are comparable to the ones from Monte Carlo simulations. Our study also shows that the DANN can achieve quite high accuracy at much lower cost, compared to the supervised learning.

Cardiac fibrillation is caused by self-sustaining spiral waves that occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. A small electrical stimulation is often sufficient to unpin these spirals but only if it is applied during the vulnerable unpinning window. Even if these unpinning windows can be inferred from data, when multiple pinned spirals exist, their unpinning windows will not generally overlap. Using phase-based reduction techniques, we formulate and solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a collection of heterogeneous obstacles. Upon synchronization, the unpinning windows overlap so that they can be simultaneously unpinned by applying an external voltage gradient pulse at an appropriate moment. Numerical validation is presented in bidomain model simulations. Results represent a proof-of-concept illustration of the proposed unpinning strategy which explicitly incorporates heterogeneity in the problem formulation and requires no real-time feedback about the system state.

The collective behavior of a binary mixture of polar self-propelled particles (SPPs) with different motile properties is studied. The binary mixture consists of slow-moving SPPs (sSPPs) of fixed velocity $v_s$ and fast-moving SPPs (fSPPs) of fixed velocity $v_f$. These SPPs interact via a short-range interaction irrespective of their types. They move following certain position and velocity update rules similar to the Vicsek model (VM) under the influence of an external noise $\eta$. The system is studied at different values of $v_f$ keeping $v_s=0.01$ constant for a fixed density $\rho =0.5$. Different phase-separated collective patterns that appear in the system over a wide range of noise $\eta$ are characterized. The fSPPs and the sSPPs are found to be orientationally phase synchronized at the steady state. We studied an orientational order-disorder transition varying the angular noise $\eta$ and identified the critical noise ${\eta }_c$ for different $v_f$. Interestingly, both the species exhibit continuous transition for $v_f<100v_s$ and discontinuous transition for $v_f>100v_s$. A new set of critical exponents is determined for the continuous transitions. However, the binary model is found to be nonuniversal as the values of the critical exponents depend on the velocity. The effect of interaction radius on the system behavior is also studied.

Active matter are a collection of units with intrinsic supply of energy that is utilized for self-propelled motion. Recent studies have confirmed that these active systems can exist in exotic phases, such as swarming, laning, jamming, and even turbulence, based on the size and density of the constituent units. An interesting question that naturally arises is whether one can identify an effective temperature for particles advected by such an active flow that is far from equilibrium. In this paper, we report using a continuum model of a dense bacterial suspension, an exact expression of the effective temperature for a distribution of interacting particles that are immersed in this suspension. We observe that this effective temperature is linear in particle diffusivity with the slope defining the particle mobility that is higher when the background fluid exhibits global polar ordering and lower when the fluid is in isotropic equilibrium. We believe our paper is a direct verification of the Einstein relation—the simplest fluctuation dissipation relation for interacting particles advected in an active matter flow.

Dispersion in porous media is of great importance in many areas of science and engineering. While dispersion in porous media has been generally well discussed in the literature, little work has been done regarding a generalization of Taylor dispersion in stratified media. In this work, we generalized the Taylor dispersion theory and Stokes flow in porous media to derive a reduced-order model for tracer dispersion in stratified porous media. Our findings revealed that for a simple case of two-layer porous media, the hydrodynamic coupling between the two layers leads to the tensorial nature of dispersion and advection. The results showed that the obtained dispersion tensor and advection are not symmetric unless both porous layers have similar thickness, porosity, and molecular diffusion. We found that the main elements of the coefficient of the dispersion tensor remain positive while the off-diagonal elements can take negative values. On the contrary, all elements of the advection matrix may take negative values. On the basis of these observations, we report the manifestation of the dispersion barrier, uphill dispersion and advection, and osmotic dispersion during tracer transport in stratified porous media. In particular, the identified uphill advection reveals that the injected tracer in one layer could be transported countercurrent to the adjacent layer. Furthermore, we have shown that in the limiting case of Darcy flow, the Taylor dispersion is absent, and the tracer mixing between the two layers is restricted to the cross-diffusive flux between them. The results revealed that the field scale mixing may not necessarily originate from the Taylor dispersion and could be due to the modified advection terms and the cross-diffusive flux between the two layers.