Polarization of opinions has been empirically noted in many online social network platforms. Traditional models of opinion dynamics, based on statistical physics principles, do not account for the emergence of polarization and echo chambers in online network platforms. A recently introduced opinion dynamics model that incorporates the homophily factor—the tendency of agents to connect with those holding similar opinions as their own—captures polarization and echo chamber effects. In this work, we provide a nonintrusive framework for mildly nudging agents in an online community to form random connections. This is shown to lead to significant depolarization of opinions and decrease the echo chamber effects. Though a mild nudge effectively avoids polarization, overdoing this leads to another undesirable effect, namely, radicalization. Further, we obtain the optimal nudge probability to avoid the extremes of polarization and radicalization outcomes.

By means of one-dimensional, electromagnetic, particle-in-cell simulations considering the effects of energetic-ion injection, we study the harmonic structure of lower hybrid waves (LHWs) driven by energetic ions under the condition where the electron plasma frequency (${\omega }_{pe}$) is smaller than the electron cyclotron frequency (${\mathrm{\Omega }}_e$). It is found that after the LHWs are excited with the wave number and frequency of ($k_1,{\omega }_1$), many harmonic LHWs are generated at ($m{k}_1,n{\omega }_1$) where $m$ and $n$ are integers, up to far beyond the lower hybrid resonance frequency, $m$ and $n\sim 10$. We show that the harmonic LHWs are generated by nonlinear wave-wave coupling between the LHWs directly excited by the energetic ions and the energetic-ion cyclotron waves above the lower hybrid resonance frequency. We also find that the harmonic LHWs can exist even after the energetic ions are artificially removed because they can be coupled with ion Bernstein waves due to bulk ions. The effect of the energetic-ion injection and the dependence of ${\omega }_{pe}/{\mathrm{\Omega }}_e$ on the development of the harmonic LHWs are investigated to compare the simulation results with an observation in Earth's magnetosphere.

Discovering the underlying mathematical-physical equations of complex systems directly from observational data has been a challenging inversion problem. We propose a data-driven framework for identifying dynamical information in stochastic diffusion or stochastic jump-diffusion systems. The probability density function is utilized to relate the Kramers-Moyal expansion to the governing equations, and the kernel density estimation method, improved by the Fourier transform idea, is used to extract the Kramers-Moyal coefficients from the time series of the state variables of the system. These coefficients provide the data expression of the governing equations of the system. Then a data-driven sparse identification algorithm is used to reconstruct the underlying dynamic equations. The proposed framework does not rely on prior assumptions, and all results are obtained directly from the data. In addition, we demonstrate its validity and accuracy using illustrative one- and two-dimensional examples.

The upper portions of the Earth's atmospheric layer, e.g., the ionospheric plasma layer, can be significantly affected by perturbations generated in the lower layers. In fact, all perturbations formed within the troposphere can easily propagate, not only horizontally within the layer but also vertically reaching the highest regions of the atmosphere far from the Earth's surface, as depicted by the Wentzel-Kramers-Brillouin (WKB) approximation of atmospheric waves. Because all perturbations generated in the atmospheric boundary layer must take into account the effects of the medium's nonlinearity and thus the effects of atmospheric turbulence, in this work the impact of a strong seismic event and the disturbances generated in the flow are analyzed by means of a fully nonlinear model which incorporates a simple parametrization of the seismic event and is based on the classical shallow water. A strict dependence was observed between the model control parameters and the vertical nonvanishing modes from the WKB approximation, and only few specific bands of excited modes are nonvanishing and can eventually propagate to the ionosphere. Moreover, the flow disturbance, generated by a seismic event, presents a multiscale nature characterized by two fixed wavelengths, and the excited modes are harmonics of such distinctive scales.

An efficient method based on the variational perturbation theory (VPT) is proposed to conveniently calculate the atomic real- and imaginary-frequency dynamic polarizabilities and the interatomic dispersion coefficients. The developed method holds the great advantage that only the system ground state wave function and corresponding radial mean values are needed. Verification of the VPT method on one- and two-electron atoms indicates that the present approximation shows good agreement with calculations based on the sophisticated sum-over-states method. We apply the VPT method to examine the approximate $Z$-scaling laws of polarizabilities and dispersion coefficients in the He isoelectronic sequence, and to investigate the plasma screening effect on these quantities for embedded atoms. Our calculation demonstrates very well that the VPT method is capable of producing reasonably accurate static and dynamic polarizabilities as well as two- and three-atom dispersion coefficients for plasma-embedded atoms in a wide range of screening parameters.

How do nonlinear clocks in time and/or space affect the fundamental properties of a stochastic process? Specifically, how precisely may ergodic processes such as fractional Brownian motion (FBM) acquire predictable nonergodic and aging features being subjected to such conditions? We address these questions in the current study. To describe different types of non-Brownian motion of particles—including power-law anomalous, ultraslow or logarithmic, as well as superfast or exponential diffusion—we here develop and analyze a generalized stochastic process of scaled-fractional Brownian motion (SFBM). The time- and space-SFBM processes are, respectively, constructed based on FBM running with nonlinear time and space clocks. The fundamental statistical characteristics such as non-Gaussianity of particle displacements, nonergodicity, as well as aging are quantified for time- and space-SFBM by selecting different clocks. The latter parametrize power-law anomalous, ultraslow, and superfast diffusion. The results of our computer simulations are fully consistent with the analytical predictions for several functional forms of clocks. We thoroughly examine the behaviors of the probability-density function, the mean-squared displacement, the time-averaged mean-squared displacement, as well as the aging factor. Our results are applicable for rationalizing the impact of nonlinear time and space properties superimposed onto the FBM-type dynamics. SFBM offers a general framework for a universal and more precise model-based description of anomalous, nonergodic, non-Gaussian, and aging diffusion in single-molecule-tracking observations.

Digital memcomputing machines (DMMs) are a new class of computing machines that employ nonquantum dynamical systems with memory to solve combinatorial optimization problems. Here, we show that the time to solution (TTS) of DMMs follows an inverse Gaussian distribution, with the TTS self-averaging with increasing problem size, irrespective of the problem they solve. We provide both an analytical understanding of this phenomenon and numerical evidence by solving instances of the 3-SAT (satisfiability) problem. The self-averaging property of DMMs with problem size implies that they are increasingly insensitive to the detailed features of the instances they solve. This is in sharp contrast to traditional algorithms applied to the same problems, illustrating another advantage of this physics-based approach to computation.

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemoresistance in the tumor by managing the ecological mechanism of competitive release of a resistant subpopulation. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of $N$ cells, with a chemotherapy control parameter, $C\left(t\right)$, which we use to dynamically impose selection pressure on the sensitive subpopulation to slow tumor growth and manage competitive release of the resistant population. The adaptive chemoschedule is designed based on the deterministic $(N\to \infty )$ adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model $(N=10\mathrm{K}\text{–}50\text{K})$ to ascertain the cumulative effect of the stochastic fluctuations on the efficacy of the adaptive schedules over multiple rounds. We quantify the stochastic fixation probability regions of the $R$ and $S$ populations in the $HSR$ trilinear phase plane as a function of the control parameter $C\in [0,1]$, showing that the size of the $R$ region increases with increasing $C$. We then implement an adaptive time-dependent schedule $C\left(t\right)$ for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles over multiple rounds of adaptive therapy. The variances increase subquadratically through several rounds before the evolutionary cycle begins to break down. Despite this, we show the stochastic adaptive schedules are more effective at delaying resistance than standard maximum tolerated dose and low-dose metronomic schedules. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes (i.e., different values of $N$) if the goal is to maintain a sustained balance among competing subpopulations of cells to avoid chemoresistance via competitive release in a stochastic environment.

We extend the Taylor-Aris dispersion theory to upscale the gas absorption into a viscous incompressible liquid flowing along an inclined surface. A reduced-order model of advection-dispersion-reaction is developed with the aid of Reynolds decomposition and cross-sectional averaging techniques. The upscaled model allowed evaluation of the dispersion, advection, and absorption kinetics as a function of the Peclet number (Pe) and the Damköhler number (Da). The transport and kinetics parameters for the limiting cases of nonabsorption and absorption dominant are also evaluated. The upscaled model is solved analytically, and the obtained solution is used to evaluate the upscaled mass transfer between the gas and liquid. The results for the overall Sherwood number identify three regions: (i) advection dominant, (ii) transition where both advection and absorption play a role, and (iii) absorption dominant. The scaling relation between the Sherwood number (Sh) and the Da for the last region was determined to follow $\mathrm{Sh}\sim {\mathrm{Da}}^{1/2}$. It is also revealed that in the first two regions, the Sherwood number versus the Peclet number exhibits a bell-shaped (or Gaussian) behavior, suggesting an optimal Pe that maximizes mass transfer between gas and liquid in these regions. The model and insights presented have the potential to be applied in a wide range of industrial separation processes involving the interaction of a gas exposed to a liquid flowing downward on an inclined surface under gravity.

We present new results on ionization by electron impacts in a dense plasma. We are interested in the density effect known as ionization potential depression and its role in atomic structure. Rather than using the well-known Stewart-Pyatt or Ecker-Kröll formulas for the ionization potential depression, we consider a distribution function of the ionization energy, which involves the plasma fluctuations due to ion dynamics. This distribution is calculated within classical molecular dynamics. The removal of the noise yields a new distribution which is composed of a small set of Gaussian peaks among which one peak is selected by considering the signal-to-noise ratio. This approach provides an ionization potential depression in good agreement with experimental results obtained at the Linac Coherent Light Source facility. Our results are also compared with other calculations. In a second part, we investigate the effects of the ionization potential depression and the fluctuations on ionization by electron impacts. We propose an expression of the cross section that is based on an average over the ionization energy distribution. This cross section can be calculated analytically. The main strength of our work is to account for the fluctuations due to ion dynamics.

Studies of multiphase fluids utilizing the lattice Boltzmann method (LBM) are typically severely restricted by the number of components or chemical species being modeled. This restriction is particularly pronounced for multiphase systems exhibiting partial miscibility and significant interfacial mass exchange, which is a common occurrence in realistic multiphase systems. Modeling such systems becomes increasingly complex as the number of chemical species increases due to the increased role of molecular interactions and the types of thermodynamic behavior that become possible. The recently introduced fugacity-based LBM [Soomro et al., Phys. Rev. E 107, 015304 (2023)] has provided a thermodynamically consistent modeling platform for multicomponent, partially miscible LBM simulations. However, until now, this fugacity-based LB model had lacked a comprehensive demonstration of its ability to accurately reproduce thermodynamic behavior beyond binary mixtures and to remove any restrictions in a number of components for multiphase LBM. In this paper we closely explore these fugacity-based LBM capabilities by showcasing comprehensive, thermodynamically consistent simulations of multiphase mixtures of up to ten chemical components. The paper begins by validating the model against the Young-Laplace equation for a droplet composed of three components. The model is then applied to study mixtures with a range of component numbers from one to six, showing agreement with rigorous thermodynamic predictions and demonstrating linear scaling of computational time with the number of components. We further investigate ternary systems in detail by exploring a wide range of temperature, pressure, and overall composition conditions to produce various characteristic ternary diagrams. In addition, the model is shown to be unrestricted in the number of phases as demonstrated through simulations of a three-component three-phase equilibrium case. The paper concludes by demonstrating simulations of a ten-component, realistic hydrocarbon mixture, achieving excellent agreement with thermodynamics for both flat interface vapor-liquid equilibrium and curved interface spinodal decomposition cases. This study represents a significant expansion of the scope and capabilities of multiphase LBM simulations that encompass multiphase systems of keen interest in engineering.

As a population grows, spreading to new environments may favor specialization. In this paper, we introduce and explore a model for specialization at the front of a colony expanding synchronously into new territory. We show through numerical simulations that, by gaining fitness through accumulating mutations, progeny of the initial seed population can differentiate into distinct specialists. With competition and selection limited to the growth front, the emerging specialists first segregate into sectors, which then expand to dominate the entire population. We quantify the scaling of the fixation time with the size of the population and observe different behaviors corresponding to distinct universality classes: unbounded and bounded gains in fitness lead to superdiffusive ($z=3/2$) and diffusive ($z=2$) stochastic wanderings of the sector boundaries, respectively.

Feedback control uses the state information of the system to actuate on it. The information used implies an effective entropy reduction of the controlled system, potentially increasing its performance. How to compute this entropy reduction has been formally shown for a general system and has been explicitly computed for spatially discrete systems. Here, we address a relevant example of how to compute the entropy reduction by information in a spatially continuous feedback-controlled system. Specifically, we consider a feedback flashing ratchet, which constitutes a paradigmatic example for the role of information and feedback in the dynamics and thermodynamics of transport induced by the rectification of Brownian motion. A Brownian particle moves in a periodic potential that is switched on and off by a controller. The controller measures the position of the particle at regular intervals and performs the switching depending on the result of the measurement. This system reaches a long-time dynamical regime with a nonzero mean particle velocity, even for a symmetric potential. Here, we calculate the efficiency at maximum power in this long-time regime, computing all the required contributions. We show how the entropy reduction can be evaluated from the entropy of the non-Markovian sequence of control actions, and we also discuss the required sampling effort for its accurate computation. Moreover, the output power developed by the particle against an external force is investigated, which—for some values of the system parameters—is shown to become larger than the input power provided by the switching of the potential. The apparent efficiency of the ratchet thus becomes higher than one, if the entropy reduction contribution is not considered. This result highlights the relevance of including the entropy reduction by information in the thermodynamic balance of feedback-controlled devices, specifically when writing the second principle. The inclusion of the entropy reduction by information leads to a well-behaved efficiency over all the range of parameters investigated.

We introduce a top-ranked cycle flux ranking scheme of network analysis to assess the performance of molecular junction solar cells. By mapping the Lindblad master equation to the quantum-transition network, we propose a microscopic Hamiltonian description underpinning the rate equations commonly used to characterize molecular photocells. Our approach elucidates the paramount significance of edge flux and unveils two pertinent electron transfer pathways that play equally important roles in robust photocurrent generation. Furthermore, we demonstrate that nonradiative loss processes impede the maximum power efficiency of photocells, which may otherwise be above the Curzon-Ahlborn limit. These findings shed light on the intricate functionalities that govern molecular photovoltaics and offer a comprehensive approach to address them in a systematic way.

Chemotaxis refers to the motion of an organism induced by chemical stimuli and is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular, autochemotaxis refers to chemotaxis mediated by a cue produced by the chemotactic particle itself. Here, we investigate the collective behavior of autochemotactic particles that are repelled by the cue and therefore migrate preferentially towards low-concentration regions. To this end, we introduce a lattice model inspired by the true self-avoiding walk which reduces to the Keller-Segel model in the continuous limit, for which we describe the rich phase behavior. We first rationalize the chemically mediated alignment interaction between walkers in the limit of stationary concentration fields, and then describe the various large-scale structures that can spontaneously form and the conditions for them to emerge, among which we find stable bands traveling at constant speed in the direction transverse to the band.

We study the diffusive behavior of interacting active particles (self-propelled) with mass $m$ in an asymmetric channel. The particles are subjected to an external oscillatory force along the length of the channel. In this setup, particles may exhibit rectification. In the absence of interaction, the mean velocity $\langle v\rangle$ of the particles shows a maximum at moderate $m$ values. It means that particles of moderate $m$ have higher velocities than the others. However, by incorporating short-range interaction between the particles, $\langle v\rangle$ exhibits an additional peak at lower $m$ values, indicating that particles of lower and moderate $m$ can be separated simultaneously from the rest. Furthermore, by tuning the interaction strength, the self-propelled velocity, and the parameters of the oscillatory force, one can selectively separate the particles of lower $m$, moderate $m$, or both. Empirical relations for estimating the optimal mass as a function of these parameters are proposed. These findings are beneficial for separating the particles of selective $m$ from the rest of the particles.

The properties of composites of mesogens and two-dimensional (2D) materials are of great interest due to their practical applications in flexible displays, optoelectronics, microelectronics, and novel nanodevices. The properties of such composites are very complex and strongly depend on the interactions between the host material and the mesogen filling. We have performed molecular dynamics simulations for 4-cyano-$4^{\prime }$-pentylbiphenyl embedded between graphene and hexagonal 2D boron nitride layers. The structural and dynamical properties of such systems were investigated in terms of the order parameters, density profiles, mean square displacement, and autocorrelation function of the single-molecule dipole moment. Our simulations have shown that the mesogenic molecules form highly stable ordered layered structures and that their dynamics are strongly related to the structural properties. We have investigated not only the effects of the polarization of the host material, but also the effects of the spatial repetition of such composites by using two models of mesogens embedded in 2D layers: the direct sheet and the structure formed by multiplying a single unit of the composite in the direction perpendicular to the substrate surface.

A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and mode II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a nontrivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean-square grain mass across rates and system sizes. Consistent scaling persists across all material properties studied, although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses and depends on elastic properties of the solid.

The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.

Cells maintain a stable size as they grow and divide. Inspired by the available experimental data, most proposed models for size homeostasis assume size-control mechanisms that act on a timescale of one generation. Such mechanisms lead to short-lived autocorrelations in size fluctuations that decay within less than two generations. However, recent evidence from comparing sister lineages suggests that correlations in size fluctuations can persist for many generations. Here we develop a minimal model that explains these seemingly contradictory results. Our model proposes that different environments result in different control parameters, leading to distinct inheritance patterns. Multigenerational memory is revealed in constant environments but obscured when averaging over many different environments. Inferring the parameters of our model from Escherichia coli size data in microfluidic experiments, we recapitulate the observed statistics. Our paper elucidates the impact of the environment on cell homeostasis and growth and division dynamics.