In this work we study the opinion evolution in a community-based population with intergroup interactions. We address two issues. First, we consider that such intergroup interactions can be negative with some probability $p$. We develop a coupled mean-field approximation that still preserves the community structure and it is able to capture the richness of the results arising from our Monte Carlo simulations: continuous and discontinuous order-disorder transitions as well as nonmonotonic ordering for an intermediate community strength. In the second part, we consider only positive interactions but with the presence of inflexible agents holding a minority opinion. We also consider an indecision noise: a probability $q$ that allows the spontaneous change of opinions to the neutral state. Our results show that the modular structure leads to a nonmonotonic global ordering as $q$ increases. This inclination toward neutrality plays a dual role: A moderated propensity to neutrality helps the initial minority to become a majority, but this noise-driven opinion switching becomes less pronounced if the agents are too susceptible to become neutral.

One of the major issues in theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thompson rumor model. Flexibility on the timescale between information and disease spreading is also included. We verify that the velocity characterizing the diffusion of information awareness greatly influences the disease prevalence. We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative timescale between disease and awareness spreading plays a crucial role in the systems' dynamics. This result is shown to be independent of the network topology. We finally calculate the epidemic threshold of our model, and show that it does not depend on the relative timescale. Our results provide a new view on how information influence disease spreading and can be used for the development of more efficient methods for disease control.

The adhesion properties and the mobility of biological cells play key roles in the propagation of cancer. These properties are expected to depend on intracellular processes and on the concentrations of chemicals inside the cell. While most existing reaction-diffusion models for cell migration consider that cell mobility and proliferation rate are constant or depend on an external diffusing species, they do not include the gene expression dynamics taking place in moving cells that affect cellular transport. In this work, we propose a multiscale model where mobility and proliferation depend explicitly on the cell's internal state. We focus more specifically on the case of cellular mobility in epithelial tissues. Wound-healing experiments have demonstrated that the loss of a key protein, E-cadherin, results in a significant increase in both mobility and invasiveness of epithelial cells, with dramatic consequences on cancer progression. We can reproduce the results of these experiments under various genetic conditions with a single set of parameters.

Stability and nonlinear evolution of rotating magnetohydrodynamic flows in the Princeton magnetorotational instability (MRI) experiment are examined using three-dimensional non-axisymmetric simulations. In particular, the effect of axial boundary conductivity on a free Stewartson-Shercliff layer (SSL) is numerically investigated using the spectral finite-element Maxwell and Navier Stokes (SFEMaNS) code. The free SSL is established by a sufficiently strong magnetic field imposed axially across the differentially rotating fluid with two rotating rings enforcing the boundary conditions. Numerical simulations show that the response of the bulk fluid flow is vastly different in the two different cases of insulating and conducting end caps. We find that, for the insulating end caps, there is a transition from stability to instability of a Kelvin-Helmholtz-like mode that saturates at an azimuthal mode number $m=1$, whereas for the conducting end caps, the reinforced coupling between the magnetic field and the bulk fluid generates a strong radially localized shear in the azimuthal velocity resulting in axisymmetric Rayleigh-like modes even at reduced thresholds for the axial magnetic field. For reference, three-dimensional nonaxisymmetric simulations have also been performed in the MRI unstable regime to compare the modal structures.

We set up the scaling theory for stably stratified turbulent fluids. For a system having infinite extent in the horizontal directions, but with a finite width in the vertical direction, this theory predicts that the inertial range can display three possible scaling behavior, which are essentially parametrized by the buoyancy frequency $N$, or dimensionless horizontal Froude number $F_h$, and the vertical length scale $l_v$ that sets the scale of variation of the velocity field in the vertical direction for a fixed Reynolds number. For very low $N$ or very high ${\mathrm{Re}}_b$ or $F_h$, and with $l_v\gg l_h$, the typical horizontal length scale, buoyancy forces are irrelevant and hence, unsurprisingly, the kinetic energy spectra show the well-known K41 scaling in the inertial range. In this regime, the local temperature behaves as a passively advected scalar, without any effect on the flow fields. For intermediate ranges of values of $N,F_h\sim O\left(1\right)$, corresponding to moderate stratification, buoyancy forces are important enough to affect the scaling. This leads to the Bolgiano-Obukhov scaling which is isotropic, when $l_v\sim l_h$. Finally, for very large $N$, corresponding to strong stratification, together with a very small $l_v$, the inertial-range flow fields effectively two-dimensionalize. The kinetic energy spectra are predicted to be anisotropic with only the horizontal part of the kinetic energy spectra following the K41 scaling. This suggests an intriguing re-entrant K41 scaling, as a function of stratification, for the horizontal components of the velocity field in this regime. The scaling theory further predicts the scaling of the thermal energy in each of these three scaling regimes. Our theory can be tested in large-scale simulations and appropriate laboratory-based experiments.

Proton radiography is a technique in high-energy density science to diagnose magnetic and/or electric fields in a plasma by firing a proton beam and detecting its modulated intensity profile on a screen. Current approaches to retrieve the integrated field from the modulated intensity profile require the unmodulated beam intensity profile before the interaction, which is rarely available experimentally due to shot-to-shot variability. In this paper, we present a statistical method to retrieve the integrated field without needing to know the exact source profile. We apply our method to experimental data, showing the robustness of our approach. Our proposed technique allows for the retrieval not only of the path-integrated fields, but also of the statistical properties of the fields.

In this second paper of a series, we discuss the dynamics of a plasma entering the precursor of an unmagnetized, relativistic collisionless pair shock. We discuss how this background plasma is decelerated and heated through its interaction with a microturbulence that results from the growth of a current filamentation instability in the shock precursor. We make use, in particular, of the reference frame ${\mathcal{R}}_{\mathrm{w}}$ in which the turbulence is mostly magnetic. This frame moves at relativistic velocities towards the shock front at rest, decelerating gradually from the far to the near precursor. In a first part, we construct a fluid model to derive the deceleration law of the background plasma expected from the scattering of suprathermal particles off the microturbulence. This law leads to the relationship ${\gamma }_{\mathrm{p}}\sim {\xi }_{\mathrm{b}}^{-1/2}$ between the background plasma Lorentz factor ${\gamma }_{\mathrm{p}}$ and the normalized pressure of the beam ${\xi }_{\mathrm{b}}$; it is found to match nicely the spatial profiles observed in large-scale 2D3V particle-in-cell simulations. In a second part, we model the dynamics of the background plasma at the kinetic level, incorporating the inertial effects associated with the deceleration of ${\mathcal{R}}_{\mathrm{w}}$ into a Vlasov-Fokker-Planck equation for pitch-angle diffusion. We show how the effective gravity in ${\mathcal{R}}_{\mathrm{w}}$ drives the background plasma particles through friction on the microturbulence, leading to efficient plasma heating. Finally, we compare a Monte Carlo simulation of our model with dedicated PIC simulations and conclude that it can satisfactorily reproduce both the heating and the deceleration of the background plasma in the shock precursor, thereby providing a successful one-dimensional description of the shock transition at the microscopic level.

In this third paper of a series, we discuss the physics of the population of accelerated particles in the precursor of an unmagnetized, relativistic collisionless pair shock. In particular, we provide a theoretical estimate of their scattering length $l_{\mathrm{scatt}}\left(p\right)$ in the self-generated electromagnetic turbulence, as well as an estimate of their distribution function. We obtain $l_{\mathrm{scatt}}\left(p\right)\approx {\gamma }_{\mathrm{p}}{\epsilon }_B^{-1}{(p/{\gamma }_{\infty }mc)}^{2}c/{\omega }_{\mathrm{p}}$, with $p$ the particle momentum in the rest frame of the shock front, ${\epsilon }_B$ the strength parameter of the microturbulence, ${\gamma }_{\mathrm{p}}$ the Lorentz factor of the background plasma relative to the shock front, and ${\gamma }_{\infty }$ its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.

Based on phase-field theory, we develop a lattice Boltzmann (LB) model for liquid-gas-solid flow from multiphase and particle dynamics algorithms. A modified bounce-back method is developed for the velocity-based LB approach. A curved boundary treatment with second-order accuracy based on velocity interpolation is developed. We propose a predictor-corrector scheme algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. In order to make the algorithm more stable, we combine the implicit particle velocity update scheme and the Galilean invariant momentum exchange method. The proposed method is validated through several single- and multicomponent fluid test cases. It was found the surface tension force associated with the interface acting on the solid structures can be captured. We simulate the sinking of a circular cylinder due to gravity, the numerical results agree well with the experimental data. Finally, we apply the method to the self-assembly process of multiple floating cylinders on water surface.

In this paper, the multicomponent lattice Boltzmann flux solver (LBFS) is developed for simulation of two-dimensional compressible viscous reacting flows. This work is based on the existing LBFS for simulation of single-component compressible flows. The present solver applies the finite volume method to discretize the multicomponent Navier-Stokes equations and evaluates the numerical flux at the cell interface by local solution of the lattice Boltzmann equation. To evaluate numerical flux, the original non-free parameter D1Q4 model in the existing LBFS is extended to the multicomponent counterpart in which the total density at the cell interface is computed directly by summing the density distribution functions, and the densities of different species are calculated from the mass fractions at the left and right sides of cell interface. The internal energy is evaluated from the enthalpy which considers the different physical properties of the species, and the temperature at the cell interface is obtained by Newton iteration. In addition, an improved switch function which takes into account the reacting effects and aspect ratio of the grid is introduced to control the numerical dissipation. Several benchmark problems are simulated to validate the present multicomponent LBFS. It is shown that the present solver is carbuncle-free for the unfavorable aspect ratio grid in the test cases here and has a satisfied performance for simulation of multicomponent compressible viscous reacting flows.

The problem of efficiently reconstructing tomographic images can be mapped into a Bayesian inference problem over the space of pixels densities. Solutions to this problem are given by pixels assignments that are compatible with tomographic measurements and maximize a posterior probability density. This maximization can be performed with standard local optimization tools when the log-posterior is a convex function, but it is generally intractable when introducing realistic nonconcave priors that reflect typical images features such as smoothness or sharpness. We introduce a new method to reconstruct images obtained from Radon projections by using expectation propagation, which allows us to approximate the intractable posterior. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, expectation propagation paired with very simple but non-log-concave priors is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.

We study the energy landscape of the traveling salesperson problem (TSP) using exact ground states and a novel linear programming approach to generate excited states with closely defined properties. We look at four different ensembles, notably the classic finite dimensional Euclidean TSP and the mean-field-like (1,2)-TSP, which has its origin directly in the mapping of the Hamiltonian circuit problem on the TSP. Our data supports previous conjectures that the Euclidean TSP does not show signatures of replica symmetry breaking neither in two nor in higher dimension. On the other hand the (1,2)-TSP exhibits some signature which does not exclude broken replica symmetry, making it a candidate for further studies in the future.

We study the behavior of a symmetric exclusion process (SEP) in the presence of stochastic resetting where the configuration of the system is reset to a steplike profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEPs strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a nontrivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we identify the resetting current in the system which emerges due to the sudden relocation of the particles to the steplike configuration and is strongly correlated to the diffusive current. We show that the average resetting current is negative, but its magnitude also grows linearly with time $t.$ We also compute the probability distributions of the diffusive current, resetting current, and total current (sum of the diffusive and the resetting currents) using the renewal approach. We demonstrate that while the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behavior.

Viscoelastically coupled excitable oscillators are used to model individually beating spatially separated cardiomyocytes surrounded by an extracellular matrix (ECM). We investigate how mechanical coupling via the ECM can synchronize two such oscillators with excitation contraction coupling and electromechanical feedback and how this synchronization depends on the rheological properties of the ECM. Extending our study to a linear chain of coupled oscillators we find a transition to synchronization as the ECM becomes stiffer. In the case of purely elastic coupling we observe antiphase chimera states.

The development of synchronization strategies for dynamical systems is an important research activity that can be applied in several different fields from locomotion control of multilimbed structures to secure communication. In the presence of chaotic systems, synchronization is more difficult to accomplish and there are different techniques that can be adopted. In this paper we considered a master-slave topology where the coupling mechanism is realized through a second-order linear dynamical system. This control scheme, recently applied to chaotic systems, is here analyzed in the presence of hyperchaotic dynamics that represent a more challenging scenario. The possibility to reach a complete synchronization and the range of allowable coupling strength is investigated comparing the effects of the dynamical coupling with a standard configuration characterized by a static gain. This methodology is also applied to weighted networks to reach synchronization regimes otherwise not obtainable with a static coupling.

During epidemic control, containment of the disease is usually achieved through increasing a devoted resource to reduce the infectiousness. However, the impact of this resource expenditure has not been studied quantitatively. For disease spread, the recovery rate can be positively correlated with the average amount of resource devoted to infected individuals. By incorporating this relation we build a novel model and find that insufficient resource leads to an abrupt increase in the infected population size, which is in marked contrast with the continuous phase transitions believed previously. Counterintuitively, this abrupt phase transition is more pronounced in less contagious diseases. Furthermore, we find that even for a single infection source, the public resource needs to be available in a significant amount, which is proportional to the total population size, to ensure epidemic containment. Our findings provide a theoretical foundation for efficient epidemic containment strategies in the early stage.

Relaxation modes are the collective modes in which all probability deviations from equilibrium states decay with the same relaxation rates. In contrast, a first passage time is the required time for arriving for the first time from one state to another. In this paper, we discuss how and why the slowest relaxation rates of relaxation modes are reconstructed from the first passage times. As an illustrative model, we use a continuous-time Markov state model of vacancy diffusion in KCl nanoclusters. Using this model, we reveal that all characteristics of the relaxations in KCl nanoclusters come from the fact that they are hybrids of two kinetically different regions of the fast surface and slow bulk diffusions. The origin of the different diffusivities turns out to come from the heterogeneity of the activation energies on the potential energy landscapes. We also develop a stationary population method to compute the mean first passage times as mean times required for pair annihilations of particle-hole pairs, which enables us to obtain the symmetric results of relaxation rates under the exchange of the sinks and the sources. With this symmetric method, we finally show why the slowest relaxation times can be reconstructed from the mean first passage times.

The study of origami-based mechanical metamaterials usually focuses on the kinematics of deployable structures made of an assembly of rigid flat plates connected by hinges. When the elastic response of each panel is taken into account, novel behaviors take place, as in the case of foldable cones ($f$-cones): circular sheets decorated by radial creases around which they can fold. These structures exhibit bistability, in the sense that they can snap through from one metastable configuration to another. In this work, we study the elastic behavior of isometric $f$-cones for any deflection and crease mechanics, which introduce nonlinear corrections to a linear model studied previously. Furthermore, we test the inextensibility hypothesis by means of a continuous numerical model that includes both the extended nature of the creases, stretching and bending deformations of the panels. The results show that this phase-field-like model could become an efficient numerical tool for the study of realistic origami structures.

Rough fractures often exhibit a broad spectrum of defect length scales ranging from the microscopic (roughness) scale to a macroscopic one (waviness) and further to the megascopic scale corresponding to the entire fracture. The influence of these multiple scales and their reciprocal interactions are expected to play a significant role on the transport properties at the megascale. Focusing on the pressure-driven slightly compressible gas slip flow, a two-scale method is presented allowing the determination of the global transmissivity of a fracture on the basis of an upscaled Reynolds model. This model is applied on a tessellation of the fracture, each tile being affected by a macroscopic transmissivity tensor which encompasses the microscale transport information as a result of the first upscaling process. Then, the megascale flow problem in this structure, made of a set of tiles characterized by a heterogeneous and anisotropic transmissivity tensor field, is solved using a boundary element method. Numerical results obtained with this two-scale method are compared to the transmissivity computed with direct simulations carried out at the microscale on the whole fracture. This is performed on two model rough fractures, namely, a spiral groove and a fractal fracture, while varying their mean apertures to investigate a wide range of the average Knudsen number characteristic of the flow at the megascale. A good agreement is obtained between the two approaches showing the robustness of the two-scale method to determine the global transmissivity of the fracture while significantly reducing the overall computational time.