We report on the construction of a granular network of particles to study the formation, evolution, and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically vibrated quasi-two-dimensional granular system. Using the data of particle positions and local order from Castillo et al. [G. Castillo, N. Mujica, and R. Soto, Phys. Rev. Lett. 109, 095701 (2012)], we extract granular clusters taken as communities of the granular network via modularity optimization. Each one of these communities is a patch of particles with a very well defined local orientational order embedded within an array of other patches forming a complex cluster network. The distributions of cluster sizes and lifespans for the cluster network depend on the distance to the liquid-solid-like phase transition of the quasi-two-dimensional granular system. Specifically, the cluster size distribution displays a scale-invariant behavior for at least a decade in cluster sizes, while cluster lifespans grow monotonically with each cluster size. We believe this systematic community analysis for clustering in granular systems can help to study and understand the spatiotemporal evolution of mesoscale structures in systems displaying out-of-equilibrium phase transitions.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. Examples for the latter include surface waves and nonlinear Schrödinger equations with cubic nonlinearity. However, numerical simulations in forced–dissipative equilibrium of two-dimensional turbulence and of a one-dimensional wave system reveal that the physical nature of their cascades is starkly different. This is demonstrated by comparing their spectra in a finite inertial range and by comparing the temporal fluctuations of their spectral fluxes. In particular, the flux fluctuations are much larger in the wave case and frequently lead to instantaneous flux values that have the opposite sign of the mean flux, a phenomenon that is completely absent in the hydrodynamic case. A simple random walk model for the dual cascade in wave turbulence is then formulated that is very successful in explaining these effects. In particular, the model is able to replicate the detailed shape of the observed turbulent spectrum in a finite inertial range, and it also offers a ready explanation for the large flux fluctuations. It is also shown that a nonlinear diffusion model for the wave system cannot explain the observed spectral shapes. Overall, this suggests that in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance.

We provide analytic expressions for the effective Coulomb logarithm for inverse bremsstrahlung absorption which predict significant corrections to the Langdon effect and overall absorption rate compared to previous estimates. The calculation of the collisional absorption rate of laser energy in a plasma by the inverse bremsstrahlung mechanism usually makes the approximation of a constant Coulomb logarithm. We dispense with this approximation and instead take into account the velocity dependence of the Coulomb logarithm, leading to a more accurate expression for the absorption rate valid in both classical and quantum conditions. In contrast to previous work, the laser intensity enters into the Coulomb logarithm. In most laser-plasma interactions the electron distribution function is super-Gaussian [Langdon, Phys. Rev. Lett. 44, 575 (1980)], and we find the absorption rate under these conditions is increased by as much as $\approx 30\%$ compared to previous estimates at low density. In many cases of interest the correction to Langdon's predicted reduction in absorption is large; for example at $Z=6$ and $T_e=400\mathrm{eV}$ the Langdon prediction for the absorption is in error by a factor of $\approx 2$. However, we also account for the additional effect of plasma screening, which predicts a reduction in absorption by a similar amount (up to $\approx 30\%$). These two effects compete to determine the overall absorption, which may be increased or decreased, depending on the conditions. The corrections can be incorporated into radiation-hydrodynamics simulation codes by replacing the familiar Coulomb logarithm with an analytic expression which depends on the super-Gaussian order “M” and the screening length.

Using a discrete element method, we investigate the phenomenon of geometric cohesion in granular systems composed of star-shaped particles with 3 to 13 arms. This was done by analyzing the stability of columns built with these particles and by studying the microstructure of these columns in terms of density and connectivity. We find that systems composed of star-shaped particles can exhibit geometric cohesion (i.e., a solidlike behavior, in the absence of adhesive forces between the grains), depending on the shape of the particles and the friction between them. This phenomenon is observed up to a given critical size of the system, from which a transition to a metastable behavior takes place. We also have evidence that geometric cohesion is closely linked to the systems' connectivity and especially to the capability of forming interlocked interactions (i.e., multicontact interactions that hinder the relative rotation of the grains). Our results contribute to the understanding of the interesting and potentially useful phenomenon of geometric cohesion. In addition, our work supplements an important set of experimental observations and sheds light on the complex behavior of real, three-dimensional, granular systems.

Even when the partial differential equation underlying a physical process can be evolved forward in time, the retrospective (backward in time) inverse problem often has its own challenges and applications. Direct adjoint looping (DAL) is the defacto approach for solving retrospective inverse problems, but it has not been applied to deterministic retrospective Navier–Stokes inverse problems in 2D or 3D. In this paper, we demonstrate that DAL is ill-suited for solving retrospective 2D Navier–Stokes inverse problems. Alongside DAL, we study two other iterative methods: simple backward integration (SBI) and the quasireversible method (QRM). As far as we know, our iterative SBI approach is novel, while iterative QRM has previously been used. Using these three iterative methods, we solve two retrospective inverse problems: 1D Korteweg–de Vries–Burgers (decaying nonlinear wave) and 2D Navier–Stokes (unstratified Kelvin–Helmholtz vortex). In both cases, SBI and QRM reproduce the target final states more accurately and in fewer iterations than DAL. We attribute this performance gap to additional terms present in SBI and QRM's respective backward integrations which are absent in DAL.

Electric fields are commonly used to control the orientation and motion of microscopic metal particles in aqueous suspensions. For example, metallodielectric Janus spheres are propelled by the induced-charge electro-osmotic flow occurring on their metallic side, the most common case in electrokinetics of exploiting symmetry breaking of surface properties for achieving net particle motion. In this work, we demonstrate that a homogeneous metal rod can translate parallel to a dielectric wall as a result of the hydrodynamic wall-particle interaction arising from the induced-charge electro-osmosis on the rod surface. The applied electric field could be either dc or low-frequency ac. The only requirement for a nonvanishing particle velocity is that the axis of the rod be inclined with respect to the wall, i.e., it cannot be neither parallel nor perpendicular. We show numerical results of the rod velocity as a function of rod orientation and distance to the wall. The maximum particle velocity is found for an orientation of between $\sim {30}^{\circ }$ and $\sim {50}^{\circ }$, depending on the position and aspect ratio of the cylinder. Particle velocities of up to tens of $\mu \mathrm{m}/\mathrm{s}$ are predicted for typical conditions in electrokinetic experiments.

Two-dimensional (2D) Kardar-Parisi-Zhang (KPZ) growth is usually investigated on substrates of lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($\xi$) are the only relevant lengths determining the scaling behavior. However, in cylindrical geometry, as well as in flat rectangular substrates $L_x\ne L_y$ and, thus, the surfaces can become correlated in a single direction, when $\xi \sim L_x\ll L_y$. From extensive simulations of several KPZ models, we demonstrate that this yields a dimensional crossover in their dynamics, with the roughness scaling as $W\sim t^{{\beta }_{\text{2D}}}$ for $t\ll t_c$ and $W\sim t^{{\beta }_{\text{1D}}}$ for $t\gg t_c$, where $t_c\sim L_x^{1/z_{2\text{D}}}$. The height distributions (HDs) also cross over from the 2D flat (cylindrical) HD to the asymptotic Tracy-Widom Gaussian orthogonal ensemble (Gaussian unitary ensemble) distribution. Moreover, 2D to one-dimensional (1D) crossovers are found also in the asymptotic growth velocity and in the steady-state regime of flat systems, where a family of universal HDs exists, interpolating between the 2D and 1D ones as $L_y/L_x$ increases. Importantly, the crossover scalings are fully determined and indicate a possible way to solve 2D KPZ models.

We formulate the knapsack problem (KP) as a statistical physics system and compute the corresponding partition function as an integral in the complex plane. The introduced formalism allows us to derive three statistical-physics-based algorithms for the KP: one based on the recursive definition of the exact partition function, another based on the large weight limit of that partition function, and a final one based on the zero-temperature limit of the second. Comparing the performances of the algorithms, we find that they do not consistently outperform (in terms of runtime and accuracy) dynamic programming, annealing, or standard greedy algorithms. However, the exact partition function is shown to reproduce the dynamic programming solution to the KP, and the zero-temperature algorithm is shown to produce a greedy solution. Therefore, although dynamic programming and greedy solutions to the KP are conceptually distinct, a statistical physics formalism introduced reveals that the large weight-constraint limit of the former leads to the latter. We conclude by discussing how to extend this formalism in order to obtain more accurate versions of the introduced algorithms and other similar combinatorial optimization problems.

This work is devoted to the emergence of a connected network of slots (cracks) on a square grid. Accordingly, extensive Monte Carlo simulations and finite-size scaling analysis have been conducted to study the site percolation of straight slots with length $l$ measured in the number of elementary cells of the grid with the edge size $L$. A special focus was made on the dependence of the percolation threshold $p_C\left(l,L\right)$ on the slot length $l$ varying in the range $1\le l\le L-2$ for the square grids with edge size in the range $50\le L\le 1000$. In this way, we found that $p_C\left(l,L\right)$ strongly decreases with increase of $l$, whereas the variations of $p_C\left(l=\mathrm{const},L\right)$ with the variation of ratio $l/L$ are very small. Consequently, we acquire the functional dependencies of the critical filling factor and percolation strength on the slot length. Furthermore, we established that the slot percolation model interpolates between the site percolation on square lattice ($l=1$) and the continuous percolation of widthless sticks ($l\to \infty$) aligned in two orthogonal directions. In this regard, we note that the critical number of widthless sticks per unit area is larger than in the case of randomly oriented sticks. Our estimates for the critical exponents indicate that the slot percolation belongs to the same universality class as standard Bernoulli percolation.

Active materials possess unique properties of being able to respond autonomously to external stimuli, yet realizing and regulating the motion behavior of active machines remains a major challenge. Conventional control approaches, including sensor control and external device control, are both complex and difficult to implement. In contrast, active materials–based self-oscillators offer distinct properties such as periodic motion and ease of regulation. Inspired by paddle boats, we have proposed a conceptual light-fueled self-paddling boat with a photothermally responsive liquid crystal elastomer (LCE)–based motor that operates under steady illumination and incorporates an LCE fiber. Based on the well-established dynamic LCE model and rotation dynamics, the dynamic equations for governing the self-paddling of the LCE-steered boat are derived, and the driving torque of the LCE-based motor and the paddling velocity of the LCE-steered boat are formulated successively. The numerical results show that two motion modes of the boat under steady illumination: the static mode and the self-paddling mode. The self-paddling regime arises from the competition between the light-fueled driving torque and the frictional torque. Moreover, the critical conditions required to trigger the self-paddling are quantitatively examined as well as the significant system parameters affecting the driving torque, angular velocity, and paddling velocity. The proposed conceptual light-fueled self-paddling LCE-steered boat exhibits benefits including customizable size and being untethered and ambient powered, which provides valuable insights into the design and application of micromachines, soft robotics, energy harvesters, and beyond.

We introduce an approach to particle breakage, wherein the particle is modeled as an aggregate of polyhedral cells with their common surfaces governed by the Griffith criterion of fracture. This model is implemented within a discrete element code to simulate and analyze the breakage behavior of a single particle impacting a rigid plane. We find that fracture dynamics involves three distinct regimes as a function of the normalized impact energy $\omega$. At low values of $\omega$, the particle undergoes elastic rebound and no cracks occur inside the particle. In the intermediate range, the particle is damaged by nucleation and propagation of cracks, and the effective restitution coefficient declines without breakup of the particle. Finally, for values of $\omega$ beyond a well-defined threshold, the particle breaks into fragments and the restitution coefficient increases with $\omega$ due to kinetic energy carried away by the fragments. We show that particle damage, restitution coefficient, and fracture efficiency (the amount of energy input consumed for particle fracture) collapse well as a function of dimensionless scaling parameters. Our data are also sufficiently accurate to scale fragment size and shape distributions. It is found that fragment masses (volumes) follow a power-law distribution with an exponent decreasing with fracture energy. Interestingly, the average elongation and flatness of fragments are very close to those observed in experiments and lunar samples at the optimal fracture efficiency.

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least half of the integration variables prior to setting up the particular Monte Carlo calculation of interest, in some cases more. Proper accounting of invariant phase space structures shows that the system's dynamics is reducible into composite stable and unstable degrees of freedom. Stable degrees of freedom behave locally in the reduced dimensional phase space exactly as an analogous integrable system would. Classification of the unstable degrees of freedom is dependent upon the degree of chaos present in the dynamics. The techniques for deriving the requisite canonical coordinate transformations are developed and shown to block diagonalize the stability matrix into irreducible parts. In doing so, it is demonstrated how to reduce the amount of sampling directions necessary in a Monte Carlo simulation. The technique is illustrated by calculating return probabilities and expectation values for different dynamical regimes of a two-degrees-of-freedom coupled quartic oscillator within a classical Wigner method framework.

We consider a system of noninteracting Brownian particles on the line with steplike initial condition and study the statistics of the occupation time on the positive half-line. We demonstrate that even at large times, the behavior of the occupation time exhibits long-lasting memory effects of the initialization. Specifically, we calculate the mean and the variance of the occupation time, demonstrating that the memory effects in the variance are determined by a generalized compressibility (or Fano factor), associated with the initial condition. In the particular case of the uncorrelated uniform initial condition we conduct a detailed study of two probability distributions of the occupation time: annealed (averaged over all possible initial configurations) and quenched (for a typical configuration). We show that at large times both the annealed and the quenched distributions admit large deviation form and we compute analytically the associated rate functions. We verify our analytical predictions via numerical simulations using importance sampling Monte Carlo strategy.

Synchronization has attracted interest in many areas where the systems under study can be described by complex networks. Among such areas is neuroscience, where it is hypothesized that synchronization plays a role in many functions and dysfunctions of the brain. We study the linear stability of synchronized states in networks of Izhikevich neurons using master stability functions (MSFs), and to accomplish that, we exploit the formalism of saltation matrices. Such a tool allows us to calculate the Lyapunov exponents of the MSF properly since the Izhikevich model displays a discontinuity within its spikes. We consider both electrical and chemical couplings as well as global and cluster synchronized states. The MSF calculations are compared with a measure of the synchronization error for simulated networks. We give special attention to the case of electric and chemical coupling, where a riddled basin of attraction makes the synchronized solution more sensitive to perturbations.

Under investigation are the three-component Gross-Pitaevskii equations in $F=1$ spinor Bose-Einstein condensates. Various localized waves' generation mechanisms have been derived from plane wave solutions using modulation instability. The perturbed continuous waves produce a large number of rogue wave structures through the split-step Fourier numerical method. Based on the known Lax pair, we construct the generalized iterative $(n,N-n)$-fold Darboux transformation to generate various high-order solutions, including the bright-dark-bright structure of rogue waves, periodic waves, and their mixed interaction structures. Numerical simulations show that rogue waves with a two-peaked structure have robust noise resistance and stable dynamical behavior. The asymptotic states of high-order rogue waves as the parameter approaches infinity are also predicted using the large parameter asymptotic technique. In addition, the position of these localized wave patterns can be controlled by some special parameters. These results may help us understand the dynamic behavior of spinor condensates for the mean-field approximation.

The resonance of $N$ linearly coupled damped Duffing oscillators with a constant frequency sinusoidal driving force acting on the first oscillator is studied analytically by calculating the fixed points of the corresponding dynamical system and numerically using a fourth-order multivariate Runge-Kutta method. For a chain with $N$ oscillators, we establish a general recursion scheme in the form of a system of equations that relates the amplitudes of the oscillators and the driving frequency, capable of describing resonance curves. We consider in detail the case of an oscillator chain with $N=2$ for high values of the driving amplitude and stiffness, and find hysteretical unstable regions in the resonance curves. In this unstable driving frequency regime, analysis of the time series reveals the presence of nonlinear normal modes visible as beating quasiperiodic oscillations.

The theory based on numerical study of the system of hydrodynamic equations, which includes the director motion, shows that under the influence of crossed electric $\mathbf{\text{E}}$ and magnetic $\mathbf{\text{B}}$ fields, the director reorients in such a way that the transient quasiperiodic patterns may arise in microsized nematic volumes if the corresponding distortion mode has the fastest response and thus suppresses all other modes, including uniform ones. It has been shown that there is a threshold value of the amplitude of the thermal fluctuations of the director over the microsized nematic film which provides the nonuniform rotation mode rather than the uniform one, whereas the lower values of the amplitude dominate the uniform mode.

This paper proposes a strategy to implement the free-energy-based wetting boundary condition within the phase-field lattice Boltzmann method. The greatest advantage of the proposed method is that the implementation of contact line motion can be significantly simplified while still maintaining good accuracy. For this purpose, the liquid-solid free energy is treated as a part of the chemical potential instead of the boundary condition, thus avoiding complicated interpolations with irregular geometries. Several numerical testing cases, including droplet spreading processes on the idea flat, inclined, and curved boundaries, are conducted, and the results demonstrate that the proposed method has good ability and satisfactory accuracy to simulate contact line motions.