Discrete Propagation Research Articles

Dynamics and Control of a Novel Discrete Internet Rumor Propagation Model in a Multilingual Environment

In the Internet age, the development of intelligent software has broken the limits of multilingual communication. Recognizing that the data collected on rumor propagation are inherently discrete, this study introduces a novel SIR discrete Internet rumor propagation model with the general nonlinear propagation function in a multilingual environment. Then, the propagation threshold R0 is obtained by the next-generation matrix method. Besides, the criteria determining the spread or demise of rumors are obtained by the stability theory of difference equations. Furthermore, combined with optimal control theory, prevention and refutation mechanisms are proposed to curb rumors. Finally, the validity and applicability of the model are demonstrated by numerical simulations and a real bilingual rumor case study.

Maximum energy dissipation-based incremental approach for structural analyses involving discrete fracture propagation in quasi-brittle materials

A maximum energy dissipation-based incremental approach (MEDIA) is proposed to overcome limit points, e.g. strong snap-backs, in the fracture analysis of quasi-brittle materials. An optimisation step is applied using an expression proposed to compute the change of dissipated energy within the discretised body when moving from one state of equilibrium to another. This expression is developed at the integration point level and uses a binary pathway vector to define all the possible solutions within that step. Due to the unique way the problem is cast, a genetic algorithm is deployed to identify the solution leading to the highest energy dissipation while following applicable thermodynamic constraints. The resulting analysis is non-iterative and purely incremental. MEDIA is particularly applicable in combination with discrete crack models. In this case, meshes are relatively coarse and each crack can be individually handled to maintain the computational cost independent of the discretisation. The equations are also cast in a direct inverse method that avoids explicitly solving the inversion of the stiffness matrices for each chromosome in the genetic optimisation. Problems having multiple snap-back effects and non-proportional loading, as well as lightly and highly reinforced concrete beams, are used to assess the suitability and efficiency of the proposed method. In contrast with other available techniques, MEDIA is shown to follow the adopted constitutive models without any energy loss due to the solution-finding process while providing adequate structural responses.

Multiple discrete crack initiation and propagation in Material Point Method

Cracks in MPM (CRAMP) is one of the most prominent discrete crack simulation methods in the Material Point Method (MPM) due to its simplicity and versatility. However, CRAMP is yet to include the capability to simulate concurrent crack initiations and propagations, as well as propagation to the edge of the material domain. The method proposed in this paper enables the simulation of multiple crack paths with CRAMP via the dynamic assignment of particles to separate grids while minimizing the number of necessary grids. It also proposes methods of evaluating crack initiation and propagation via the Rankine criterion. The proposed methods are then implemented in an in-house Convected Particle Domain Interpolation (CPDI) MPM developed at Aalto University.To verify the integrity of the CPDI algorithm, our CPDI code with the proposed method implemented simulated a CPDI vortex. Furthermore, six fracture-simulation verification test cases were carried out: (1) through-crack in an infinite plate; (2) mode-I propagation; (3) initiation; (4) initiation with large deformations; (5) merging; (6) multiple initial cracks; and (7) radially-cracked thick ring. All these verification tests show successful initiation, propagation, merging, crack opening, and agreement with the results from the literature, as well as the convergence of various parameters with the expected rates.

Wireless Network Scheduling With Discrete Propagation Delays: Theorems and Algorithms

Wireless Network Scheduling With Discrete Propagation Delays: Theorems and Algorithms

Flame propagation modes for iron particle clusters in air — Part I: Transition from continuous to discrete propagation mode under weak convection effects

Iron powder can serve as an energy carrier and help generate heat and power in a clean and sustainable manner. In this paper, we analyze one of the challenges related to iron combustion: the mode of flame propagation. Depending on the conditions, an iron dust flame can propagate in either the continuous mode, with neighboring particles burning simultaneously, or in a discrete mode, with each particle burning separately, i.e. as a percolating wave. We use particle-resolved simulations including the heterogeneous reaction of iron with oxygen and detailed transport models. Simulations are carried out with multiple particles in a single row with hot gas at the inlet for initiating combustion under weak convection effects. Continuous and discrete flame propagation modes are identified and the particle distance, at which the transition from the continuous to the discrete propagation mode occurs, is calculated for different particle diameters. It is found that the transition from one mode to another occurs close to stoichiometry and the maximum flame reaction front speed is within the range of experiments with similarly sized particles. The flame propagation mode transitions to the discrete mode for larger particles at slightly lower particle distances than smaller particles due to higher thermal inertia. The discreteness parameter is modified to take into account the effect of heating from burnt particles on the unburnt ones. This results in an overall adequate prediction of the numerically found transitional distances under weak convection effects.Novelty and significance: As a carbon-free energy carrier, there is a great requirement for exploring the fundamental and application aspects of iron combustion. One critical issue for the heterogeneous combustion of iron is the mode of flame propagation. While previous studies have relied on simplified models and simplifying assumptions, in this work, we carry out detailed boundary layer resolved simulations of multiple particles with varying distances between the particles. Beyond a critical particle spacing, the mode of flame propagation transitions from the continuous mode where multiple particles burn simultaneously, to the discrete mode where the particles burn standalone. The scaling of such a transition is improved with the help of appropriate temperature based properties and the length scale. Our work is significant in understanding the fundamentals of flame propagation in iron clusters and can help in the development of Euler–Lagrangian models where tens of thousands of particles need to be simulated.

Analytical evaluations of the path integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator.

By using the recently derived universal discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically and evaluated numerically at each imaginary time step for any short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth-order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing thermodynamic energy, converges extremely slowly with an increasing number of beads.

Flame propagation modes for iron particle clusters in air, Part II: Transition from continuous to discrete propagation mode under strong convection effects

Combustion of iron powder is a promising option for clean and sustainable generation of heat and power. However, a fundamental understanding of the flame propagation mode is missing, especially under strong convection effects. In part I of this work, we analyzed the modes of flame propagation under weak convection effects and estimated the discreteness parameter as a ratio of the particle burn time to the conduction timescale. We found that both, the selection of temperature at which thermal properties are evaluated, and the selected length scale, are critical for a reliable prediction of the transitional particle spacing indicating the transition from the continuous to the discrete mode. In this paper, we extend our previous work by studying the effect of convection on inter-particle heat and mass transfer using boundary layer resolved numerical simulations. It is shown that for increasing convection, iron flames transition from the continuous to the discrete mode at higher particle distances. Taking into account both diffusion and convection-dominated heat transfer, an extension for the scaling of transitional particle spacing of part I is proposed. Furthermore, since iron flames could experience varying ranges of particle distances at different velocities in a practical flame, a regime diagram is constructed which is based on the Péclet number and the particle spacing with a boundary separating the two modes of flame propagation. The regime diagram offers orientation for simulations of large-scale flames using Euler–Lagrange methods where boundary layers around the particles are not resolved.

Anatomy of path integral Monte Carlo: Algebraic derivation of the harmonic oscillator's universal discrete imaginary-time propagator and its sequential optimization.

The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free propagators into one in the presence of interaction, derives the discrete propagator by simple algebra without doing any integration. This discrete propagator is universal, having the same two hyperbolic coefficient functions for all short-time propagators. Individual short-time propagator only modifies the coefficient function's argument, its portal parameter, whose convergent order is the same as the thermodynamic energy. Moreover, the thermodynamic energy can be given in a closed form for any short-time propagator. Since the portal parameter can be systematically optimized by matching the expansion of the product of the two coefficients, any short-time propagator can be optimized sequentially, order by order, by matching the product coefficient's expansion alone, without computing the energy. Previous empirical findings on the convergence of fourth and sixth-order propagators can now be understood analytically. An eight-order convergent short-time propagator is also derived.

Analysis on sound absorption in Sonic Black Holes

Exploration of Acoustic black holes (ABHs) for sound wave manipulation is referred to as Sonic black holes (SBHs). Different from the ideal SBH structure with continuously varied wave propagation boundary formed by putting extensive number of rings inside, the wave trapping and energy dissipation mechanism of practically realized SBH structure with discrete varied wave propagation boundary formed by quite limited number of rings inside are still not clear. To fill the gap, finite element simulations are performed to assess the sound absorption performance of a practical discrete SBH structure and explore the sound absorption mechanism behind. The validity of the FEM results is demonstrated through comparisons with experimental data obtained through impedance tube tests. Analyses reveal that the physical mechanism underpinning the sound absorption of practically realized SBH device is attributed to the combined effects of the ABH-induced wave speed changes, energy trapping and the spatially graded local resonances of series cavities formed by the space between two adjacent rings. While shedding light on the underlying sound attenuation mechanism, studies provide guidelines for further investigations on SBH structures.

On the gravitational diagram technique in the discrete setup

This paper is in the spirit of our work on the consequences of the Regge calculus, where some edge length scale arises as an optimal initial point of the perturbative expansion after functional integration over connection. Now consider the perturbative expansion itself. To obtain an algorithmizable diagram technique, we consider the simplest periodic simplicial structure with a frozen part of the variables (“hypercubic”). After functional integration over connection, the system is described by the metric [Formula: see text] at the sites. We parameterize [Formula: see text] so that the functional measure becomes Lebesgue. The discrete diagrams are free from ultraviolet divergences and reproduce (for ordinary, non-Planck external momenta) those continuum counterparts that are finite. We give the parametrization of [Formula: see text] up to terms, providing, in particular, additional three-graviton and two-graviton-two-matter vertices, which can give additional one-loop corrections to the Newtonian potential. The edge length scale is [Formula: see text], where [Formula: see text] defines the free factor [Formula: see text] in the measure and should be a large parameter to ensure the true action after integration over connection. We verify the important fact that the perturbative expansion does not contain increasing powers of [Formula: see text] if its initial point is chosen close enough to the maximum point of the measure, thus justifying this choice. Discrete propagators depend on the Barbero–Immirzi parameter [Formula: see text], which determines the ratio of timelike and spacelike elementary length scales. The existing estimates of [Formula: see text] allow the propagator poles to have real energy for any (real) spatial momenta.

An enriched mixed finite element model for the simulation of microseismic and acoustic emissions in fractured porous media with multi‐phase flow and thermal coupling

AbstractA novel mixed enriched finite element model is developed for coupled non‐linear thermo‐hydro‐mechanical simulation of fractured porous media with three‐phase flow and thermal coupling. Simulation of induced acoustic emission (AE) and microseismic emission (ME) due to tensile fracturing and shear slip instability of pre‐existing fracture interfaces is carried out and the numerical results of the emitted signals are analysed. The mathematical model is based on the generalized Biot's theory for coupled interaction of solid and fluid phases. A computationally robust non‐linear solver is developed to handle the severe non‐linearities arising from fluid saturations, relative permeabilities of fluids, constitutive models of interfaces and convective thermal coupling. To model pre‐existing natural fractures and faults, discrete fracture propagation and nucleation of cracks (micro‐cracking) independently of the original mesh topology, a local Partition‐of‐Unity (PU) finite element method, namely, the Phantom Node Method (PNM) is implemented. The cohesive fracture modelling scheme is implemented to account for the non‐linear behaviour of fracturing and localization, and to rectify the non‐physical stress singularity condition at the fracture tip. Effects of different system parameters on fracturing, shear‐slip instability and the associated induced AEs and MEs are investigated through various numerical results.

STENCIL-NET for equation-free forecasting from data

We present an artificial neural network architecture, termed STENCIL-NET, for equation-free forecasting of spatiotemporal dynamics from data. STENCIL-NET works by learning a discrete propagator that is able to reproduce the spatiotemporal dynamics of the training data. This data-driven propagator can then be used to forecast or extrapolate dynamics without needing to know a governing equation. STENCIL-NET does not learn a governing equation, nor an approximation to the data themselves. It instead learns a discrete propagator that reproduces the data. It therefore generalizes well to different dynamics and different grid resolutions. By analogy with classic numerical methods, we show that the discrete forecasting operators learned by STENCIL-NET are numerically stable and accurate for data represented on regular Cartesian grids. A once-trained STENCIL-NET model can be used for equation-free forecasting on larger spatial domains and for longer times than it was trained for, as an autonomous predictor of chaotic dynamics, as a coarse-graining method, and as a data-adaptive de-noising method, as we illustrate in numerical experiments. In all tests, STENCIL-NET generalizes better and is computationally more efficient, both in training and inference, than neural network architectures based on local (CNN) or global (FNO) nonlinear convolutions.

Thermal inertia effect of reactive sources on one-dimensional discrete combustion wave propagation

In the present work, the discrete flame model developed by Shoshin et al. (Doklady Akademii Nauk SSSR, 1986) and further scrutinized by Tang et al. (Combustion Theory and Modelling, 2009) is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on the speeds, propagation limits, and near-limits dynamics of one-dimensional discrete combustion waves is studied using the new model. It is found that, with the increase of particle thermal inertia, the propagation velocity of the discrete flame decreases due to the smaller heating rate of the particles. Besides, particle thermal inertia extends the propagation limits compared to the prediction of the old model. Furthermore, it is mathematically proven that the nonphysical branch of the solutions for the discrete flame speeds, found using the old discrete model, is a set of solutions for the propagation limits of steady-state discrete flames with particle thermal inertia included. The flame speed predicted using the new model is also compared with that determined analytically using a continuum model considering the thermal inertia of the condensed phase, attributed to Goroshin et al. (Combustion and Flame, 1996). We find that the discrete flame speeds predicted by the both models become closer to each other with increasing particle thermal inertia. Finally, the two models converge regardless of the discrete nature of the heat sources when particle thermal inertia is large enough so that can limit the flame propagation. The particle thermal inertia controlled flames could be regarded as a new kind of combustion regime.

Size effect on the FPZ length in notched beams: Mesoscopic method and theoretical analytical

A microscopic finite element model of three-point bending (TPB) notched lightweight concrete beams is established in this paper. The behavior of discrete crack initiation and propagation in notched beams is simulated based on the cohesive and interface frictional coupling model. The correctness of the microscopic model is verified by the experimental data from related literature, and the length evolution of the fracture process zone (FPZ) during the loading process of the microscopic notched beams is performed. Meanwhile, the evolution laws of macroscopic and mesoscopic characteristic parameters such as the crack-height ratio, porosity, lightweight aggregate strength, and the lightweight aggregate volume fraction on the FPZ length of the mesoscopic notched beams are studied. In addition, the size effect of the FPZ of the mesoscopic notched beams is analyzed. The size effect law based on the critical distance line criterion is derived and the effect of high-order terms of the stress field is considered. The functional relationship between the nominal strength, FPZ length, and notched beam height is obtained to explain the size effect phenomenon. The results show that the FPZ length obtained by the mesoscopic method is in good agreement with the FPZ length obtained by the critical distance line criterion.

A Knowledge-Based Adaptive Discrete Water Wave Optimization for Solving Cloud Workflow Scheduling

Workflow scheduling in cloud environments has become a significant topic in both commercial and industrial applications. However, it is still an extraordinarily challenge to generate effective and economical scheduling schemes under the deadline constraint especially for the large scale workflow applications. To address the issue, this paper investigates the cloud workflow scheduling problem with the aim of minimizing the whole cost of workflow execution whereas maintaining its execution time under a predetermined deadline. A novel knowledge-based adaptive discrete water wave optimization (KADWWO) algorithm is developed based on the problem-specific knowledge of cloud workflow scheduling. In the proposed KADWWO, a discrete propagation operator is designed based on the idle time knowledge of hourly-based cost model to adaptively explore the huge search space. The adaptive refraction operator is employed to avoid stagnation and expand the available resource pool. Meanwhile, the dynamic grouping based breaking operator is designed to exploit the excellent block structure knowledge of task allocation scheme and corresponding resource to intensify the local region and accelerate convergence. Extensive simulation experiments on the well-known scientific workflow demonstrate that the KADWWO approach outperforms several recent state-of-the-art algorithms.

Optical fiber with fractional orbital angular momentum.

A design method for the creation of photons with fractional orbital angular momentum (FOAM) is reported through the use of a metal-wedge optical fiber. The main focus was on a limiting zero-degree metal wedge, the case of light beams carrying ±ℏ2 OAM per photon. We compared this ideal case with a one-degree metal wedge in hopes of encouraging experimentalists to fabricate this type of waveguide. Various intensity and the Poynting vector plots for different modes and varying wedge angles were obtained and analyzed. We found that the Poynting vectors in the transverse direction for the zero and one degree metal wedges were essentially identical. In addition, as the metal wedge angle was increased, the real propagation constant decreased. Furthermore, the metal wedge enables a new method to obtain a local field enhancement in the center of the core of this waveguide, thus providing a wide range of applications in other fields. Finally, we found discrete complex propagation constants leading to discrete leaky modes with potentially an infinite number of these modes.

3D Interconnected Magnetic Nanowire Networks as Potential Integrated Multistate Memristors.

Interconnected magnetic nanowire (NW) networks offer a promising platform for three-dimensional (3D) information storage and integrated neuromorphic computing. Here we report discrete propagation of magnetic states in interconnected Co nanowire networks driven by magnetic field and current, manifested in distinct magnetoresistance (MR) features. In these networks, when only a few interconnected NWs were measured, multiple MR kinks and local minima were observed, including a significant minimum at a positive field during the descending field sweep. Micromagnetic simulations showed that this unusual feature was due to domain wall (DW) pinning at the NW intersections, which was confirmed by off-axis electron holography imaging. In a complex network with many intersections, sequential switching of nanowire sections separated by interconnects was observed, along with stochastic characteristics. The pinning/depinning of the DWs can be further controlled by the driving current density. These results illustrate the promise of such interconnected networks as integrated multistate memristors.

Observations of the Discrete Propagation of a Mesoscale Convective System during RELAMPAGO–CACTI

Abstract During the early morning hours of 5 November 2018, a mature mesoscale convective system (MCS) propagated discretely over the second-most populous province of Argentina, Córdoba Province, during the Remote Sensing of Electrification, Lightning, and Mesoscale/Microscale Processes with Adaptive Ground Observations–Cloud, Aerosol, and Complex Terrain Interactions (RELAMPAGO–CACTI) joint field campaigns. Storm behavior was modified by the Sierras de Córdoba, a north–south-oriented regional mountain chain located in the western side of the province. Here, we present observational evidence of the discrete propagation event and the impact of the mountains on the associated physical processes. As the mature MCS moved northeastward and approached the windward side of the mountains, isolated convective cells developed downstream in the mountain lee, 20–50 km ahead of the main convective line. Cells were initiated by an undular bore, which formed as the MCS cold pool moved over the mountain ridge and perturbed the leeside nocturnal, low-level stable layer. The field of isolated cells organized into a new MCS, which continued to move northeastward, while the parent storm decayed as it traversed the mountains. Only the southern portion of the storm propagated discretely, due to variability in mountain height along the chain. In the north, taller mountain peaks prevented the MCS cold pool from moving over the terrain and perturbing the stable layer. Consequently, no bore was generated, and no discrete propagation occurred in this region. To the south, the MCS cold pool was able to traverse the lower-relief mountains, and the discrete propagation was successful.

FE2 methodology for discrete cohesive crack propagation in heterogenous materials

To study the discrete crack growth of heterogeneous materials, a dual-scale discrete fracture calculation method is proposed in this paper. An equivalent cohesive energy criterion is proposed for the FE2 model based on the characteristics of the fracture zone. The representative volume element (RVE) with a cohesive zone is embedded into the Gauss points of the macro-element to replace the full FE model of the discrete crack. Therefore, the dual-scale method of discrete fractures not only improves the dual-scale modeling of discrete cracks but also greatly reduces the computational cost. We further demonstrate that the built-in capabilities of commercial software are naturally compatible with this method. Finally, the fracture process of a two-phase heterogeneous material containing a zirconium alloy matrix and hydride was studied using the dual-scale method. The macro-fracture direction was related to the precipitation direction of the brittle hydrides. This conclusion is consistent with existing experimental observations.

Improved discrete plant propagation algorithm for solving the traveling salesman problem

The primary goal of traveling salesman problem (TSP) is for a salesman to visit many cities and return to the starting city via a sequence of potential shortest paths. Subsequently, conventional algorithms are inadequate for large-scale problems; thus, metaheuristic algorithms have been proposed. A recent metaheuristic algorithm that has been implemented to solve TSP is the plant propagation algorithm (PPA), which belongs to the rose family. In this research, this existing PPA is modified to solve TSP. Although PPA is claimed to be successful, it suffers from the slow convergence problem, which significantly impedes its applicability for getting good solution. Therefore, the proposed partial-partitioned greedy algorithm (PPGA) offers crossover and three mutation operations (flip, swap, and slide), which allow local and global search and seem to be wise methods to help PPA in solving the TSP. The PPGA performance is evaluated on 10 separate datasets available in the literature and compared with the original PPA. In terms of distance, the computational results demonstrate that the PPGA outperforms the original PPA in nine datasets which assures that it is 90% better than PPA. PPGA produces good solutions when compared with other algorithms in the literature, where the average execution time reduces by 10.73%.