Discrete Coupling Research Articles

A partitioned material point method and discrete element method coupling scheme

Mass-movement hazards involving fast and large soil deformation often include huge rocks or other significant obstacles increasing tremendously the risks for humans and infrastructures. Therefore, numerical investigations of such disasters are in high economic demand for prediction as well as for the design of countermeasures. Unfortunately, classical numerical approaches are not suitable for such challenging multiphysics problems. For this reason, in this work we explore the combination of the Material Point Method, able to simulate elasto-plastic continuum materials and the Discrete Element Method to accurately calculate the contact forces, in a coupled formulation. We propose a partitioned MPM-DEM coupling scheme, thus the solvers involved are treated as black-box solvers, whereas the communication of the involved sub-systems is shifted to the shared interface. This approach allows to freely choose the best suited solver for each model and to combine the advantages of both physics in a generalized manner. The examples validate the novel coupling scheme and show its applicability for the simulation of large strain flow events interacting with obstacles.

Primal and mixed finite element formulations for the relaxed micromorphic model

The classical Cauchy continuum theory is suitable to model highly homogeneous materials. However, many materials, such as porous media or metamaterials, exhibit a pronounced microstructure. As a result, the classical continuum theory cannot capture their mechanical behaviour without fully resolving the underlying microstructure. In terms of finite element computations, this can be done by modelling the entire body, including every interior cell. The relaxed micromorphic continuum offers an alternative method by instead enriching the kinematics of the mathematical model. The theory introduces a microdistortion field, encompassing nine extra degrees of freedom for each material point. The corresponding elastic energy functional contains the gradient of the displacement field, the microdistortion field and its Curl (the micro-dislocation). Therefore, the natural spaces of the fields are [H1]3 for the displacement and [H(curl)]3 for the microdistortion, leading to unusual finite element formulations. In this work we describe the construction of appropriate finite elements using Nédélec and Raviart–Thomas subspaces, encompassing solutions to the orientation problem and the discrete consistent coupling condition. Further, we explore the numerical behaviour of the relaxed micromorphic model for both a primal and a mixed formulation. The focus of our benchmarks lies in the influence of the characteristic length Lc and the correlation to the classical Cauchy continuum theory.

A novel continuum–discrete multiscale coupling method for strain localization of lipid bio-membrane under tension

A novel continuum–discrete multiscale coupling method for strain localization of lipid bio-membrane under tension

Numerical Simulation on the Evolution of Tailings Pond Dam Failure Based on GDEM Method

Because of the continuous exploitation of metal minerals and the limited availability of land resources, many tailings ponds have been expanded. It is of great importance to dynamically calculate the critical parameters of flooding and sand velocity after a collapse, and quickly determine the dangerous area downstream on reducing the hidden dangers for an accident. In view of the limitations of the single finite element and discrete element methods for the simulation of tailings pond instability, the authors use the finite element and discrete element coupling method (GDEM) for the first time to carry out a dynamical process for numerical simulation of the evolution of a tailings pond collapse. The sediment movement and submerged range were compared with the results of the Volume of Fluid (VOF) method. The comparison shows that the change in drainage flow at the dam foundation position and the depth change in the downstream sensitive point after the dam break are consistent with the VOF calculation results, which indicates that the GDEM can be used as an effective means for the analysis of tailings dam failure. The calculation results of this method can provide technical support for the determination of dangerous areas downstream of tailings ponds and the safety management of key areas.

Simulation and experiment of tomato pollen particles release and motion characteristics based on optical flow target tracking method

Due to the reduction of the amount of natural pollinators, it is necessary to study the method and mechanism of greenhouse tomato mechanical vibration supplementary pollination. The release process and motion characteristics of pollen particles are very important for precision tomato supplementary pollination. In this paper, the pollen particles release and motion simulation model based on discrete element and hydrodynamics coupling method is established. The pollen particles position and trajectories detection algorithm based on optical flow target tracking method is designed. Compared with the detection results of high speed photography system, the relative error of pollen distribution range angle and pollen motion velocity of the simulation model is 7.94% and 8.87%, which shows the rationality and reliability of the established simulation model. Through the comprehensive analysis of the high speed photography observation results and simulation results, it can be concluded that the trend of pollen particles trajectories are vertical downward with random direction change, and greater vibration amplitude cause greater distribution range angle of pollen particles. There is no obvious trend of velocity change during the release process of each single pollen particle, and the relationship between vibration amplitude and average velocity of pollen particles is not obvious. The research results and the established model of this paper provide a mechanism basis for tomato mechanical vibration supplementary pollination and lay a foundation for the optimization of mechanical pollination method.

Design of a New Dimension-Changeable Hyperchaotic Model Based on Discrete Memristor

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic map and Sine map (CLS) is proposed. The new chaotic model is constructed by cascade operation in which the output of the Logistic map is used as the input of the Sine map. Additionally, the one-dimensional map is extended to any dimension through the coupling modulation. In order to further increase the complexity and stability of CLS, the discrete memristor model is introduced to construct a discrete memristor-based coupling model with a Logistic map and a Sine map (MCLS). By analyzing the Lyapunov exponents, bifurcation diagram, complexity, and the 0–1 test result, the comparison result between CLS and MCLS is obtained. The dynamics performance analysis shows that the Lyapunov exponents and bifurcation diagrams present symmetrical distribution with variations of some parameters. The MCLS has parameters whose values can be set in a wider range and can generate more complex and more stable chaotic sequences. It proves that the proposed discrete memristor-based closed-loop coupling model can produce any higher dimension hyperchaotic system and the discrete memristor model can effectively improve the performance of discrete chaotic map and make this hyperchaotic system more stable.

Microscopic fabric evolution and macroscopic deformation response of gangue solid waste filler considering block shape under different confining pressures.

The irregular shape of gangue blocks will affect the coordination structure between blocks in the crushed gangue accumulation body, and then affect the engineering mechanical properties of crushed gangue in the process of load-bearing compression. In this paper, through CT scanning experiment, particle flow numerical simulation experiment, and comprehensive application of image processing, 3D reconstruction, FLAC/PFC3D continuum—discrete coupling technology, the gangue digital 3D model and the numerical model of crushed gangue particle flow under triaxial compression condition considering the real shape of the block were obtained. The microscopic fabric evolution law and macroscopic deformation response characteristics of crushed gangue considering triaxial compression condition and different confining pressures were studied. The results show that: (1) the bearing capacity of crushed gangue materials increases with the increase of confining pressure; (2) the block aggregate in the gangue sample is gradually compacted, and the lateral deformation of the sample is changed from “extruding to the axis” to “bulging to the periphery”; (3) the vertical movement of the block decreases gradually from the top to the bottom of the sample, and there is a “triangle area” of block displacement at the top and bottom of the sample; the larger the confining pressure, the smaller the vertical displacement range at the top of the sample; (4) the process of “instability and failure—optimization and reconstruction” of skeleton force chain structure occurs constantly; as confining pressure increases, the stability of skeleton force chain structure and the bearing capacity of crushed gangue sample increases; (5) under the same strain state, the greater the confining pressure, the higher the fragmentation degree of the sample. This study reveals the internal mechanism of macro deformation of crushed gangue under the triaxial compression from the perspective of the mesoscopic fabric evolution. The research results are of great significance for the selection of crushed gangue in engineering application. In addition, the research results also have a significant impact on promoting the reasonable disposal and resource utilization of gangue solid waste and protecting the ecological environment of mining areas.

Uncovering the non-equilibrium stationary properties in sparse Boolean networks

Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the linear threshold model. However, because of the computational complexity of the method, the analysis has been limited to systems where the largest number of neighbours is small. We devise an efficient implementation of the dynamic cavity method which substantially reduces the computational complexity of the method for systems with discrete couplings. Our approach opens up the possibility to investigate the dynamic properties of networks with fat-tailed degree distribution. We exploit this new implementation to study properties of the non-equilibrium steady-state. We extend the dynamic cavity approach to calculate the pairwise correlations induced by different motifs in the network. Our results suggest that just two basic motifs of the network are able to accurately describe the entire statistics of observed correlations. Finally, we investigate models defined on networks containing bi-directional interactions. We observe that the stationary state associated with networks with symmetric or anti-symmetric interactions is biased towards the active or inactive state respectively, even if independent interaction entries are drawn from a symmetric distribution. This phenomenon, which can be regarded as a form of spontaneous symmetry-breaking, is peculiar to systems formulated in terms of Boolean variables, as opposed to Ising spins.

Bimorphic Floquet topological insulators.

Topological theories have established a unique set of rules that govern the transport properties in a wide variety of wave-mechanical settings. In a marked departure from the established approaches that induce Floquet topological phases by specifically tailored discrete coupling protocols or helical lattice motions, we introduce a class of bimorphic Floquet topological insulators that leverage connective chains with periodically modulated on-site potentials to reveal rich topological features in the system. In exploring a 'chain-driven' generalization of the archetypical Floquet honeycomb lattice, we identify a rich phase structure that can host multiple non-trivial topological phases associated simultaneously with both Chern-type and anomalous chiral states. Experiments carried out in photonic waveguide lattices reveal a strongly confined helical edge state that, owing to its origin in bulk flat bands, can be set into motion in a topologically protected fashion, or halted at will, without compromising its adherence to individual lattice sites.

Adaptive search strategy based chemical reaction optimization scheme for task scheduling in discrete multiphysical coupling applications

Parallel computing problems of multiphysical coupling applications based on discrete grids can be equivalently transformed into parallel computing problems based on a directed acyclic graph (DAG). Due to the problem of the discrete high-dimensional grids of the multiphysical coupling application, the directed data dependencies usually have parallelism. Moreover, this kind of scheduling problem based on DAG is NP-hard problem. Heuristic algorithms are often used to achieve optimal execution order scheduling of tasks and mapping between tasks and processors. In this paper, we propose an improved chemical reaction optimization algorithm based on adaptive search strategy (ASSCRO), which is used to solve the DAG task scheduling problem of discrete multiphysical coupling applications. ASSCRO is divided into two phases. The first phase is used to search the directed execution order of the tasks, and the second phase aims to use the heuristic strategy to map the tasks to the processors efficiently. In the four basic reactions of CRO, the algorithm can cover a larger search solution space by using an adaptive search strategy, it can obtain a better solution, and achieve less overhead and superior performance than the state-of-the-art. We conducted the experiment that applied our ASSCRO to deal with the multiphysical coupling applications. The experimental results showed that the proposed algorithm outperforms other algorithms in multiple metrics when dealing with DAG scheduling problems.

Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging

We explore the aging transition in a network of globally coupled Stuart-Landau oscillators under a discrete time-dependent coupling. In this coupling, the connections among the oscillators are turned ON and OFF in a systematic manner, having either a symmetric or an asymmetric time interval. We discover that depending upon the time period and duty cycle of the ON-OFF intervals, the aging region shrinks drastically in the parameter space, therefore promoting restoration of oscillatory dynamics from the aging. In the case of symmetric discrete coupling (where the ON-OFF intervals are equal), the aging zone decreases significantly with the resumption of dynamism with an increasing time period of the ON-OFF intervals. On the other hand, in the case of asymmetric coupling (where the ON-OFF intervals are not equal), we find that the ratio of the ON and OFF intervals controls the aging dynamics: the aging state is revoked more effectively if the interval of the OFF state is greater than the ON state. Finally, we study the transition in aging using a discrete pulse coupling: we note that the pulse interval plays a crucial role in determining the aging region. For all the cases of discrete time-dependent couplings, the aging regions are shrinking and the rhythmicity gets enhanced in a controlled manner. Our findings suggest that this type of coupling can act as a noninvasive way to restore the oscillatory dynamics from an aging state in a network of coupled oscillators.

A 2D discrete moisture diffusion model for simulating desiccation fracturing of soil

The desiccation fracturing of soil is widespread, which affects the migration of rainwater in the soil, and the stability of slopes or other projects. This paper proposes a simple two-dimensional (2D) discrete moisture diffusion model considering the influence of fractures on moisture migration. The moisture diffusion model is used in conjunction with the finite discrete element method (FDEM) to create a 2D discrete moisture diffusion-fracture coupling model, which is implemented in a GPU parallel multiphysics finite-discrete element software, namely MultiFracS. The coupled model is made up of three parts: a 2D discrete moisture diffusion model that takes into account the influence of fractures on moisture migration, a shrinkage deformation and stress computation, and an FDEM fracture mechanical computation. First, the moisture distribution in the system is analyzed using the moisture diffusion model. The shrinkage stress resulting from the moisture change is then computed. Finally, the shrinkage stress is added to the governing equation of FDEM to perform the fracture mechanical computation. Desiccation fracturing of the soil can be modeled using the processes outlined above. The paper firstly verifies the correctness of the 2D discrete moisture diffusion model to deal with the moisture migration in a continuous media, a media with impervious fractures or permeable fractures. Then, we give a principle that is used to determine the moisture exchange coefficient of the unbroken joint element through the parameter sensitivity analysis. Moreover, typical shrinkage deformation and stress problems and soil desiccation fracturing experiments are simulated. The simulation results are in good agreement with the analytical solutions and experiment results, verifying the effectiveness of the 2D discrete moisture diffusion-fracture coupling model to deal with shrinkage deformation and stress problems and the desiccation fracturing of soil. The coupled model provides a powerful solution tool to study the desiccation fracturing of soil.

Numerical simulation of erosion and fatigue failure the coal gangue paste filling caused to pumping pipes

The mechanical behavior of high-viscosity coal gangue paste (CGP) has been studied, while computational fluid dynamics and discrete element coupling method (DEM-CFD) was employed for it. Through the bidirectional coupling of particles and fluid, the force among different particles in the pipe and the effect of collisions were analyzed. The particle-pipe or particle–wall collision force has been solved by coupling the finite element method with discrete element method (DEM-FEM). The mechanical analysis of pipe’s life is realized, which was based on the fracture and fatigue analysis software NCODE, in which the actual pipe material parameters used in engineering were considered. The numerical simulation results show that the erosion of the flow field in the pipe (inlet and elbow) is serious, and the life of the parts will be greatly shortened. The simulation results agree with the results of field test very well. Hence, this numerical simulation method can be used to simulate the pipe erosion and wear, estimate the pipe’s life, and predict the positions of the failure.

Water Supply and Regulation of Underground Reservoir in Coal Mine considering Coal-Water Occurrence Relationship

Water supply prediction and control is one of the key issues in exploitation of coal mine underground reservoirs (CMUR). In order to investigate the water supply for underground reservoirs in coal mines, the aquifers were classified into three types (types I, II, and III) according to the relative location of aquifers. The discrete element fluid structure coupling numerical simulation model is constructed according to the classification results. The numerical simulation parameters are inversed based on the surface subsidence data and the advance support pressure, and then, the disturbed characteristics and water pressure variation law of different types of aquifers are studied. The research results show that the maximum water inflow of type III, type II, and type I aquifers is 739 m3/h, 377 m3/h, and 279 m3/h, respectively. The dynamic calculation process of underground reservoir capacity under mining disturbance is refined, and the regulation and storage methods of underground reservoir are preliminarily put forward.

Discrete element simulations on the damaged surface hydrodynamics of tungsten powders with inert Ar gas

Ejecta of micrometer-sized particles from a shocked damaged metal surface into a gas environment are widely observed in the engineering fields. Investigating the transport of ejecta particles in the converging geometries is a challenging scientific issue. Rousculp et al. [“Damaged surface hydrodynamics (DSH) flash report,” Report No. LA-UR-15-22889, 2015] have studied the transport of shock-launched tungsten powders from a cylindrical metal surface into an inert gas. In the so-called damaged surface hydrodynamic experiments, the effect of gas species on powder transport was investigated. Distinctive phenomena were observed in all cases in which particles aggregated into radial spikes or stripes with an azimuthal modulation of n > 20, though the initial powder coating was highly controlled and the shock loading was believed to be azimuthally uniform. In this work, discrete element method coupling with magneto-hydrodynamic simulations was employed to explore the mechanism behind the experimental phenomena. Results showed that stripes may be originated from the non-uniform initial distribution and small velocity difference of particles. The intense particle collision during the shock launching caused the microstripe-like structures, which merged into macroscopic ones observed in the subsequent particle transport process. Lagrange tracking revealed the stripes at different moments consisted of different particles. Oblique collisions played an important role in the long-term transport of ejecta particles in the convergence geometries, while the drag force of gas showed little influence. This work will promote the understanding of dense particle–gas flow in converging geometries.

Numerical study on P-wave propagation across the jointed rock masses by the combined finite-discrete element method

The combined finite-discrete element method (FDEM) is an advanced finite and discrete element coupling method. This study further applies it to the problem of stress wave propagation in the jointed rock mass. Firstly, the fundamental theory of FDEM is briefly described and the methods commonly used in FDEM to characterize structural planes are comprehensively analyzed. Then, based on the viscous boundary condition (VBC), the viscous-spring boundary condition (VSBC) is added to absorb the reflected wave at the artificial boundary and restore the residual displacement to meet the actual engineering. In addition, the application range of the VBC and VSBC is verified, which indicates that the VBC and VSBC in the improved FDEM can be well applied not only to the continuum range but also to the case of the new fracture formed. Finally, several classic models are solved to verify the stress wave propagation across different types of joints by FDEM. The results reveal that results from FDEM agree well with analytical solutions based on the displacement discontinuity model and numerical solutions from universal distinct element code (UDEC), which means that the improved FDEM can capably and accurately simulate wave propagation in the jointed rock mass.

Analysis of the Hopfield Model with Discrete Coupling

Growing demand for high-speed Ising-computing-specific hardware has prompted a need for determining how the accuracy depends on a hardware implementation with physically limited resources. For instance, in digital hardware such as field-programmable gate arrays, as the number of bits representing the coupling strength is reduced, the density of integrated Ising spins and the speed of computing can be increased while the calculation accuracy becomes lower. To optimize the accuracy-efficiency trade-off, we have to estimate the change in performance of the Ising computing machine depending on the number of bits representing the coupling strength. In this study, we tackle this issue by focusing on the Hopfield model with discrete coupling. The Hopfield model is a canonical Ising computing model. Previous studies have analyzed the effect of a few nonlinear functions (e.g. sign) for mapping the coupling strength on the Hopfield model with statistical mechanics methods, but not the effect of discretization of the coupling strength in detail. Here, we derived the order parameter equations of the Hopfield model with discrete coupling by using the replica method and clarified the relationship between the number of bits representing the coupling strength and the critical memory capacity. In this paper, we used the replica method for the Hopfield model with general nonlinear coupling (Sompolinsky (1986)) to analyze the model with a multi-bit discrete coupling strength, and we novelly derived the de Almeida-Thouless line of the model with general nonlinear coupling.

Coherent single-photon scattering spectra for a giant-atom waveguide-QED system beyond the dipole approximation

We investigate the single-photon scattering spectra of a giant atom coupled to a one dimensional waveguide via multiple connection points or a continuous coupling region. Using a full quantum mechanical method, we obtain the general analytic expressions for the single-photon scattering coefficients, which are valid in both the Markovian and the non-arkovian regimes. We summarize the influences of the non-dipole effects, mainly caused by the phases accumulated by photons traveling between coupling points, on the scattering spectra. We find that under the Markovian limit, the phase decay is detuning-independent, resulting in Lorentzian lineshapes characterized by the Lamb shifts and the effective decay rates. While in the non-Markovian regime, the accumulated phases become detuning-dependent, giving rise to non-Lorentzian lineshapes, characterized by multiple side peaks and total transmission points. Another interesting phenomenon in the non-Markovian regime is generation of broad photonic band gap by a single giant atom. We further generalize the case of discrete coupling points to the continuum limit with atom coupling to the waveguide via a continuous area, and analyze the scattering spectra for some typical distributions of coupling strength.

Research on time synchronization of linear pulse-coupled oscillators model with delay in nearest neighbor wireless multi-hop networks

Time synchronicity works as a popular requirement in wireless sensor networks. Pulse-coupled oscillators similar to firefly flashing and synchronization via discrete pulse coupling are widely used in wireless sensor networks. In this article, we have studied the time synchronization with communication delay in the nearest neighbor network of distributed sensors, based on the pulse-coupled oscillators model of synchronicity achieved by biological systems. First, we present a linear pulse-coupled oscillators model with coupling delay and the model is used to analyze the wireless sensor networks synchronization with communication delay. Second, we mathematically analyze the firing behaviors in the linear pulse-coupled oscillators network using the delayed excitatory coupling and track the synchronization process of the two and multi-oscillators and obtain the synchronization conditions from the regression mapping. Finally, through the proposed model implementation in the wireless sensor networks simulation framework, we demonstrate that the multi-oscillators system can be synchronized from a random starting stage distribution under linear phase responding functions and the nearest neighbor communication. The results show that our approach can achieve clock synchronization in wireless sensor networks with delayed nearest neighbor communication.

A review on metal additive manufacturing: modeling and application of numerical simulation for heat and mass transfer and microstructure evolution

Metal additive manufacturing technology has been widely used in prototyping, parts manufacturing and repairing. Metal additive manufacturing is a multi-scale and multi-physical coupling process with complex physical phenomena of heat and mass transfer and microstructure evolution. It is hard to directly observe the dynamic behavior and microstructure evolution of molten pool during additive manufacturing. Therefore, numerical simulation of additive manufacturing process is significant since it can efficiently and pertinently predict and analyze the physical phenomena in the process of metal additive manufacturing, and provide a reference for technological parameters selection. In this review, the research progress of numerical simulation of metal additive manufacturing is discussed. Various aspects of numerical simulation models are reviewed, including: (1) Introduction of basic control method and physical description of numerical simulation models; (2) Comparison of various heat and mass transfer models based on different physical assumptions (heat conduction model; heat flux coupling model; discrete powder particle heat flux coupling model); (3) Applications of various microstructure evolution models [phase field (PF), cellular automata (CA), and Monte Carlo (MC)]. Finally, the development trend of numerical simulation of metal additive manufacturing, including the thermal-flow-solid coupling model and deep learning for numerical model, is analyzed.