Podlozhnyuk, Alexander; Pirker, Stefan; Kloss, Christoph
2016-09-01
Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particle-particle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particle-wall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.
Podlozhnyuk, Alexander; Pirker, Stefan; Kloss, Christoph
2017-01-01
Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particle-particle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particle-wall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.
Energy Technology Data Exchange (ETDEWEB)
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Superquadric Similarity Measure with Spherical Harmonics in 3D Object Recognition
Institute of Scientific and Technical Information of China (English)
XINGWeiwei; LIUWeibin; YUANBaozong
2005-01-01
This paper proposes a novel approach for superquadric similarity measure in 3D object recognition. The 3D objects are represented by a composite volumetric representation of Superquadric (SQ)-based geons, which are the new and powerful volumetric models adequate for 3D recognition. The proposed approach is processed through three stages: first, a novel sampling algorithm is designed for searching Chebyshev nodes on superquadric surface to construct the discrete spherical function representing superquadric 3D shape; secondly, the fast Spherical Harmonic Transform is performed on the discrete spherical function to obtain the rotation invariant descriptor of superquadric; thirdly, the similarity of superquadrics is measured by computing the L2 difference between two obtained descriptors. In addition, an integrated processing framework is presented for 3D object recognition with SQ-based geons from the real 3D data, which implements the approach proposed in this paper for shape similarity measure between SQ-based geons. Evaluation experiments demonstrate that the proposed approach is very efficient and robust for similarity measure of superquadric models. The research lays a foundation for developing SQ-based 3D object recognition systems.
Superquadric Based Hierarchical Reconstruction for Virtualizing Free Form Objects from 3D Data
Institute of Scientific and Technical Information of China (English)
LIU Weibin; YUAN Baozong
2001-01-01
The superquadric description is usedin modeling the virtual objects in AVR (from ActualReality to Virtual Reality).However,due to the in-trinsic property,the superquadric and its deforma-tion extensions (DSQ) are not flexible enough to de-scribe precisely the complex objects with asymmetryand free form surface.To solve the problem,a hierar-chical reconstruction approach in AVR for virtualizingthe objects with superquadric based models from 3Ddata is developed.Firstly,an initial approximation isproduced by a superquadric fit to the 3D data.Then,the crude superquadric fit is refined by fitting theresidue (distance map) with global and local DirectManipulation of Free-Form Deformation (DMFFD).The key elements of the hierarchical method,includ-ing superquadric fit to 3D data,mathematical detailsand the recursive-fitting algorithm for DMFFD,com-putation of distance maps,adaptive refinement anddecimation of polygon mesh under DMFFD,are pro-posed.An implementation example of hierarchicalreconstruction is presented.The proposed approachis shown competent and efficient for virtualizing thecomplex objects into virtual environment.
A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil
Lane, John E.; Metzger, Philip T.; Wilkinson, R. Allen
2010-01-01
As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.
Soltanbeigi, Behzad; Podlozhnyuk, Alexander; Ooi, Jin Y.; Kloss, Christoph; Papanicolopulos, Stefanos-Aldo
2017-06-01
In the current study, complex-shaped particles are simulated with the Discrete Element Method (DEM) using two different approaches, namely Multi-spheres (MS) and Superquadrics (SQ). Both methods have been used by researchers to represent the shape of real particles. However, despite the growing popularity of utilizing MS and SQ particles in DEM simulations, few insights have been given on the comparison of the macro scale characteristics arising from the two methods. In this respect, initially the characteristics of the two shape representation methods are evaluated in a direct shear test simulation. The results suggest that controlling the sharpness of the edges for SQ particles can lead to a good agreement with the results of MS particles. This way, a set of SQ and MS particles, which are numerically calibrated in the shear tester, are obtained. Furthermore, the macro-scale responses of the numerically calibrated particles are assessed during a slow shearing scenario, which is achieved through simulating quasi-static flow of the particles from a flat-bottom silo. The results for mass discharge, flow profile and wall pressure show a good quantitative agreement. These findings suggest that the numerically calibrated MS and SQ particles in the shear tester can provide similar bulk-scale flow properties. Moreover, the results highlight that surface bumpiness for MS particles and corner sharpness for SQ particles change the characteristics of particles and play a significant role in the shear strength of the material composed of these particles.
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis of the...
Discrete elements for 3D microfluidics.
Bhargava, Krisna C; Thompson, Bryant; Malmstadt, Noah
2014-10-21
Microfluidic systems are rapidly becoming commonplace tools for high-precision materials synthesis, biochemical sample preparation, and biophysical analysis. Typically, microfluidic systems are constructed in monolithic form by means of microfabrication and, increasingly, by additive techniques. These methods restrict the design and assembly of truly complex systems by placing unnecessary emphasis on complete functional integration of operational elements in a planar environment. Here, we present a solution based on discrete elements that liberates designers to build large-scale microfluidic systems in three dimensions that are modular, diverse, and predictable by simple network analysis techniques. We develop a sample library of standardized components and connectors manufactured using stereolithography. We predict and validate the flow characteristics of these individual components to design and construct a tunable concentration gradient generator with a scalable number of parallel outputs. We show that these systems are rapidly reconfigurable by constructing three variations of a device for generating monodisperse microdroplets in two distinct size regimes and in a high-throughput mode by simple replacement of emulsifier subcircuits. Finally, we demonstrate the capability for active process monitoring by constructing an optical sensing element for detecting water droplets in a fluorocarbon stream and quantifying their size and frequency. By moving away from large-scale integration toward standardized discrete elements, we demonstrate the potential to reduce the practice of designing and assembling complex 3D microfluidic circuits to a methodology comparable to that found in the electronics industry.
Discrete Element Analysis of Huangtupo Landslide
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
On the basis of the deep geology and the geological structure of Huangtupo landslide, an ancient landslide in the reservoir of the Three Gorges, the geo-environmental model of the landslide is established to analyze quantitatively the sliding mechanism by using the discrete element method. It is concluded that interbedding structure of soft and hard formation consists of the main geological background,which induced the arching of the formation under gravity. Stability analysis of different loadings shows that the ground building weight on the middle slope may restrain the extension of shear sliding zone below, but may activate the foot area which will reduce the safety factor of the front.
New discrete element models for elastoplastic problems
Institute of Scientific and Technical Information of China (English)
Ming Cheng; Weifu Liu; Kaixin Liu
2009-01-01
The discrete element method (DEM) has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application, The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the inter-element parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method (FEM) and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.
New discrete element models for elastoplastic problems
Cheng, Ming; Liu, Weifu; Liu, Kaixin
2009-10-01
The discrete element method (DEM) has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the inter-element parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method (FEM) and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.
Discrete Element Modelling of Floating Debris
Mahaffey, Samantha; Liang, Qiuhua; Parkin, Geoff; Large, Andy; Rouainia, Mohamed
2016-04-01
Flash flooding is characterised by high velocity flows which impact vulnerable catchments with little warning time and as such, result in complex flow dynamics which are difficult to replicate through modelling. The impacts of flash flooding can be made yet more severe by the transport of both natural and anthropogenic debris, ranging from tree trunks to vehicles, wheelie bins and even storage containers, the effects of which have been clearly evident during recent UK flooding. This cargo of debris can have wide reaching effects and result in actual flood impacts which diverge from those predicted. A build-up of debris may lead to partial channel blockage and potential flow rerouting through urban centres. Build-up at bridges and river structures also leads to increased hydraulic loading which may result in damage and possible structural failure. Predicting the impacts of debris transport; however, is difficult as conventional hydrodynamic modelling schemes do not intrinsically include floating debris within their calculations. Subsequently a new tool has been developed using an emerging approach, which incorporates debris transport through the coupling of two existing modelling techniques. A 1D hydrodynamic modelling scheme has here been coupled with a 2D discrete element scheme to form a new modelling tool which predicts the motion and flow-interaction of floating debris. Hydraulic forces arising from flow around the object are applied to instigate its motion. Likewise, an equivalent opposing force is applied to fluid cells, enabling backwater effects to be simulated. Shock capturing capabilities make the tool applicable to predicting the complex flow dynamics associated with flash flooding. The modelling scheme has been applied to experimental case studies where cylindrical wooden dowels are transported by a dam-break wave. These case studies enable validation of the tool's shock capturing capabilities and the coupling technique applied between the two numerical
Discrete Element Modeling for Mobility and Excavation
Knuth, M. A.; Hopkins, M. A.
2011-12-01
The planning and completion of mobility and excavation efforts on the moon requires a thorough understanding of the planetary regolith. In this work, a discrete element method (DEM) model is created to replicate those activities in the laboratory and for planning mission activities in the future. The crux of this work is developing a particle bed that best replicates the regolith tool/wheel interaction seen in the laboratory. To do this, a DEM geotechnical triaxial strength cell was created allowing for comparison of laboratory JSC-1a triaxial tests to DEM simulated soils. This model relies on a triangular lattice membrane covered triaxial cell for determining the macroscopic properties of the modeled granular material as well as a fast and efficient contact detection algorithm for a variety of grain shapes. Multiple grain shapes with increasing complexity (ellipsoid, poly-ellipsoid and polyhedra) have been developed and tested. This comparison gives us a basis to begin scaling DEM grain size and shape to practical values for mobility and excavation modeling. Next steps include development of a DEM scoop for percussive excavation testing as well as continued analysis of rover wheel interactions using a wide assortment of grain shape and size distributions.
Discrete element simulation of crushable rockfill materials
Institute of Scientific and Technical Information of China (English)
Lei SHAO; Shi-chun CHI; Liang-jing ZHOU; Yu-zan WANG
2013-01-01
A discrete element method was used to study the evolution of particle crushing in a rockfill sample subjected to triaxial shear. A simple procedure was developed to generate clusters with arbitrary shapes, which resembled real rockfill particles. A theoretical method was developed to define the failure criterion for an individual particle subjected to an arbitrary set of contact forces. Then, a series of numerical tests of large-scale drained triaxial tests were conducted to simulate the behaviors of the rockfill sample. Finally, we examined the development of micro-characteristics such as particle crushing, contact characteristics, porosity, deformation, movement, and energy dissipation. The simulation results were partially compared with the laboratory experiments, and good agreement was achieved, demonstrating that the particle crushing model proposed can be used to simulate the drained triaxial test of rockfill materials. Based on a comparison of macro behaviors of the rockfill sample and micro structures of the particles, the microscopic mechanism of the rockfill materials subjected to triaxial shear was determined qualitatively. It is shown that the crushing rate, rather than the number of crushed particles, can be used to reflect the relationship between macro- and micro-mechanical characteristics of rockfill materials. These research results further develop our understanding of the deformation mechanism of rockfill materials.
Discrete element modeling of subglacial sediment deformation
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.; Tulaczyk, Slawek; Larsen, Nicolaj K.; Tylmann, Karol
2013-12-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis of the material dynamics and the shear zone development during progressive shear strain. The geometry of the heterogeneous stress network is visible in the form of force-carrying grain bridges and adjacent, volumetrically dominant, inactive zones. We demonstrate how the shear zone thickness and dilation depend on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elastoplastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain.
Discrete element simulation of crushable rockfill materials
Directory of Open Access Journals (Sweden)
Lei SHAO
2013-04-01
Full Text Available A discrete element method was used to study the evolution of particle crushing in a rockfill sample subjected to triaxial shear. A simple procedure was developed to generate clusters with arbitrary shapes, which resembled real rockfill particles. A theoretical method was developed to define the failure criterion for an individual particle subjected to an arbitrary set of contact forces. Then, a series of numerical tests of large-scale drained triaxial tests were conducted to simulate the behaviors of the rockfill sample. Finally, we examined the development of micro-characteristics such as particle crushing, contact characteristics, porosity, deformation, movement, and energy dissipation. The simulation results were partially compared with the laboratory experiments, and good agreement was achieved, demonstrating that the particle crushing model proposed can be used to simulate the drained triaxial test of rockfill materials. Based on a comparison of macro behaviors of the rockfill sample and micro structures of the particles, the microscopic mechanism of the rockfill materials subjected to triaxial shear was determined qualitatively. It is shown that the crushing rate, rather than the number of crushed particles, can be used to reflect the relationship between macro- and micro-mechanical characteristics of rockfill materials. These research results further develop our understanding of the deformation mechanism of rockfill materials.
Discrete Element Modeling of Complex Granular Flows
Movshovitz, N.; Asphaug, E. I.
2010-12-01
Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material's flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive. For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia's PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated. We demonstrate the code's ability to physically model granular materials in the three regimes
A distortional semi-discretized thin-walled beam element
DEFF Research Database (Denmark)
Andreassen, Michael Joachim; Jönsson, Jeppe
2013-01-01
Due to the increased consumption of thin-walled structural elements there has been increasing focus and need for more detailed calculations as well as development of new approaches. In this paper a thin-walled beam element including distortion of the cross section is formulated. The formulation...... is based on a generalized beam theory (GBT), in which the classic Vlasov beam theory for analysis of open and closed thin-walled cross sections is generalized by including distortional displacements. The beam element formulation utilizes a semi-discretization approach in which the cross section...... is discretized into wall elements and the analytical solutions of the related GBT beam equations are used as displacement functions in the axial direction. Thus the beam element contains the semi-analytical solutions. In three related papers the authors have recently presented the semi-discretization approach...
Isolated and coupled superquadric loop antennas for mobile communications applications
Jensen, Michael A.; Rahmat-Samii, Yahya
1993-01-01
This work provides an investigation of the performance of loop antennas for use in mobile communications applications. The analysis tools developed allow for high flexibility by representing the loop antenna as a superquadric curve, which includes the case of circular, elliptical, and rectangular loops. The antenna may be in an isolated environment, located above an infinite ground plane, or placed near a finite conducting plate or box. In cases where coupled loops are used, the two loops may have arbitrary relative positions and orientations. Several design examples are included to illustrate the versatility of the analysis capabilities. The performance of coupled loops arranged in a diversity scheme is also evaluated, and it is found that high diversity gain can be achieved even when the antennas are closely spaced.
The Numerical Integration of Discrete Functions on a Triangular Element
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
With the application of Hammer integral formulas of a continuousfunction on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
Modeling rammed earth wall using discrete element method
Bui, T.-T.; Bui, Q.-B.; Limam, A.; Morel, J.-C.
2016-03-01
Rammed earth is attracting renewed interest throughout the world thanks to its "green" characteristics in the context of sustainable development. Several research studies have thus recently been carried out to investigate this material. Some of them attempted to simulate the rammed earth's mechanical behavior by using analytical or numerical models. Most of these studies assumed that there was a perfect cohesion at the interface between earthen layers. This hypothesis proved to be acceptable for the case of vertical loading, but it could be questionable for horizontal loading. To address this problem, discrete element modeling seems to be relevant to simulate a rammed earth wall. To our knowledge, no research has been conducted thus far using discrete element modeling to study a rammed earth wall. This paper presents an assessment of the discrete element modeling's robustness for rammed earth walls. Firstly, a brief description of the discrete element modeling is presented. Then the parameters necessary for discrete element modeling of the material law of the earthen layers and their interfaces law following the Mohr-Coulomb model with a tension cut-off and post-peak softening were given. The relevance of the model and the material parameters were assessed by comparing them with experimental results from the literature. The results showed that, in the case of vertical loading, interfaces did not have an important effect. In the case of diagonal loading, model with interfaces produced better results. Interface characteristics can vary from 85 to 100% of the corresponding earthen layer's characteristics.
A discrete element model for simulating saturated granular soil
Institute of Scientific and Technical Information of China (English)
Mahan Lamei; Ali Asghar Mirghasemi
2011-01-01
A numerical model is developed to simulate saturated granular soil,based on the discrete element method.Soil particles are represented by Lagrangian discrete elements,and pore fluid,by appropriate discrete elements which represent alternately Lagrangian mass of water and Eulerian volume of space.Macroscale behavior of the model is verified by simulating undrained biaxial compression tests.Micro-scale behavior is compared to previous literature through pore pressure pattern visualization during shear tests,it is demonstrated that dynamic pore pressure patterns are generated by superposed stress waves.These pore-pressure patterns travel much faster than average drainage rate of the pore fluid and may initiate soil fabric change,ultimately leading to liquefaction in loose sands.Thus,this work demonstrates a tool to roughly link dynamic stress wave patterns to initiation of liquefaction phenomena.
Extracting Superquadric-based Geon Description for 3D Object Recognition
Institute of Scientific and Technical Information of China (English)
XINGWeiwei; LIUWeibin; YUANBaozong
2005-01-01
Geons recognition is one key issue in developing 3D object recognition system based on Recognition by components (RBC) theory. In this paper, we present a novel approach for extracting superquadric-based geon description of 3D volumetric primitives from real shape data, which integrates the advantages of deformable superquadric models reconstruction and SVM-based classification. First, Real-coded genetic algorithm (RCGA) is used for superquadric fitting to 3D data and the quantitative parametric information is obtained; then a new sophisticated feature set is derived from superquadric parameters obtained for the next step; and SVM-based classification is proposed and implemented for geons recognition and the qualitative geometric information is obtained. Furthermore, the knowledge-based feedback of SVM network is introduced for improving the classification performance. Ex-perimental results obtained show that our approach is efficient and precise for extracting superquadric-based geon description from real shape data in 3D object recognition. The results are very encouraging and have significant benefit for developing the general 3D object recognition system.
Discrete Element Simulation of Asphalt Mastics Based on Burgers Model
Institute of Scientific and Technical Information of China (English)
LIU Yu; FENG Shi-rong; HU Xia-guang
2007-01-01
In order to investigate the viscoelastic performance of asphalt mastics, a micro-mechanical model for asphalt mastics was built by applying Burgers model to discrete element simulation and constructing Burgers contact model. Then the numerical simulation of creep tests was conducted, and results from the simulation were compared with the analytical solution for Burgers model. The comparision snowed that the two results agreed well with each other, suggesting that discrete element model based on Burgers model could be employed in the numerical simulation for asphalt mastics.
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression...... of the grains. This is true even of the resilient (or reversible) deformations. It is also interesting because the Discrete Element Method models resilient and plastic deformations as well as failure in a single process.The paper describes two types of calculations. One on a small sample of angular elements...... subjected to a pulsating (repeated) biaxial loading and another of a larger sample of circular element subjected to a plate load. Both cases are two dimensional, i.e. plane strain.The repeated biaxial loading showed a large increase in plastic strain for the first load pulse at a given load level...
Discrete element modelling of fluidised bed spray granulation
Goldschmidt, M.J.V.; Weijers, G.G.C.; Boerefijn, R.; Kuipers, J.A.M.
2003-01-01
A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid¿solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Microsca
Discrete element modelling of fluidised bed spray granulation
Goldschmidt, M.J.V.; Weijers, G.G.C.; Boerefijn, R.; Kuipers, J.A.M.
2002-01-01
A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid-solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Micro sc
Analysis of bender element test interpretation using the discrete element method
O’Donovan, J.; O’Sullivan, C.; Marketos, G.; Muir Wood, D.
2015-01-01
While bender element testing is now well-established as a laboratory technique to determine soil stiffness, a robust technique to interpret the data remains elusive. A discrete element method (DEM) model of a face-centred cubic packing of uniform spheres was created to simulate bender element tests
New Discrete Element Models for Three-Dimensional Impact Problems
Institute of Scientific and Technical Information of China (English)
SHAN Li; CHENG Ming; LIU Kai-xin; LIU Wei-Fu; CHEN Shi-Yang
2009-01-01
Two 3-D numerical models of the discrete element method(DEM)for impact problems are proposed.The models can calculate not only the impact problems of continuum and non-continuum,but also the transient process from continuum to non-continuum.The stress wave propagation in a concrete block and a dynamic splitting process of a marble disc under impact loading are numerically simulated with the proposed models.By comparing the numerical results with the corresponding results obtained by the finite element method(FEM)and the experiments,it is proved that the models are reliable for three-dimensional impact problems.
Certain Discrete Element Methods in Problems of Fracture Mechanics
Directory of Open Access Journals (Sweden)
P. P. Procházka
2002-01-01
Full Text Available In this paper two discrete element methods (DEM are discussed. The free hexagon element method is considered a powerful discrete element method, which is broadly used in mechanics of granular media. It substitutes the methods for solving continuum problems. The great disadvantage of classical DEM, such as the particle flow code (material properties are characterized by spring stiffness, is that they have to be fed with material properties provided from laboratory tests (Young's modulus, Poisson's ratio, etc.. The problem consists in the fact that the material properties of continuum methods (FEM, BEM are not mutually consistent with DEM. This is why we utilize the principal idea of DEM, but cover the continuum by hexagonal elastic, or elastic-plastic, elements. In order to complete the study, another one DEM is discussed. The second method starts with the classical particle flow code (PFC - which uses dynamic equilibrium, but applies static equilibrium. The second method is called the static particle flow code (SPFC. The numerical experience and comparison numerical with experimental results from scaled models are discussed in forthcoming paper by both authors.
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette
2010-02-23
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.
A Review of Discrete Element Method Research on Particulate Systems
Mahmood, A. A.; Elektorowicz, M.
2016-07-01
This paper summarizes research done using the Discrete Element Method (DEM) and explores new trends in its use on Particulate systems. The rationale for using DEM versus the traditional continuum-based approach is explained first. Then, DEM application is explored in terms of geotechnical engineering and mining engineering materials, since particulate media are mostly associated with these two disciplines. It is concluded that no research to date had addressed the issue of using the DEM to model the strength and weathering characteristics of peaty soil-slag-Portland cement-fly ash combinations.
From discrete elements to continuum fields: Extension to bidisperse systems
Tunuguntla, Deepak R.; Thornton, Anthony R.; Weinhart, Thomas
2016-07-01
Micro-macro transition methods can be used to, both, calibrate and validate continuum models from discrete data obtained via experiments or simulations. These methods generate continuum fields such as density, momentum, stress, etc., from discrete data, i.e. positions, velocity, orientations and forces of individual elements. Performing this micro-macro transition step is especially challenging for non-uniform or dynamic situations. Here, we present a general method of performing this transition, but for simplicity we will restrict our attention to two-component scenarios. The mapping technique, presented here, is an extension to the micro-macro transition method, called coarse-graining, for unsteady two-component flows and can be easily extended to multi-component systems without any loss of generality. This novel method is advantageous; because, by construction the obtained macroscopic fields are consistent with the continuum equations of mass, momentum and energy balance. Additionally, boundary interaction forces can be taken into account in a self-consistent way and thus allow for the construction of continuous stress fields even within one element radius of the boundaries. Similarly, stress and drag forces can also be determined for individual constituents of a multi-component mixture, which is critical for several continuum applications, e.g. mixture theory-based segregation models. Moreover, the method does not require ensemble-averaging and thus can be efficiently exploited to investigate static, steady and time-dependent flows. The method presented in this paper is valid for any discrete data, e.g. particle simulations, molecular dynamics, experimental data, etc.; however, for the purpose of illustration we consider data generated from discrete particle simulations of bidisperse granular mixtures flowing over rough inclined channels. We show how to practically use our coarse-graining extension for both steady and unsteady flows using our open-source coarse
3D mode discrete element method with the elastoplastic model
Institute of Scientific and Technical Information of China (English)
2012-01-01
The three-dimensional mode-deformable discrete element method (3MDEM) is an extended distinct element approach under the assumptions of small strain,finite displacement,and finite rotation of blocks.The deformation of blocks is expressed by the combination of the deformation modes in 3MDEM.In this paper,the elastoplastic constitutive relationship of blocks is implemented on the 3MDEM platform to simulate the integrated process from elasticity to plasticity and finally to fracture.To overcome the shortcomings of the conventional criterion for contact fracturing,a new criterion based on plastic strain is introduced.This approach is verified by two numerical examples.Finally,a cantilever beam is simulated as a comprehensive case study,which went through elastic,elastoplastic,and discontinuous fracture stages.
An implicit finite element method for discrete dynamic fracture
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Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Discrete element modelling of sediment falling in water.
Wang, Dong; Ho-Minh, Dao; Tan, Danielle S
2016-11-01
The Discrete Element Method (DEM) is a discrete, particle-based method commonly used in studies involving granular media, e.g. sediment transport, and geomechanics. It is heavily dependent on particle properties, and one important component is the force model, which relates the relative positions and velocities of the simulated particles to the forces they experience. In this paper we model a collection of lightly compacted granular material, released at a short distance above a flat base in a quiescent fluid --similar to the process whereby sediment tailings are released back into the sea during nodule harvesting. We employ different typical force models, and consider how their varying components affect the simulated outcome. The results are compared with a physical experiment of similar dimensions. We find that a realistic simulation is achieved when the force model considers the local solid fraction in the drag force, and incorporates the hydrodynamic effect of neighbouring particles. The added mass effect increases the accuracy of the outcome, but does not contribute significantly in a qualitative sense.
7th International Conference on Discrete Element Methods
Feng, Yuntian; Mustoe, Graham
2017-01-01
This book presents the latest advances in Discrete Element Methods (DEM) and technology. It is the proceeding of 7th International Conference on DEM which was held at Dalian University of Technology on August 1 - 4, 2016. The subject of this book are the DEM and related computational techniques such as DDA, FEM/DEM, molecular dynamics, SPH, Meshless methods, etc., which are the main computational methods for modeling discontinua. In comparison to continua which have been already studied for a long time, the research of discontinua is relatively new, but increases dramatically in recent years and has already become an important field. This book will benefit researchers and scientists from the academic fields of physics, engineering and applied mathematics, as well as from industry and national laboratories who are interested in the DEM. .
Adaptive model reduction for nonsmooth discrete element simulation
Servin, Martin
2015-01-01
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined used for deriving and conditions for when and where to apply model reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5 - 50 times for model reduction level between 70 - 95 %.
Adaptive model reduction for nonsmooth discrete element simulation
Servin, Martin; Wang, Da
2016-03-01
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined and used to derive conditions for when and where to apply reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5-50 times for model reduction level between 70-95 %.
Discrete Element Method Simulations for Complex Granular Flows
Guo, Yu; Curtis, Jennifer Sinclair
2015-01-01
This review article focuses on the modeling of complex granular flows employing the discrete element method (DEM) approach. The specific topic discussed is the application of DEM models for the study of the flow behavior of nonspherical, flexible, or cohesive particles, including particle breakage. The major sources of particle cohesion—liquid induced, electrostatics, van der Waals forces—and their implementation into DEM simulations are covered. These aspects of particle flow are of great importance in practical applications and hence are the significant foci of research at the forefront of current DEM modeling efforts. For example, DEM simulations of nonspherical grains can provide particle stress information needed to develop constitutive models for continuum-based simulations of large-scale industrial processes.
A modified discrete element model for sea ice dynamics
Institute of Scientific and Technical Information of China (English)
LI Baohui; LI Hai; LIU Yu; WANG Anliang; JI Shunying
2014-01-01
Considering the discontinuous characteristics of sea ice on various scales, a modified discrete element mod-el (DEM) for sea ice dynamics is developed based on the granular material rheology. In this modified DEM, a soft sea ice particle element is introduced as a self-adjustive particle size function. Each ice particle can be treated as an assembly of ice floes, with its concentration and thickness changing to variable sizes un-der the conservation of mass. In this model, the contact forces among ice particles are calculated using a viscous-elastic-plastic model, while the maximum shear forces are described with the Mohr-Coulomb fric-tion law. With this modified DEM, the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths. The thicknesses, concentrations and velocities of ice particles are obtained, and then reasonable dynamic process is analyzed. The sea ice dynamic process is also simulated in a vortex wind field. Taking the influence of thermodynamics into account, this modified DEM will be improved in the future work.
Discrete element modelling of pebble packing in pebble bed reactors
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Suikkanen, Heikki, E-mail: heikki.suikkanen@lut.fi; Ritvanen, Jouni, E-mail: jouni.ritvanen@lut.fi; Jalali, Payman, E-mail: payman.jalali@lut.fi; Kyrki-Rajamäki, Riitta, E-mail: riitta.kyrki-rajamaki@lut.fi
2014-07-01
Highlights: • A discrete element method code is developed for pebble bed reactor analyses. • Methods are established to extract packing information at various spatial scales. • Packing simulations inside annular core geometry are done varying input parameters. • The restitution coefficient has the strongest effect on the resulting packing density. • Detailed analyses reveal local densification especially near the walls. - Abstract: It is important to understand the packing characteristics and behaviour of the randomly packed pebble bed to further analyse the reactor physical and thermal-hydraulic behaviour and to design a safe and economically feasible pebble bed reactor. The objective of this work was to establish methods to model and analyse the pebble packing in detail to provide useful tools and data for further analyses. Discrete element method (DEM) is a well acknowledged method for analysing granular materials, such as the fuel pebbles in a pebble bed reactor. In this work, a DEM computer code was written specifically for pebble bed analyses. Analysis methods were established to extract data at various spatial scales from the pebble beds resulting from the DEM simulations. A comparison with available experimental data was performed to validate the DEM implementation. To test the code implementation in full-scale reactor calculations, DEM packing simulations were done in annular geometry with 450,000 pebbles. Effects of the initial packing configuration, friction and restitution coefficients and pebble size distribution to the resulting pebble bed were investigated. The packing simulations revealed that from the investigated parameters the restitution coefficient had the largest effect on the resulting average packing density while other parameters had smaller effects. Detailed local packing density analysis of pebble beds with different average densities revealed local variations especially strong in the regions near the walls. The implemented DEM
Matsumoto, Takuma; Ogata, Kazuyuki; Yahiro, Masanobu
2009-01-01
We present a practical way of smoothing discrete breakup S-matrix elements calculated by the continuum-discretized coupled-channel method (CDCC). This method makes the smoothing procedure much easier. The reliability of the smoothing method is confirmed for the three-body breakup reactions, 58Ni(d,pn) at 80 MeV and 12C(6He,4He2n) at 229.8 MeV.
Mechanics of a crushable pebble assembly using discrete element method
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Annabattula, R.K., E-mail: ratna.annabattula@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany); Gan, Y., E-mail: yixiang.gan@sydney.edu.au [School of Civil Engineering, University of Sydney, 2006 NSW, Sydney (Australia); Zhao, S. [College of Mechanical and Electronics Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018 (China); Kamlah, M., E-mail: marc.kamlah@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany)
2012-11-15
The influence of crushing of individual pebbles on the overall strength of a pebble assembly is investigated using discrete element method. An assembly comprising of 5000 spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation. Then, the pebble assembly is subjected to uni-axial compression ({epsilon}{sub 33}=1.5%) with periodic boundary conditions. The crushable pebble assembly shows a significant difference in stress-strain response in comparison to a non-crushable pebble assembly. The analysis shows that a ideal plasticity like behaviour (constant stress with increase in strain) is the characteristic of a crushable pebble assembly with sudden damage. The damage accumulation law plays a critical role in determining the critical stress while the critical number of completely failed pebbles at the onset of critical stress is independent of such a damage law. Furthermore, a loosely packed pebble assembly shows a higher crush resistance while the critical stress is insensitive to the packing factor ({eta}) of the assembly.
Discrete Element Crowd Model for Pedestrian Evacuation Through an Exit
Lin, Peng; Lo, Siuming
2016-01-01
A series of accidents caused by crowd within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on discrete element method, a granular dynamic model, in which human body is simplified as self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of human body is simulated by applying the second Newton's law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, clogging phenomenon occurs more easily when the velocity of desired is high and the exit may as a result be totally blocked at a desired velocity of 1.6m/s or above, leading to fas...
Applications of the discrete element method in mechanical engineering
Energy Technology Data Exchange (ETDEWEB)
Fleissner, Florian, E-mail: fleissner@itm.uni-stuttgart.de; Gaugele, Timo, E-mail: gaugele@itm.uni-stuttgart.de; Eberhard, Peter [University of Stuttgart, Institute of Engineering and Computational Mechanics (Germany)], E-mail: eberhard@itm.uni-stuttgart.de
2007-08-15
Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples.
Discrete element crowd model for pedestrian evacuation through an exit
Peng, Lin; Jian, Ma; Siuming, Lo
2016-03-01
A series of accidents caused by crowds within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on the discrete element method, a granular dynamic model, in which the human body is simplified as a self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of the human body is simulated by applying the second Newton’s law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, the clogging phenomenon occurs more easily when the desired velocity is high and the exit may as a result be totally blocked at a desired velocity of 1.6 m/s or above, leading to faster-to-frozen effect. Project supported by the National Natural Science Foundation of China (Grant Nos. 71473207, 51178445, and 71103148), the Research Grant Council, Government of Hong Kong, China (Grant No. CityU119011), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2682014CX103 and 2682014RC05).
Discrete Element Model for Suppression of Coffee-Ring Effect
Xu, Ting; Lam, Miu Ling; Chen, Ting-Hsuan
2017-02-01
When a sessile droplet evaporates, coffee-ring effect drives the suspended particulate matters to the droplet edge, eventually forming a ring-shaped deposition. Because it causes a non-uniform distribution of solid contents, which is undesired in many applications, attempts have been made to eliminate the coffee-ring effect. Recent reports indicated that the coffee-ring effect can be suppressed by a mixture of spherical and non-spherical particles with enhanced particle-particle interaction at air-water interface. However, a model to comprehend the inter-particulate activities has been lacking. Here, we report a discrete element model (particle system) to investigate the phenomenon. The modeled dynamics included particle traveling following the capillary flow with Brownian motion, and its resultant 3D hexagonal close packing of particles along the contact line. For particles being adsorbed by air-water interface, we modeled cluster growth, cluster deformation, and cluster combination. We found that the suppression of coffee-ring effect does not require a circulatory flow driven by an inward Marangoni flow at air-water interface. Instead, the number of new cluster formation, which can be enhanced by increasing the ratio of non-spherical particles and the overall number of microspheres, is more dominant in the suppression process. Together, this model provides a useful platform elucidating insights for suppressing coffee-ring effect for practical applications in the future.
Discrete element modelling of screw conveyor-mixers
Directory of Open Access Journals (Sweden)
Jovanović Aca
2015-01-01
Full Text Available Screw conveyors are used extensively in food, plastics, mineral processing, agriculture and processing industries for elevating and/or transporting bulk materials over short to medium distances. Despite their apparent simplicity in design, the transportation action is very complex for design and constructors have tended to rely heavily on empirical performance data. Screw conveyor performance is affected by its operating conditions (such as: the rotational speed of the screw, the inclination of the screw conveyor, and its volumetric fill level. In this paper, horizontal, several single-pitch screw conveyors with some geometry variations in screw blade was investigated for mixing action during transport, using Discrete Element Method (DEM. The influence of geometry modifications on the performance of screw conveyor was examined, different screw designs were compared, and the effects of geometrical variations on mixing performances during transport were explored. During the transport, the particle tumbles down from the top of the helix to the next free surface and that segment of the path was used for auxiliary mixing action. The particle path is dramatically increased with the addition of three complementary helices oriented in the same direction as screw blades (1458.2 mm compared to 397.6 mm in case of single flight screw conveyor Transport route enlarges to 1764.4 mm, when installing helices oriented in the opposite direction from screw blades. By addition of straight line blade to single flight screw conveyor, the longest particle path is being reached: 2061.6 mm [Projekat Ministarstva nauke Republike Srbije, br. TR-31055
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Generation of Random Particle Packings for Discrete Element Models
Abe, S.; Weatherley, D.; Ayton, T.
2012-04-01
An important step in the setup process of Discrete Element Model (DEM) simulations is the generation of a suitable particle packing. There are quite a number of properties such a granular material specimen should ideally have, such as high coordination number, isotropy, the ability to fill arbitrary bounding volumes and the absence of locked-in stresses. An algorithm which is able to produce specimens fulfilling these requirements is the insertion based sphere packing algorithm originally proposed by Place and Mora, 2001 [2] and extended in this work. The algorithm works in two stages. First a number of "seed" spheres are inserted into the bounding volume. In the second stage the gaps between the "seed" spheres are filled by inserting new spheres in a way so they have D+1 (i.e. 3 in 2D, 4 in 3D) touching contacts with either other spheres or the boundaries of the enclosing volume. Here we present an implementation of the algorithm and a systematic statistical analysis of the generated sphere packings. The analysis of the particle radius distribution shows that they follow a power-law with an exponent ≈ D (i.e. ≈3 for a 3D packing and ≈2 for 2D). Although the algorithm intrinsically guarantees coordination numbers of at least 4 in 3D and 3 in 2D, the coordination numbers realized in the generated packings can be significantly higher, reaching beyond 50 if the range of particle radii is sufficiently large. Even for relatively small ranges of particle sizes (e.g. Rmin = 0.5Rmax) the maximum coordination number may exceed 10. The degree of isotropy of the generated sphere packing is also analysed in both 2D and 3D, by measuring the distribution of orientations of vectors joining the centres of adjacent particles. If the range of particle sizes is small, the packing algorithm yields moderate anisotropy approaching that expected for a face-centred cubic packing of equal-sized particles. However, once Rmin 2D and 3D. The analysis demonstrates that this space
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Application of Discrete Element Methods to the Problem of Rock Bumps
Directory of Open Access Journals (Sweden)
P. P. Procházka
2002-01-01
Full Text Available This paper is a continuation of a previous paper by the authors. Applications of two discrete element methods (DEM to several fields of geotechnics are discussed. The free hexagon element method is considered a powerful discrete element method, and is widely used in mechanics of granular media. It substitutes the methods for solving continuum problems. In order to complete the study, other discrete element methods are discussed. The second method starts with the classical particle flow code (PFC, which uses dynamic equilibrium, but we apply static equilibrium in our case. The second method is called the static particle flow code (SPFC. The numerical experiences and comparison with experimental results from scaled models are discussed.
Partition of the contact force network obtained in discrete element simulations of element tests
Huang, Xin; O'Sullivan, Catherine; Hanley, Kevin J.; Kwok, Chung-Yee
2017-04-01
The transmission of stress within a granular material composed of rigid spheres is explored using the discrete element method. The contribution of contacts to both deviatoric stress and structural anisotropy is investigated. The influences of five factors are considered: inter-particle friction coefficient, loading regime, packing density, contact model, and boundary conditions. The data generated indicate that using the above-average normal contact force criterion to decompose the contact force network into two subsets with distinct contributions to stress transmission and structural anisotropy is not robust. The characteristic normal contact forces marking the transition from negative to positive contribution to the overall deviatoric stress and structural anisotropy are not unique values but vary during shearing. Once the critical state is attained (i.e., once shearing continues at a constant deviator stress and solid fraction), the characteristic normal contact force remains approximately constant and this critical state characteristic normal force is observed to decrease with increasing inter-particle friction. The characteristic normal contact force considering the contribution to deviatoric stress has a power-law relationship with the mean effective stress at the critical state.
Partition of the contact force network obtained in discrete element simulations of element tests
Huang, Xin; O'Sullivan, Catherine; Hanley, Kevin J.; Kwok, Chung-Yee
2016-01-01
The transmission of stress within a granular material composed of rigid spheres is explored using the discrete element method. The contribution of contacts to both deviatoric stress and structural anisotropy is investigated. The influences of five factors are considered: inter-particle friction coefficient, loading regime, packing density, contact model, and boundary conditions. The data generated indicate that using the above-average normal contact force criterion to decompose the contact force network into two subsets with distinct contributions to stress transmission and structural anisotropy is not robust. The characteristic normal contact forces marking the transition from negative to positive contribution to the overall deviatoric stress and structural anisotropy are not unique values but vary during shearing. Once the critical state is attained (i.e., once shearing continues at a constant deviator stress and solid fraction), the characteristic normal contact force remains approximately constant and this critical state characteristic normal force is observed to decrease with increasing inter-particle friction. The characteristic normal contact force considering the contribution to deviatoric stress has a power-law relationship with the mean effective stress at the critical state.
Energy Technology Data Exchange (ETDEWEB)
Rousseau, J.
2009-07-15
That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)
The use of discrete orthogonal projections in boundary element methods
Brandts, J.
2001-01-01
In recent papers by Sloan and Wendland Grigorie and Sloan and Grigorie Sloan and Brandts a formalismwas developed that serves many important and interesting applications in boundary element methods the commutator property for splines Based on superapproximation results this property is for exam
Wang, Dafang; Kirby, Robert M; Johnson, Chris R
2011-06-01
We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L(2) norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.
Discrete Element Method, a Tool to Investigate Complex Material Behaviour in Material Forming
Iordanoff, Ivan; Iliescu, Daniel; Charles, Jean-Luc; NÉAUPORT, Jérome
2010-01-01
International audience; Discrete Model is based on the description of the physical state (velocity, position, temperature, magnetic moment, electric potential ..) of a large number of discrete elements that form the media to be studied. It is not based on a continuous description of the media. Then, it is particularly well adapted to describe media evolution driven by discontinuous phenomena : - multi fracturation problems like abrasion process and composite machining, - description of multi ...
Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers
Malik, Mujeeb; Liao, Wei; Li, Fei; Choudhari, Meelan
2015-01-01
Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.
Finite Element Calculation of Discrete Stratified Fluid Vibrations
Directory of Open Access Journals (Sweden)
Ko Ko Win
2016-01-01
Full Text Available Many publications, which consider a problem of small vibrations of an incompressible ideal fluid, completely filling the stationary cylindrical tank, have the long lists of references in the field concerned. This paper uses the finite element method to consider vibrations of three incompressible fluids, defines natural frequencies of vibrations, and builds the vibration forms of the interface surface of fluids for the double-tone vibrations. It shows how the vibration frequency depends on the ratios of vibrating fluid density and thicknesses of fluid layers and compares the numerical calculation results with the analytically obtained exact values.The paper describes a variational formulation of the problem concerning the natural vibrations of immiscible fluids and using the finite element method provides a numerical implementation to define the fixed values of the functional that meets the variational problem. The reliability of the numerical results obtained is proved by their approximation to the result of calculating frequencies derived from the solutions of the problem of natural vibrations of fluid in a cylindrical vessel with a different fluid depth. To perform all numerical calculations was used the Matlab software.
Stochastic structural model of rock and soil aggregates by continuum-based discrete element method
Institute of Scientific and Technical Information of China (English)
WANG; Yuannian; ZHAO; Manhong; LI; Shihai; J.G.; Wang
2005-01-01
This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.
Generalized Rayleigh quotient and finite element two-grid discretization schemes
Institute of Scientific and Technical Information of China (English)
2009-01-01
This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
Generalized Rayleigh quotient and finite element two-grid discretization schemes
Institute of Scientific and Technical Information of China (English)
YANG YiDu; FAN XinYue
2009-01-01
This study discusses generalized Rayleigh quotient and high efficiency finite element dis-cretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
Level set discrete element method for three-dimensional computations with triaxial case study
Kawamoto, Reid; Andò, Edward; Viggiani, Gioacchino; Andrade, José E.
2016-06-01
In this paper, we outline the level set discrete element method (LS-DEM) which is a discrete element method variant able to simulate systems of particles with arbitrary shape using level set functions as a geometric basis. This unique formulation allows seamless interfacing with level set-based characterization methods as well as computational ease in contact calculations. We then apply LS-DEM to simulate two virtual triaxial specimens generated from XRCT images of experiments and demonstrate LS-DEM's ability to quantitatively capture and predict stress-strain and volume-strain behavior observed in the experiments.
Discrete Element Method simulations of standing jumps in granular flows down inclines
Directory of Open Access Journals (Sweden)
Méjean Ségolène
2017-01-01
Full Text Available This paper describes a numerical set-up which uses Discrete Element Method to produce standing jumps in flows of dry granular materials down a slope in two dimensions. The grain-scale force interactions are modeled by a visco-elastic normal force and an elastic tangential force with a Coulomb threshold. We will show how it is possible to reproduce all the shapes of the jumps observed in a previous laboratory study: diffuse versus steep jumps and compressible versus incompressible jumps. Moreover, we will discuss the additional measurements that can be done thanks to discrete element modelling.
Modeling of asphalt by means of discrete element method – an initial study
DEFF Research Database (Denmark)
Feng, Huan; Hededal, Ole; Stang, Henrik
type of numerical simulation method which allows the finite displacement and rotation of discrete particles, making it an excellent tool to simulate the complex micro interaction between aggregate particles within an asphalt mixture, [3],[4] . In this research, PFC3D – a commercial DEM program...... of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples...
Institute of Scientific and Technical Information of China (English)
ZHANG Xiang-wei; TAKEUCHI Kuniyoshi; CHEN Jing
2007-01-01
In this article, the finite element solution of quasi-three-dimensional (quasi-3-D) groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model (FEM) is the results choosing the small time step or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3-D groundwater flow problems if the criteria are satisfied.
A stable and optimal complexity solution method for mixed finite element discretizations
Brandts, J.; Stevenson, R.
2001-01-01
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inho- mogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally g
Study of the Internal Mechanical response of an asphalt mixture by 3-D Discrete Element Modeling
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Hofko, Bernhard
2015-01-01
In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional Discrete Element Method (DEM). The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties for ...
CSIR Research Space (South Africa)
Govender, Nicolin
2013-01-01
Full Text Available in nature and cannot be described by a closed form solution for more than a few particles. A popular and successful approach in simulating the underlying dynamics of GM is by using the Discrete Element Method (DEM). Computational viable simulations...
Discrete element simulation of mill charge in 3D using the BLAZE-DEM GPU framework
CSIR Research Space (South Africa)
Govender, Nicolin
2015-08-01
Full Text Available The Discrete Element Method (DEM) simulation of charge motion in ball, semi autogenous (SAG) and autogenous mills has advanced to a stage where the effects of lifter design, power draft and product size can be evaluated with sufficient accuracy...
Discrete element study of granulation in a spout-fluidized bed
Link, J.M.; Godlieb, W.; Deen, N.G.; Kuipers, J.A.M.
2007-01-01
In this work a discrete element model (DEM) is presented for the description of the gas–liquid–solid flow in a spout-fluidized bed including all relevant phenomena for the study of granulation. The model is demonstrated for the case of a granulation process in a flat spout-fluidized bed, containing
A stable and optimal complexity solution method for mixed finite element discretizations
Brandts, J.; Stevenson, R.
2002-01-01
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inho- mogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally g
Flow Dynamics of green sand in the DISAMATIC moulding process using Discrete element method (DEM)
DEFF Research Database (Denmark)
Hovad, Emil; Larsen, P.; Walther, Jens Honore
2015-01-01
The DISAMATIC casting process production of sand moulds is simulated with DEM (discrete element method). The main purpose is to simulate the dynamics of the flow of green sand, during the production of the sand mould with DEM. The sand shot is simulated, which is the first stage of the DISAMATIC...
DEFF Research Database (Denmark)
Hovad, Emil; Spangenberg, Jon; Larsen, P.
2016-01-01
The discrete element method (DEM) is applied to simulate the dynamics of the flow of green sand while filling a mould using the DISAMATIC process. The focus is to identify relevant physical experiments that can be used to characterize the material properties of green sand in the numerical model...
Dynamic Analysis of Deep-Ocean Mining Pipe System by Discrete Element Method
Institute of Scientific and Technical Information of China (English)
LI Yan; LIU Shao-jun; LI Li
2007-01-01
The dynamic analysis of a pipe system is one of the most crucial problems for the entire mining system.A discrete element method (DEM) is proposed for the analysis of a deep-ocean mining pipe system,including the lift pipe,pump,buffer and flexible hose.By the discrete element method,the pipe is divided into some rigid elements that are linked by flexible connectors.First,two examples representing static analysis and dynamic analysis respectively are given to show that the DEM model is feasible.Then the three-dimensional DEM model is used for dynamic analysis of the mining pipe system.The dynamic motions of the entire mining pipe system under different work conditions are discussed.Some suggestions are made for the actual operation of deep-ocean mining systems.
Dispersion Analysis of Gravity Waves in Fluid Media Discretized by Energy-Orthogonal Finite Elements
José Brito Castro, Francisco
2014-11-01
This article studies the dispersion of gravity waves in fluid media discretized by the finite element method. The element stiffness matrix is split into basic and higher-order components which are respectively related to the mean and deviatoric components of the gradient of displacement potential. This decomposition is applied to the kinetic energy. The dispersion analysis yields a correlation between the higher-order kinetic energy and the kinetic energy error. The use of this correlation as a reference to apply the higher-order energy as an error indicator for the sloshing modes computed by the finite element method is explored.
A minimal coupled fluid-discrete element model for bedload transport
Maurin, Raphael; Chareyre, Bruno; Frey, Philippe
2016-01-01
A minimal Lagragian two-phase model to study turbulent bedload transport focusing on the granular phase is presented, and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively low Shields numbers, for which no suspension occurs. A discrete element method for the granular phase is coupled with a one dimensional volume-averaged two-phase momentum equation for the fluid phase. The coupling between the discrete granular phase and the continuous fluid phase is discussed, and a consistent averaging formulation adapted to bedload transport is introduced. An original simple discrete random walk model is proposed to account for the fluid velocity fluctuations. The model is compared with experiments considering both classical sediment transport rate as a function of the Shields number, and depth profiles of solid velocity, volume fraction, and transport rate density, from existing bedload transport experiments in inclined flume. The results s...
Anssari-Benam, Afshin; Bucchi, Andrea; Bader, Dan L
2015-09-18
Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues. Copyright © 2015 Elsevier Ltd. All rights reserved.
Application of the control volume mixed finite element method to a triangular discretization
Naff, R.L.
2012-01-01
A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.
Rahmouni, Lyes; Cools, Kristof; Andriulli, Francesco P
2016-01-01
In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages in several real case scenarios. Unfortunately however, it is widely reported that the accuracy of standard BEM schemes is limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly discretized EEG forward problems, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several ...
Discrete element simulation of powder compaction in cold uniaxial pressing with low pressure
Rojek, Jerzy; Nosewicz, Szymon; Jurczak, Kamila; Chmielewski, Marcin; Bochenek, Kamil; Pietrzak, Katarzyna
2016-11-01
This paper presents numerical studies of powder compaction in cold uniaxial pressing. The powder compaction in this work is considered as an initial stage of a hot pressing process so it is realized with relatively low pressure (up to 50 MPa). Hence the attention has been focused on the densification mechanisms at this range of pressure and models suitable for these conditions. The discrete element method employing spherical particles has been used in the numerical studies. Numerical simulations have been performed for two different contact models—the elastic Hertz-Mindlin-Deresiewicz model and the plastic Storåkers model. Numerical results have been compared with the results of laboratory tests of the die compaction of the NiAl powder. Comparisons have shown that the discrete element method is capable to represent properly the densification mechanisms by the particle rearrangement and particle deformation.
Abushaikha, Ahmad S.; Voskov, Denis V.; Tchelepi, Hamdi A.
2017-10-01
We present a new fully-implicit, mixed-hybrid, finite-element (MHFE) discretization scheme for general-purpose compositional reservoir simulation. The locally conservative scheme solves the coupled momentum and mass balance equations simultaneously, and the fluid system is modeled using a cubic equation-of-state. We introduce a new conservative flux approach for the mass balance equations for this fully-implicit approach. We discuss the nonlinear solution procedure for the proposed approach, and we present extensive numerical tests to demonstrate the convergence and accuracy of the MHFE method using tetrahedral elements. We also compare the method to other advanced discretization schemes for unstructured meshes and tensor permeability. Finally, we illustrate the applicability and robustness of the method for highly heterogeneous reservoirs with unstructured grids.
Application of the extended discrete element method (XDEM) in the melting of a single particle
Baniasadi, Mehdi; Baniasadi, Maryam; Peters, Bernhard
2017-07-01
In this contribution, a new method referred to as Extended Discrete Element Method (XDEM) is usedto model melting of a single particle in the fluid media. The XDEM as a Lagrangian-Eulerian framework is the extension of Discrete Element Method (DEM) by considering thermodynamic state such as temperature distribution and is able to link with Computational Fluid Dynamics (CFD) for fluid phase. In order to provide more accurate results, multiscale method was used. The model is validated by comparing predicted results with existing experimental data for melting of a single ice particle in a water bath. In addition, the model has the capability to be extended to the packed bed of particles with different size and properties to produce different liquid phases.
Discrete/Finite Element Modelling of Rock Cutting with a TBM Disc Cutter
Labra, Carlos; Rojek, Jerzy; Oñate, Eugenio
2017-03-01
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool-rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.
Numerical simulation of liquefaction behaviour of granular materials using Discrete Element Method
Indian Academy of Sciences (India)
T G Sitharam; S V Dinesh
2003-09-01
In this paper, numerical simulation of 3-dimensional assemblies of 1000 polydisperse sphere particles using Discrete Element Method (DEM) is used to study the liquefaction behaviour of granular materials. Numerical simulations of cyclic triaxial shear tests under undrained conditions are performed at different confining pressures under constant strain amplitude. Results obtained in these numerical simulations indicate that with increase in confining pressure there is an increase in liquefaction resistance.
Finite-Element-Based Discretization and Regularization Strategies for 3D Inverse Electrocardiography
Wang, Dafang; Kirby, Robert M.; Johnson, Chris R.
2011-01-01
We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of ...
Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal Evolution of the MIZ
2015-09-30
dynamic and thermodynamic processes governing the seasonal evolution of the marginal ice zone (MIZ) and (b) forecasting conditions in the MIZ in...STATEMENT A. Approved for public release; distribution is unlimited. Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal ...spatial variability of the surface stress fields to icepack evolution. • Evaluate the DEM’s effectiveness in simulating the seasonal evolution of the
Optimization of Zoom Lens with Discrete State of Liquid Lens Elements by Using Genetic Algorithm
Directory of Open Access Journals (Sweden)
Cheng-Mu Tsai
2015-01-01
Full Text Available This paper is to employ liquid lens elements to design a lens with zoom function by using the genetic algorithm (GA optimization. The liquid lens elements used in the proposal can apply voltage adjustment to generate the electrical field that induces the liquid with electric conductivity to vary the surface curvature between two different kinds of liquids. According to the voltage level, the liquid lens element makes the discrete variation of the curvature and thickness realize the zoom function without moving the lens groups so that the overall length can be reduced. However, it is difficult to design the zoom lens under the discrete variation of the curvature and thickness in the liquid lens elements and the mechanical space that is constantly limited. The GA offers a flexible way for lens optimization. We regarded the spot size as the fitness function to look for the optimum curvatures, thickness, and the corresponding statuses of liquid lens elements for the zoom lens. As a result, the zoom lens with constant space can be realized by running the selection, crossover, and mutation operation in the GA optimization.
Korneev, V. G.
2012-09-01
BPS is a well known an efficient and rather general domain decomposition Dirichlet-Dirichlet type preconditioner, suggested in the famous series of papers Bramble, Pasciak and Schatz (1986-1989). Since then, it has been serving as the origin for the whole family of domain decomposition Dirichlet-Dirichlet type preconditioners-solvers as for h so hp discretizations of elliptic problems. For its original version, designed for h discretizations, the named authors proved the bound O(1 + log2 H/ h) for the relative condition number under some restricting conditions on the domain decomposition and finite element discretization. Here H/ h is the maximal relation of the characteristic size H of a decomposition subdomain to the mesh parameter h of its discretization. It was assumed that subdomains are images of the reference unite cube by trilinear mappings. Later similar bounds related to h discretizations were proved for more general domain decompositions, defined by means of coarse tetrahedral meshes. These results, accompanied by the development of some special tools of analysis aimed at such type of decompositions, were summarized in the book of Toselli and Widlund (2005). This paper is also confined to h discretizations. We further expand the range of admissible domain decompositions for constructing BPS preconditioners, in which decomposition subdomains can be convex polyhedrons, satisfying some conditions of shape regularity. We prove the bound for the relative condition number with the same dependence on H/ h as in the bound given above. Along the way to this result, we simplify the proof of the so called abstract bound for the relative condition number of the domain decomposition preconditioner. In the part, related to the analysis of the interface sub-problem preconditioning, our technical tools are generalization of those used by Bramble, Pasciak and Schatz.
Failure analysis of pebble bed reactors during earthquake by discrete element method
Energy Technology Data Exchange (ETDEWEB)
Keppler, Istvan, E-mail: keppler.istvan@gek.szie.hu [Department of Mechanics and Engineering Design, Szent István University, Páter K.u.1., Gödöllő H-2103 (Hungary)
2013-05-15
Highlights: ► We evaluated the load acting on the central reflector beam of a pebble bed reactor. ► The load acting on the reflector beam highly depends on fuel element distribution. ► The contact force values do not show high dependence on fuel element distribution. ► Earthquake increases the load of the reflector, not the contact forces. -- Abstract: Pebble bed reactors (PBR) are graphite-moderated, gas-cooled nuclear reactors. PBR reactors use a large number of spherical fuel elements called pebbles. From mechanical point of view, the arrangement of “small” spherical fuel elements in a container poses the same problem, as the so-called silo problem in powder technology and agricultural engineering. To get more exact information about the contact forces arising between the fuel elements in static and dynamic case, we simulated the static case and the effects of an earthquake on a model reactor by using discrete element method. We determined the maximal contact forces acting between the individual fuel elements. We found that the value of the maximal bending moment in the central reflector beam has a high deviation from the average value even in static case, and it can significantly increase in case of an earthquake. Our results can help the engineers working on the design of such types of reactors to get information about the contact forces, to determine the dust production and the crush probability of fuel elements within the reactor, and to model different accident scenarios.
Mesoscale dynamic coupling of finite- and discrete-element methods for fluid-particle interactions.
Srivastava, S; Yazdchi, K; Luding, S
2014-08-06
A new method for two-way fluid-particle coupling on an unstructured mesoscopically coarse mesh is presented. In this approach, we combine a (higher order) finite-element method (FEM) on the moving mesh for the fluid with a soft sphere discrete-element method for the particles. The novel feature of the proposed scheme is that the FEM mesh is a dynamic Delaunay triangulation based on the positions of the moving particles. Thus, the mesh can be multi-purpose: it provides (i) a framework for the discretization of the Navier-Stokes equations, (ii) a simple tool for detecting contacts between moving particles, (iii) a basis for coarse-graining or upscaling, and (iv) coupling with other physical fields (temperature, electromagnetic, etc.). This approach is suitable for a wide range of dilute and dense particulate flows, because the mesh resolution adapts with particle density in a given region. Two-way momentum exchange is implemented using semi-empirical drag laws akin to other popular approaches; for example, the discrete particle method, where a finite-volume solver on a coarser, fixed grid is used. We validate the methodology with several basic test cases, including single- and double-particle settling with analytical and empirical expectations, and flow through ordered and random porous media, when compared against finely resolved FEM simulations of flow through fixed arrays of particles.
Pennec, Fabienne; Alzina, Arnaud; Tessier-Doyen, Nicolas; Naitali, Benoit; Smith, David S.
2012-11-01
This work is about the calculation of thermal conductivity of insulating building materials made from plant particles. To determine the type of raw materials, the particle sizes or the volume fractions of plant and binder, a tool dedicated to calculate the thermal conductivity of heterogeneous materials has been developped, using the discrete element method to generate the volume element and the finite element method to calculate the homogenized properties. A 3D optical scanner has been used to capture plant particle shapes and convert them into a cluster of discret elements. These aggregates are initially randomly distributed but without any overlap, and then fall down in a container due to the gravity force and collide with neighbour particles according to a velocity Verlet algorithm. Once the RVE is built, the geometry is exported in the open-source Salome-Meca platform to be meshed. The calculation of the effective thermal conductivity of the heterogeneous volume is then performed using a homogenization technique, based on an energy method. To validate the numerical tool, thermal conductivity measurements have been performed on sunflower pith aggregates and on packed beds of the same particles. The experimental values have been compared satisfactorily with a batch of numerical simulations.
Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo
2015-10-01
The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.
Aorta modeling with the element-based zero-stress state and isogeometric discretization
Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi
2016-11-01
Patient-specific arterial fluid-structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight
Aorta modeling with the element-based zero-stress state and isogeometric discretization
Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi
2017-02-01
Patient-specific arterial fluid-structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight
Institute of Scientific and Technical Information of China (English)
CHANG Wei-Tze; HSIEH Shang-Hsien; YANG Fu-Ling; CHEN Chuin-Shan
2008-01-01
This paper proposes a numerical scheme that employs the discrete element method (DEM) to simulate the motion of a wet granular flow down an inclined channel.To account for the liquid influences on the dynamics between paired particles,this paper presents a wet soft-sphere contact model with liquid-modified parameters.The developed scheme takes full advantage of DEM and avoids the expensive simula-tion of the solid-liquid interactions with conventional Navier-Stokes equation solver.This wet contact model has been implemented in an in-housed parallel discrete objects simulation system-KNIGHT and ANNE/IRIS口to compute the dynamic behaviors of both dry and wet granular particles flowing down an in-dined channel.
Institute of Scientific and Technical Information of China (English)
LUO Zhen-dong; ZHOU Yan-jie; ZHU Jiang
2007-01-01
The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical modes by the following governing nonlinear partial differential equations containing velocity vector,temperature field,pressure field,and gas mass field.The mixed finite element(MFE)method is employed to study the system of equations for the vapor deposition chemical reaction processes.The semidiscrete and fully discrete MFE formulations are derived.And the existence and convergence(error estimate)of the semidiscrete and fully discrete MFE solutions are deposition chemical reaction processes,the numerical solutions of the velocity vector,the temperature field,the pressure field,and the gas mass field can be found out simultaneonsly.Thus,these researches are not only of important theoretical means,but also of extremely extensive applied vistas.
Casas, Guillermo; Mukherjee, Debanjan; Celigueta, Miguel Angel; Zohdi, Tarek I.; Onate, Eugenio
2015-11-01
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.
Casas, Guillermo; Mukherjee, Debanjan; Celigueta, Miguel Angel; Zohdi, Tarek I.; Onate, Eugenio
2017-04-01
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.
Directory of Open Access Journals (Sweden)
Zainorizuan Mohd Jaini
2013-12-01
Full Text Available Innovative technologies have resulted in more effective ceramic composite as high rate loading-resistance and protective layer. The ceramic composite layer consists of ceramic frontal plate that bonded by softer-strong reinforced polymer network, consequently gains the heterogeneous condition. These materials serve specific purposes of defeating high rate loading and maintaining the structural integrity of the layer. Further due to the lack of a constituent material and tedious problem in heterogonous material modelling, a numerical homogenization is employed to analyse the isotropic material properties of ceramic composite layer in homogenous manner. The objective of this study is to derive a constitutive law of the ceramic composite using the multi-scale analysis. Two-dimensional symmetric macrostructure of the ceramic composite was numerically modelled using the hybrid finite-discrete element method to investigate the effective material properties and strength profile. The macrostructure was modelled as brittle material with nonlinear material properties. The finite element method is incorporated with a Rankine-Rotating Crack approach and discrete element to model the fracture onset. The prescribed uniaxial and biaxial loadings were imposed along the free boundaries to create different deformations. Due to crack initiation on the macrostructure, the averaged stresses were calculated to plot the stress-strain curves and the effective yield stress surface. From the multi-scale analysis, the rate-dependency of Mohr-Coulomb constitutive law was derived for the ceramic composite layer.
Energy Technology Data Exchange (ETDEWEB)
Svyatskiy, Daniil [Los Alamos National Laboratory; Shashkov, Mikhail [Los Alamos National Laboratory; Kuzmin, D [DORTMUND UNIV
2008-01-01
A new approach to the design of constrained finite element approximations to second-order elliptic problems is introduced. This approach guarantees that the finite element solution satisfies the discrete maximum principle (DMP). To enforce these monotonicity constrains the sufficient conditions for elements of the stiffness matrix are formulated. An algebraic splitting of the stiffness matrix is employed to separate the contributions of diffusive and antidiffusive numerical fluxes, respectively. In order to prevent the formation of spurious undershoots and overshoots, a symmetric slope limiter is designed for the antidiffusive part. The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes. The recovery of nodal gradients is performed by means of a lumped-mass L{sub 2} projection. The proposed slope limiting strategy preserves the consistency of the underlying discrete problem and the structure of the stiffness matrix (symmetry, zero row and column sums). A positivity-preserving defect correction scheme is devised for the nonlinear algebraic system to be solved. Numerical results and a grid convergence study are presented for a number of anisotropic diffusion problems in two space dimensions.
Determination of contact parameters for discrete element method simulations of granular systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Both linear-spring-dashpot (LSD) and non-linear Hertzian-spring-dnshpot (HSD) contact models are commonly used for the calculation of contact forces in Discrete Element Method (DEM) simulations of granular systems.Despite the popularity of these models, determination of suitable values for the contact parameters of the simulated particles such as stiffness, damping coefficient, coefficient of restitution, and simulation time step,is not altogether obvious.In this work the relationships between these contact parameters for a model system where a particle impacts on a flat base are examined.Recommendations are made concerning the determination of these contact parameters for use in DEM simulations.
Directory of Open Access Journals (Sweden)
F. Nicot
2002-01-01
Full Text Available The search of improvement of protective techniques against natural phenomena such as snow avalanches continues to use classic methods for calculating flexible structures. This paper deals with a new method to design avalanche protection nets. This method is based on a coupled analysis of both net structure and snow mantle by using a Discrete Element Method. This has led to the development of computational software so that avalanche nets can be easily designed. This tool gives the evolution of the forces acting in several parts of the work as a function of the snow situation.
Cleary, Paul W; Prakash, Mahesh
2004-09-15
Particle-based simulation methods, such as the discrete-element method and smoothed particle hydrodynamics, have specific advantages in modelling complex three-dimensional (3D) environmental fluid and particulate flows. The theory of both these methods and their relative advantages compared with traditional methods will be discussed. Examples of 3D flows on realistic topography illustrate the environmental application of these methods. These include the flooding of a river valley as a result of a dam collapse, coastal inundation by a tsunami, volcanic lava flow and landslides. Issues related to validation and quality data availability are also discussed.
Coupled discrete element and smoothed particle hydrodynamics simulations of the die filling process
Breinlinger, Thomas; Kraft, Torsten
2016-11-01
Die filling is an important part of the powder compaction process chain, where defects in the final part can be introduced—or prevented. Simulation of this process is therefore a goal for many part producers and has been studied by some researchers already. In this work, we focus on the influence of the surrounding air on the powder flow. We demonstrate the implementing and coupling of the discrete element method for the granular powder and the smoothed particle hydrodynamics method for the gas flow. Application of the method to the die filling process is demonstrated.
Impact of Interaction Laws and Particle Modeling in Discrete Element Simulations
Cao, Hong-Phong; Renouf, Mathieu; Dubois, Frédéric
2009-06-01
To describe the evolution of divided media, Discrete Elements Methods (DEMs) appear as one of the most appropriate tools. Medium evolution is directly related to assumptions about local contact area, body deformations and contact interactions. In some circumstance such assumptions have a strong influence on the macroscopic behaviour of the media and consequently become questionable. Using the Contact Dynamics framework, the paper presents how classical assumptions could be extended to avoid numerical effects. A reflection is proposed taking into account both physical and numerical aspects. Static and dynamic configuration have been used to illustrate the paper purposes.
Karrech, Ali; Bonnet, Guy; Chevoir, François; Roux, Jean-Noel; Canou, Jean; Dupla, Jean-Claude
2008-01-01
This paper deals with the vibration of granular materials due to cyclic external excitation. It highlights the effect of the acceleration on the settlement speed and proves the existence of a relationship between settlement and loss of contacts in partially confined granular materials under vibration. The numerical simulations are carried out using the Molecular Dynamics method, where the discrete elements consist of polygonal grains. The data analyses are conducted based on multivariate autoregressive models to describe the settlement and permanent contacts number with respect to the number of loading cycles.
Damping of rotating beams with particle dampers: Discrete element method analysis
Els, D. N. J.
2013-06-01
The performance of particle dampers (PDs) under centrifugal loads was investigated. A test bench consisting of a rotating cantilever beam with a particle damper at the tip was developed (D. N. J. Els, AIAA Journal 49, 2228-2238 (2011)). Equal mass containers with different depths, filled with a range of uniform-sized steel ball bearings, were used as particle dampers. The experiments were duplicated numerically with a discrete element method (DEM) model, calibrated against the experimental data. The DEM model of the rotating beam with a PD at the tip captured the performance of the PD very well over a wide range of tests with different configurations and rotation velocities.
A TWO-SCALE HIGHER-ORDER FINITE ELEMENT DISCRETIZATION FOR SCHRODINGER EQUATION
Institute of Scientific and Technical Information of China (English)
Huajie Chen; Fang Liu; Aihui Zhou
2009-01-01
In this paper,a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schr(o)dinger equation on tensor product domains.With the scheme,the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids.It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method.
Brocklehurst, Paul; Adeniran, Ismail; Yang, Dongmin; Sheng, Yong; Zhang, Henggui; Ye, Jianqiao
2015-01-01
Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca(2+) concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.
A minimal coupled fluid-discrete element model for bedload transport
Maurin, R.; Chauchat, J.; Chareyre, B.; Frey, P.
2015-11-01
A minimal Lagrangian two-phase model to study turbulent bedload transport focusing on the granular phase is presented and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively low Shields numbers, for which no suspension occurs. A discrete element method for the granular phase is coupled with a one dimensional volume-averaged two-phase momentum equation for the fluid phase. The coupling between the discrete granular phase and the continuous fluid phase is discussed, and a consistent averaging formulation adapted to bedload transport is introduced. An original simple discrete random walk model is proposed to account for the fluid velocity fluctuations. The model is compared with experiments considering both classical sediment transport rate as a function of the Shields number, and depth profiles of solid velocity, volume fraction, and transport rate density, from existing bedload transport experiments in inclined flume. The results successfully reproduce the classical 3/2 power law, and more importantly describe well the depth profiles of the granular phase, showing that the model is able to reproduce the particle scale mechanisms. From a sensitivity analysis, it is shown that the fluctuation model allows to reproduce a realistic critical Shields number, and that the influence of the granular parameters on the macroscopic results is weak. Nevertheless, the analysis of the corresponding depth profiles reveals an evolution of the depth structure of the granular phase with varying restitution and friction coefficients, which denotes the non-trivial underlying physical mechanisms.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Yang, B; Zika, M R
2005-07-15
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
Directory of Open Access Journals (Sweden)
Enan Chi
2015-06-01
Full Text Available The fracture and fragmentation of rock materials are basic and important problem in geomechanics and blasting engineering. An approach, which can simulate the process of fracture and fragmentation of rock materials, is introduced in this work. A beam–particle model is first introduced in the frame of the discrete element method. In the beam–particle model, the neighboring elements are connected by beams. Consequently, a beam network is formed in the particle system. The strength characteristics of rock materials are reflected by the beam network. The strength criterion was then built to verify whether a beam exists or not. The process of rock fracture and fragmentation is described by the gradual disappearance of beams. Finally, two cases were presented to indicate the validity of the method proposed in this work.
Multiple-contact discrete-element model for simulating dense granular media
Brodu, Nicolas; Dijksman, Joshua A.; Behringer, Robert P.
2015-03-01
This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable MC-DEM method retains all the advantages of discrete-element method simulations and does not require the use of costly finite-element methods. The new model closely reproduces our recent experimental measurements, including contact force distributions in full 3D, at all compression levels of the packing up to the experimental maximum limit of 13%. Comparisons with classic simulations using the nondeformable spheres approach, as well as with alternative models for interactions between multiple contacts, are provided. The success of our model, compared to these alternatives, demonstrates that interactions between multiple contacts on each grain must be included for dense granular packings.
Zohdi, T. I.
2016-03-01
In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.
Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method
Institute of Scientific and Technical Information of China (English)
CHEN Jun; PAN Tongyan; CHEN Jingya; HUANG Xiaoming; LU Yang
2012-01-01
A user-defined three-dimensional (3D) discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete (AC).The 3D discrete element method (DEM) model of AC was constructed employing a user-defined computer program developed using the "Fish" language in PFC3D.Important microstructural features of AC were modeled,including aggregate gradation,air voids and mastic.The irregular shape of aggregate particle was modeled using a clump of spheres.The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test,based on which the dynamic modulus and phase angle were calculated from the output stressstrain relationship.The effects of air void content,aggregate stiffness and volumetric fraction on AC modulus were further investigated.The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies.The userdefined 3D model also demonstrated significant improvement over the general existing two-dimensional models.
Institute of Scientific and Technical Information of China (English)
Kevin J. Hanley; Catherine O'Sullivan; Edmond P. Byrne; Kevin Cronin
2012-01-01
Infant formula is usually produced in an agglomerated powder form.These agglomerates are subjected to many transient forces following their manufacture.These can be difficult to quantify experimentally because of their small magnitudes and short durations.Numerical models have the potential to address this gap in the experimental data.The objective of the research described here was to calibrate a discrete element model for these agglomerates using experimental data obtained for quasi-static loading,and to use this model to study the mechanics of the particle response in detail.The Taguchi method was previously proposed as a viable calibration approach for discrete element models.In this work,the method was assessed for calibration of the model parameters (e.g.,bond stiffnesses and strengths) considering three responses: the force at failure,strain at failure and agglomerate stiffness.The Weibull moduli for the simulation results and the experimental data were almost identical following calibration and the 37％ characteristic stresses were similar.An analysis of the energy terms in the model provided useful insight into the model response.The bond energy and the normal force exerted on the platens were strongly correlated,and bond breakage events coincided with the highest energy dissipation rates.
THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS
Institute of Scientific and Technical Information of China (English)
LiuKaixin; GaoLingtian
2003-01-01
A three-dimensional discrete element model of the connective type is presented. Moreover, a three- dimensional numerical analysis code, which can carry out the transitional process from connective model (for continuum) to contact model (for non-continuum), is developed for simulating the mechanical process from continuum to non-continuum. The wave propagation process in a concrete block (as continuum) made of cement grout under impact loading is numerically simulated with this code. By comparing its numerical results with those by LS-DYNA, the calculation accuracy of the model and algorithm is proved. Furthermore, the failure process of the concrete block under quasi-static loading is demonstrated, showing the basic dynamic transitional process from continuum to non-continuum. The results of calculation can be displayed by animation. The damage modes are similar to the experimental results. The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum. It also shows that the discrete element method (DEM) will have broad prospects for development and application.
Institute of Scientific and Technical Information of China (English)
马涛; 张德育; 张垚; 赵永利; 黄晓明
2016-01-01
The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions (PFC3D) based on three-dimensional discrete element method. A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate. And then, modeling algorithm and method for graded aggregates were built. Based on the combination of modeling of coarse aggregates, asphalt mastic and air voids, three-dimensional virtual sample of asphalt mixture was modeled by using PFC3D. Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC3D. By comparison of the testing results between virtual tests and actual laboratory tests, the validity of the microstructure modeling and virtual test built in this study was verified. Additionally, compared with laboratory test, the virtual test is easier to conduct and has less variability. It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.
Martin, Hugo; Mangeney, Anne; Farin, Maxime; Richard, Patrick
2016-04-01
The mechanical behavior of granular flows is still an open issue. In particular, quantitative agreement between the detailed dynamics of the flow and laboratory experiments is necessary to better constrain the performance and limits of the models. We propose here to compare quantitatively the flow profiles and the force during granular column collapse simulated using Discrete Element Models and laboratory experiments. These small scale experiments are performed with dry granular material released initially from a cylinder on a sloping plane. The flow profiles and the acoustic signal generated by the granular impacts and stresses on the plane are recorded systematically [Farin et al., 2015]. These experiments are simulated using the Discrete Element Method Modys [Richard et al., 2000]. We show that the effect of the removing gate should be taken into account in the model in order to quantatively reproduce the flow dynamics. Furthermore we compare the simulated and observed acoustic signals that are generated by the fluctuating stresses exerted by the grains on the substrate in different frequency bands. [1] P. Richard et Luc Oger. 2000 Etude de la géométrie de milieux granulaires modèles tridimensionnels par simulation numérique. [2] Farin, M., Mangeney, A., Toussaint, R., De Rosny, J., Shapiro, N., Dewez, T., Hibert, C., Mathon, C., Sedan, O., Berger. 2015, Characterization of rockfalls from seismic signal: insights from laboratory experiments
Novel Discrete Element Method for 3D non-spherical granular particles.
Seelen, Luuk; Padding, Johan; Kuipers, Hans
2015-11-01
Granular materials are common in many industries and nature. The different properties from solid behavior to fluid like behavior are well known but less well understood. The main aim of our work is to develop a discrete element method (DEM) to simulate non-spherical granular particles. The non-spherical shape of particles is important, as it controls the behavior of the granular materials in many situations, such as static systems of packed particles. In such systems the packing fraction is determined by the particle shape. We developed a novel 3D discrete element method that simulates the particle-particle interactions for a wide variety of shapes. The model can simulate quadratic shapes such as spheres, ellipsoids, cylinders. More importantly, any convex polyhedron can be used as a granular particle shape. These polyhedrons are very well suited to represent non-rounded sand particles. The main difficulty of any non-spherical DEM is the determination of particle-particle overlap. Our model uses two iterative geometric algorithms to determine the overlap. The algorithms are robust and can also determine multiple contact points which can occur for these shapes. With this method we are able to study different applications such as the discharging of a hopper or silo. Another application the creation of a random close packing, to determine the solid volume fraction as a function of the particle shape.
Discrete element modeling of ice loads on ship hulls in broken ice fields
Institute of Scientific and Technical Information of China (English)
JI Shunying; LI Zilin; LI Chunhua; SHANG Jie
2013-01-01
Ice loads on a ship hull affect the safety of the hull structure and the ship maneuvering performance in ice-covered regions. A discrete element method (DEM) is used to simulate the interaction between drifting ice floes and a moving ship. The pancake ice floes are modelled with three-dimensional (3-D) dilated disk elements considering the buoyancy, drag force and additional mass induced by the current. The ship hull is modelled with 3D disks with overlaps. Ice loads on the ship hull are determined through the contact detection between ice floe element and ship hull element and the contact force calculation. The influences of different ice conditions (current velocities and directions, ice thicknesses, concentrations and ice floe sizes) and ship speeds are also examined on the dynamic ice force. The simulated results are compared qualitatively well with the existing field data and other numerical results. This work can be helpful in the ship structure design and the navigation security in ice-covered fields.
Institute of Scientific and Technical Information of China (English)
WANG Zhuolin; LIN Feng; GU Xianglin
2008-01-01
A two-dimensional mesoscopic numerical method to simulate the failure process of concrete under compression was developed based on the discrete element method by modifying the dgid body-spdng model proposed by Nagai et al.In the calculation model,aggregates or aggregate elements inside the concrete were simplified as rigid bodies with regular polygon profiles,which were surrounded by mortar polygons or mortar elements.All of the adjacent elements were connected by springs.According to the random distribution of aggregates,the mesh was generated by using Voronoi diagram method.Plastic behavior after the elastic limit for a spring was considered to set up the constitutive model of the spring,and Mohr-Coulomb criterion was adopted to judge the failure of a spdng.Simulation examples show that the proposed method can be used to predict the mechanical behavior of concrete under compression descriptively and quantitatively both for small deformation problems and for larger deformation problems.
A Stable Parametric Finite Element Discretization of Two-Phase Navier--Stokes Flow
Barrett, John W; Nürnberg, Robert
2013-01-01
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element approximation of the evolving interface is then coupled to a standard finite element approximation of the two-phase Navier--Stokes equations in the bulk. Here enriching the pressure approximation space with the help of an XFEM function ensures good volume conservation properties for the two phase regions. In addition, the mesh quality of the parametric approximation of the interface in general does not deteriorate over time, and an equidistribution property can be shown for a semidiscrete continuous-in-time variant of our scheme in two space dimensions. Moreover, our finite element approximation can be shown to be uncondit...
Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell
Energy Technology Data Exchange (ETDEWEB)
Earl Mattson; Hai Huang; Michael Conway; Lisa O' Connell
2014-02-01
The study of propped fracture conductivity began in earnest with the development of the Cooke cell which later became part of the initial API standard. Subsequent developments included a patented multicell design to conduct 4 tests in a press at the same time. Other modifications have been used by various investigators. Recent studies by the Stim-Lab proppant consortium have indicated that the flow field across a Cooke proppant conductivity testing cell may not be uniform as initially believed which resulted is significantly different conductivity results. Post test analysis of low temperature metal alloy injections at the termination of proppant testing prior to the release of the applied stress suggest that higher flow is to be expected along the sides and top of the proppant pack than compared to the middle of the pack. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate proppant rearrangement during stress loading in the Cooke conductivity cell and the resulting porosity field. Analysis of these simulations are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues such as how these effects are manifested in proppant concentration testing results. The 2-D DEM model was constructed to represent a realistic cross section of the Cooke cell with a distribution of four material properties, three that represented the Cooke cell (steel, sandstone,square rings), and one representing the proppant. In principle, Cooke cell materials can be approximated as assemblies of independent discrete elements (particles) of various sizes and material properties that interact via cohesive interactions, repulsive forces, and frictional forces. The macroscopic behavior can then be modeled as the collective behavior of many interacting discrete elements. This DEM model is particularly suitable for modeling proppant
Carbonate fracture stratigraphy: An integrated outcrop and 2D discrete element modelling study
Spence, Guy; Finch, Emma
2013-04-01
Constraining fracture stratigraphy is important as natural fractures control primary fluid flow in low matrix permeability naturally fractured carbonate hydrocarbon reservoirs. Away from the influence of folds and faults, stratigraphic controls are known to be the major control on fracture networks. The fracture stratigraphy of carbonate nodular-chert rhythmite successions are investigated using a Discrete Element Modelling (DEM) technique and validated against observations from outcrops. Comparisons are made to the naturally fractured carbonates of the Eocene Thebes Formation exposed in the west central Sinai of Egypt, which form reservoir rocks in the nearby East Ras Budran Field. DEM allows mechanical stratigraphy to be defined as the starting conditions from which forward numerical modelling can generate fracture stratigraphy. DEM can incorporate both stratigraphic and lateral heterogeneity, and enable mechanical and fracture stratigraphy to be characterised separately. Stratally bound stratified chert nodules below bedding surfaces generate closely spaced lateral heterogeneity in physical properties at stratigraphic mechanical interfaces. This generates extra complexity in natural fracture networks in addition to that caused by bed thickness and lithological physical properties. A series of representative geologically appropriate synthetic mechanical stratigraphic models were tested. Fracture networks generated in 15 DEM experiments designed to isolate and constrain the effects of nodular chert rhythmites on carbonate fracture stratigraphy are presented. The discrete element media used to model the elastic strengths of rocks contain 72,866 individual elements. Mechanical stratigraphies and the fracture networks generated are placed in a sequence stratigraphic framework. Nodular chert rhythmite successions are shown to be a distinct type of naturally fractured carbonate reservoir. Qualitative stratigraphic rules for predicting the distribution, lengths, spacing
Discrete-element modelling: methods and applications in the environmental sciences.
Richards, Keith; Bithell, Mike; Dove, Martin; Hodge, Rebecca
2004-09-15
This paper introduces a Theme Issue on discrete-element modelling, based on research presented at an interdisciplinary workshop on this topic organized by the National Institute of Environmental e-Science. The purpose of the workshop, and this collection of papers, is to highlight the opportunities for environmental scientists provided by (primarily) off-lattice methods in the discrete-element family, and to draw on the experiences of research communities in which the use of these methods is more advanced. Applications of these methods may be conceived in a wide range of situations where dynamic processes involve a series of fundamental entities (particles or elements) whose interaction results in emergent macroscale structures. Indeed, the capacity of these methods to reveal emergent properties at the meso- and macroscale, that reflect microscale interactions, is a significant part of their attraction. They assist with the definition of constitutive material properties at scales beyond those at which measurement and theory have been developed, and help us to understand self-organizing behaviours. The paper discusses technical issues including the contact models required to represent collision behaviour, computational aspects of particle tracking and collision detection, and scales at which experimental data are required and choices about modelling style must be made. It then illustrates the applicability of DEM and other forms of individual-based modelling in environmental and related fields as diverse as mineralogy, geomaterials, mass movement and fluvial sediment transport processes, as well as developments in ecology, zoology and the human sciences where the relationship between individual behaviour and group dynamics can be explored using a partially similar methodological framework.
Derakhshani, S. M.; Schott, D. L.; Lodewijks, G.
2013-06-01
Dust emissions can have significant effects on the human health, environment and industry equipment. Understanding the dust generation process helps to select a suitable dust preventing approach and also is useful to evaluate the environmental impact of dust emission. To describe these processes, numerical methods such as Computational Fluid Dynamics (CFD) are widely used, however nowadays particle based methods like Discrete Element Method (DEM) allow researchers to model interaction between particles and fluid flow. In this study, air flow over a stockpile, dust emission, erosion and surface deformation of granular material in the form of stockpile are studied by using DEM and CFD as a coupled method. Two and three dimensional simulations are respectively developed for CFD and DEM methods to minimize CPU time. The standard κ-ɛ turbulence model is used in a fully developed turbulent flow. The continuous gas phase and the discrete particle phase link to each other through gas-particle void fractions and momentum transfer. In addition to stockpile deformation, dust dispersion is studied and finally the accuracy of stockpile deformation results obtained by CFD-DEM modelling will be validated by the agreement with the existing experimental data.
Discrete element method of improved performance of railway ballast bed using elastic sleeper
Institute of Scientific and Technical Information of China (English)
高亮; 罗奇; 徐旸; 井国庆; 蒋函珂
2015-01-01
With the development of high-speed and heavy-haul railway in China, problems like insufficient thickness of ballast bed and overlarge track stiffness are obvious. Ballast may break into small particles and their contact status will deteriorate under cyclic loading, resulting in ballast degradation. Discrete element method (DEM) was used to research improved performance of ballast bed using elastic sleeper. Clusters were generated by bonding spheres to model real ballasts, while broken bonds were utilized to distinguish breakage. Two kinds of ballast beds with elastic sleeper and conventional sleeper were established, respectively. After applying cyclic loading to the models, differences of mechanical properties between two models were analyzed by contrasting their dynamic behavior indexes, such as particle contact force, sleeper settlement, vibration velocity and acceleration, breakage characteristic. The results illustrate that compared with conventional sleeper, elastic sleeper increases sleeper settlement, while reduces ballast vibration and contact force between particles, which could depress ballast breakage.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The phenomenon of the soil plug usually rising inside the suction foundations during suction penetration was quantitatively described and predicted. The formation process of the soil plug was simulated and calculated by DEM (discrete element method) model. The seepage flow, the self-weight of soil, the friction on the chamber wall as well as the suction inside the chamber are considered as the main external forces in the process. The results are compared with a set of laboratory model tests performed by using three soil types (sand, silty clay and clay) in the Bohai Sea area. The heights of soil plug from numerical estimations are lower than those from model test results, mainly because the suction pressure and friction resistance are applied in an ideal way under the numerical simulation.
Modelling Gas Diffusion from Breaking Coal Samples with the Discrete Element Method
Directory of Open Access Journals (Sweden)
Dan-Ling Lin
2015-01-01
Full Text Available Particle scale diffusion is implemented in the discrete element code, Esys-Particle. We focus on the question of how to calibrate the particle scale diffusion coefficient. For the regular 2D packing, theoretical relation between micro- and macrodiffusion coefficients is derived. This relation is then verified in several numerical tests where the macroscopic diffusion coefficient is determined numerically based on the half-time of a desorption scheme. To further test the coupled model, we simulate the diffusion and desorption in the circular sample. The numerical results match the analytical solution very well. An example of gas diffusion and desorption during sample crushing and fragmenting is given at the last. The current approach is the first step towards a realistic and comprehensive modelling of coal and gas outbursts.
Particle stratification and penetration of a linear vibrating screen by the discrete element method
Institute of Scientific and Technical Information of China (English)
Xiao Jianzhang; Tong Xin
2012-01-01
A simulation of stratification and penetration was performed over a range of structural parameters that included screen width,aperture size,inclination angle,and wire diameter.The discrete element method (DEM) was used for the simulations.The terms stratification and penetration are defined and the change in fine particle concentration is discussed.Mathematical models relating fine particle ratio to time are established using the least squares method.The effect of structural parameters on fine particle ratio is analyzed.Stratification and penetration rate are discussed by considering the time derivative of the fine particle ratio.The conclusions are:an increase in inclination or wire diameter has a positive effect on particle stratifying; The optimal screen width is 40 mm for particle stratification; The inclination angle has a negative effect on the penetration; The effect of wire diameter and screen width on the penetration rate is negligible.
Directory of Open Access Journals (Sweden)
T. Lukas
2014-12-01
Full Text Available The combined finite–discrete element method (FDEM belongs to a family of methods of computational mechanics of discontinua. The method is suitable for problems of discontinua, where particles are deformable and can fracture or fragment. The applications of FDEM have spread over a number of disciplines including rock mechanics, where problems like mining, mineral processing or rock blasting can be solved by employing FDEM. In this work, a novel approach for the parallelization of two-dimensional (2D FDEM aiming at clusters and desktop computers is developed. Dynamic domain decomposition based parallelization solvers covering all aspects of FDEM have been developed. These have been implemented into the open source Y2D software package and have been tested on a PC cluster. The overall performance and scalability of the parallel code have been studied using numerical examples. The results obtained confirm the suitability of the parallel implementation for solving large scale problems.
A hybrid mortar virtual element method for discrete fracture network simulations
Benedetto, Matías Fernando; Berrone, Stefano; Borio, Andrea; Pieraccini, Sandra; Scialò, Stefano
2016-02-01
The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN) is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to "weakly" impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries.
Spellings, Matthew; Anderson, Joshua A; Glotzer, Sharon C
2016-01-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks-Chandler-Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
A discrete element model for soil-sweep interaction in three different soils
DEFF Research Database (Denmark)
Chen, Y; Munkholm, Lars Juhl; Nyord, Tavs
2013-01-01
Soil–tool interactions are at the centre of many agricultural field operations, including slurry injection. Understanding of soil–tool interaction behaviours (soil cutting forces and soil disturbance) is important for designing high performance injection tools. A discrete element model was develo....... The calibrated model was validated using the soil disturbance characteristics measured in those three soils. The simulations agreed well with the measurements with relative errors below 10% in most cases....... were measured. The measured draught and vertical forces were used in calibrations of the most sensitive model parameter, particle stiffness. The calibrated particle stiffness was 0.75 × 103 N m−1 for the coarse sand, 2.75 × 103 N m−1 for the loamy sand, and 6 × 103 N m−1 for the sandy loam...
Spellings, Matthew; Marson, Ryan L.; Anderson, Joshua A.; Glotzer, Sharon C.
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks-Chandler-Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
An overset mesh approach for 3D mixed element high-order discretizations
Brazell, Michael J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.
2016-10-01
A parallel high-order Discontinuous Galerkin (DG) method is used to solve the compressible Navier-Stokes equations in an overset mesh framework. The DG solver has many capabilities including: hp-adaption, curved cells, support for hybrid, mixed-element meshes, and moving meshes. Combining these capabilities with overset grids allows the DG solver to be used in problems with bodies in relative motion and in a near-body off-body solver strategy. The overset implementation is constructed to preserve the design accuracy of the baseline DG discretization. Multiple simulations are carried out to validate the accuracy and performance of the overset DG solver. These simulations demonstrate the capability of the high-order DG solver to handle complex geometry and large scale parallel simulations in an overset framework.
Discrete Element Simulation of Elastoplastic Shock Wave Propagation in Spherical Particles
Directory of Open Access Journals (Sweden)
M. Shoaib
2011-01-01
Full Text Available Elastoplastic shock wave propagation in a one-dimensional assembly of spherical metal particles is presented by extending well-established quasistatic compaction models. The compaction process is modeled by a discrete element method while using elastic and plastic loading, elastic unloading, and adhesion at contacts with typical dynamic loading parameters. Of particular interest is to study the development of the elastoplastic shock wave, its propagation, and reflection during entire loading process. Simulation results yield information on contact behavior, velocity, and deformation of particles during dynamic loading. Effects of shock wave propagation on loading parameters are also discussed. The elastoplastic shock propagation in granular material has many practical applications including the high-velocity compaction of particulate material.
Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and tests
Richardson, Derek C; Murdoch, Naomi; Michel, Patrick
2013-01-01
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular "atmosphere" that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to ...
Huang, Yueqin; Cheng, Yi Pik; Coop, Matthew
2017-06-01
The Discrete Element Method (DEM) was used to simulate the mechanical behaviour of a reservoir sandstone. Triaxial tests were carried out using 3D-DEM to simulate the stress-strain behaviour of a sandstone with comparisons made between the numerical tests and the laboratory tests. The influence of isotropic unloading was investigated, which was found to have impacts on bond breakages and was successfully captured in the 3D shearing processes. It was found that bond breakages correlated strongly with the stress-strain behaviour of the sandstone affecting the peak strength. It was also found that unloading affected the bond breakages, which then changed the mechanical behaviour of sandstone. The tangent stiffnesses of simulated virgin and cored samples under different confining stresses were compared. From the tangent stiffnesses, gross yield envelopes and the yielding surfaces for unloaded samples and virgin samples were plotted and analysed in detail.
Approximation of mechanical properties of sintered materials with discrete element method
Dosta, Maksym; Besler, Robert; Ziehdorn, Christian; Janßen, Rolf; Heinrich, Stefan
2017-06-01
Sintering process is a key step in ceramic processing, which has strong influence on quality of final product. The final shape, microstructure and mechanical properties, e.g. density, heat conductivity, strength and hardness are depending on the sintering process. In order to characterize mechanical properties of sintered materials, in this contribution we present a microscale modelling approach. This approach consists of three different stages: simulation of the sintering process, transition to final structure and modelling of mechanical behaviour of sintered material with discrete element method (DEM). To validate the proposed simulation approach and to investigate products with varied internal structures alumina powder has been experimentally sintered at different temperatures. The comparison has shown that simulation results are in a very good agreement with experimental data and that the novel strategy can be effectively used for modelling of sintering process.
A Discrete Element Model of Armor Glass Fragmentation and Comminution Failure Under Compression
Energy Technology Data Exchange (ETDEWEB)
Xu, Wei [Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland Washington 99354; Sun, Xin [Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland Washington 99354
2016-02-15
Because of its exceptional compressive resistance and crystal-clear appearance, lightweight glass has been traditionally used in transparent armor applications. However, due to its brittle nature, glass fails differently from ductile materials in the sense that glass fragmentation occurs instantly ahead of the projectile tip upon penetration. The effective residual strength of the armor glass then inevitably relies on the damaged glass strength within such comminuted zones with confinement from the surrounding intact materials. Physical understanding of damaged glass strength therefore becomes highly critical to the further development of armor designs. In the present study, a discrete element based modeling framework has been developed to understand and predict the evolution of compressive damages and residual strength of armor glasses. With the characteristic fragmentation and comminution failures explicitly resolved, their influences on the mechanical degradation of the loaded glass materials have been evaluated. The effects of essential loading conditions and material properties have also been investigated.
Institute of Scientific and Technical Information of China (English)
AN Xi-Zhong
2007-01-01
The crystallization, corresponding to the fcc structure (with packing density p ≈ 0.74), of smooth equal hard spheres under batch-wised feeding and three-dimensional interval vibration is numerically obtained by using the discrete element method. The numerical experiment shows that the ordered packing can be realized by proper control of the dynamic parameters such as batch of each feeding § and vibration amplitude A. The radial distribution function and force network are used to characterize the ordered structure. The defect formed during vibrated packing is characterized as well The results in our work fill the gap of getting packing density between random close packing and fcc packing in phase diagram which provides an effective way of theoretically investigating the complex process and mechanism of hard sphere crystallization and its dynamics.
Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles
Institute of Scientific and Technical Information of China (English)
Ehsan Seyedi Hosseininia
2012-01-01
In the present article,we study the effect of inherent anisotropy,i.e.,initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials,by numerical simulation of several biaxial compression tests using the discrete element method (DEM).Particle shape is considered to be irregular convex-polygonal.The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading.As experimental tests have already shown,numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies.Comparison of simulations with tests using oval particles,shows that angularity influences both the mobilized shear strength and the volume change regime,which originates from the interlocking resistance between particles.
Discrete element modelling approach to assessment of granular properties in concrete
Institute of Scientific and Technical Information of China (English)
Piet STROEVEN; Huan HE; Martijn STROEVEN
2011-01-01
This paper presents the technological relevance of a concurrent algorithm-based discrete element modelling (DEM)system, HADES. This new system is the successor of SPACE that is limited to spherical grains only. It can realistically simulate the packing of arbitrary-shaped particles up to the fully compacted state. Generation of families of such particles, i.e., generally representing aggregate of fluvial origin and crushed rock, respectively, and the forming way of particulate structure are described.Similarly shaped particles are proposed for simulation of cement paste because of conformity with experimental results obtained by the X-ray tomography method. Technologically relevant territories inside and outside concrete technology are presently explored in this efficient, reliable, and economic way. Some results obtained by this DEM approach are presented.
Discrete element method study of fuel relocation and dispersal during loss-of-coolant accidents
Govers, K.; Verwerft, M.
2016-09-01
The fuel fragmentation, relocation and dispersal (FFRD) during LOCA transients today retain the attention of the nuclear safety community. The fine fragmentation observed at high burnup may, indeed, affect the Emergency Core Cooling System performance: accumulation of fuel debris in the cladding ballooned zone leads to a redistribution of the temperature profile, while dispersal of debris might lead to coolant blockage or to debris circulation through the primary circuit. This work presents a contribution, by discrete element method, towards a mechanistic description of the various stages of FFRD. The fuel fragments are described as a set of interacting particles, behaving as a granular medium. The model shows qualitative and quantitative agreement with experimental observations, such as the packing efficiency in the balloon, which is shown to stabilize at about 55%. The model is then applied to study fuel dispersal, for which experimental parametric studies are both difficult and expensive.
Institute of Scientific and Technical Information of China (English)
Ji Xu; Jing hai Li; Hua biao Qi; Xiao jian Fang; Li qiang Lu; Wei Ge; Xiao wei Wang; Ming Xu; Fei guo Chen; Xian feng He
2011-01-01
Real-time simulation of industrial equipment is a huge challenge nowadays.The high performance and fine-grained parallel computing provided by graphics processing units (GPUs) bring us closer to our goals.In this article,an industrial-scale rotating drum is simulated using simplified discrete element method (DEM) without consideration of the tangential components of contact force and particle rotation.A single GPU is used first to simulate a small model system with about 8000 particles in real-time,and the simulation is then scaled up to industrial scale using more than 200 GPUs in a 1D domain-decomposition parallelization mode.The overall speed is about 1/11 of the real-time.Optimization of the communication part of the parallel GPU codes can speed up the simulation further,indicating that such real-time simulations have not only methodological but also industrial implications in the near future.
Energy Technology Data Exchange (ETDEWEB)
Spellings, Matthew [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Marson, Ryan L. [Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Anderson, Joshua A. [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Glotzer, Sharon C., E-mail: sglotzer@umich.edu [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States)
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
DEFF Research Database (Denmark)
Hærvig, Jakob; Kleinhans, Ulrich; Wieland, Christoph
2017-01-01
Discrete Element Method (DEM) simulations are a promising approach to accurately predict agglomeration and deposition of micron-sized adhesive particles. However, the mechanistic models in DEM combined with high particle stiffness for most common materials require time step sizes in the order...... particle stiffness to experimental data. Then two well-defined test cases are investigated to show the applicability of the guidelines. When introducing a reduced particle stiffness in DEM simulations by reducing the effective Young's modulus from E to Emod, the surface energy density γ in the adhesive...... is important, the commonly used adhesive rolling resistance torque model proposed by Dominik and Tielens [2,3], Krijt et al. [4] can be used by modifying the contact radius ratio (a/a0)3/2 to (amod/a0,mod)3/2, while keeping the other terms unaltered in the description of the rolling resistance torque Mr...
Han, Xuesong
2014-09-01
Machining technology about ceramics has been developed very fast over recent years due to the growing industrial demand of higher machining accuracy and better surface quality of ceramic elements, while the nature of hard and brittle ceramics makes it difficult to acquire damage-free and ultra-smooth surface. Ceramic bulk can be treated as an assemblage of discrete particles bonded together randomly as the micro-structure of ceramics consists of crystal particles and pores, and the inter-granular fracture of the ceramics can be naturally represented by the separation of particles due to breakage of bonds. Discrete element method (DEM) provides a promising approach for constructing an effective model to describe the tool-workpiece interaction and can serve as a predicting simulation tool in analyzing the complicated surface generation mechanism and is employed in this research to simulate the mechanical polishing process of ceramics and surface integrity. In this work, a densely packed particle assembly system of the polycrystalline Si3N4 has been generated using bonded-particle model to represent the ceramic workpiece numerically. The simulation results justify that the common critical depth of cut cannot be used as the effective parameters for evaluating brittle to ductile transformation in ceramic polishing process. Therefore, a generalized criterion of defining the range of ductile regime machining has been developed based on the numerical results. Furthermore, different distribution of pressure chain is observed with different depth of cut which ought to have intense relationship with special structure of ceramics. This study also justified the advantage of DEM model in its capability of revealing the mechanical behaviors of ceramics at micro-scale.
Indian Academy of Sciences (India)
Rajesh P Nair; C Lakshmana Rao
2012-04-01
One-dimensional discrete element model for the ballistic impact is used to determine the depth of penetration of a bullet on a thick target. Discrete Element Method (DEM) is a numerical tool where a continuum is modelled as a network of masses connected by normal springs. A one-dimensional discrete element model is developed to obtain the displacements and forces associated with the ballistic impact on a thick target. The depth of penetration of the penetrator into the target is calculated from these DEM results. The simulated results of depth of penetration are found to be in reasonable agreement with the simulation results of other numerical approaches that are available in the literature.
The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil
Meade, Andrew J., Jr.
1992-01-01
A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.
Energy Technology Data Exchange (ETDEWEB)
Herbold, E. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Walton, O. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Homel, M. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
This document serves as a final report to a small effort where several improvements were added to a LLNL code GEODYN-L to develop Discrete Element Method (DEM) algorithms coupled to Lagrangian Finite Element (FE) solvers to investigate powder-bed formation problems for additive manufacturing. The results from these simulations will be assessed for inclusion as the initial conditions for Direct Metal Laser Sintering (DMLS) simulations performed with ALE3D. The algorithms were written and performed on parallel computing platforms at LLNL. The total funding level was 3-4 weeks of an FTE split amongst two staff scientists and one post-doc. The DEM simulations emulated, as much as was feasible, the physical process of depositing a new layer of powder over a bed of existing powder. The DEM simulations utilized truncated size distributions spanning realistic size ranges with a size distribution profile consistent with realistic sample set. A minimum simulation sample size on the order of 40-particles square by 10-particles deep was utilized in these scoping studies in order to evaluate the potential effects of size segregation variation with distance displaced in front of a screed blade. A reasonable method for evaluating the problem was developed and validated. Several simulations were performed to show the viability of the approach. Future investigations will focus on running various simulations investigating powder particle sizing and screen geometries.
Numerical simulation of two-dimensional spouted bed with draft plates by discrete element method
Institute of Scientific and Technical Information of China (English)
Yongzhi ZHAO; Yi CHENG; Maoqiang JIANG; Yong JIN
2008-01-01
A discrete element method (DEM)-computa-tional fluid dynamics (CFD) two-way coupling method was employed to simulate the hydrodynamics in a two-dimensional spouted bed with draft plates. The motion of particles was modeled by the DEM and the gas flow was modeled by the Navier-Stokes equation. The interactions between gas and particles were considered using a two-way coupling method. The motion of particles in the spouted bed with complex geometry was solved by com-bining DEM and boundary element method (BEM). The minimal spouted velocity was obtained by the BEM-DEM-CFD simulation and the variation of the flow pat-tern in the bed with different superficial gas velocity was studied. The relationship between the pressure drop of the spouted bed and the superficial gas velocity was achieved from the simulations. The radial profile of the averaged vertical velocities of particles and the profile of the aver-aged void fraction in the spout and the annulus were stat-istically analyzed. The flow characteristics of the gas-solid system in the two-dimensional spouted bed were clearly described by the simulation results.
Finite-element discretization of 3D energy-transport equations for semiconductors
Energy Technology Data Exchange (ETDEWEB)
Gadau, Stephan
2007-07-01
In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and
Heege, J.H. ter; Orlic, B.; Hoedeman, G.C.
2015-01-01
Wellbore zonal isolation is particularly important for subsurface storage of CO2, where well integrity must be ensured for very long time spans. In this study, three dimensional discrete element models of wellbore systems have been used to simulate failure and damage of wellbore cement and surroundi
Calvert, S.C.; Taale, H.; Hoogendoorn, S.P.
2014-01-01
In this contribution the Core Probability Framework (CPF) is introduced with the application of the Discrete-Element Core Probability Model (DE-CPM) as a new DNL for dynamic macroscopic modelling of stochastic traffic flow. The model is demonstrated for validation in a test case and for computationa
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2015-01-01
In this paper, the viscoelastic behavior of asphalt mixture was studied by using discrete element method. The dynamic properties of asphalt mixture were captured by implementing Burger’s contact model. Different ways of taking into account of the normal and shear material properties of asphalt mi...
Bokhove, O.
2003-01-01
Free boundaries in shallow-water equations demarcate the time-dependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous finite element discretization of the one-dimensional or symm
Boutt, D. F.; McPherson, B. J.
2001-12-01
The micromechanics of sedimentary rock deformation are a fundamental aspect of many research fields, ranging from geotechnical engineering to petroleum recovery and hazardous waste disposal. Laboratory triaxial tests yield information concerning macroscopic behaviors but are not capable of quantifying micromechanical processes such as microcracking and localization. Thus, to quantify micromechanical processes we employed the discrete element method (DEM) of rock deformation, calibrated with triaxial test results. This DEM simulates rock using rigid disc shaped particles bonded at contacts between particles. Previous studies demonstrated that this type of DEM can qualitatively and quantitatively mimic macroscopic behaviors of triaxial tests. An important conclusion of these studies is that a number of particles must be bonded together with higher bond strengths than the surrounding particles to achieve a steeper strength envelope of rocks. This process, termed clustering, is the focus of this study. We hypothesize that since clusters posses a more complicated geometry, they may increase failure strength at elevated confining pressures by interlocking and creating a higher apparent friction. An alternative hypothesis is that the clusters change force chain development by allowing chains to persist longer in specimens. This ultimately causes failure to occur at higher strengths compared to unclustered material. A systematic study comparing effects of cluster shape, particle friction, and force chain development was undertaken. Several model simulations with various cluster shapes and sizes were compared with each other as well as single particle models with high friction coefficients (>1). Preliminary results suggest that the organization of the particle clusters play a key role in increasing the strength envelope. Particle friction coefficients needed to increase slopes of the strength envelopes are well beyond those of geological materials measured in the laboratory
Yeom, Seungcheol; Sjoblom, Kurt
2016-12-01
The mechanical nature of crust formation as a result of raindrop impacts was simulated within a discrete element modeling environment. Simulations were conducted in two-dimensions (2D) using both linear and non-linear elastic contact models. The 2D approach was found to minimize the computational effort required and maximize the number of particles in the soil profile. For the non-linear model, the effect of the coefficient of restitution (COR) for soil-rain and soil-soil was investigated. Finally, the comparison between the linear and nonlinear elastic contact model was presented. The simulation indicated that the COR for rain-soil had negligible effect on the crust development but the computational time was exponentially increased with increasing coefficient value. In contrast, the COR for soil-soil had a dominant influence on the crust development. To validate the numerical results, a micro computerized tomography (microCT) technique was applied to characterize the changes in pore structure to a USCS SP soil after exposure under a rainfall simulator. Additionally, the effect of cyclic wetting and drying (without rainfall) on the changes in porosity was investigated. The experimental results showed that the rainfall simulator sufficiently densified the soil but the effect of cyclic wetting and drying was negligible. The numerical simulations showed similar changes in porosity along the depth of the soil profile as compared with the experimental results thus validating the DEM technique to simulate crust development.
Discrete element method analysis of lateral resistance of fouled ballast bed
Institute of Scientific and Technical Information of China (English)
徐旸; 高亮; 张艳荣; 尹辉; 蔡小培
2016-01-01
The lateral resistance of sleeper plays an important role in ensuring the stability of a railway track, which may change in the operation of railway, due to the fouling in the ballast bed. In this work, discrete element method was adopted to investigate the effect of fouling on the lateral resistance of sleeper. The shape information of ballast was captured by method of three-dimensional vision reconstruction. In order to calibrate the mechanical parameters and verify the models, a lateral resistance field test was carried out by using a custom-made device. The contact force distributions in the different parts of sleeper as well as the interaction between ballast and sleeper were discussed in depth. The results show that fouling of ballast bed evidently reduces the lateral resistance of sleeper and the decreasing degree is also related to the fouled position of ballast bed, in the order of shoulder > bottom > side. Therefore, the effect of fouling, especially the fouling in the ballast shoulder, on the lateral resistance of sleeper, should be taken into account in ballast track maintenance work.
Sun, Zhuang; Espinoza, D. Nicolas; Balhoff, Matthew T.
2016-11-01
During CO2 injection into geological formations, petrophysical and geomechanical properties of host formations can be altered due to mineral dissolution and precipitation. Field and laboratory results have shown that sandstone and siltstone can be altered by CO2-water mixtures, but few quantitative studies have been performed to fully investigate underlying mechanisms. Based on the hypothesis that CO2-water mixtures alter the integrity of rock structure by attacking cements rather than grains, we attempt to explain the degradation of cementation due to long-term contact with CO2 and water and mechanisms for changes in rock mechanical properties. Many sandstones, including calcite-cemented quartzitic sandstone, chlorite-cemented quartzitic sandstone, and hematite-cemented quartzitic sandstone, contain interparticle cements that are more readily affected by CO2-water mixtures than grains. A model that couples the discrete element method and the bonded-particle model is used to perform simulations of indentation tests on synthetic rocks with crystal and random packings. The model is verified against the analytical cavity expansion model and validated against laboratory indentation tests on Entrada sandstone with and without CO2 alteration. Sensitivity analysis is performed for cementation microscopic parameters including stiffness, size, axial, and shear strength. The simulation results indicate that the CO2-related degradation of mechanical properties in bleached Entrada sandstone can be attributed to the reduction of cement size rather than cement strength. Our study indicates that it is possible to describe the CO2-related rock alteration through particle-scale mechanisms.
Yan, Zilin; Wilkinson, Sam K; Stitt, Edmund H; Marigo, Michele
2016-11-20
Mixing and segregation in a Freeman FT4 powder rheometer, using binary mixtures with varied particle size ratio and volume fraction, were studied using the Discrete Element Method (DEM). As the blade moves within the particle bed, size induced segregations can occur via a sifting mechanism. A larger particle size ratio and/or a larger volume fraction of large particles lead to a quicker segregation process. A higher particle velocity magnitude can promote the segregation process and the rate for the segregation index increases in the radial direction: from the centre towards the outer layer. In the current DEM simulations, it is shown that the change in flow energy associated with segregation and mixing depends on the choice of frictional input parameters. FT4 is proposed as a potential tool to compare and rank the segregation tendency for particulate materials with distinct differences in flow energy of each component. This is achieved by measuring the flow energy gradient after a number of test cycles for mixing powders with different flow properties. Employing the FT4 dynamic powder characterisation can be advantageous to establish blending performances in an industrial context.
Yushi, Zou; Xinfang, Ma; Tong, Zhou; Ning, Li; Ming, Chen; Sihai, Li; Yinuo, Zhang; Han, Li
2017-09-01
Hydraulic fracture (HF) height containment tends to occur in layered formations, and it significantly influences the entire HF geometry or the stimulated reservoir volume. This study aims to explore the influence of preexisting bedding planes (BPs) on the HF height growth in layered formations. Laboratory fracturing experiments were performed to confirm the occurrence of HF height containment in natural shale that contains multiple weak and high-permeability BPs under triaxial stresses. Numerical simulations were then conducted to further illustrate the manner in which vertical stress, BP permeability, BP density(or spacing), pump rate, and fluid viscosity control HF height growth using a 3D discrete element method-based fracturing model. In this model, the rock matrix was considered transversely isotropic and multiple BPs can be explicitly represented. Experimental and numerical results show that the vertically growing HF tends to be limited by multi-high-permeability BPs, even under higher vertical stress. When the vertically growing HF intersects with the multi-high-permeability BPs, the injection pressure will be sharply reduced. If a low pumping rate or a low-viscosity fluid is used, the excess fracturing fluid leak-off into the BPs obviously decreases the rate of pressure build up, which will then limit the growth of HF. Otherwise, a higher pumping rate and/or a higher viscosity will reduce the leak-off time and fluid volume, but increase the injection pressure to drive the HF to grow and to penetrate through the BPs.
Coupled Large Eddy Simulation and Discrete Element Model for Particle Saltation
Liu, X.; Liu, D.; Fu, X.
2016-12-01
Particle saltation is the major mode of motion for sediment transport. The quantification of the characteristics of saltation, either as an individual particle or as a group, is of great importance to our understanding of the transport process. In the past, experiments and numerical models have been performed to study the saltation length, height, and velocity under different turbulent flow and rough bed conditions. Most previous numerical models have very restrictive assumptions. For example, many models assumed Log-law flow velocity profiles to drive the motion of particles. Others assumed some "splash-function" which assigns the reflection angle for the rebounding of the saltating particle after each collision with bed. This research aims to relax these restrictions by a coupled eddy-resolving flow solver and a discrete element model. The model simulates the fully four-way coupling among fluid, particles, and wall. The model is extensively validated on both the turbulent flow field and saltation statistics. The results show that the two controlling factors for particle saltation are turbulent fluctuations and bed collision. Detailed quantification of these two factors will be presented. Through the statistics of incidence reflection angles, a more physical "splash-function" is obtained in which the reflection angle follows an asymmetric bimodal distribution for a given incidence angle. The higher mode is always located on the upstream side of the bed particle, while the lower one is always on the downstream surface.
Optimizing the Pipe Diameter of the Pipe Belt Conveyor Based on Discrete Element Method
Guo, Yong-cun; Wang, Shuang; Hu, Kun; Li, De-yong
2016-03-01
In order to increase the transport volume of the pipe belt conveyor and reduce lateral pressure of the supporting roller set, this study aims to optimize the pipe diameter of the pipe belt conveyor. A mechanical model of the pipe belt conveyor with six supporting roller sets in the belt bearing section was built based on the infinitesimal method, and the formula for calculating the lateral pressure of each supporting roller was deduced on the basis of reasonable assumption. Simulated analysis was carried out on the operation process of the pipe belt conveyor by using the discrete element method. The result showed that, when the other conditions were certain, as the pipe diameter increased, the average lateral pressure of the supporting roller set increased, with a gradually decreasing increment, which was consistent with the calculated result of the theoretical formula. An optimized pipe diameter under the current conditions was obtained by fitting the curve of the formula for calculating the transport volume of the pipe belt conveyor and its simulation curve. It provided a certain reference value for improving the transport efficiency and prolonging the service life of the pipe belt conveyor.
Directory of Open Access Journals (Sweden)
Maitraye Sen
2017-04-01
Full Text Available A discrete element model (DEM has been developed for an industrial batch bin blender in which three different types of materials are mixed. The mixing dynamics have been evaluated from a model-based study with respect to the blend critical quality attributes (CQAs which are relative standard deviation (RSD and segregation intensity. In the actual industrial setup, a sensor mounted on the blender lid is used to determine the blend composition in this region. A model-based analysis has been used to understand the mixing efficiency in the other zones inside the blender and to determine if the data obtained near the blender-lid region are able to provide a good representation of the overall blend quality. Sub-optimal mixing zones have been identified and other potential sampling locations have been investigated in order to obtain a good approximation of the blend variability. The model has been used to study how the mixing efficiency can be improved by varying the key processing parameters, i.e., blender RPM/speed, fill level/volume and loading order. Both segregation intensity and RSD reduce at a lower fill level and higher blender RPM and are a function of the mixing time. This work demonstrates the use of a model-based approach to improve process knowledge regarding a pharmaceutical mixing process. The model can be used to acquire qualitative information about the influence of different critical process parameters and equipment geometry on the mixing dynamics.
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Institute of Scientific and Technical Information of China (English)
Qi Zhao; Andrea Lisjak; Omid Mahabadi; Qinya Liu; Giovanni Grasselli
2014-01-01
Hydraulic fracturing (HF) technique has been extensively used for the exploitation of unconventional oil and gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formations by fluid injection, which creates an interconnected fracture network and increases the hydrocarbon production. Meanwhile, microseismic (MS) monitoring is one of the most effective approaches to eval-uate such stimulation process. In this paper, the combined finite-discrete element method (FDEM) is adopted to numerically simulate HF and associated MS. Several post-processing tools, including frequency-magnitude distribution (b-value), fractal dimension (D-value), and seismic events clustering, are utilized to interpret numerical results. A non-parametric clustering algorithm designed specifically for FDEM is used to reduce the mesh dependency and extract more realistic seismic information. Simulation results indicated that at the local scale, the HF process tends to propagate following the rock mass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to the maximum in-situ stress.
Energy Technology Data Exchange (ETDEWEB)
Herrmann, K.P. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik; Mueller, W.H. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mechanical and Chemical Engineering; Neumann, S. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik
2001-07-01
The objective of our contribution is to present the discrete Fouriertransformation (DFT) as a serious alternative for the numerical computation of local stresses and strains in a two dimensional representative volume element (RVE) containing heterogeneities of complex shape and high volume fractions. The methodology is based on the application of the so-called ''equivalent inclusion method'' (Mura 1987). This method is used to devolve the original problem onto the determination of an auxiliary strain field which is related to the stresses by virtue of a spatially constant auxiliary stiffness tensor. The resulting partial differential equations (PDE) are firstly approximated by difference schemes leading to a linear system of equations (LSE) to solve. Two different types of difference schemes for an approximation are presented, a 9-pixelstar which is well-known in this context and a new one which uses 21 pixel for the numerical approach in order to increase the quality of the numerical solution. In a second step the DFT has been used which allows to solve the LSE analytically, obtaining a functional relation for the auxiliary strain field. Finally the solution of this equation is determined approximately by virtue of a Neumann iteration procedure. Different heterogeneity problems are considered where the accuracy of both difference stars is checked by existing analytical solutions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [Universiyt of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind
2015-10-01
The interaction between hydraulic fractures (HF) and natural fractures (NF) will lead to complex fracture networks due to the branching and merging of natural and hydraulic fractures in unconventional reservoirs. In this paper, a newly developed hydraulic fracturing simulator based on discrete element method is used to predict the generation of complex fracture network in the presence of pre-existing natural fractures. By coupling geomechanics and reservoir flow within a dual lattice system, this simulator can effectively capture the poro-elastic effects and fluid leakoff into the formation. When HFs are intercepting single or multiple NFs, complex mechanisms such as direct crossing, arresting, dilating and branching can be simulated. Based on the model, the effects of injected fluid rate and viscosity, the orientation and permeability of NFs and stress anisotropy on the HF-NF interaction process are investigated. Combined impacts from multiple parameters are also examined in the paper. The numerical results show that large values of stress anisotropy, intercepting angle, injection rate and viscosity will impede the opening of NFs.
Nye, Ben; Kulchitsky, Anton V; Johnson, Jerome B
2014-01-01
This paper describes a new method for representing concave polyhedral particles in a discrete element method as unions of convex dilated polyhedra. This method offers an efficient way to simulate systems with a large number of (generally concave) polyhedral particles. The method also allows spheres, capsules, and dilated triangles to be combined with polyhedra using the same approach. The computational efficiency of the method is tested in two different simulation setups using different efficiency metrics for seven particle types: spheres, clusters of three spheres, clusters of four spheres, tetrahedra, cubes, unions of two octahedra (concave), and a model of a computer tomography scan of a lunar simulant GRC-3 particle. It is shown that the computational efficiency of the simulations degrades much slower than the increase in complexity of the particles in the system. The efficiency of the method is based on the time coherence of the system, and an efficient and robust distance computation method between polyhedra as particles never intersect for dilated particles. PMID:26300584
Discrete Element Method simulations of the saturation of aeolian sand transport
Pähtz, Thomas; Carneiro, Marcus V; Araújo, Nuno A M; Herrmann, Hans J
2015-01-01
The saturation length of aeolian sand transport ($L_s$), characterizing the distance needed by wind-blown sand to adapt to changes in the wind shear, is essential for accurate modeling of the morphodynamics of Earth's sandy landscapes and for explaining the formation and shape of sand dunes. In the last decade, it has become a widely-accepted hypothesis that $L_s$ is proportional to the characteristic distance needed by transported particles to reach the wind speed (the ``drag length''). Here we challenge this hypothesis. From extensive numerical Discrete Element Method simulations, we find that, for medium and strong winds, $L_s\\propto V_s^2/g$, where $V_s$ is the saturated value of the average speed of sand particles traveling above the surface and $g$ the gravitational constant. We show that this proportionality is consistent with a recent analytical model, in which the drag length is just one of four similarly important length scales relevant for sand transport saturation.
Discrete element simulation of charging and mixed layer formation in the ironmaking blast furnace
Mitra, Tamoghna; Saxén, Henrik
2016-11-01
The burden distribution in the ironmaking blast furnace plays an important role for the operation as it affects the gas flow distribution, heat and mass transfer, and chemical reactions in the shaft. This work studies certain aspects of burden distribution by small-scale experiments and numerical simulation by the discrete element method (DEM). Particular attention is focused on the complex layer-formation process and the problems associated with estimating the burden layer distribution by burden profile measurements. The formation of mixed layers is studied, and a computational method for estimating the extent of the mixed layer, as well as its voidage, is proposed and applied on the results of the DEM simulations. In studying a charging program and its resulting burden distribution, the mixed layers of coke and pellets were found to show lower voidage than the individual burden layers. The dynamic evolution of the mixed layer during the charging process is also analyzed. The results of the study can be used to gain deeper insight into the complex charging process of the blast furnace, which is useful in the design of new charging programs and for mathematical models that do not consider the full behavior of the particles in the burden layers.
Discrete-element model for the interaction between ocean waves and sea ice.
Xu, Zhijie; Tartakovsky, Alexandre M; Pan, Wenxiao
2012-01-01
We present a discrete-element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice potentially can lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice explicitly is modeled by a DEM method where sea ice is modeled by densely packed spherical particles with finite sizes. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing naturally can be represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean waves, the model provides information for the spatial distribution and time evolution of stress and microfractures and the fragment size distribution. We demonstrate that the fraction of broken bonds α increases with increasing wave amplitude. In contrast, the ice fragment size l decreases with increasing amplitude. This information is important for the understanding of the breakup of individual ice floes and floe fragment size.
Maxwell, R; Ata, S; Wanless, E J; Moreno-Atanasio, R
2012-09-01
Three dimensional Discrete Element Method (DEM) computer simulations have been carried out to analyse the kinetics of collision of multiple particles against a stationary bubble and the sliding of the particles over the bubble surface. This is the first time that a computational analysis of the sliding time and particle packing arrangements of multiple particles on the surface of a bubble has been carried out. The collision kinetics of monodisperse (33 μm in radius) and polydisperse (12-33 μm in radius) particle systems have been analysed in terms of the time taken by 10%, 50% and 100% of the particles to collide against the bubble. The dependencies of these collision times on the strength of hydrophobic interactions follow relationships close to power laws. However, minimal sensitivity of the collision times to particle size was found when linear and square relationships of the hydrophobic force with particles radius were considered. The sliding time for single particles has corroborated published theoretical expressions. Finally, a good qualitative comparison with experiments has been observed with respect to the particle packing at the bottom of the bubble after sliding demonstrating the usefulness of computer simulations in the studies of particle-bubble systems.
Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design
Deng, Zongquan; Cui, Jinsheng; Hou, Xuyan; Jiang, Shengyuan
2017-03-01
The efficiency and precision of parameter calibration in discrete element method (DEM) are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity (ETC) of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design (CCD) is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.
Parallel computing of discrete element method on multi-core processors
Institute of Scientific and Technical Information of China (English)
Yusuke Shigeto; Mikio Sakai
2011-01-01
This paper describes parallel simulation techniques for the discrete element method (DEM) on multi-core processors.Recently,multi-core CPU and GPU processors have attracted much attention in accelerating computer simulations in various fields.We propose a new algorithm for multi-thread parallel computation of DEM,which makes effective use of the available memory and accelerates the computation.This study shows that memory usage is drastically reduced by using this algorithm.To show the practical use of DEM in industry,a large-scale powder system is simulated with a complicated drive unit.We compared the performance of the simulation between the latest GPU and CPU processors with optimized programs for each processor.The results show that the difference in performance is not substantial when using either GPUs or CPUs with a multi-thread parallel algorithm.In addition,DEM algorithm is shown to have high scalability in a multi-thread parallel computation on a CPU.
Numerical sedimentation particle-size analysis using the Discrete Element Method
Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.
2015-12-01
Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.
Discrete element modeling of sand behavior in a biaxial shear test
Institute of Scientific and Technical Information of China (English)
Zhi-yi HUANG; Zhong-xuan YANG; Zhen-yu WANG
2008-01-01
The mechanical behavior of sand is very complex,and depends on factors including confining pressure,density,and drainage condition.A soil mass Call be contractive or dilative when subjected to shear loading,and eventually reaches an ultimate state,referred to as the critical state in soil mechanics.Conventional approach to explore the mechanical behavior of sand mainly relies on the experimental tests in laboratory.This paper gives an alternative view to this subject using discrete element method (DEM),which has attracted much attention in recent years.The implementation of the DEM is carried out by a series of numerical tests on granular assemblies with varying initial densities and confining pressures,under different test configurations.The results demonstrate that such numerical simulations can produce correct responses of the sand behavior in general,including the critical state response,as compared to experimental observations.In addition,the DEM can further provide details of the microstructure evolutions during shearing processes,and the resulting induced anisotropy can be fully captured and quantified in the particle scale.
Dry granular avalanche down a flume: Choice of discrete element simulation parameters
Yang, F.-L.; Chang, W. T.; Huang, Y. T.; Hsieh, S. H.; Chen, C. S.
2013-12-01
This paper presents a method to assign soft-sphere contact model parameters in a discrete-element simulation with which we can reproduce the experimentally measured avalanche dynamics of finite dry granular mass down a flume. We adopt the simplest linear model in which interaction force is decomposed along or tangent to the contact normal. The model parameters are chosen uniquely to satisfy theoretical models or to meet experimental evidences at either the particle or the bulk size level. The normal mode parameters are chosen specifically to ensure Hertzian contact time (but not its force-displacement history) and the resulting loss of particle kinetic energy, characterized by a measured coefficient of restitution, for each pair of colliding surfaces. We follow the literature to assign the tangential spring constant according to an elasticity model but propose a method to assign the friction coefficient using a measured bulk property that characterizes the bulk discharge volume flow rate. The linear contact model with the assigned parameters are evaluated by comparing the simulated bulk avalanche dynamics down three slopes to the experimental data, including instantaneous particle trajectories and bulk unsteady velocity profile. Satisfying quantitative agreement can be obtained except at the free surface and the early-time front propagation velocity.
High-speed laminar-turbulent boundary layer transition induced by a discrete roughness element
Iyer, Prahladh; Mahesh, Krishnan
2013-11-01
Direct numerical simulation (DNS) is used to study laminar to turbulent transition induced by a discrete hemispherical roughness element in a high-speed laminar boundary layer. The simulations are performed under conditions matching the experiments of Danehy et al. (AIAA Paper 2009-394, 2009) for free-stream Mach numbers of 3.37, 5.26 and 8.23. It is observed that the Mach 8.23 flow remains laminar downstream of the roughness, while the lower Mach numbers undergo transition. The Mach 3.37 flow undergoes transition closer to the bump when compared with Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in Cf and Ch (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in Cf until 20 D downstream. The mean van Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 show good agreement with available data. A local Reynolds number based on the wall properties is seen to correlate with the onset of transition for the cases considered. Partially supported by NASA.
A discrete element based simulation framework to investigate particulate spray deposition processes
Mukherjee, Debanjan
2015-06-01
© 2015 Elsevier Inc. This work presents a computer simulation framework based on discrete element method to analyze manufacturing processes that comprise a loosely flowing stream of particles in a carrier fluid being deposited on a target surface. The individual particulate dynamics under the combined action of particle collisions, fluid-particle interactions, particle-surface contact and adhesive interactions is simulated, and aggregated to obtain global system behavior. A model for deposition which incorporates the effect of surface energy, impact velocity and particle size, is developed. The fluid-particle interaction is modeled using appropriate spray nozzle gas velocity distributions and a one-way coupling between the phases. It is found that the particle response times and the release velocity distribution of particles have a combined effect on inter-particle collisions during the flow along the spray. It is also found that resolution of the particulate collisions close to the target surface plays an important role in characterizing the trends in the deposit pattern. Analysis of the deposit pattern using metrics defined from the particle distribution on the target surface is provided to characterize the deposition efficiency, deposit size, and scatter due to collisions.
Directory of Open Access Journals (Sweden)
Qi Zhao
2014-12-01
Full Text Available Hydraulic fracturing (HF technique has been extensively used for the exploitation of unconventional oil and gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formations by fluid injection, which creates an interconnected fracture network and increases the hydrocarbon production. Meanwhile, microseismic (MS monitoring is one of the most effective approaches to evaluate such stimulation process. In this paper, the combined finite-discrete element method (FDEM is adopted to numerically simulate HF and associated MS. Several post-processing tools, including frequency-magnitude distribution (b-value, fractal dimension (D-value, and seismic events clustering, are utilized to interpret numerical results. A non-parametric clustering algorithm designed specifically for FDEM is used to reduce the mesh dependency and extract more realistic seismic information. Simulation results indicated that at the local scale, the HF process tends to propagate following the rock mass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to the maximum in-situ stress.
Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures
Directory of Open Access Journals (Sweden)
Behzad Majidi
2016-05-01
Full Text Available Rheological properties of pitch and pitch/coke mixtures at temperatures around 150 °C are of great interest for the carbon anode manufacturing process in the aluminum industry. In the present work, a cohesive viscoelastic contact model based on Burger’s model is developed using the discrete element method (DEM on the YADE, the open-source DEM software. A dynamic shear rheometer (DSR is used to measure the viscoelastic properties of pitch at 150 °C. The experimental data obtained is then used to estimate the Burger’s model parameters and calibrate the DEM model. The DSR tests were then simulated by a three-dimensional model. Very good agreement was observed between the experimental data and simulation results. Coke aggregates were modeled by overlapping spheres in the DEM model. Coke/pitch mixtures were numerically created by adding 5, 10, 20, and 30 percent of coke aggregates of the size range of 0.297–0.595 mm (−30 + 50 mesh to pitch. Adding up to 30% of coke aggregates to pitch can increase its complex shear modulus at 60 Hz from 273 Pa to 1557 Pa. Results also showed that adding coke particles increases both storage and loss moduli, while it does not have a meaningful effect on the phase angle of pitch.
Directory of Open Access Journals (Sweden)
Spyridon Liakas
2017-08-01
Full Text Available The particulate discrete element method (DEM can be employed to capture the response of rock, provided that appropriate bonding models are used to cement the particles to each other. Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors. Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional (2D models. In situ rock formations are often heterogeneous, thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis. In situ stress states are basically three-dimensional (3D, and therefore it is important to develop 3D models for this purpose. This paper revisits an earlier experimental study on heterogeneous specimens, of which the relative proportions of weaker material (siltstone and stronger, harder material (sandstone were varied in a controlled manner. Using a 3D DEM model with the parallel bond model, virtual heterogeneous specimens were created. The overall responses in terms of variations in strength and stiffness with different percentages of weaker material (siltstone were shown to agree with the experimental observations. There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations, suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
Borehole Breakouts Induced in Arkosic Sandstones and a Discrete Element Analysis
Lee, H.; Moon, T.; Haimson, B. C.
2016-04-01
A series of laboratory drilling experiments were conducted on two arkosic sandstones (Tenino and Tablerock) under polyaxial far-field stress conditions (σ h ≠ σ H ≠ σ v ). V-shaped breakouts, aligned with the σ h direction and revealing stress-dependent dimensions (width and length), were observed in the sandstones. The microscale damage pattern leading to the breakouts, however, is different between the two, which is attributed to the difference in their cementation. The dominant micromechanism in Tenino sandstone is intergranular microcracking occurring in clay minerals filling the spaces between clastic grains. On the other hand, intra- and transgranular microcracking taking place in the grain itself prevails in Tablerock sandstone. To capture the grain-scale damage and reproduce the failure localization observed around the borehole in the laboratory, we used a discrete element (DE) model in which a grain breakage algorithm was implemented. The microparameters needed in the numerical model were calibrated by running material tests and comparing the macroscopic responses of the model to the ones measured in the laboratory. It is shown that DE modeling is capable of simulating the microscale damage of the rock and replicating the localized damage zone observed in the laboratory. In addition, the numerically induced breakout width is determined at a very early stage of the damage localization and is not altered for the rest of the failure process.
Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations
Institute of Scientific and Technical Information of China (English)
Christoph R. Müller; Daniel J. Holland; James R. Third; Andrew J. Sederman; John S. Dennis; Lynn F. Gladden
2011-01-01
This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and twophase granular systems,such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes.The unique capability of MR to not only image the solids' distribution (voidage) but also the velocity of the particulate phase is clearly shown,it is demonstrated that MR can provide measurements over different length and time scales.With the MR equipment used for the studies summarized here,temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres,respectively.Besides providing crucial data required for an improved understanding of the underlying physics of granular flows,multi-scale MR measurements were also used to validate numerical simulations of granular systems.It is shown that predictions of time-averaged properties,such as voidage and velocity of the particulate phase,made using the Discrete Element Model agree very well with MR measurements.
Simulation of growth normal fault sandbox tests using the 2D discrete element method
Chu, Sheng-Shin; Lin, Ming-Lang; Huang, Wen-Chao; Nien, Wei-Tung; Liu, Huan-Chi; Chan, Pei-Chen
2015-01-01
A fault slip can cause the deformation of shallow soil layers and destroy infrastructures. The Shanchiao Fault on the west side of the Taipei Basin is one such fault. The activities of the Shanchiao Fault have caused the quaternary sediment beneath the Taipei Basin to become deformed, damaging structures, traffic construction, and utility lines in the area. Data on geological drilling and dating have been used to determine that a growth fault exists in the Shanchiao Fault. In an experiment, a sandbox model was built using noncohesive sandy soil to simulate the existence of a growth fault in the Shanchiao Fault and forecast the effect of the growth fault on shear-band development and ground differential deformation. The experimental results indicated that when a normal fault contains a growth fault at the offset of the base rock, the shear band develops upward beside the weak side of the shear band of the original-topped soil layer, and surfaces considerably faster than that of the single-topped layer. The offset ratio required is approximately one-third that of the single-cover soil layer. In this study, a numerical simulation of the sandbox experiment was conducted using a discrete element method program, PFC2D, to simulate the upper-covering sand layer shear-band development pace and the scope of a growth normal fault slip. The simulation results indicated an outcome similar to that of the sandbox experiment, which can be applied to the design of construction projects near fault zones.
Modeling reservoir geomechanics using discrete element method : Application to reservoir monitoring
Energy Technology Data Exchange (ETDEWEB)
Alassi, Haitham Tayseer
2008-09-15
Understanding reservoir geomechanical behavior is becoming more and more important for the petroleum industry. Reservoir compaction, which may result in surface subsidence and fault reactivation, occurs during reservoir depletion. Stress changes and possible fracture development inside and outside a depleting reservoir can be monitored using time-lapse (so-called '4D') seismic and/or passive seismic, and this can give valuable information about the conditions of a given reservoir during production. In this study we will focus on using the (particle-based) Discrete Element Method (DEM) to model reservoir geomechanical behavior during depletion and fluid injection. We show in this study that DEM can be used in modeling reservoir geomechanical behavior by comparing results obtained from DEM to those obtained from analytical solutions. The match of the displacement field between DEM and the analytical solution is good, however there is mismatch of the stress field which is related to the way stress is measured in DEM. A good match is however obtained by measuring the stress field carefully. We also use DEM to model reservoir geomechanical behavior beyond the elasticity limit where fractures can develop and faults can reactivate. A general technique has been developed to relate DEM parameters to rock properties. This is necessary in order to use correct reservoir geomechanical properties during modeling. For any type of particle packing there is a limitation that the maximum ratio between P- and S-wave velocity Vp/Vs that can be modeled is 3 . The static behavior for a loose packing is different from the dynamic behavior. Empirical relations are needed for the static behavior based on numerical test observations. The dynamic behavior for both dense and loose packing can be given by analytical relations. Cosserat continuum theory is needed to derive relations for Vp and Vs. It is shown that by constraining the particle rotation, the S-wave velocity can be
Coupled large eddy simulation and discrete element model of bedload motion
Furbish, D.; Schmeeckle, M. W.
2011-12-01
We combine a three-dimensional large eddy simulation of turbulence to a three-dimensional discrete element model of turbulence. The large eddy simulation of the turbulent fluid is extended into the bed composed of non-moving particles by adding resistance terms to the Navier-Stokes equations in accordance with the Darcy-Forchheimer law. This allows the turbulent velocity and pressure fluctuations to penetrate the bed of discrete particles, and this addition of a porous zone results in turbulence structures above the bed that are similar to previous experimental and numerical results for hydraulically-rough beds. For example, we reproduce low-speed streaks that are less coherent than those over smooth-beds due to the episodic outflow of fluid from the bed. Local resistance terms are also added to the Navier-Stokes equations to account for the drag of individual moving particles. The interaction of the spherical particles utilizes a standard DEM soft-sphere Hertz model. We use only a simple drag model to calculate the fluid forces on the particles. The model reproduces an exponential distribution of bedload particle velocities that we have found experimentally using high-speed video of a flat bed of moving sand in a recirculating water flume. The exponential distribution of velocity results from the motion of many particles that are nearly constantly in contact with other bed particles and come to rest after short distances, in combination with a relatively few particles that are entrained further above the bed and have velocities approaching that of the fluid. Entrainment and motion "hot spots" are evident that are not perfectly correlated with the local, instantaneous fluid velocity. Zones of the bed that have recently experienced motion are more susceptible to motion because of the local configuration of particle contacts. The paradigm of a characteristic saltation hop length in riverine bedload transport has infused many aspects of geomorphic thought, including
Directory of Open Access Journals (Sweden)
Haitao Cao
2014-01-01
Full Text Available We propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM, a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by C0 piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards’ equation to show the efficiency and accuracy of the proposed method.
A parallel Discrete Element Method to model collisions between non-convex particles
Rakotonirina, Andriarimina Daniel; Delenne, Jean-Yves; Wachs, Anthony
2017-06-01
In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called "glued-convex method" (in the sense clumping convex bodies together), as an extension of the popular "glued-spheres" method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor.
Modeling of crack propagation in weak snowpack layers using the discrete element method
Directory of Open Access Journals (Sweden)
J. Gaume
2015-01-01
Full Text Available Dry-snow slab avalanches are generally caused by a sequence of fracture processes including (1 failure initiation in a weak snow layer underlying a cohesive slab, (2 crack propagation within the weak layer and (3 tensile fracture through the slab which leads to its detachment. During the past decades, theoretical and experimental work has gradually led to a better understanding of the fracture process in snow involving the collapse of the structure in the weak layer during fracture. This now allows us to better model failure initiation and the onset of crack propagation, i.e. to estimate the critical length required for crack propagation. On the other hand, our understanding of dynamic crack propagation and fracture arrest propensity is still very limited. For instance, it is not uncommon to perform field measurements with widespread crack propagation on one day, while a few days later, with very little changes to the snowpack, crack propagation does not occur anymore. Thus far, there is no clear theoretical framework to interpret such observations, and it is not clear how and which snowpack properties affect dynamic crack propagation. To shed more light on this issue, we performed numerical propagation saw test (PST experiments applying the discrete element (DE method and compared the numerical results with field measurements based on particle tracking. The goal is to investigate the influence of weak layer failure and the mechanical properties of the slab on crack propagation and fracture arrest propensity. Crack propagation speeds and distances before fracture arrest were derived from the DE simulations for different snowpack configurations and mechanical properties. Then, the relation between mechanical parameters of the snowpack was taken into account so as to compare numerical and experimental results, which were in good agreement, suggesting that the simulations can reproduce crack propagation in PSTs. Finally, an in-depth analysis of the
Investigation of Crack Propagation in Rock using Discrete Sphero-Polyhedral Element Method
Behraftar, S.; Galindo-torres, S. A.; Scheuermann, A.; Li, L.; Williams, D.
2014-12-01
In this study a micro-mechanical model is developed to study the fracture propagation process in rocks. The model is represented by an array of bonded particles simulated by the Discrete Sphero-Polyhedral Element Model (DSEM), which was introduced by the authors previously and has been shown to be a suitable technique to model rock [1]. It allows the modelling of particles of general shape, with no internal porosity. The motivation behind using this technique is the desire to microscopically investigate the fracture propagation process and study the relationship between the microscopic and macroscopic behaviour of rock. The DSEM method is used to model the Crack Chevron Notch Brazilian Disc (CCNBD) test suggested by the International Society of Rock Mechanics (ISRM) for determining the fracture toughness of rock specimens. CCNBD samples with different crack inclination angles, are modelled to investigate their fracture mode. The Crack Mouth Opening Displacement (CMOD) is simulated and the results are validated using experimental results obtained from a previous study [2]. Fig. 1 shows the simulated and experimental results of crack propagation for different inclination angles of CCNBD specimens. The DSEM method can be used to predict crack trajectory and quantify crack propagation during loading. References: 1. Galindo-Torres, S. A., et al. "Breaking processes in three-dimensional bonded granular materials with general shapes." Computer Physics Communications 183.2 (2012): 266-277. 2. Erarslan, N., and D. J. Williams. "Mixed-mode fracturing of rocks under static and cyclic loading." Rock mechanics and rock engineering 46.5 (2013): 1035-1052.
Coupled discrete element modeling of fluid injection into dense granular media
Zhang, Fengshou; Damjanac, Branko; Huang, Haiying
2013-06-01
The coupled displacement process of fluid injection into a dense granular medium is investigated numerically using a discrete element method (DEM) code PFC2D® coupled with a pore network fluid flow scheme. How a dense granular medium behaves in response to fluid injection is a subject of fundamental and applied research interests to better understand subsurface processes such as fluid or gas migration and formation of intrusive features as well as engineering applications such as hydraulic fracturing and geological storage in unconsolidated formations. The numerical analysis is performed with DEM executing the mechanical calculation and the network model solving the Hagen-Poiseuille equation between the pore spaces enclosed by chains of particles and contacts. Hydromechanical coupling is realized by data exchanging at predetermined time steps. The numerical results show that increase in the injection rate and the invading fluid viscosity and decrease in the modulus and permeability of the medium result in fluid flow behaviors displaying a transition from infiltration-governed to infiltration-limited and the granular medium responses evolving from that of a rigid porous medium to localized failure leading to the development of preferential paths. The transition in the fluid flow and granular medium behaviors is governed by the ratio between the characteristic times associated with fluid injection and hydromechanical coupling. The peak pressures at large injection rates when fluid leakoff is limited compare well with those from the injection experiments in triaxial cells in the literature. The numerical analysis also reveals intriguing tip kinematics field for the growth of a fluid channel, which may shed light on the occurrence of the apical inverted-conical features in sandstone and magma intrusion in unconsolidated formations.
Fish Passage though Hydropower Turbines: Simulating Blade Strike using the Discrete Element Method
Energy Technology Data Exchange (ETDEWEB)
Richmond, Marshall C.; Romero Gomez, Pedro DJ
2014-12-08
mong the hazardous hydraulic conditions affecting anadromous and resident fish during their passage though turbine flows, two are believed to cause considerable injury and mortality: collision on moving blades and decompression. Several methods are currently available to evaluate these stressors in installed turbines, i.e. using live fish or autonomous sensor devices, and in reduced-scale physical models, i.e. registering collisions from plastic beads. However, a priori estimates with computational modeling approaches applied early in the process of turbine design can facilitate the development of fish-friendly turbines. In the present study, we evaluated the frequency of blade strike and nadir pressure environment by modeling potential fish trajectories with the Discrete Element Method (DEM) applied to fish-like composite particles. In the DEM approach, particles are subjected to realistic hydraulic conditions simulated with computational fluid dynamics (CFD), and particle-structure interactions—representing fish collisions with turbine blades—are explicitly recorded and accounted for in the calculation of particle trajectories. We conducted transient CFD simulations by setting the runner in motion and allowing for better turbulence resolution, a modeling improvement over the conventional practice of simulating the system in steady state which was also done here. While both schemes yielded comparable bulk hydraulic performance, transient conditions exhibited a visual improvement in describing flow variability. We released streamtraces (steady flow solution) and DEM particles (transient solution) at the same location from where sensor fish (SF) have been released in field studies of the modeled turbine unit. The streamtrace-based results showed a better agreement with SF data than the DEM-based nadir pressures did because the former accounted for the turbulent dispersion at the intake but the latter did not. However, the DEM-based strike frequency is more
Duan, K.; Kwok, C. Y.
2016-04-01
The aim of this study is to better understand the mechanisms controlling the initiation, propagation, and ultimate pattern of borehole breakouts in shale formation when drilled parallel with and perpendicular to beddings. A two-dimensional discrete element model is constructed to explicitly represent the microstructure of inherently anisotropic rocks by inserting a series of individual smooth joints into an assembly of bonded rigid discs. Both isotropic and anisotropic hollow square-shaped samples are generated to represent the wellbores drilled perpendicular to and parallel with beddings at reduced scale. The isotropic model is validated by comparing the stress distribution around borehole wall and along X axis direction with analytical solutions. Effects of different factors including the particle size distribution, borehole diameter, far-field stress anisotropy, and rock anisotropy are systematically evaluated on the stress distribution and borehole breakout propagation. Simulation results reveal that wider particle size distribution results in the local stress perturbations which cause localization of cracks. Reduction of borehole diameter significantly alters the crack failure from tensile to shear and raises the critical pressure. Rock anisotropy plays an important role on the stress state around wellbore which lead to the formation of preferred cracks under hydrostatic stress. Far-field stress anisotropy plays a dominant role in the shape of borehole breakout when drilled perpendicular to beddings while a secondary role when drilled parallel with beddings. Results from this study can provide fundamental insights on the underlying particle-scale mechanisms for previous findings in laboratory and field on borehole stability in anisotropic rock.
Influence of mobile shale on thrust faults: Insights from discrete element simulations
Dean, S. L.; Morgan, J. K.
2013-12-01
We use two-dimensional discrete element method (DEM) simulations to study the effects of a two-layer mechanical stratigraphy on a gravitationally collapsing passive margin. The system consists of an upslope sedimentary wedge, overlying an extensional zone that is linked at depth with a downslope fold and thrust belt. The behavior of the system is dependent on the material properties and thickness of the competent units. The models are initially composed of a mobile shale unit overlain by a pre-delta unit. In DEM materials, the bulk rheology of the granular material is a product of the particle interactions, depending on a range of parameters, including friction and elastic moduli. Natural mobile shales underlying deltas are presumed to be viscous, and are therefore represented in DEM as very weak non-cohesive particles. The unbonded particles respond to loading by moving to areas of lower stress, i.e. out from beneath a growing sediment wedge. The bulk motion of the particles therefore flows away from the upslope extensional zone. Apparent viscosity is introduced in DEM materials due to time dependent numerical parameters such as viscous damping of particle motions. We characterized this apparent viscosity of this mobile shale unit with a series of shear box tests, with varying shear strain rates. The mobile shale particles have a viscosity of about 108 Pa*s, which is low for mobile shale. The low viscosity of our numerical materials can be compensated for by scaling time in our models, because the simulations are driven by sedimentary loading. By increasing the sedimentation rate by many orders of magnitude, we can approximate the natural values of shear stress in our simulations. Results are compared with the Niger Delta type locale for shale tectonics. The simulations succeed in creating an overall linked extensional-contractional system, as well as creating individual structures such as popups and intersecting forethrusts and backthrusts. In addition, toe
Mandal, Sandip; Khakhar, D. V.
2016-10-01
Granular materials handled in industries are typically non-spherical in shape and understanding the flow of such materials is important. The steady flow of mono-disperse, frictional, inelastic dumbbells in two-dimensions is studied by soft sphere, discrete element method simulations for chute flow and shear cell flow. The chute flow data are in the dense flow regime, while the shear cell data span a wide range of solid fractions. Results of a detailed parametric study for both systems are presented. In chute flow, increase in the aspect ratio of the dumbbells results in significant slowing of the flow at a fixed inclination and in the shear cell it results in increase in the shear stress and pressure for a fixed shear rate. The flow is well-described by the μ-I scaling for inertial numbers as high as I = 1, corresponding to solid fractions as low as ϕ = 0.3, where μ is the effective friction (the ratio of shear stress to pressure) and I is the inertial number (a dimensionless shear rate scaled with the time scale obtained from the local pressure). For a fixed inertial number, the effective friction increases by 60%-70% when aspect ratio is increased from 1.0 (sphere) to 1.9. At low values of the inertial number, there is little change in the solid fraction with aspect ratio of the dumbbells, whereas at high values of the inertial number, there is a significant increase in solid fraction with increase in aspect ratio. The dense flow data are well-described by the Jop-Forterre-Pouliquen model [P. Jop et al., Nature 441, 727-730 (2006)] with the model parameters dependent on the dumbbell aspect ratio. The variation of μ with I over the extended range shows a maximum in the range I ∈ (0.4, 0.5), while the solid fraction shows a faster than linear decrease with inertial number. A modified version of the JFP model for μ(I) and a power law model for ϕ(I) is shown to describe the combined data over the extended range of I.
Bedload Transport on Steep Slopes with Coupled Modeling Based on the Discrete Element Method
Chauchat, J.; Maurin, R.; Chareyre, B.; Frey, P.
2014-12-01
After more than a century of research, a clear understanding of the physical processes involved in sediment transport problems is still lacking. In particular, modeling of intergranular interactions and fluid-particle interactions in bedload transport need to be improved. In this contribution, we propose a simple numerical model coupling a Discrete Element Method (DEM) for the grain dynamics with a simple 1D vertical fluid phase model inspired from the two-phase approach [1] in order to contribute to this open question. The Reynolds stress is parameterized by a mixing length model which depends on the integral of the grain volume fraction. The coupling between the grains and the fluid phase is essentially achieved through buoyancy and drag forces. The open source DEM code Yade [2] is used with a linear spring-dashpot contact law that allows the description of the behavior of the particles from the quasi-static to the dynamical state. The model is compared with classical results [3] and with particle-scale experimental results obtained in the quasi-2D flume at IRSTEA, Grenoble [4]. We discuss the closures of the model and the sensitivity to the different physical and numerical parameters. [1] Revil-Baudard, T. and J. Chauchat. A two-phase model for sheet flow regime based on dense granular flow rheology. Journal of Geophysical Research: Oceans, 118(2):619-634, 2013. [2] Šmilauer V. , E. Catalano, B. Chareyre, S. Dorofeenko, J. Duriez, A. Gladky, J. Kozicki, C . Modenese, L. Scholtès, L. Sibille, J. Str.nský, and K. Thoeni. Yade Documentation (V. Šmilauer, ed.), The Yade Project, 1st ed., http://yade-dem.org/doc/., 2010. [3] Meyer-Peter, E. and R. Müller. Formulas for bed-load transport. In Proc. 2nd Meeting, pages 39-64. IAHR, 1948. [4] Frey, P. Particle velocity and concentration profiles in bedload experiments on a steep slope. Earth Surface Processes and Landforms, 39(5):646-655, 2014.
Fish passage through hydropower turbines: Simulating blade strike using the discrete element method
Richmond, M. C.; Romero-Gomez, P.
2014-03-01
Among the hazardous hydraulic conditions affecting anadromous and resident fish during their passage though hydro-turbines two common physical processes can lead to injury and mortality: collisions/blade-strike and rapid decompression. Several methods are currently available to evaluate these stressors in installed turbines, e.g. using live fish or autonomous sensor devices, and in reduced-scale physical models, e.g. registering collisions from plastic beads. However, a priori estimates with computational modeling approaches applied early in the process of turbine design can facilitate the development of fish-friendly turbines. In the present study, we evaluated the frequency of blade strike and rapid pressure change by modeling potential fish trajectories with the Discrete Element Method (DEM) applied to fish-like composite particles. In the DEM approach, particles are subjected to realistic hydraulic conditions simulated with computational fluid dynamics (CFD), and particle-structure interactions-representing fish collisions with turbine components such as blades-are explicitly recorded and accounted for in the calculation of particle trajectories. We conducted transient CFD simulations by setting the runner in motion and allowing for unsteady turbulence using detached eddy simulation (DES), as compared to the conventional practice of simulating the system in steady state (which was also done here for comparison). While both schemes yielded comparable bulk hydraulic performance values, transient conditions exhibited an improvement in describing flow temporal and spatial variability. We released streamtraces (in the steady flow solution) and DEM particles (transient solution) at the same locations where sensor fish (SF) were released in previous field studies of the advanced turbine unit. The streamtrace- based results showed a better agreement with SF data than the DEM-based nadir pressures did because the former accounted for the turbulent dispersion at the
Energy Technology Data Exchange (ETDEWEB)
Romero Gomez, Pedro DJ; Richmond, Marshall C.
2014-04-17
Evaluating the consequences from blade-strike of fish on marine hydrokinetic (MHK) turbine blades is essential for incorporating environmental objectives into the integral optimization of machine performance. For instance, experience with conventional hydroelectric turbines has shown that innovative shaping of the blade and other machine components can lead to improved designs that generate more power without increased impacts to fish and other aquatic life. In this work, we used unsteady computational fluid dynamics (CFD) simulations of turbine flow and discrete element modeling (DEM) of particle motion to estimate the frequency and severity of collisions between a horizontal axis MHK tidal energy device and drifting aquatic organisms or debris. Two metrics are determined with the method: the strike frequency and survival rate estimate. To illustrate the procedure step-by-step, an exemplary case of a simple runner model was run and compared against a probabilistic model widely used for strike frequency evaluation. The results for the exemplary case showed a strong correlation between the two approaches. In the application case of the MHK turbine flow, turbulent flow was modeled using detached eddy simulation (DES) in conjunction with a full moving rotor at full scale. The CFD simulated power and thrust were satisfactorily comparable to experimental results conducted in a water tunnel on a reduced scaled (1:8.7) version of the turbine design. A cloud of DEM particles was injected into the domain to simulate fish or debris that were entrained into the turbine flow. The strike frequency was the ratio of the count of colliding particles to the crossing sample size. The fish length and approaching velocity were test conditions in the simulations of the MHK turbine. Comparisons showed that DEM-based frequencies tend to be greater than previous results from Lagrangian particles and probabilistic models, mostly because the DEM scheme accounts for both the geometric
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 曾庆存; 谢正辉
2004-01-01
The mixed finite element (MFE) methods for a shallow water equation system consisting of water dynamics equations, silt transport equation, and the equation of bottom topography change were derived. A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established. The existence and convergence of MFE solution of the discrete current velocity, elevation of the bottom topography, thickness of fluid column, and mass rate of sediment is demonstrated.
Roux, A; Laporte, S; Lecompte, J; Gras, L-L; Iordanoff, I
2016-01-25
The muscle-tendon complex (MTC) is a multi-scale, anisotropic, non-homogeneous structure. It is composed of fascicles, gathered together in a conjunctive aponeurosis. Fibers are oriented into the MTC with a pennation angle. Many MTC models use the Finite Element Method (FEM) to simulate the behavior of the MTC as a hyper-viscoelastic material. The Discrete Element Method (DEM) could be adapted to model fibrous materials, such as the MTC. DEM could capture the complex behavior of a material with a simple discretization scheme and help in understanding the influence of the orientation of fibers on the MTC׳s behavior. The aims of this study were to model the MTC in DEM at the macroscopic scale and to obtain the force/displacement curve during a non-destructive passive tensile test. Another aim was to highlight the influence of the geometrical parameters of the MTC on the global mechanical behavior. A geometrical construction of the MTC was done using discrete element linked by springs. Young׳s modulus values of the MTC׳s components were retrieved from the literature to model the microscopic stiffness of each spring. Alignment and re-orientation of all of the muscle׳s fibers with the tensile axis were observed numerically. The hyper-elastic behavior of the MTC was pointed out. The structure׳s effects, added to the geometrical parameters, highlight the MTC׳s mechanical behavior. It is also highlighted by the heterogeneity of the strain of the MTC׳s components. DEM seems to be a promising method to model the hyper-elastic macroscopic behavior of the MTC with simple elastic microscopic elements. Copyright © 2015 Elsevier Ltd. All rights reserved.
Discrete element modeling approach to porosimetry for durability risk estimation of concrete
Stroeven, P.; Le, N.L.B.; Stroeven, M.; Sluys, L.J.
2011-01-01
The paper introduces a novel approach to porosimetry in virtual concrete, denoted as random node structuring (RNS). The fresh state of this particulate material is produced by the DEM system HADES. Hydration simulation is a hybrid approach making use of wellknown discretization and vector methods. P
Kovács, M; Lindgren, F
2012-01-01
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.
Kulchitsky, A. V.; Johnson, J.; Duvoy, P.; Wilkinson, A.; Creager, C. M.
2012-12-01
For in situ resource utilization on the Moon, asteroids, Mars, or other space body it is necessary to be able to simulate the interaction of mobile platforms and excavation machines with the regolith for engineering design, planning, and operations. For accurate simulations, tools designed to measure regolith properties will need to be deployed and interpreted. Two such tools are the penetrometer, used to measure a soil strength index as a function of depth, and the bevameter, used to characterize regolith surface properties of strength, friction and sinkage. The penetrometer interrogates regolith properties from the surface to a depth limited only by the capabilities of the instrument to penetrate the regolith while a bevameter interrogates only the upper few centimeters needed to describe a mobility platform's traction and sinkage. Interpretation of penetrometer and bevameter data can be difficult, especially on low gravity objects. We use the discrete element method (DEM) model to simulate the large regolith deformations and failures associated with the tests to determine regolith properties. The DEM simulates granular material behavior using large aggregates of distinct particles. Realistic physics of particle-particle interaction introduces many granular specific phenomena such as interlocking and force chain formation that cannot be represented using continuum methods. In this work, experiments using a cone penetrometer test (CPT) and bevameter on lunar simulants JSC-1A and GRC-1 were performed at NASA Glenn Research Center. These tests were used to validate the physics in the COUPi DEM model. COUPi is a general physical DEM code being developed to model machine/regolith interactions as part of a NASA Lunar Science Institute sponsored project on excavation and mobility modeling. The experimental results were used in this work to build an accurate model to simulate the lunar regolith. The CPT consists of driving an instrumented cone with opening angle of 60
Discrete element method based scale-up model for material synthesis using ball milling
Santhanam, Priya Radhi
Mechanical milling is a widely used technique for powder processing in various areas. In this work, a scale-up model for describing this ball milling process is developed. The thesis is a combination of experimental and modeling efforts. Initially, Discrete Element Model (DEM) is used to describe energy transfer from milling tools to the milled powder for shaker, planetary, and attritor mills. The rolling and static friction coefficients are determined experimentally. Computations predict a quasisteady rate of energy dissipation, E d, for each experimental configuration. It is proposed that the milling dose defined as a product of Ed and milling time, t, divided by the mass of milled powder, mp characterizes the milling progress independently of the milling device or milling conditions used. Once the milling dose is determined for one experimental configuration, it can be used to predict the milling time required to prepare the same material in any milling configuration, for which Ed is calculated. The concept is validated experimentally for DEM describing planetary and shaker mills. For attritor, the predicted Ed includes substantial contribution from milling tool interaction events with abnormally high forces (>103 N). The energy in such events is likely dissipated to heat or plastically deform milling tools rather than refine material. Indeed, DEM predictions for the attritor correlate with experiments when such events are ignored in the analysis. With an objective of obtaining real-time indicators of milling progress, power, torque, and rotation speed of the impeller of an attritor mill are measured during preparation of metal matrix composite powders in the subsequent portion of this thesis. Two material systems are selected and comparisons made between in-situ parameters and experimental milling progress indicators. It is established that real-time measurements can certainly be used to describe milling progress. However, they need to be interpreted carefully
Zhao, Xuzhe
High efficiency hydrogen storage method is significant in development of fuel cell vehicle. Seeking for a high energy density material as the fuel becomes the key of wide spreading fuel cell vehicle. LiBH4 + MgH 2 system is a strong candidate due to their high hydrogen storage density and the reaction between them is reversible. However, LiBH4 + MgH 2 system usually requires the high temperature and hydrogen pressure for hydrogen release and uptake reaction. In order to reduce the requirements of this system, nanoengineering is the simple and efficient method to improve the thermodynamic properties and reduce kinetic barrier of reaction between LiBH4 and MgH2. Based on ab initio density functional theory (DFT) calculations, the previous study has indicated that the reaction between LiBH4 and MgH2 can take place at temperature near 200°C or below. However, the predictions have been shown to be inconsistent with many experiments. Therefore, it is the first time that our experiment using ball milling with aerosol spraying (BMAS) to prove the reaction between LiBH4 and MgH2 can happen during high energy ball milling at room temperature. Through this BMAS process we have found undoubtedly the formation of MgB 2 and LiH during ball milling of MgH2 while aerosol spraying of the LiBH4/THF solution. Aerosol nanoparticles from LiBH 4/THF solution leads to form Li2B12H12 during BMAS process. The Li2B12H12 formed then reacts with MgH2 in situ during ball milling to form MgB 2 and LiH. Discrete element modeling (DEM) is a useful tool to describe operation of various ball milling processes. EDEM is software based on DEM to predict power consumption, liner and media wear and mill output. In order to further improve the milling efficiency of BMAS process, EDEM is conducted to make analysis for complicated ball milling process. Milling speed and ball's filling ratio inside the canister as the variables are considered to determine the milling efficiency. The average and maximum
Directory of Open Access Journals (Sweden)
J. Ochoa-Avendaño
2017-01-01
Full Text Available This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.
Matuttis, Hans-Georg
2014-01-01
Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particlesProvides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulationHighlights the numerical tricks and pitfalls that are usually only realized after years of experience, with relevant simple experiment
Monteiro, André O.
2013-09-25
The mechanical response to a uniaxial compressive force of a single carbon nanotube (CNT) filled (or partially-filled) with ZnS has been modelled. A semi-empirical approach based on the finite element method was used whereby modelling outcomes were closely matched to experimental observations. This is the first example of the use of the continuum approach to model the mechanical behaviour of discrete filled CNTs. In contrast to more computationally demanding methods such as density functional theory or molecular dynamics, our approach provides a viable and expedite alternative to model the mechanics of filled multi-walled CNTs. © 2013 Springer Science+Business Media New York.
Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems
Knabner, Peter; Summ, Gerhard
2016-01-01
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite element method with augmented Crouzeix-Raviart ansatz space. We discuss the reduction of unknowns by static condensation and propose Newton's method for the solution of local and global systems. Finally, we show, how such a nonlinear problem arises from the mixe...
Bosch, Jessica
2014-04-01
We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach. © 2014 Elsevier Inc.
Directory of Open Access Journals (Sweden)
Qingdong Zeng
2015-10-01
Full Text Available Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM is applied to capture fluid flow in the fractured porous media, which represents fractures explicitly and avoids calculating shape factor for cross flow. In addition, the extended finite element method (XFEM is applied to capture solid deformation due to the discontinuity caused by fractures. More importantly, this model captures the change of fractures aperture during the simulation, and then adjusts fluid flow in the fractures. The final linear equation set is derived and solved for a 2D plane strain problem. Results show that the combination of discrete fracture model and extended finite element method is suited for simulating coupled deformation and fluid flow in fractured porous media.
Institute of Scientific and Technical Information of China (English)
CHEN Jun; PAN Tongyan; HUANG Xiaoming
2011-01-01
We established a user-defined micromechanical model using discrete element method (DEM) to investigate the cracking behavior of asphalt concrete (AC).Using the “Fish” language provided in the particle flow code in 3-Demensions (PFC3D),the air voids and mastics in asphalt concrete were realistically built as two distinct phases.With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes,the three-dimensional (3D) discrete element model was able to account for aggregate gradation and fraction.Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation.A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature,i e,-10 ℃ and 15 ℃.The predicted results of the numerical simulation were compared with laboratory experimental measurements.Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures.Based on the DEM model,the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.
Institute of Scientific and Technical Information of China (English)
HOU Shuguang; ZHANG Dong; HUANG Xiaoming; ZHAO Yongli
2015-01-01
The micro-mechanical response of asphalt mixtures was studied using the discrete element method. The discrete element sample of stone mastic asphalt was generated first and the vehicle load was applied to the sample. A user-written program was coded with the FISH language in PFC3D to extract the contact forces within the sample and the displacements of the particles. Then, the contact forces within the whole sample, in asphalt mastic, in coarse aggregates and between asphalt mastic and coarse aggregates were investigated. Finally, the movement of the particles in the sample was analyzed. The sample was divided into 15 areas and a figure was drawn to show how the balls move in each area according to the displacements of the balls in each area. The displacements of asphalt mastic balls and coarse aggregates were also analyzed. The experimental results explain how the asphalt mixture bears vehicle load and the potential reasons why the rutting forms from a micro-mechanical view.
Osterberg, Erich C; Handley, Michael J; Sneed, Sharon B; Mayewski, Paul A; Kreutz, Karl J
2006-05-15
We present a novel ice/firn core melter system that uses fraction collectors to collect discrete, high-resolution (32 trace elements by inductively coupled plasma sectorfield mass spectrometry (ICP-SMS), and stable oxygen and hydrogen isotopes by isotope ratio mass spectrometry (IRMS). The new continuous melting with discrete sampling (CMDS) system preserves an archive of each sample, reduces the problem of incomplete particle dissolution in ICP-SMS samples, and provides more precise trace element data than previous ice melter models by using longer ICP-SMS scan times and washing the instrument between samples. CMDS detection limits are similar to or lower than those published for ice melter systems coupled directly to analytical instruments and are suitable for analyses of polar and mid-low-latitude ice cores. Analysis of total calcium and sulfur by ICP-SMS and calcium ion, sulfate, and methanesulfonate by IC from the Mt. Logan Prospector-Russell Col ice core confirms data accuracy and coregistration of the split fractions from each sample. The reproducibility of all data acquired by the CMDS system is confirmed by replicate analyses of parallel sections of the GISP2 D ice core.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The soil plug phenomenon involving the rising of the surface soil inside the bucket chamber under the suction pressure and seepage forces was simulated and calculated by deformable discrete element method (DDEM) models. The seepage forces, the effective gravity of soil, the friction on the chamber wall and the suction inside the chamber are considered as the main external forces of DDEM specimen. Three typical types of soil (silty clay, silt and sand) in the Bohai Sea are set as the main environmental conditions in the formation process of soil plug. It is found that the heights of soil plug simulated by DDEM models are 161.85 mm in silty clay, 125.22 mm in silt and 167.56 mm in sand, which are close to model test results and higher than those estimated by discrete element method (DEM). DDEM is an effective method to estimate and predict the heights of soil plug before suction penetration of bucket foundations on site.
Gao, F. Q.; Kang, H. P.
2016-04-01
When rock failure is unavoidable, the designer of engineering structures must know and account for the residual strength of the rock mass. This is particularly relevant in underground coal mine openings. Pre-existing discontinuities play an important role in the mechanical behavior of rock masses and thus it is important to understand the effects of such pre-existing discontinuities on the residual strength. For this purpose, the present study demonstrates a numerical analysis using a discrete element method simulation. The numerical results indicate that fracture intensity has no significant influence on the residual strength of jointed rock masses, independent of confining conditions. As confining pressures increase, both peak and residual strengths increase, with residual strength increasing at a faster rate. The finding was further demonstrated by analyzing documented laboratory compressive test data from a variety of rocks along with field data from coal pillars. A comprehensive interpretation of the finding was conducted using a cohesion-weakening-friction-strengthening (CWFS) model. The effect of rock bolts on rock mass strength was also evaluated by using a discrete element method model which suggested that rock bolts can significantly increases residual strength but have limited effect on increasing the peak strength of rock masses.
Gardiner, Bruce S; Wong, Kelvin K L; Joldes, Grand R; Rich, Addison J; Tan, Chin Wee; Burgess, Antony W; Smith, David W
2015-10-01
This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.
Directory of Open Access Journals (Sweden)
Bruce S Gardiner
2015-10-01
Full Text Available This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus and extracellular matrix (e.g. collagen are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties. Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings. Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.
Daya Sagar, B S
2010-02-01
Spatial interpolation is one of the demanding techniques in Geographic Information Science (GISci) to generate interpolated maps in a continuous manner by using two discrete spatial and/or temporal data sets. Noise-free data (thematic layers) depicting a specific theme at varied spatial or temporal resolutions consist of connected components either in aggregated or in disaggregated forms. This short paper provides a simple framework: 1) to categorize the connected components of layered sets of two different time instants through their spatial relationships and the Hausdorff distances between the companion-connected components and 2) to generate sequential maps (interpolations) between the discrete thematic maps. Development of the median set, using Hausdorff erosion and dilation distances to interpolate between temporal frames, is demonstrated on lake geometries mapped at two different times and also on the bubonic plague epidemic spread data available for 11 consecutive years. We documented the significantly fair quality of the median sets generated for epidemic data between alternative years by visually comparing the interpolated maps with actual maps. They can be used to visualize (animate) the spatiotemporal behavior of a specific theme in a continuous sequence.
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Hashemnia, Kamyar
A new laser displacement probe was developed to measure the impact velocities of particles within vibrationally-fluidized beds. The sensor output was also used to measure bulk flow velocity along the probe window and to provide a measure of the media packing. The displacement signals from the laser sensors were analyzed to obtain the probability distribution functions of the impact velocity of the particles. The impact velocity was affected by the orientation of the laser probe relative to the bulk flow velocity, and the density and elastic properties of the granular media. The impact velocities of the particles were largely independent of their bulk flow speed and packing density. Both the local impact and bulk flow velocities within a tub vibratory finisher were predicted using discrete element modelling (DEM) and compared to the measured values for spherical steel media. It was observed that the impact and bulk flow velocities were relatively insensitive to uncertainties in the contact coefficients of friction and restitution. It was concluded that the predicted impact and bulk flow velocities were dependent on the number of layers in the model. Consequently, the final DE model mimicked the key aspects of the experimental setup, including the submerged laser sensor. The DE method predictions of both impact velocity and bulk flow velocity were in reasonable agreement with the experimental measurements, with maximum differences of 20% and 30%, respectively. Discrete element modeling of granular flows is effective, but requires large numerical models. In an effort to reduce computational effort, this work presents a finite element (FE) continuum model of a vibrationally-fluidized granular flow. The constitutive equations governing the continuum model were calibrated using the discrete element method (DEM). The bulk flow behavior of the equivalent continuum media was then studied using both Lagrangian and Eulerian FE formulations. The bulk flow velocities predicted
Seismic evaluation of lead caves using no-tension discrete model with interface elements
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Khaleel, M.A.; Deibler, J.E.; Koontz, D.A.
1995-07-01
This paper investigates quasi-static behavior of lead cave walls radiation shields made by stacking lead bricks. The bricks have high stiffness, whereas the joints are weak and incapable of supporting tension. Global behavior of this kind of wall is strongly influenced by size friction coefficient of the brick elements. The general finite element code ANSYS was used for the analysis of the lead caves. A series of 2-D models that spanned the range of height-to-width aspect ratios of the cave wall were constructed. Two types of contact elements were incorporated in the model. The point-to-point contact element was used to represent contact in the horizontal direction. This element permits either compression in the direction normal to the surfaces or opening of a gap. The point-to-surface contact element was chosen to represent contact in the vertical direction. This element allows sliding in addition to the compression or gap formation normal to the surface. A series of static analyses were performed for each model. A l-g. vertical acceleration representing gravity was applied. The lateral acceleration was increased until the solution would not converge. This acceleration is defined as the critical lateral acceleration. This was achieved with a set of load steps with increasing lateral load. The critical acceleration was found to depend on the wall aspect ratio. For a wall with an aspect ratio up to three, the maximum acceleration is above the required 0.1 g. The wall failure mechanisms were also identified based on the numerical results. The two failure modes are the rotation and loss of interlocking among the blocks or silding of upper layers of the wall.
Institute of Scientific and Technical Information of China (English)
Ding Rui; Jiang Meiqun; Peng Daping
2005-01-01
The boundary element approximation of the parabolic variational inequalities of the second kind is discussed. First, the parabolic variational inequalities of the second kind can be reduced to an elliptic variational inequality by using semidiscretization and implicit method in time; then the existence and uniqueness for the solution of nonlinear non-differentiable mixed variational inequality is discussed. Its corresponding mixed boundary variational inequality and the existence and uniqueness of its solution are yielded. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.
Institute of Scientific and Technical Information of China (English)
ZHANG; Lei; WEI; Zuoan; LIU; Xiaoyu; LI; Shihai
2005-01-01
Three-dimensional discrete element face-to-face contact model with fissure water pressure is established in this paper and the model is used to simulate three-stage process of landslide under fissure water pressure in the opencast mine, according to the actual state of landslide in Panluo iron mine where landslide happened in 1990 and was fathered in 1999. The calculation results show that fissure water pressure on the sliding surface is the main reason causing landslide and the local soft interlayer weakens the stability of slope. If the discrete element method adopts the same assumption as the limit equilibrium method, the results of two methods are in good agreement; while if the assumption is not adopted in the discrete element method, the critical φ numerically calculated is less than the one calculated by use of the limit equilibrium method for the sameC. Thus, from an engineering point of view, the result from the discrete element model simulation is safer and has more widely application since the discrete element model takes into account the effect of rock mass structures.
Tian, Wenyi; Yuan, Xiaoming
2016-11-01
Linear inverse problems with total variation regularization can be reformulated as saddle-point problems; the primal and dual variables of such a saddle-point reformulation can be discretized in piecewise affine and constant finite element spaces, respectively. Thus, the well-developed primal-dual approach (a.k.a. the inexact Uzawa method) is conceptually applicable to such a regularized and discretized model. When the primal-dual approach is applied, the resulting subproblems may be highly nontrivial and it is necessary to discuss how to tackle them and thus make the primal-dual approach implementable. In this paper, we suggest linearizing the data-fidelity quadratic term of the hard subproblems so as to obtain easier ones. A linearized primal-dual method is thus proposed. Inspired by the fact that the linearized primal-dual method can be explained as an application of the proximal point algorithm, a relaxed version of the linearized primal-dual method, which can often accelerate the convergence numerically with the same order of computation, is also proposed. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the new algorithms. Their efficiency is verified by some numerical results.
Cil, Mehmet B.; Alshibli, Khalid A.
2015-02-01
The constitutive behavior and deformation characteristics of uncemented granular materials are to a large extent derived from the fabric or geometry of the particle structure and the interparticle friction resulting from normal forces acting on particles or groups of particles. Granular materials consist of discrete particles with a fabric (microstructure) that changes under loading. Synchrotron micro-computed tomography (SMT) has emerged as a powerful non-destructive 3D scanning technique to study geomaterials. In this paper, SMT was used to acquire in situ scans of the oedometry test of a column of three silica sand particles. The sand is known as ASTM 20-30 Ottawa sand, and has a grain size between US sieves #20 (0.841 mm) and #30 (0.595 mm). The characteristics and evolution of particle fracture in sand were examined using SMT images, and a 3D discrete element method (DEM) was used to model the fracture behavior of sand particles. It adopts the bonded particle model to generate a crushable agglomerate that consists of a large number of small spherical sub-particles. The agglomerate shape matches the 3D physical shape of the tested sand particles by mapping the particle morphology from the SMT images. The paper investigates and discusses the influence of agglomerate packing (i.e., the number and size distribution of spherical sub-particles that constitute the agglomerate) and agglomerate shape on the fracture behavior of crushable particles.
Directory of Open Access Journals (Sweden)
Jayaprakash Jaganathan
2014-10-01
Full Text Available The application of fibre reinforced polymer (FRP composites for retrofitting and strengthening of existing reinforced concrete (RC structures has fascinated the attention of researchers and engineers in the recent decades. This paper presents the results of experimental and finite element (FE investigation of shear behaviour of reinforced concrete T-beams repaired with externally bonded bi-directional discrete carbon fibre fabric (CFF strips. The reinforced concrete T-beams were tested under four point bending system to investigate the performance of CFF shear strengthening scheme in terms of ultimate load carrying capacity. These beams were modelled using LUSAS software. To evaluate the behaviour of the simulated models, the predicted results were compared with the experimental results. The experimental results show that the gain in shear capacity of the CFF repaired beams ranged between 20% and 40% over the control beam. Thus, it can be concluded that the externally bonded CFF strips significantly increased the shear capacity of CFF repaired beams. It was generally observed that the developed FE model shows better agreement with the experimental results. The results of load-deflection profile, cracking pattern, modes of failure, and strain distribution in discrete CFF strips are presented.
Least-squares finite element discretizations of neutron transport equations in 3 dimensions
Energy Technology Data Exchange (ETDEWEB)
Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)
1996-12-31
The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.
Institute of Scientific and Technical Information of China (English)
陈普庆; 夏伟; 周照耀; 朱权利; 李元元
2004-01-01
The application of a combined finite-discrete element modeling approach to simulate the three-dimensional microscopic compaction behavior of single-layer metal powder system was described. The process was treated as a static problem, with kinematical component being neglected. Due to ill condition, Cholesky's method failed to solve the system equations, while conjugate gradient method was tried and yielded good results. Deformation of the particles was examined and compared with the results of physical modeling experiments. In both cases, the inner particles were deformed from sphere to polygonal column, with the edges turning from arc to straight line. The edge number of a particle was equal to the number of particles surrounding it. And the experiments show that the ductile metal particles can be densified only by their plastic deformation without the occurrence of rearrangement phenomenon.
Energy Technology Data Exchange (ETDEWEB)
Tao, Liang; McCurdy, C.W.; Rescigno, T.N.
2008-11-25
We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.
Xue, W.-M.; Atluri, S. N.
1985-01-01
In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.
Directory of Open Access Journals (Sweden)
Jae-Hong Pyo
2013-01-01
Full Text Available The stabilized Gauge-Uzawa method (SGUM, which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow.
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2016-01-01
modulus. Three different approaches have been used and compared for calibrating the Burger's contact model. Values of the dynamic modulus and phase angle of asphalt mixtures were predicted by conducting DE simulation under dynamic strain control loading. The excellent agreement between the predicted......In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional discrete element method. Combined with Burger's model, three contact models were used for the construction of constitutive asphalt mixture model with viscoelastic properties...... in the commercial software PFC3D, including the slip model, linear stiffness-contact model, and contact bond model. A macro-scale Burger's model was first established and the input parameters of Burger's contact model were calibrated by adjusting them so that the model fitted the experimental data for the complex...
Institute of Scientific and Technical Information of China (English)
LI; Shihai; LIAN; Zhenzhong; J.; G.; Wang
2005-01-01
This paper studies the stability of jointed rock slopes by using our improved three-dimensional discrete element methods (DEM) and physical modeling. Results show that the DEM can simulate all failure modes of rock slopes with different joint configurations. The stress in each rock block is not homogeneous and blocks rotate in failure development. Failure modes depend on the configuration of joints. Toppling failure is observed for the slope with straight joints and sliding failure is observed for the slope with staged joints. The DEM results are also compared with those of limit equilibrium method (LEM). Without considering the joints in rock masses, the LEM predicts much higher factor of safety than physical modeling and DEM. The failure mode and factor of safety predicted by the DEM are in good agreement with laboratory tests for any jointed rock slope.
Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.
2016-04-01
Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that
Ji, S.; Hanes, D.M.; Shen, H.H.
2009-01-01
In this study, we report a direct comparison between a physical test and a computer simulation of rapidly sheared granular materials. An annular shear cell experiment was conducted. All parameters were kept the same between the physical and the computational systems to the extent possible. Artificially softened particles were used in the simulation to reduce the computational time to a manageable level. Sensitivity study on the particle stiffness ensured such artificial modification was acceptable. In the experiment, a range of normal stress was applied to a given amount of particles sheared in an annular trough with a range of controlled shear speed. Two types of particles, glass and Delrin, were used in the experiment. Qualitatively, the required torque to shear the materials under different rotational speed compared well with those in the physical experiments for both the glass and the Delrin particles. However, the quantitative discrepancies between the measured and simulated shear stresses were nearly a factor of two. Boundary conditions, particle size distribution, particle damping and friction, including a sliding and rolling, contact force model, were examined to determine their effects on the computational results. It was found that of the above, the rolling friction between particles had the most significant effect on the macro stress level. This study shows that discrete element simulation is a viable method for engineering design for granular material systems. Particle level information is needed to properly conduct these simulations. However, not all particle level information is equally important in the study regime. Rolling friction, which is not commonly considered in many discrete element models, appears to play an important role. ?? 2009 Elsevier Ltd.
A Study of Three Intrinsic Problems of the Classic Discrete Element Method Using Flat-Joint Model
Wu, Shunchuan; Xu, Xueliang
2016-05-01
Discrete element methods have been proven to offer a new avenue for obtaining the mechanics of geo-materials. The standard bonded-particle model (BPM), a classic discrete element method, has been applied to a wide range of problems related to rock and soil. However, three intrinsic problems are associated with using the standard BPM: (1) an unrealistically low unconfined compressive strength to tensile strength (UCS/TS) ratio, (2) an excessively low internal friction angle, and (3) a linear strength envelope, i.e., a low Hoek-Brown (HB) strength parameter m i . After summarizing the underlying reasons of these problems through analyzing previous researchers' work, flat-joint model (FJM) is used to calibrate Jinping marble and is found to closely match its macro-properties. A parametric study is carried out to systematically evaluate the micro-parameters' effect on these three macro-properties. The results indicate that (1) the UCS/TS ratio increases with the increasing average coordination number (CN) and bond cohesion to tensile strength ratio, but it first decreases and then increases with the increasing crack density (CD); (2) the HB strength parameter m i has positive relationships to the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle, but a negative relationship to the average coordination number (CN); (3) the internal friction angle increases as the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle increase; (4) the residual friction angle has little effect on these three macro-properties and mainly influences post-peak behavior. Finally, a new calibration procedure is developed, which not only addresses these three problems, but also considers the post-peak behavior.
Karampinos, Efstratios; Hadjigeorgiou, John; Turcotte, Pascal
2016-12-01
Structurally defined squeezing mechanisms in hard rock mining often result in buckling failures and large deformations. In mining drives, the primary objective is to mitigate and manage, in a cost-effective way, as opposed to arrest the deformation. This paper is a contribution to an improved understanding of the impact of several reinforcement scenarios in structurally controlled deformations in hard rock mines. The influence of reinforcement in the 3D discrete element method is explored, extending previous numerical work that has captured the squeezing buckling mechanism driven by foliation and high stresses in the selected mine site. A comprehensive strategy for explicitly modelling rock reinforcement using the DEM was developed and implemented in a series of 3D numerical models. The models were calibrated based on field testing of reinforcement and observations at the LaRonde Mine. They were used to investigate the influence of different reinforcement strategies at different deformation stages. The numerical results were in agreement with the field observations and demonstrated the practical implications of using yielding reinforcement elements. This was supported by field data where the use of yielding bolts reduced the drift convergence and rehabilitation. The methodology is applicable to other mine sites facing structurally controlled large deformations.
Guan, P. B.; Tingatinga, E. A.; Longalong, R. E.; Saguid, J.
2016-09-01
During the past decades, the complexity of conventional methods to perform seismic performance assessment of buildings led to the development of more effective approaches. The rigid body spring-discrete element method (RBS-DEM) is one of these approaches and has recently been applied to the study of the behavior of reinforced concrete (RC) buildings subjected to strong earthquakes. In this paper, the governing equations of RBS-DEM planar elements subjected to lateral loads and horizontal ground motion are presented and used to replicate the hysteretic behavior of experimental RC columns. The RBS-DEM models of columns are made up of rigid components connected by systems of springs that simulate axial, shear, and bending behavior of an RC section. The parameters of springs were obtained using Response-2000 software and the hysteretic response of the models of select columns from the Pacific Earthquake Engineering Research (PEER) Structural Performance Database were computed numerically. Numerical examples show that one-component models were able to simulate the initial stiffness reasonably, while the displacement capacity of actual columns undergoing large displacements were underestimated.
Crystal plasticity finite element modeling of discrete twin evolution in polycrystalline magnesium
Cheng, Jiahao; Ghosh, Somnath
2017-02-01
This paper develops an advanced, image-based crystal plasticity finite element (CPFE) model, for predicting explicit twin formation and associated heterogeneous deformation in single crystal and polycrystalline microstructures of hexagonal close-packed or hcp materials, such as magnesium. Twin formation is responsible for premature failure of many hcp materials. The physics of nucleation, propagation and growth of explicit twins are considered in the CPFE formulation. The twin nucleation model is based on dissociation of sessile dislocations into stable twin loops, while propagation is assumed by atoms shearing on twin planes and shuffling to reduce the thermal activation energy barrier. The explicit twin evolution model however has intrinsic issues of low computational efficiency. Very fine simulation time steps with enormous computation costs are required to simulate the fast propagating twin bands and associated strain localization. To improve the computational efficiency, a multi-time scale subcycling algorithm is developed. It decomposes the computational domain into sub-domains of localized twins requiring very fine time-steps and complementary domains of relatively low resolution. Each sub-domain updates the stress and the deformation-dependent variables in different rates, followed by a coupling at the end of every coarse time step to satisfy global equilibrium. A 6-fold increase in computing speed is obtained for a polycrystalline Mg microstructure simulation in this paper. CPFE simulations of high purity Mg microstructures are compared with experiments with very good agreement in stress-strain response as well as heterogeneous twin formation with strain localization.
High-speed boundary layer transition induced by a discrete roughness element
Iyer, Prahladh; Mahesh, Krishnan
2011-11-01
The effect of a hemispherical bump on a Mach 3.37 laminar boundary layer is studied using DNS for three conditions with k / δ = 2.54, 0.25 and 0.125, where k is the roughness height. The simulation parameters are based on the experiment by Danehy et. al. (AIAA-2009-394). The flow downstream of the roughness is transitional for all the three conditions accompanied by a rise in skin friction and heat transfer. Upon interaction with the roughness element, the boundary layer separates to form a series of spanwise vortices upstream and a shear layer. These vortices wrap around the roughness to yield a system of streamwise vortices downstream. Perturbation of the shear layer due to the vortices results in the formation of hairpin-shaped vortices further downstream of the roughness. While hairpin vortices were observed in both the center plane and off-symmetry planes on either side for the smallest δ case, they were observed only in the center plane for the other cases. This work was supported by NASA under the hypersonics NRA program under grant NNX08AB33A.
Discrete element simulation of localized deformation in stochastic distributed granular materials
Institute of Scientific and Technical Information of China (English)
2008-01-01
The deformation in granular material under loading conditions is a problem of great interest currently. In this paper,the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modi-fied distinct element method under the plane strain conditions,and the influences of the confining pressure,the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded,based on the numerical simulation testing,that two crossed shear sliding planes may occur inside the granular assembly,and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes,it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last,the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail.
Discrete element simulation of localized deformation in stochastic distributed granular materials
Institute of Scientific and Technical Information of China (English)
WANG DengMing; ZHOU YouHe
2008-01-01
The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modi-fied distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail.
Calantoni, Joseph; Holland, K Todd; Drake, Thomas G
2004-09-15
Sediment transport in oscillatory boundary layers is a process that drives coastal geomorphological change. Most formulae for bed-load transport in nearshore regions subsume the smallest-scale physics of the phenomena by parametrizing interactions amongst particles. In contrast, we directly simulate granular physics in the wave-bottom boundary layer using a discrete-element model comprised of a three-dimensional particle phase coupled to a one-dimensional fluid phase via Newton's third law through forces of buoyancy, drag and added mass. The particulate sediment phase is modelled using discrete particles formed to approximate natural grains by overlapping two spheres. Both the size of each sphere and the degree of overlap can be varied for these composite particles to generate a range of non-spherical grains. Simulations of particles having a range of shapes showed that the critical angle--the angle at which a grain pile will fail when tilted slowly from rest--increases from approximately 26 degrees for spherical particles to nearly 39 degrees for highly non-spherical composite particles having a dumbbell shape. Simulations of oscillatory sheet flow were conducted using composite particles with an angle of repose of approximately 33 degrees and a Corey shape factor greater than about 0.8, similar to the properties of beach sand. The results from the sheet-flow simulations with composite particles agreed more closely with laboratory measurements than similar simulations conducted using spherical particles. The findings suggest that particle shape may be an important factor for determining bed-load flux, particularly for larger bed slopes.
Shearing fluid-filled granular media: A coupled discrete element - continuous approach
Goren, L.; Aharonov, E.; Sparks, D.; Toussaint, R.; Marder, E.
2012-04-01
Fluid-filled granular layers are abundant in the Earth's shallow crust as saturated soils and poorly consolidated hillslope material, and as fluid-filled fault gouge layers. When such grains-fluid systems are subjected to excitation by the passage of seismic waves, tectonic loading, or gravitational loading they exhibit a highly non-trivial dynamical behavior that may lead to instabilities in the form of soil liquefaction, debris flow mobilization, and earthquakes. In order to study the basic coupled mechanics of fluid-filled granular media and the dynamical processes that are responsible for the emergence of instabilities we develop a model that couples granular dynamics (DEM) algorithm with a continuous Eulerian grid-based solver. The two components of the model represent the two phases (grains and fluid) in two different scales. Each grain is represented by a single element in the granular dynamics component, where grains interact by elastic collisions and frictional sliding. The compressible pore fluid is represented on a coarser Darcy scale grid that is super-imposed over the grains layer. The pore space geometry set by the evolving granular packing is used to define smooth porosity and permeability fields, and the individual grain velocities are interpolated to define a smooth field of a solid-fraction velocity. The porosity, permeability, and solid velocity fields are used in the continuous fluid grid-based solver to find pore fluid velocity and pressure. Pore fluid pressure gradients are interpolated back from the fluid grid to individual grains, where they enter the grains force balance equation as seepage forces. Boundary conditions are specified separately for the two phases. For the pore fluid we test two end-member drainage conditions: completely drained system (with infinite boundary permeability) and completely undrained system (with zero boundary permeability). For the grains, two-dimensional time dependent stress and velocity conditions are
Memon, Shahbaz; Vallot, Dorothée; Zwinger, Thomas; Neukirchen, Helmut
2017-04-01
Scientific communities generate complex simulations through orchestration of semi-structured analysis pipelines which involves execution of large workflows on multiple, distributed and heterogeneous computing and data resources. Modeling ice dynamics of glaciers requires workflows consisting of many non-trivial, computationally expensive processing tasks which are coupled to each other. From this domain, we present an e-Science use case, a workflow, which requires the execution of a continuum ice flow model and a discrete element based calving model in an iterative manner. Apart from the execution, this workflow also contains data format conversion tasks that support the execution of ice flow and calving by means of transition through sequential, nested and iterative steps. Thus, the management and monitoring of all the processing tasks including data management and transfer of the workflow model becomes more complex. From the implementation perspective, this workflow model was initially developed on a set of scripts using static data input and output references. In the course of application usage when more scripts or modifications introduced as per user requirements, the debugging and validation of results were more cumbersome to achieve. To address these problems, we identified a need to have a high-level scientific workflow tool through which all the above mentioned processes can be achieved in an efficient and usable manner. We decided to make use of the e-Science middleware UNICORE (Uniform Interface to Computing Resources) that allows seamless and automated access to different heterogenous and distributed resources which is supported by a scientific workflow engine. Based on this, we developed a high-level scientific workflow model for coupling of massively parallel High-Performance Computing (HPC) jobs: a continuum ice sheet model (Elmer/Ice) and a discrete element calving and crevassing model (HiDEM). In our talk we present how the use of a high
Directory of Open Access Journals (Sweden)
Mustafa Ucgul
2015-09-01
Full Text Available The energy required for tillage processes accounts for a significant proportion of total energy used in crop production. In many tillage processes decreasing the draft and upward vertical forces is often desired for reduced fuel use and improved penetration, respectively. Recent studies have proved that the discrete element modelling (DEM can effectively be used to model the soil–tool interaction. In his study, Fielke (1994 [1] examined the effect of the various tool cutting edge geometries, namely; cutting edge height, length of underside rub, angle of underside clearance, on draft and vertical forces. In this paper the experimental parameters of Fielke (1994 [1] were simulated using 3D discrete element modelling techniques. In the simulations a hysteretic spring contact model integrated with a linear cohesion model that considers the plastic deformation behaviour of the soil hence provides better vertical force prediction was employed. DEM parameters were determined by comparing the experimental and simulation results of angle of repose and penetration tests. The results of the study showed that the simulation results of the soil-various tool cutting edge geometries agreed well with the experimental results of Fielke (1994 [1]. The modelling was then used to simulate a further range of cutting edge geometries to better define the effect of sweep tool cutting edge geometry parameters on tillage forces. The extra simulations were able to show that by using a sharper cutting edge with zero vertical cutting edge height the draft and upward vertical force were further reduced indicating there is benefit from having a really sharp cutting edge. The extra simulations also confirmed that the interpolated trends for angle of underside clearance as suggested by Fielke (1994 [1] where correct with a linear reduction in draft and upward vertical force for angle of underside clearance between the ranges of −25 and −5°, and between −5 and 0°. The
Luding, Stefan
2008-01-01
One challenge of today's research is the realistic simulation of granular materials, like sand or powders, consisting of millions of particles. In this article, the discrete element method (DEM), as based on molecular dynamics methods, is introduced. Contact models are at the physical basis of DEM.
Lei, Qinghua; Latham, John-Paul; Xiang, Jiansheng
2016-12-01
An empirical joint constitutive model (JCM) that captures the rough wall interaction behaviour of individual fractures associated with roughness characteristics observed in laboratory experiments is combined with the solid mechanical model of the finite-discrete element method (FEMDEM). The combined JCM-FEMDEM formulation gives realistic fracture behaviour with respect to shear strength, normal closure, and shear dilatancy and includes the recognition of fracture length influence as seen in experiments. The validity of the numerical model is demonstrated by a comparison with the experimentally established empirical solutions. A 2D plane strain geomechanical simulation is conducted using an outcrop-based naturally fractured rock model with far-field stresses loaded in two consecutive phases, i.e. take-up of isotropic stresses and imposition of two deviatoric stress conditions. The modelled behaviour of natural fractures in response to various stress conditions illustrates a range of realistic behaviour including closure, opening, shearing, dilatancy, and new crack propagation. With the increase in stress ratio, significant deformation enhancement occurs in the vicinity of fracture tips, intersections, and bends, where large apertures can be generated. The JCM-FEMDEM model is also compared with conventional approaches that neglect the scale dependency of joint properties or the roughness-induced additional frictional resistance. The results of this paper have important implications for understanding the geomechanical behaviour of fractured rocks in various engineering activities.
Pestiaux, A.; Kärnä, T.; Melchior, S.; Lambrechts, J.; Remacle, J. F.; Deleersnijder, E.; Fichefet, T.
2012-04-01
The discretization of the Gent-McWilliams velocity and isopycnal diffusion with a discontinuous Galerkin finite element method is presented. Both processes are implemented in an ocean model thanks to a tensor related to the mesoscale eddies. The antisymmetric part of this tensor is computed from the Gent-McWilliams velocity and is subsequently included in the tracer advection equation. This velocity can be constructed to be divergence-free. The symmetric part that describes the diapycnal and isopycnal diffusions requires a special treatment. A stable and physically sound isopycnal tracer diffusion scheme is needed. Here, an interior penalty method is chosen that enables to build stable diffusion terms. However, due to the strong anisotropy of the diffusion, the common-usual penalty factor by Ern et al. (2008) is not sufficient. A novel method for computing the penalty term of Ern is then proposed for diffusion equations when both the diffusivity and the mesh are strongly anisotropic. Two test cases are resorted to validate the methodology and two more realistic applications illustrate the diapycnal and isopycnal diffusions, as well as the Gent-McWilliams velocity.
Directory of Open Access Journals (Sweden)
Guodong Liu
2013-01-01
Full Text Available Modular pebble-bed nuclear reactor (MPBNR technology is promising due to its attractive features such as high fuel performance and inherent safety. Particle motion of fuel and graphite pebbles is highly associated with the performance of pebbled-bed modular nuclear reactor. To understand the mechanism of pebble’s motion in the reactor, we numerically studied the influence of number ratio of fuel and graphite pebbles, funnel angle of the reactor, height of guide ring on the distribution of pebble position, and velocity by means of discrete element method (DEM in a two-dimensional MPBNR. Velocity distributions at different areas of the reactor as well as mixing characteristics of fuel and graphite pebbles were investigated. Both fuel and graphite pebbles moved downward, and a uniform motion was formed in the column zone, while pebbles motion in the cone zone was accelerated due to the decrease of the cross sectional flow area. The number ratio of fuel and graphite pebbles and the height of guide ring had a minor influence on the velocity distribution of pebbles, while the variation of funnel angle had an obvious impact on the velocity distribution. Simulated results agreed well with the work in the literature.
Energy Technology Data Exchange (ETDEWEB)
Huang, Hai; Plummer, Mitchell; Podgorney, Robert
2013-02-01
Advancement of EGS requires improved prediction of fracture development and growth during reservoir stimulation and long-term operation. This, in turn, requires better understanding of the dynamics of the strongly coupled thermo-hydro-mechanical (THM) processes within fractured rocks. We have developed a physically based rock deformation and fracture propagation simulator by using a quasi-static discrete element model (DEM) to model mechanical rock deformation and fracture propagation induced by thermal stress and fluid pressure changes. We also developed a network model to simulate fluid flow and heat transport in both fractures and porous rock. In this paper, we describe results of simulations in which the DEM model and network flow & heat transport model are coupled together to provide realistic simulation of the changes of apertures and permeability of fractures and fracture networks induced by thermal cooling and fluid pressure changes within fractures. Various processes, such as Stokes flow in low velocity pores, convection-dominated heat transport in fractures, heat exchange between fluid-filled fractures and solid rock, heat conduction through low-permeability matrices and associated mechanical deformations are all incorporated into the coupled model. The effects of confining stresses, developing thermal stress and injection pressure on the permeability evolution of fracture and fracture networks are systematically investigated. Results are summarized in terms of implications for the development and evolution of fracture distribution during hydrofracturing and thermal stimulation for EGS.
Directory of Open Access Journals (Sweden)
A. Herman
2015-07-01
Full Text Available This paper presents theoretical foundations, numerical implementation and examples of application of a two-dimensional Discrete-Element bonded-particle Sea Ice model DESIgn. In the model, sea ice is represented as an assemblage of objects of two types: disk-shaped "grains", and semi-elastic bonds connecting them. Grains move on the sea surface under the influence of forces from the atmosphere and the ocean, as well as interactions with surrounding grains through a direct contact (Hertzian contact mechanics and/or through bonds. The model has an option of taking into account quasi-threedimensional effects related to space- and time-varying curvature of the sea surface, thus enabling simulation of ice breaking due to stresses resulting from bending moments associated with surface waves. Examples of the model's application to simple sea ice deformation and breaking problems are presented, with an analysis of the influence of the basic model parameters ("microscopic" properties of grains and bonds on the large-scale response of the modeled material. The model is written as a toolbox suitable for usage with the open-source numerical library LIGGGHTS. The code, together with a full technical documentation and example input files, is freely available with this paper and on the Internet.
Tran, Quoc Anh; Chevalier, Bastien; Benz, Miguel; Breul, Pierre; Gourvès, Roland
2017-06-01
The recent technological developments made on the light dynamic penetration test Panda 3 ® provide a dynamic load-penetration curve σp - sp for each impact. This curve is influenced by the mechanical and physical properties of the investigated granular media. In order to analyze and exploit the load-penetration curve, a numerical model of penetration test using 3D Discrete Element Method is proposed for reproducing tests in dynamic conditions in granular media. All parameters of impact used in this model have at first been calibrated by respecting mechanical and geometrical properties of the hammer and the rod. There is a good agreement between experimental results and the ones obtained from simulations in 2D or 3D. After creating a sample, we will simulate the Panda 3 ®. It is possible to measure directly the dynamic load-penetration curve occurring at the tip for each impact. Using the force and acceleration measured in the top part of the rod, it is possible to separate the incident and reflected waves and then calculate the tip's load-penetration curve. The load-penetration curve obtained is qualitatively similar with that obtained by experimental tests. In addition, the frequency analysis of the measured signals present also a good compliance with that measured in reality when the tip resistance is qualitatively similar.
Herman, Agnieszka
2016-04-01
This paper presents theoretical foundations, numerical implementation and examples of application of the two-dimensional Discrete-Element bonded-particle Sea Ice model - DESIgn. In the model, sea ice is represented as an assemblage of objects of two types: disk-shaped "grains" and semi-elastic bonds connecting them. Grains move on the sea surface under the influence of forces from the atmosphere and the ocean, as well as interactions with surrounding grains through direct contact (Hertzian contact mechanics) and/or through bonds. The model has an experimental option of taking into account quasi-three-dimensional effects related to the space- and time-varying curvature of the sea surface, thus enabling simulation of ice breaking due to stresses resulting from bending moments associated with surface waves. Examples of the model's application to simple sea ice deformation and breaking problems are presented, with an analysis of the influence of the basic model parameters ("microscopic" properties of grains and bonds) on the large-scale response of the modeled material. The model is written as a toolbox suitable for usage with the open-source numerical library LIGGGHTS. The code, together with full technical documentation and example input files, is freely available with this paper and on the Internet.
Zou, Zongxing; Tang, Huiming; Xiong, Chengren; Su, Aijun; Criss, Robert E.
2017-10-01
The Jiweishan rockslide of June 5, 2009 in China provides an important opportunity to elucidate the kinetic characteristics of high-speed, long-runout debris flows. A 2D discrete element model whose mechanical parameters were calibrated using basic field data was used to simulate the kinetic behavior of this catastrophic landslide. The model output shows that the Jiweishan debris flow lasted about 3 min, released a gravitational potential energy of about 6 × 10^13 J with collisions and friction dissipating approximately equal amounts of energy, and had a maximum fragment velocity of 60-70 m/s, almost twice the highest velocity of the overall slide mass (35 m/s). Notable simulated characteristics include the high velocity and energy of the slide material, the preservation of the original positional order of the slide blocks, the inverse vertical grading of blocks, and the downslope sorting of the slide deposits. Field observations that verify these features include uprooted trees in the frontal collision area of the air-blast wave, downslope reduction of average clast size, and undamaged plants atop huge blocks that prove their lack of downslope tumbling. The secondary acceleration effect and force chains derived from the numerical model help explain these deposit features and the long-distance transport. Our back-analyzed frictions of the motion path in the PFC model provide a reference for analyzing and predicting the motion of similar geological hazards.
2017-01-01
We report a computational fluid dynamics–discrete element method (CFD-DEM) simulation study on the interplay between mass transfer and a heterogeneous catalyzed chemical reaction in cocurrent gas-particle flows as encountered in risers. Slip velocity, axial gas dispersion, gas bypassing, and particle mixing phenomena have been evaluated under riser flow conditions to study the complex system behavior in detail. The most important factors are found to be directly related to particle cluster formation. Low air-to-solids flux ratios lead to more heterogeneous systems, where the cluster formation is more pronounced and mass transfer more influenced. Falling clusters can be partially circumvented by the gas phase, which therefore does not fully interact with the cluster particles, leading to poor gas–solid contact efficiencies. Cluster gas–solid contact efficiencies are quantified at several gas superficial velocities, reaction rates, and dilution factors in order to gain more insight regarding the influence of clustering phenomena on the performance of riser reactors. PMID:28553011
Marson, Ryan; Spellings, Matthew; Anderson, Joshua; Glotzer, Sharon
2014-03-01
Faceted shapes, such as polyhedra, are commonly created in experimental systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystalline nucleation and growth, vacancy motion, and glassy dynamics, are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We report the first implementation of DEM MD intended for thermodynamic nanoscale simulation. Our method is implemented in parallel on the GPU within the HOOMD-Blue framework. By decomposing the force calculation into its components, this implementation can take advantage of massive data parallelism, enabling optimal use of the GPU for even relatively small systems while achieving a speedup of 60 times over a single CPU core. This method is a natural extension of classical molecular dynamics into the realm of faceted particles, and allows simulation of disparate size scales ranging from the nanoscale to granular particulates, all within the same framework.
Directory of Open Access Journals (Sweden)
Goh Wei Pin
2017-01-01
Full Text Available The size distribution, shape and aspect ratio of particles are the common factors that affect their packing in a particle bed. Agitated powder beds are commonly used in the process industry for various applications. The stresses arising as a result of shearing the bed could result in undesirable particle breakage with adverse impact on manufacturability. We report on our work on analysing the stress distribution within an agitated particle bed with several particle aspect ratios by the Discrete Element Method (DEM. Rounded cylinders with different aspect ratios are generated and incorporated into the DEM simulation. The void fraction of the packing of the static and agitated beds with different particle aspect ratios is analysed. Principal and deviatoric stresses are quantified in the regions of interest along the agitating impeller blade for different cases of particle aspect ratios. The relationship between the particle aspect ratio and the stress distribution of the bed over the regions of interest is then established and will be presented.
Smart, Kevin J.; Wyrick, Danielle Y.; Ferrill, David A.
2011-04-01
Pit craters, circular to elliptical depressions that lack a raised rim or ejecta deposits, are common on the surface of Mars. Similar structures are also found on Earth, Venus, the Moon, and smaller planetary bodies, including some asteroids. While it is generally accepted that these pits form in response to material drainage into a subsurface void space, the primary mechanism(s) responsible for creating the void is a subject of debate. Previously proposed mechanisms include collapse into lave tubes, dike injection, extensional fracturing, and dilational normal faulting. In this study, we employ two-dimensional discrete element models to assess both extensional fracturing and dilational normal faulting as mechanisms for forming pit craters. We also examine the effect of mechanical stratigraphy (alternating strong and weak layers) and variation in regolith thickness on pit morphology. Our simulations indicate that both extensional fracturing and dilational normal faulting are viable mechanisms. Both mechanisms lead to generally convex (steepening downward) slope profiles; extensional fracturing results in generally symmetric pits, whereas dilational normal faulting produces strongly asymmetric geometries. Pit width is established early, whereas pit depth increases later in the deformation history. Inclusion of mechanical stratigraphy results in wider and deeper pits, particularly for the dilational normal faulting, and the presence of strong near-surface layers leads to pits with distinct edges as observed on Mars. The modeling results suggest that a thicker regolith leads to wider but shallower pits that are less distinct and may be more difficult to detect in areas of thick regolith.
Palha, Artur
2016-01-01
In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular grids.
Palha, A.; Gerritsma, M.
2017-01-01
In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured triangular grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular triangular grids.
Lisjak, Andrea; Tatone, Bryan S. A.; Mahabadi, Omid K.; Grasselli, Giovanni; Marschall, Paul; Lanyon, George W.; Vaissière, Rémi de la; Shao, Hua; Leung, Helen; Nussbaum, Christophe
2016-05-01
The analysis and prediction of the rock mass disturbance around underground excavations are critical components of the performance and safety assessment of deep geological repositories for nuclear waste. In the short term, an excavation damaged zone (EDZ) tends to develop due to the redistribution of stresses around the underground openings. The EDZ is associated with an increase in hydraulic conductivity of several orders of magnitude. In argillaceous rocks, sealing mechanisms ultimately lead to a partial reduction in the effective hydraulic conductivity of the EDZ with time. The goal of this study is to strengthen the understanding of the phenomena involved in the EDZ formation and sealing in Opalinus Clay, an indurated claystone currently being assessed as a host rock for a geological repository in Switzerland. To achieve this goal, hybrid finite-discrete element method (FDEM) simulations are performed. With its explicit consideration of fracturing processes, FDEM modeling is applied to the HG-A experiment, an in situ test carried out at the Mont Terri underground rock laboratory to investigate the hydro-mechanical response of a backfilled and sealed microtunnel. A quantitative simulation of the EDZ formation process around the microtunnel is first carried out, and the numerical results are compared with field observations. Then, the re-compression of the EDZ under the effect of a purely mechanical loading, capturing the increase of swelling pressure from the backfill onto the rock, is considered. The simulation results highlight distinctive rock failure kinematics due to the bedded structure of the rock mass. Also, fracture termination is simulated at the intersection with a pre-existing discontinuity, representing a fault plane oblique to the bedding orientation. Simulation of the EDZ re-compression indicates an overall reduction of the total fracture area as a function of the applied pressure, with locations of ineffective sealing associated with self
Falkingham, Peter L; Gatesy, Stephen M
2014-12-23
Locomotion over deformable substrates is a common occurrence in nature. Footprints represent sedimentary distortions that provide anatomical, functional, and behavioral insights into trackmaker biology. The interpretation of such evidence can be challenging, however, particularly for fossil tracks recovered at bedding planes below the originally exposed surface. Even in living animals, the complex dynamics that give rise to footprint morphology are obscured by both foot and sediment opacity, which conceals animal-substrate and substrate-substrate interactions. We used X-ray reconstruction of moving morphology (XROMM) to image and animate the hind limb skeleton of a chicken-like bird traversing a dry, granular material. Foot movement differed significantly from walking on solid ground; the longest toe penetrated to a depth of ∼5 cm, reaching an angle of 30° below horizontal before slipping backward on withdrawal. The 3D kinematic data were integrated into a validated substrate simulation using the discrete element method (DEM) to create a quantitative model of limb-induced substrate deformation. Simulation revealed that despite sediment collapse yielding poor quality tracks at the air-substrate interface, subsurface displacements maintain a high level of organization owing to grain-grain support. Splitting the substrate volume along "virtual bedding planes" exposed prints that more closely resembled the foot and could easily be mistaken for shallow tracks. DEM data elucidate how highly localized deformations associated with foot entry and exit generate specific features in the final tracks, a temporal sequence that we term "track ontogeny." This combination of methodologies fosters a synthesis between the surface/layer-based perspective prevalent in paleontology and the particle/volume-based perspective essential for a mechanistic understanding of sediment redistribution during track formation.
Zeeb, Conny; Frühwirt, Thomas; Konietzky, Heinz
2015-04-01
Key to a successful exploitation of deep geothermal reservoirs in a petrothermal environment is the hydraulic stimulation of the host rock to increase permeability. The presented research investigates the fracture propagation and interaction during hydraulic stimulation of multiple fractures in a highly anisotropic stress field. The presented work was conducted within the framework of the OPTIRISS project, which is a cooperation of industry partners and universities in Thuringia and Saxony (Federal States of Germany) and was funded by the European Fond for Regional Development. One objective was the design optimization of the subsurface geothermal heat exchanger (SGHE) by means of numerical simulations. The presented simulations were conducted applying 3DEC (Itasca™), a software tool based on the discrete element method. The simulation results indicate that the main direction of fracture propagation is towards lower stresses and thus towards the biosphere. Therefore, barriers might be necessary to limit fracture propagation to the designated geological formation. Moreover, the hydraulic stimulation significantly alters the stresses in the vicinity of newly created fractures. Especially the change of the minimum stress component affects the hydraulic stimulation of subsequent fractures, which are deflected away from the previously stimulated fractures. This fracture deflection can render it impossible to connect all fractures with a second borehole for the later production. The results of continuative simulations indicate that a fracture deflection cannot be avoided completely. Therefore, the stage alignment was modified to minimize fracture deflection by varying (1) the pauses between stages, (2) the spacing's between adjacent stages, and (3) the angle between stimulation borehole and minimum stress component. An optimum SGHE design, which implies that all stimulated fractures are connected to the production borehole, can be achieved by aligning the stimulation
Yoon, Jeoung Seok; Zang, Arno; Zimmermann, Günter; Stephansson, Ove
2016-04-01
, Ellsworth WL, Stump BW, Hayward C, Frohlich C, Oldham HR, Olson JE, Magnani MB, Brokaw C, Luetgert JH, 2015, Causal factors for seismicity near Azle, Texas, nature communications 6:6728, DOI: 10.1038/ncomms7728 [3] Yoon JS, Zimmermann G, Zang A, Stephansson O, 2015, Discrete element modeling of fluid injection-induced seismicity and activation of nearby fault, Can Geotech J 52: 1457-1465, DOI: 10.1139/cgj-2014-0435.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
examples on regular languages. Apply these concepts to new problems. Finite state machines: Define a finite state machine as a 6-tuble; describe simple finite state machines by tables and graphs; pattern recognition by finite state machines; minimizing the number of states in a finite state machine......The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... of natural numbers. Apply these concepts to new problems. Division and factorizing: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Regular languages: Define a language from the elements of a set; define a regular language; form strings from a regular language; construct...
Directory of Open Access Journals (Sweden)
Akimov Pavel
2016-01-01
Full Text Available The distinctive paper is devoted to the two-dimensional semi-analytical solution of boundary problems of analysis of shear walls with the use of discrete-continual finite element method (DCFEM. This approach allows obtaining the exact analytical solution in one direction (so-called “basic” direction, also decrease the size of the problem to one-dimensional common finite element analysis. Two numerical examples of structural analysis with the use of DCFEM are considered, conventional finite element method (FEM is used for verification purposes. The presented examples show some of the advantages of the suggested approach to semianalytical analysis of the shear wall. Future development of DCFEM, particularly associated with multigrid approach, is under consideration as well.
Institute of Scientific and Technical Information of China (English)
Yin-nianHe
2004-01-01
In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a H1-optimal velocity approximation and a L2-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small,nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, one linear Stokes problem on the fine mesh with mesh size h <
Institute of Scientific and Technical Information of China (English)
Pooya Hamdi; Doug Stead; Davide Elmo
2015-01-01
abstract Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks are usually observed in crystalline rocks in two forms: natural and stress-induced; the amount of stress-induced microcracking increases with depth and in-situ stress. Laboratory results indicate that the physical properties of rocks such as strength, deformability, P-wave velocity and permeability are influenced by increase in microcrack intensity. In this study, the finite-discrete element method (FDEM) is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network (mDFN) approach. The characteristics of the microcracks required to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial, triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data. The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the me-chanical behavior and resultant fracture pattern. An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope. Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement. Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone, and the frictional strength component remains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. The importance of microcrack heterogeneity in reproducing
Zampini, Stefano
2016-06-02
Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically established that are independent of the number of subdomains of the decomposition. The core of the methods resides in the design of a larger and partially discontinuous finite element space that allows for fast application of the preconditioner, where Cholesky factorizations of the subdomain finite element problems are additively combined with a coarse, global solver. Multilevel and highly-scalable algorithms can be obtained by replacing the coarse Cholesky solver with a coarse BDDC preconditioner. BDDC methods have the remarkable ability to control the condition number, since the coarse space of the preconditioner can be adaptively enriched at the cost of solving local eigenproblems. The proper identification of these eigenproblems extends the robustness of the methods to any heterogeneity in the distribution of the coefficients of the PDEs, not only when the coefficients jumps align with the subdomain boundaries or when the high contrast regions are confined to lie in the interior of the subdomains. The specific adaptive technique considered in this paper does not depend upon any interaction of discretization and partition; it relies purely on algebraic operations. Coarse space adaptation in BDDC methods has attractive algorithmic properties, since the technique enhances the concurrency and the arithmetic intensity of the preconditioning step of the sparse implicit solver with the aim of controlling the number of iterations of the Krylov method in a black-box fashion, thus reducing the number of global synchronization steps and matrix vector multiplications needed by the iterative solver; data movement and memory bound kernels in the solve phase can be thus limited at the expense of extra local ops during the setup of
Zhang, Rong; Verkruysse, Wim; Aguilar, Guillermo; Nelson, J Stuart
2005-09-07
Both diffusion approximation (DA) and Monte Carlo (MC) models have been used to simulate light distribution in multilayered human skin with or without discrete blood vessels. However, no detailed comparison of the light distribution, heat generation and induced thermal damage between these two models has been done for discrete vessels. Three models were constructed: (1) MC-based finite element method (FEM) model, referred to as MC-FEM; (2) DA-based FEM with simple scaling factors according to chromophore concentrations (SFCC) in the epidermis and vessels, referred to as DA-FEM-SFCC; and (3) DA-FEM with improved scaling factors (ISF) obtained by equalizing the total light energy depositions that are solved from the DA and MC models in the epidermis and vessels, respectively, referred to as DA-FEM-ISF. The results show that DA-FEM-SFCC underestimates the light energy deposition in the epidermis and vessels when compared to MC-FEM. The difference is nonlinearly dependent on wavelength, dermal blood volume fraction, vessel size and depth, etc. Thus, the temperature and damage profiles are also dramatically different. DA-FEM-ISF achieves much better results in calculating heat generation and induced thermal damage when compared to MC-FEM, and has the advantages of both calculation speed and accuracy. The disadvantage is that a multidimensional ISF table is needed for DA-FEM-ISF to be a practical modelling tool.
Profit, Matthew; Dutko, Martin; Yu, Jianguo; Cole, Sarah; Angus, Doug; Baird, Alan
2016-04-01
This paper presents a novel approach to predict the propagation of hydraulic fractures in tight shale reservoirs. Many hydraulic fracture modelling schemes assume that the fracture direction is pre-seeded in the problem domain discretisation. This is a severe limitation as the reservoir often contains large numbers of pre-existing fractures that strongly influence the direction of the propagating fracture. To circumvent these shortcomings, a new fracture modelling treatment is proposed where the introduction of discrete fracture surfaces is based on new and dynamically updated geometrical entities rather than the topology of the underlying spatial discretisation. Hydraulic fracturing is an inherently coupled engineering problem with interactions between fluid flow and fracturing when the stress state of the reservoir rock attains a failure criterion. This work follows a staggered hydro-mechanical coupled finite/discrete element approach to capture the key interplay between fluid pressure and fracture growth. In field practice, the fracture growth is hidden from the design engineer and microseismicity is often used to infer hydraulic fracture lengths and directions. Microseismic output can also be computed from changes of the effective stress in the geomechanical model and compared against field microseismicity. A number of hydraulic fracture numerical examples are presented to illustrate the new technology.
Stühler, Sven; Fleissner, Florian; Eberhard, Peter
2016-11-01
We present an extended particle model for the discrete element method that on the one hand is tetrahedral in shape and on the other hand is capable to describe deformations. The deformations of the tetrahedral particles require a framework to interrelate the particle strains and resulting stresses. Hence, adaptations from the finite element method were used. This allows to link the two methods and to adequately describe material and simulation parameters separately in each scope. Due to the complexity arising of the non-spherical tetrahedral geometry, all possible contact combinations of vertices, edges, and surfaces must be considered by the used contact detection algorithm. The deformations of the particles make the contact evaluation even more challenging. Therefore, a robust contact detection algorithm based on an optimization approach that exploits temporal coherence is presented. This algorithm is suitable for general {R}^{{n}} simplices. An evaluation of the robustness of this algorithm is performed using a numerical example. In order to create complex geometries, bonds between these deformable particles are introduced. This coupling via the tetrahedra faces allows the simulation bonding of deformable bodies composed of several particles. Numerical examples are presented and validated with results that are obtained by the same simulation setup modeled with the finite element method. The intention of using these bonds is to be able to model fracture and material failure. Therefore, the bonds between the particles are not lasting and feature a release mechanism based on a predefined criterion.
Directory of Open Access Journals (Sweden)
Vadim N. Glinskiy
2017-05-01
Full Text Available In memory of an outstanding palaeoichthyologist Elga Mark-Kurik The range of diversity of psammosteids from the family Psammosteidae is still poorly known. Here a new species, Psammosteus ramosus sp. nov. Glinskiy, from the Amata Regional Stage of the Main Devonian Field is described. Its morphology, ornamentation, histology of exoskeletal plates, and micromeric elements are compared with those of other representatives of the family Psammosteidae. The comparison shows a close relationship of the new species with Psammosteus falcatus Obruchev, P. kiaeri Halstead Tarlo and P. pectinatus Obruchev, a group of species that is significantly different from other representatives of the genus Psammosteus and constitutes a separate evolutionary lineage. On the basis of morphological and histological features we here differentiate in the fields of tesserae of Psammosteidae the discrete micromeric elements of the ‘basic type’, known in Psammosteus bergi (Obruchev, P. levis Obruchev, P. livonicus Obruchev, P. maeandrinus Agassiz, P. megalopteryx (Trautschold, P. praecursor Obruchev and Karelosteus weberi Obruchev, and micromeric elements of the ‘progressive type’, known in Psammosteus falcatus, P. cf. kiaeri and P. ramosus sp. nov. Glinskiy.
1983-11-01
element u.-lei is readily applied to such flows. For lully developed flow V = 0, and U and H are functions of y only (i.e., J ■ U(y) and H ■ H(y...included, application of the basic momentum theorem yields T b |£| . / w+ Jb \\ T r ’dx’ I W < s,av where T is the average shear stress
大西, 泰史
2017-01-01
The purpose of this study is to perform to earth pressure coefficient calculation simulation using the Distinct Element Method (DEM). Earth pressure theory has been established since long ago and is still in use. Therefore, simulation based on Coulomb and Rankine's theory of earth pressure is carried out to confirm usability of DEM. As a result of the static earth pressure coefficient calculation simulation, good results were obtained. However, in the passive earth pressure coefficient calcul...
Directory of Open Access Journals (Sweden)
L. Jones Tarcius Doss
2012-01-01
Full Text Available A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.
Gui, Y. L.; Zhao, Z. Y.; Zhou, H. Y.; Wu, W.
2016-10-01
In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [Idaho National Lab. (INL), Idaho Falls, ID (United States); Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Mattson, Earl [Idaho National Lab. (INL), Idaho Falls, ID (United States); Wang, Herb F. [Univ. of Wisconsin, Madison, WI (United States); Haimson, Bezalel C. [Univ. of Wisconsin, Madison, WI (United States); Doe, Thomas W. [Golder Associates Inc., Redmond, VA (United States); Oldenburg, Curtis M. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Dobson, Patrick F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-02-01
Aimed at supporting the design of hydraulic fracturing experiments at the kISMET site, ~1500 m below ground in a deep mine, we performed pre-experimental hydraulic fracturing simulations in order to estimate the breakdown pressure, propagation pressure, fracture geometry, and the magnitude of induced seismicity using a newly developed fully coupled three-dimensional (3D) network flow and quasi-static discrete element model (DEM). The quasi-static DEM model, which is constructed by Delaunay tessellation of the rock volume, considers rock fabric heterogeneities by using the “disordered” DEM mesh and adding random perturbations to the stiffness and tensile/shear strengths of individual DEM elements and the elastic beams between them. A conjugate 3D flow network based on the DEM lattice is constructed to calculate the fluid flow in both the fracture and porous matrix. One distinctive advantage of the model is that fracturing is naturally described by the breakage of elastic beams between DEM elements. It is also extremely convenient to introduce mechanical anisotropy into the model by simply assigning orientation-dependent tensile/shear strengths to the elastic beams. In this paper, the 3D hydraulic fracturing model was verified against the analytic solution for a penny-shaped crack model. We applied the model to simulate fracture propagation from a vertical open borehole based on initial estimates of rock mechanical properties and in-situ stress conditions. The breakdown pressure and propagation pressure are directly obtained from the simulation. In addition, the released elastic strain energies of individual fracturing events were calculated and used as a conservative estimate for the magnitudes of the potential induced seismic activities associated with fracturing. The comparisons between model predictions and experimental results are still ongoing.
Zou, Feng; Yuan, De-Yi; Gao, Chao; Liao, Ting; Chen, Wen-Tao; Han, Zhi-Qiang; Zhang, Lin
2014-04-01
In order to elucidate the nutrition of Camellia olei fera at pollination and fertilization stages, the contents of mineral elements were determined by auto discrete analyzers and atomic absorption spectrophotometer, and the change in the contents of mineral elements was studied and analysed under the condition of self- and cross-pollination. The results are showed that nine kinds of mineral elements contents were of "S" or "W" type curve changes at the pollination and fertilization stages of Camellia olei fera. N, K, Zn, Cu, Ca, Mn element content changes showed "S" curve under the self- and out-crossing, the content of N reaching the highest was 3.445 8 mg x g(-1) in self-pollination of 20 d; K content reaching the highest at the cross-pollination 20 d was 6.275 5 mg x g(-1); Zn content in self-pollination of 10 d reaching the highest was 0.070 5 mg x g(-1); Cu content in the cross-pollination of 5 d up to the highest was 0.061 0 mg x g(-1); Ca content in the cross-pollination of 15 d up to the highest was 3.714 5 mg x g(-1); the content of Mn reaching the highest in self-pollination 30 d was 2. 161 5 mg x g(-1). Fe, P, Mg element content changes was of "S" type curve in selfing and was of "W" type curve in outcrossing, Fe content in the self-pollination 10 d up to the highest was 0.453 0 mg x g(-1); P content in self-pollination of 20 d reaching the highest was 6.731 8 mg x g(-1); the content of Mg up to the highest in self-pollination 25 d was 2.724 0 mg x g(-1). The results can be used as a reference for spraying foliar fertilizer, and improving seed setting rate and yield in Camellia olei fera.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
铁路散体道床捣固作业的离散元分析∗%Discrete Element Analysis of Railway Ballast under Tamping Operation
Institute of Scientific and Technical Information of China (English)
周陶勇; 胡斌
2016-01-01
捣固作业是铁路散体道床养护维修作业中一项重要的工作，由于铁路散体道床是由形状大小各异的散粒体道砟组成的，这就给捣固效果的研究带来了一定的困难。为了从微观尺度上对铁路散体道床捣固作业进行研究，运用离散元分析方法，创建了铁路散体道床捣固作业的离散元分析模型，分析了捣固作业过程中道砟的流动趋势和道床的密实程度。分析表明，在捣固作业过程中，轨枕之间的道砟向轨枕下方有空隙的地方流动，轨枕下方捣固区域的道床密实程度得到了提高。%Tamping operation is an important work in the railway ballast maintenance and repair operations,because the railway ballast is composed of various shapes and sizes of granular ballast gravel,which bring some difficulty to research the tamping effect.In order to study on railway ballast under tamping operation from micro scale,the discrete element analysis model of railway ballast under tamping operation is created using discrete element method,and the research is done on the motion trend of ballast gravel and compaction degree of railway ballast during the tamping process.The analysis shows that the ballast gravels between sleepers are moved to fill the voids under sleeper and the ballast compactness in tamping area un-der sleeper is also improved during tamping process.
Directory of Open Access Journals (Sweden)
Tran Quoc Anh
2017-01-01
Full Text Available The recent technological developments made on the light dynamic penetration test Panda 3 ® provide a dynamic load–penetration curve σp – sp for each impact. This curve is influenced by the mechanical and physical properties of the investigated granular media. In order to analyze and exploit the load-penetration curve, a numerical model of penetration test using 3D Discrete Element Method is proposed for reproducing tests in dynamic conditions in granular media. All parameters of impact used in this model have at first been calibrated by respecting mechanical and geometrical properties of the hammer and the rod. There is a good agreement between experimental results and the ones obtained from simulations in 2D or 3D. After creating a sample, we will simulate the Panda 3 ®. It is possible to measure directly the dynamic load–penetration curve occurring at the tip for each impact. Using the force and acceleration measured in the top part of the rod, it is possible to separate the incident and reflected waves and then calculate the tip’s load-penetration curve. The load–penetration curve obtained is qualitatively similar with that obtained by experimental tests. In addition, the frequency analysis of the measured signals present also a good compliance with that measured in reality when the tip resistance is qualitatively similar.
Discrete element contact model of vibratory feeder and its research%振动给料机的离散元接触模型及研究
Institute of Scientific and Technical Information of China (English)
吴昊; 杨亚罗
2011-01-01
The particulate discrete element method (DEM) is a new method of analysing the mechanical behavior of granular materials in various applications. The contact model is the basis of DEM, and dry granular model is currently used for simulation. According to the theory of DEM and the analysis of various granular models and their application to the vibratory feeder, the model proves applicable to the dry granular iron ore in the vibratory feeder, and it is simple and practical.%颗粒离散元法是分析散体力学行为的新方法,其应用涵盖诸多工程领域.接触模型是离散元法的基础,目前多采用干球颗粒模型模拟.根据离散元法的理论和各种颗粒作用模型及其在振动给料机中的应用分析可知,它适用于振动给料机干颗粒铁矿石物料,且简单实用.
Sheikh, Bahman; Pak, Ali
2015-05-01
Permeability of porous materials is an important characteristic which is extensively used in various engineering disciplines. There are a number of issues that influence the permeability coefficient among which the porosity, size of particles, pore shape, tortuosity, and particle size distribution are of great importance. In this paper a C++ GPU code based on three-dimensional lattice Boltzmann method (LBM) has been developed and used for investigating the effects of the above mentioned factors on the permeability coefficient of granular materials. Multirelaxation time collision scheme of the LBM equations is used in the simulator, which is capable of modeling the exact position of the fluid-solid interface leading to viscosity-independent permeabilities and better computational stability due to separation of the relaxations of various kinetic models. GPU-CPU parallel processing has been employed to reduce the computational time associated with three-dimensional simulations. Soil samples have been prepared using the discrete element method. The obtained results have demonstrated the importance of employing the concept of effective porosity instead of total porosity in permeability relationships. The results also show that a threshold porosity exists below which the connectivity of the pores vanishes and the permeability of the soils reduces drastically.
Virgo, Simon; Abe, Steffen; Urai, Janos L.
2016-03-01
We present the results of a comparative study of loading conditions on the interactions between extension fractures and veins. We model the fracture behavior of brittle discrete element materials each containing a tabular vein body of variable orientation and strength in two different loading conditions. The first is uniaxial tension, applied with servo-controlled sidewalls. The second is a boudinage boundary condition in which a tensile triaxial stress state is induced in the brittle model volume by quasi-viscous extensional deformation in the adjacent layers. Most of the fracture- vein interactions observed in uniaxial tension also exists in boudinage boundary conditions. However, the importance of each interaction mechanism for a given configuration of relative strength and misorientation of the vein may differ according to the loading mechanism. Nucleation and internal deflection is under both boundary conditions the dominating fracture-vein interaction style in weak veins. In uniaxial tension models, strong veins tend to alter the fracture path by external deflection, while under boudinage loading these veins are more likely overcome by the fracture step over mechanism. Dynamic bifurcation of fractures was observed in uniaxial tension models but never for boudinage boundary conditions. This is because the acceleration of fracture tips in these conditions is suppressed by interaction with distributed fractures as well as viscous damping by the neighboring layers.
Flach, S
1998-01-01
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattic...
Directory of Open Access Journals (Sweden)
Xiaolin Huang
2016-12-01
Full Text Available This paper numerically investigates the seismic response of the filled joint under high amplitude stress waves using the combined finite-discrete element method (FDEM. A thin layer of independent polygonal particles are used to simulate the joint fillings. Each particle is meshed using the Delaunay triangulation scheme and can be crushed when the load exceeds its strength. The propagation of the 1D longitude wave through a single filled joint is studied, considering the influences of the joint thickness and the characteristics of the incident wave, such as the amplitude and frequency. The results show that the filled particles under high amplitude stress waves mainly experience three deformation stages: (i initial compaction stage; (ii crushing stage; and (iii crushing and compaction stage. In the initial compaction stage and crushing and compaction stage, compaction dominates the mechanical behavior of the joint, and the particle area distribution curve varies little. In these stages, the transmission coefficient increases with the increase of the amplitude, i.e., peak particle velocity (PPV, of the incident wave. On the other hand, in the crushing stage, particle crushing plays the dominant role. The particle size distribution curve changes abruptly with the PPV due to the fragments created by the crushing process. This process consumes part of wave energy and reduces the stiffness of the filled joint. The transmission coefficient decreases with increasing PPV in this stage because of the increased amount of energy consumed by crushing. Moreover, with the increase of the frequency of the incident wave, the transmission coefficient decreases and fewer particles can be crushed. Under the same incident wave, the transmission coefficient decreases when the filled thickness increases and the filled particles become more difficult to be crushed.
Tseng, C. H.; Chan, Y. C.; Jeng, C. J.; Hsieh, Y. C.
2015-12-01
Slope failure is a widely observed phenomenon in hill and mountainous areas in Taiwan, which is characterized by high erosion rates (up to 60 mm/yr) due to its climatic and geographical conditions. Slope failure events easily occur after intense rainfall, especially resulting from typhoons and accordingly cause a great loss of human lives and property. At the northern end of the Western Foothill belt in northern Taiwan, Huafan University campus (121.692448˚ E, 24.980724˚ N ) is founded on a dip slope, ~20˚ toward southwest, being composed of early Miocene alternations of sandstone and shale. Data from continuous monitoring over the years by means of inclinometers and groundwater gauges reveal that creep of 6-10 mm of the slope occurred when precipitation exceeded 300 mm during typhoons' striking. In addition, extension cracks on the ground are also found within and on the edge of the campus. Furthermore, potential slip surfaces are detected shown by rock cores to exist 10 and 30 m in depth as well. To understand the kinematic behaviors of the rock slope failure beneath the university campus, a 3D discrete element mothed is applied in this study. Results of the modeling indicate that creeping is the primary behavior pattern when the friction coefficient reduces owing to rise of groundwater during rainstorms. However, rapid slip may take place under influences of earthquake with large magnitude. Suggestions for preventing the slope creep are to construct catchpits to drainage runoff and lower the groundwater table and ground anchors through the slip surfaces to stabilize the slide blocks.
Simonson, Scott; Hua, Peng; Luobin, Yan; Zhi, Chen
2016-04-01
Important to the evolution of Danxia landforms is how the rock cliffs are in large part shaped by rock collapse events, ranging from small break offs to large collapses. Quantitative research of Danxia landform evolution is still relatively young. In 2013-2014, Chinese and Slovak researchers conducted joint research to measure deformation of two large rock walls. In situ measurements of one rock wall found it to be stable, and Ps-InSAR measurements of the other were too few to be validated. Research conducted this year by Chinese researchers modeled the stress states of a stone pillar at Mt. Langshan, in Hunan Province, that toppled over in 2009. The model was able to demonstrate how stress states within the pillar changed as the soft basal layer retreated, but was not able to show the stress states at the point of complete collapse. According to field observations, the back side of the pillar fell away from the entire cliff mass before the complete collapse, and no models have been able to demonstrate the mechanisms behind this behavior. A further understanding of the mechanisms controlling rockfall events in Danxia landforms is extremely important because these stunning sceneries draw millions of tourists each year. Protecting the tourists and the infrastructure constructed to accommodate tourism is of utmost concern. This research will employ a UAV to as universally as possible photograph a stone pillar at Mt. Langshan that stands next to where the stone pillar collapsed in 2009. Using the recently developed structure-from-motion technique, a 3D model of the pillar will be constructed in order to extract geometrical data of the entire slope and its structural fabric. Also in situ measurements will be taken of the slope's toe during the field work exercises. These data are essential to constructing a realistic discrete element model using the 3DEC code and perform a kinematic analysis of the rock mass. Intact rock behavior will be based on the Mohr Coulomb
Discrete Stein characterizations and discrete information distances
Ley, Christophe
2012-01-01
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
COREX3000竖炉布料的离散元模型%Discrete Element Model for Charging Process of COREX 3000 Shaft
Institute of Scientific and Technical Information of China (English)
李强; 冯明霞; 邹宗树
2012-01-01
The gas distribution in a shaft furnace dominates the temperature profile, gas utilization ratio, metallization degree and is the only means for regulating the gas flow distribution. Through introducing kinematic theory of granular, a numerical simulation model of burden distribution in the shaft furnace of COREX 3000 was developed by means of discrete element method (DEM) based on the Newton second law and soft-sphere contact model. The model can intuitively and visually reproduce the charging process, and quantitatively access the material flow trajectories, landing and forming process of the burden surface shape. Applying the model to further analyze the mixing charging process of two different diameter particle, obtained the charge movement process and the formation of the stockpile and found that size segregation is serious. Therefore, the model provides an important research base established model to find and optimize the charge patterns.%竖炉内煤气流的分布主宰着其内温度分布、煤气利用率和金属化率的高低，其上部调节方式仅有布料模式。通过引入离散颗粒动力学理论，基于经典牛顿力学和颗粒碰撞软球模型建立了针对COREX3000竖炉布料过程的离散元数值模拟模型，模型直观可视化再现装料过程，可定量获得料流轨迹、炉料落点及形成料堆的过程。应用模型进一步分析混装2种不同粒径颗粒，获得了炉料运动及形成的料堆过程，发现混装布料过程粒度偏析严重。建立的模型可为寻找和优化合理的布料模式提供重要研究基础。
Discrete Element Simulation of Wet Particles Flow Behavior in Riser%提升管内湿颗粒流动特性的离散元模拟
Institute of Scientific and Technical Information of China (English)
朱卫兵; 李锦时; 王猛; 孙巧群
2013-01-01
采用离散单元法模拟了二维提升管内湿颗粒的流动和团聚特性。考虑颗粒所受重力、颗粒间(颗粒与壁面间)的碰撞力、摩擦力、液桥力以及气体对颗粒的曳力和浮力。预测提升管内湿颗粒的流动行为，得到不同含湿量下颗粒浓度和轴向速度的分布，并且定量分析了湿颗粒的团聚特性。结果显示：湿颗粒在提升管内呈现边壁浓、中心稀的环核流动结构；由于液桥力的存在，提升管内湿颗粒出现团聚现象，且颗粒以单颗粒和聚团2种方式运动；含湿量对颗粒聚团存在时间、聚团时间份额和聚团生成频率有较大的影响。%The wet particles flow and agglomerate characteristics in a two-dimensional riser was numerically simulated by discrete element method (DEM). The force acting on particle included gravity, particle-particle or particle-wall interactions (i.e. contact force, friction force and liquid bridge force), drag force and pressure gradient force. In this paper, the flow behavior of wet particles was predicted, and the distribution characteristics of particle concentration and axial velocity at various moisture contents were obtained. Then, agglomeration characteristics of wet particles were analyzed quantitatively. The results indicate that a core-annulus flow structure with a dense phase near the walls, and a dilute phase in the center are formed in wet particles riser. The results show that due to existence of the liquid bridge force, it appears wet particles agglomeration phenomenon, and the motions of wet particles in the riser have two ways with single particles and agglomerates. There are significant influences of moisture content on agglomerate duration time, agglomerate time fraction and frequency of agglomerate occurrence.
Energy Technology Data Exchange (ETDEWEB)
Fynn, K.A.; Faraone, L. [Univ. of Western Australia, Nedlands (Australia). Dept. of Electrical and Electronic Engineering; Bajaj, J. [Rockwell International Science Center, Thousand Oaks, CA (United States)
1995-10-01
The non-destructive optical characterization technique of Laser-Beam-Induced-Current (LBIC) imaging has proven useful in qualitatively assessing electrically active defects and localized non-uniformities in HgCdTe materials and devices used for infrared photovoltaic arrays. To further the development of a quantitative working model for LBIC, this paper focuses on the application of the technique to photovoltaic structures that are represented by a discrete element equivalent circuit. For this particular case the LBIC signal arises due to the lateral photovoltaic effect in non-uniformly illuminated open-circuit photodiodes. The outcomes of the model predict all of the experimentally observed geometrical features of the LBIC image and signal. Furthermore, the model indicates that the LBIC signal has an extremely weak dependence on the p-n junction reverse saturation current, and shows a linear dependence with laser power. This latter feature may be useful for non-contact measurement of the quantum efficiency of individual photodiodes within a large two-dimensional focal plane array. The decay of the LBIC signal outside the physical boundary of the p-n junction is of the same form as the roll-off in the short circuit photoresponse and, therefore, can be used to extract the diffusion length of minority carriers. Experimental data are obtained from an arsenic implanted p-on-n junction fabricated on MBE grown Hg{sub 1{minus}x}Cd{sub x}Te material with an x-value of 0.3. The p-on-n diode is shown to be uniform and of high quality with an R{sub o}A product of 1 {times} 10{sup 8} {Omega}{center_dot}cm{sup 2} at 77 K. The validity of the simple model developed in this paper, is confirmed by the excellent agreement with experimental results. Consequently, the LBIC technique is shown to be an appropriate diagnostic tool for non-contact quantitative analysis of semiconductor materials and devices.
基于颗粒尺度的离散颗粒传热模型%Heat transfer model for particles with discrete element method
Institute of Scientific and Technical Information of China (English)
卜昌盛; 陈晓平; 刘道银; 段钰锋
2012-01-01
颗粒间传热在诸多工业过程中有着十分重要的作用.详细考虑颗粒间传热机理,对颗粒间各传热途径建模,包括颗粒内部导热、颗粒粗糙表面传热、颗粒表面气膜及接触颗粒间隙气膜传热,并与离散颗粒模型(DEM)耦合,建立颗粒尺度下离散颗粒传热模型.以固定床为对象,考察颗粒粒径、颗粒比热容、颗粒热导率及压缩负载对固定床有效传热系数的影响,并将本文计算值和文献的实验值及模型预测值对比,结果表明,该模型可定量预测固定床有效传热系数.本文建立的离散颗粒传热模型为合理预测颗粒体系内的传热提供了一种有效方法.%Heat conduction in granular assemblies plays an important role in industrial applications. In this paper, the details of heat transfer mechanism are considered in particle scale. The conduction resistances of solid interior, rough surface, gas film between solids, and gas-gap between contacted surfaces are modeled and coupled with discrete element method to deduce a heat transfer model. Numerical simulations are performed to investigate the effects of particle diameter, specific thermal capacity, thermal conductivity of particles and compressive load on effective thermal conductivity (ETC) in fixed beds. The predicted ETC is compared with experimental and simulated data in literature, indicating that the presented model can predict ETC satisfactorily, which provides a useful tool for studying heat transfer in particle assemblies.
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
Directory of Open Access Journals (Sweden)
Augusto Hernández Vidal
2011-12-01
Full Text Available In order to strengthen the concept of municipal autonomy, this essay proposes an extensive interpretation of administrative discretion. Discretion is the exercise of free judgment given by law to authorities for performing official acts. This legislative technique seems to be suitable whenever the legislative is intended to legislate over the essential core of municipal autonomy. This way, an eventual abuse of that autonomy could be avoided, for the disproportional restriction of the local faculty to oversee the local issues. This alternative is presented as a tool to provide with dynamism the performing of administrative activities as well, aiming to assimilate public administration new practices.
Institute of Scientific and Technical Information of China (English)
李林涛; 谭援强; 姜胜强
2012-01-01
采用离散元法(DEM),用BPM(Bonded-particle model)模型分别建立并校准SiC陶瓷基体和碳纤维离散元模型,采用位移软化接触模型表征层间和纤维/基体之间的界面元损伤双线性本构关系.通过DCB试验(Double cantilever beam virtual test)和微滴脱黏试验分别对其界面强度进行收敛试验,动态地观察了塑性变形、裂纹扩展及界面脱黏过程.结果表明,位移软化接触模型可以很好地表征界面损伤过程,采用离散元法可以很好地动态模拟较复杂复合材料的损坏过程.%With the aid of BPM (Bonded-particle model), the discrete element models of SiC ceramics matrix and carbon fiber were set up and calibrated separately by the discrete element method(DEM). The bilinear cohesive law of interface element damage in interlayer and on matrix/fiber interface was characterized using displacement-softening contact models, and then calibrated by DCB test (Double cantilever beam virtual test) and microbond test, respectively. Plastic deformation, crac-king growth situation and dynamic processes of interface debonding were observed in these simulation tests. The results show that the displacement-softening contact model could characterize in-terfacial damage process nicely, and discrete element method could simulate dynamic damage process for more complex composite materials admirably.
Jia, Pin; Cheng, Linsong; Huang, Shijun; Xu, Zhongyi; Xue, Yongchao; Cao, Renyi; Ding, Guanyang
2017-08-01
This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the
Discrete element simulation of gas-solids flow behavior in riser%提升管内气固流动特性的离散元模拟
Institute of Scientific and Technical Information of China (English)
王猛; 朱卫兵; 孙巧群; 张小彬; 周金哲
2013-01-01
The gas-solids flow behavior in a two-dimensional riser was numerically simulated by combining computational fluid dynamics (CFD) and discrete element method (DEM).In particular,gas turbulence was investigated by standard k-ε two-equation model,and van der Waals force and rolling friction between particles were also considered.In the present study,the flow behavior of particles and gas was analyzed,distribution of particle concentration,velocity,granular temperature and gas velocity were obtained,and the effect of operating conditions on solids flow was also studied.The results indicated that particles flow showed significant non-uniformity in the riser,clustering was observed near the wall.The typical coreannulus flow structure with a dense phase near the wall and a dilute phase in the center was formed.In the vertical direction,it was divided into a dilute region in the upper zone and a dense region near the bottom in the riser.The results showed a certain amount of some backmixing of both particle and gas phase.Furthermore,it was demonstrated that particle velocity increased and particle concentration decreased with increasing superficial gas velocity,and particles had more non-uniform distributions.Larger solids mass flux led to more non-uniform solids distributions and higher particle concentration,while particle velocity was insensitive to change of solids mass flux.Simulated results were in qualitative agreement with experimental observations.%采用离散单元法模型对二维提升管内气固流动特性进行了数值模拟.利用标准k-ε模型模拟气相的湍流流动,考虑了颗粒间的van der Waals力和滚动摩擦的作用.通过对颗粒和气体流动行为的分析,得到了颗粒浓度、速度、温度及气体速度等的分布,研究了表观气速和颗粒循环速率对颗粒流动的影响.结果显示:颗粒在提升管内呈现边壁浓、中心稀的环核流动及上稀下浓的流动结构；气固两相都存在一定程度
Institute of Scientific and Technical Information of China (English)
张红梅; 肖映雄; 欧阳媛
2012-01-01
Higher-order conforming finite elements can effectively overcome the poisson-Locking in linear elasticity,which is call and Locking-free finite elements. But when compared with the linear element,it often requires more computer storage and has a higher computational complexity. For the Locking-free (quartic) finite element discretization in linear elasticity,a general two-level method is proposed by analyzing the relationship between the quadratic finite element space and the quartic finite element space and by taking advantage of the special nature of the finite element's basi functions,such as compactly supported. First,the quadratic element is chosen as the coarse level space. Secon'd,by combining the selective reduced integration and some efficient smoothers,then,obtain the two-level method is obtained in which the element is chosen as the coarse level space for the Locking-free finite element discretization with better robustness and high efficiency. The numerical results show the efficiency of the resulting method.%高次协调元能有效克服弹性力学问题的闭锁( Locking)现象,称这种单元为无闭锁(Locking—free)有限元,但它与线性元相比,往往需要更多的计算机存储单元,具有更高的计算复杂性.针对弹性力学问题Locking—free(四次)有限元离散系统的求解,本文通过分析四次有限元与二次有限元空间之间的关系,并利用有限元基函数的特殊性质,如紧支集性,建立一种以二次有限元(P2)为粗水平空间的两水平方法;然后,利用减缩积分方案,以P2／P0元作为四次元空间的粗水平空间,并结合有效的磨光算子,为Locking—free有限元离散系统设计具有更好计算效率和鲁棒性的求解方法.数值实验结果验证了算法的有效性.
Nehl, T. W.
1980-12-01
A discrete state space model of a power conditioner fed permanent magnet brushless dc motor for aerospace and electric vehicle applications is developed. The parameters which describe that machine portion of this model are derived from a two dimensional nonlinear magnetic field analysis using the finite element method. The model predicts the instantaneous mechanical and electrical behavior of a prototype electromechanical actuator for possible use on board the shuttle orbiter. The model is also used to simulate the instantaneous performance of an advanced electric vehicle propulsion unit. The results of the computer simulations are compared with experimental test data and excellent agreement between the two is found in all cases.
Institute of Scientific and Technical Information of China (English)
潘成杰
2016-01-01
At present in structural strength analysis of underground dump truck, the pre-estimate of applied stress usually depends on experience and simple calculation, leading to large deviation. In the paper, the discrete element method is introduced to the finite element strength check. The coal material's discrete element model is established to simulate the material loaded process, and acquire the applied force of the truck body from coal material discrete element. Then the finite element software is used to conduct coupling and strength checking with the obtained data. The method can accurately apply the force of coal material to the finite element model, get the stress and strain of the vehicle body, and obtain the credible force of the hopper according to the calculation scale factor.%针对目前运矿车结构强度分析，施加载荷环节往往依靠经验或简单计算进行预估，分析结果不能完全真实地反映车体实际受力情况。将离散元方法引入到设备有限元强度校核中，建立煤料离散元模型，通过模拟装载过程，获取煤料离散单元对车体的作用力，然后将数据导入到有限元软件中进行耦合，进行强度校核。该方法真实地将煤料对车体的作用力准确地施加到有限元模型中，可得到车体应力应变，以及根据计算比例因子，得到料斗所受可信作用力。该研究将为改进运矿车的设计和使用性能，提高产品生产效率，提供强大依据。
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Institute of Scientific and Technical Information of China (English)
邱流潮; 张之豪; 袁林娟
2015-01-01
A discrete element method-based simulation platform for dry and wet particulate systems, DEMSIM,is introduced in this paper.In the case of dry particulate systems,DEMSIM has the ability to model the elastic and plastic contact of granular systems in two and three dimensions.For particulate system with few liquid,a liquid bridge model is applied in this simulation platform.In addition,a numerical method coupling discrete element method (DEM)with computational fluid dynamics (CFD)is developed to simulate particle-liquid flow in DEMSIM.The liquid motion was considered as a weakly compressible flow solved using CFD solvers while the discrete particle motion is solved using DEM in which the particle-particle interaction are based on theoretical contact mechanics thereby enabling particles to be directly specified using realistic material properties such as friction and elasticity.Several numerical examples are presented to verify the simulation platform by comparing the numerical results with theoretic solution and experimental data in the literature.The results demonstrate the ability to simulate the dynamics of the dry and wet particulate systems.%介绍了基于离散元法的干湿颗粒系统仿真软件 DEMSIM。对于干颗粒系统,DEMSIM 可以分析二维和三维颗粒系统的弹性和塑性接触碰撞过程；对于湿颗粒系统,DEMSIM 采用传统的液桥模型；对于颗粒-流体系统,DEMSIM 采用 CFD-DEM 细观耦合模型模拟。一系列典型算例的模拟分析,验证了干湿颗粒系统仿真软件DEMSIM 的精度和有效性。
Institute of Scientific and Technical Information of China (English)
鲍鹏; 李丽; 赵捷
2008-01-01
Based on the principle of deformation dynamics, a new discrete element model for deformable bodies is established in this paper. From the side-side contact relation and the dynamic relaxation method, theoretical formulas are derived and the corresponding calculation program is worked out according to the discrete element method (DEM). From the astringency of the calculation results in the static problem, the validity of the calculation program and the selected parameters is verified, and the motive reaction of the underground structure under artificial seismic wave is solved.%基于变形体动力学原理,建立了新的可变形块体单元模型.根据离散元法原理,采用边-边接触关系及动态松弛法,推导出其理论公式并编制了计算程序;由静力问题计算结果的收敛性,验证了计算程序和计算参数选取的正确性,求出了地下结构在人工地震波作用下的动力反应.
Gong, Yongmei; Zwinger, Thomas; Åström, Jan; Gladstone, Rupert; Schellenberger, Thomas; Altena, Bas; Moore, John
2017-04-01
The outlet glacier at Basin 3, Austfonna ice-cap entered its active surge phase in autumn 2012. We assess the evolution of the basal friction during the surge through inverse modelling of basal friction coefficients using recent velocity observation from 2012 to 2014 in a continuum ice dynamic model Elmer/ice. The obtained basal friction coefficient distributions at different time instances are further used as a boundary condition in a discrete element model (HiDEM) that is capable of computing fracturing of ice. The inverted basal friction coefficient evolution shows a gradual 'unplugging' of the stagnant frontal area and northwards and inland expansion of the fast flowing region in the southern basin. The validation between the modeled crevasses distribution and the satellite observation in August 2013 shows a good agreement in shear zones inland and at the frontal area. Crevasse distributions of the summer before and after the glacier reached its maximum velocity in January 2013 (August 2012 and August 2014, respectively) are also evaluated. Previous studies suggest the triggering and development of the surge are linked to surface melt water penetrating through ice to form an efficient basal hydrology system thereby triggering a hydro- thermodynamic feedback. This preliminary offline coupling between a continuum ice dynamic model and a discrete element model will give a hint on future model development of linking supra-glacial to sub-glacial hydrology system.
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Institute of Scientific and Technical Information of China (English)
鲍春永; 赵啦啦; 刘万英; 杨康康
2016-01-01
Particle discrete element method is a kind of numerical simulation method widely used in the research of granular material mechanics behaviour.Computation efficiency is one of the main factors that restricts its development and application.In this paper,we build a hopper model by using Pro/E software,and use Stream DEM software to study the stimulations of discrete element method in regard to hopper’s particles filling process.We also compare the operation processes and results of CPU-based and GPU-based acceleration algorithms. Results show that the GPU-based computer graphics acceleration algorithm can dramatically improve the computation efficiency of the simulation process of particle discrete element method.When the number of particles to be filled reaches 130 000,its computational efficiency improves over 10 times than that of the CPU-based acceleration algorithm.%颗粒离散元法是一种广泛应用于研究颗粒物料力学行为的数值模拟方法，而计算效率是制约其发展和应用的主要因素之一。通过Pro／E软件建立了料斗模型，利用Stream DEM软件对料斗的颗粒充填过程进行离散元法模拟研究，并对基于CPU 和GPU加速算法的运算过程和结果进行对比。结果表明，基于GPU的计算机图形学加速算法可大幅提高颗粒离散元法模拟过程的运算效率。当填充颗粒数量达到13万时，其运算效率比基于CPU的运算效率提高了10倍以上。
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Liu, Peiyuan [Univ. of Colorado, Boulder, CO (United States); Brown, Timothy [Univ. of Colorado, Boulder, CO (United States); Fullmer, William D. [Univ. of Colorado, Boulder, CO (United States); Hauser, Thomas [Univ. of Colorado, Boulder, CO (United States); Hrenya, Christine [Univ. of Colorado, Boulder, CO (United States); Grout, Ray [National Renewable Energy Lab. (NREL), Golden, CO (United States); Sitaraman, Hariswaran [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2016-01-29
Five benchmark problems are developed and simulated with the computational fluid dynamics and discrete element model code MFiX. The benchmark problems span dilute and dense regimes, consider statistically homogeneous and inhomogeneous (both clusters and bubbles) particle concentrations and a range of particle and fluid dynamic computational loads. Several variations of the benchmark problems are also discussed to extend the computational phase space to cover granular (particles only), bidisperse and heat transfer cases. A weak scaling analysis is performed for each benchmark problem and, in most cases, the scalability of the code appears reasonable up to approx. 103 cores. Profiling of the benchmark problems indicate that the most substantial computational time is being spent on particle-particle force calculations, drag force calculations and interpolating between discrete particle and continuum fields. Hardware performance analysis was also carried out showing significant Level 2 cache miss ratios and a rather low degree of vectorization. These results are intended to serve as a baseline for future developments to the code as well as a preliminary indicator of where to best focus performance optimizations.
Energy Technology Data Exchange (ETDEWEB)
Smith, Jovanca J.; Bishop, Joseph E.
2013-11-01
This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed at Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.
Energy Technology Data Exchange (ETDEWEB)
Hrovat, M.F.; Grosse, K.H.; Seemann, R. [ALD Vacuum Technologies GmbH, Hanau (Germany)
2008-07-01
The thorium resources in the world are relatively large. According to the IAEA-NEA-publication ''Red Book'' they amount to 4.5 10E6 metric tons and are about 4 times greater than the resources of Uranium. The fuel element described in this paper could be used in light water reactor (LWR) preferably in pressurized water reactor (PWR). The seed (feed) rods contain uranium 235 as fissionable material and the blanket (breed) rods contain thorium and uranium. The thorium in the blanket rods is converted to fissionable U-233 by irradiation with thermal neutrons. The U-233 produced is a valuable fissionable material and is characterized by high revalues, where t is defined as the number of fission neutrons per absorption in fissile materials. By optimized configuration and loading of the seed- and blanket rods the thorium is converted to U-233 and the U-238 is converted to fissionable Plutonium isotopes. Consequently more fissionable material is generated than is used. The fuel cycle is also flexible. Thus U-235, Pu-239 or weapons-grade Plutonium can be used.Based on knowledge obtained in the development of fuel elements for material test reactors (MTR), high temperature reactors (HTR) and light water reactors (LWR), a new design of fuel element suitable for thorium employment in PWR is described.
Discrete integrable systems and deformations of associative algebras
Energy Technology Data Exchange (ETDEWEB)
Konopelchenko, B G [Dipartimento di Fisica, Universita del Salento and INFN, Sezione di Lecce, 73100 Lecce (Italy)], E-mail: konopel@le.infn.it
2009-10-30
Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.
2014-01-01
valid OMB control number. 1. REPORT DATE 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE A Polynomial-Based...solve Eq. (2.5) is kept under control by a sufficiently effective preconditioner. The RTB test case is an example of a dynamical scenario that can be run...program element 121670. We also would like to thank Michal Kopera and several anonymous reviewers for their helpful sug- gestions for improving the
Conservative discretization of the Landau collision integral
Hirvijoki, Eero
2016-01-01
We describe a density, momentum, and energy conserving discretization of the nonlinear Landau collision integral. Our algorithm is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem.
Discretization of topological spaces
Amini, Massoud; Golestani, Nasser
2014-01-01
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compact...
Li, Zhan-Ke; Li, Jian-Wei; Cooke, David R.; Danyushevsky, Leonid; Zhang, Lejun; O'Brien, Hugh; Lahaye, Yann; Zhang, Wen; Xu, Hai-Jun
2016-12-01
The Haopinggou deposit in the Xiong'ershan district, southern margin of the North China Craton, comprises numerous Au and Ag-Pb-Zn veins hosted in metamorphic rocks of the Late Archean to early Paleoproterozoic Taihua Group. Two stages of mineralization have been recognized: Stage 1 pyrite-quartz veins and Stage 2 Pb-Zn-sulfide veins. Some pyrite-quartz veins are surrounded or cut by Pb-Zn-sulfide veins, others occur as independent veins. Six generations of pyrite have been identified at Haopinggou: Py1 to Py3 in Stage 1 and Py4 to Py6 in Stage 2. Pyrites from Stage 1 are enriched in Au, As, Co, Ni, and Bi, whereas Stage 2 pyrites contain higher Ag, Pb, Zn, Sn, and Sb. Invisible Au mostly occurs as lattice-bound gold in Py2 (up to 92 ppm Au) and Py3 (up to 127 ppm Au) and has a close relationship with As. Native Au grains are also present in Py3 and likely resulted from mobilization and reprecipitation of the invisible Au previously locked in the precursor pyrite. This view is supported by extensive plastic deformation in Stage 1 pyrite as revealed by electron backscatter diffraction analysis. In Stage 2, Ag is mostly present as lattice-bound silver closely associated with Sb in galena (up to 798 ppm Ag). A variety of silver minerals are also present as inclusions within galena or as interstitial grains. These silver minerals were likely formed via Ag-Cu exchange reaction between tetrahedrite and galena or represent exsolution from galena due to a temperature decrease. Pb isotopic compositions differ remarkably between Stage 1 and Stage 2 sulfides, indicating different sources of lead. Pb in Stage 2 Pb-Zn-sulfide veins is consistent with the Haopinggou porphyry close to the veins. The field, textural, compositional, and lead isotopic data led us to conclude that the early gold-bearing pyrite-quartz veins and late silver-bearing Pb-Zn-sulfide veins likely formed from distinct fluid systems related to discrete mineralization events. Our study suggests that Au and Ag
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Center for Efficient Exascale Discretizations Software Suite
Energy Technology Data Exchange (ETDEWEB)
2017-08-30
The CEED Software suite is a collection of generally applicable software tools focusing on the following computational motives: PDE discretizations on unstructured meshes, high-order finite element and spectral element methods and unstructured adaptive mesh refinement. All of this software is being developed as part of CEED, a co-design Center for Efficient Exascale Discretizations, within DOE's Exascale Computing Project (ECP) program.
Lu, An; Hsieh, Pei-Chen; Wu, Liang-Chun; Lin, Ming-Lang
2017-04-01
Earthquake and rainfall weakening potential sliding surface are common causes of dip slope failure. But in recent years, certain dip slopes failure, for example dip slope sliding without rain on the roadside of Formosa Freeway in northern Taiwan, are caused by uplift groundwater in vertical joints eventually weakening the potential sliding surface. The mechanism of sliding failure should be analyzed in more detail. Furthermore, prestress dissipating in anchors causing dip slope failure is also considered in this study. In this study, conceptual model is simplified from the case of Formosa Freeway in northern Taiwan and the main control factors including angle of slope, stratum, attitude of joints. In addition, drilling data, such as hydraulic conductivity, strength, friction angle and cohesion, are utilized to discuss mechanism and dominant factors of dip slope failure caused by uplift groundwater in vertical joints. UDEC(Universal Distinct Element Code) which is particularly well suited to problems involving jointed media and has been used extensively in stability analysis of jointed rock slopes is utilized in this study. The influence of external factors such as groundwater pressure on block sliding and deformation can also be simulated in UDEC. When the results from numerical simulation fit the condition of slope failure on the roadside of Formosa Freeway, the influence of prestress dissipating in anchors on slope stability is considered subsequently. Finally, simulation results by UDEC are compared with previous research results by FLAC, and discuss the difference between each other.
Directory of Open Access Journals (Sweden)
Jorge Mauricio Ruiz Vera
2013-03-01
Full Text Available The Derrida-Lebowitz-Speer-Spohn (DLSS equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS es una ecuación de evolución no lineal de cuarto orden. Esta aparece en el estudio de las fluctuaciones de interface de sistemas de espín y en la modelación de semicoductores cuánticos. En este artículo, se presenta una discretización por elementos finitos para una formulación exponencial de la ecuación DLSS abordada como un sistema acoplado de ecuaciones. Usando la información disponible acerca del fenómeno físico, se establecen las condiciones de contorno para el sistema acoplado. Se demuestra la existencia de la solución discreta global en el tiempo via un argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta un test del orden de convergencia de la discretización porpuesta.
Institute of Scientific and Technical Information of China (English)
赵艳敏; 石东洋
2011-01-01
The infinite dimensional Hamiltonian system of three-dimensional vector wave equation is given and a new numerical approximate scheme is proposed in this paper. Based on the Gauss-Lobatto-Legendre polynomial, the spatial discretization scheme for the proposed infinite dimensional system is established by virtue of the vector spectral element method, and then a finite dimensional Hamiltonian system is attained. Moreover, in order to preserve the structure and energy of the system, the full discretization scheme of the finite dimensional system is derived by utilizing the symplectic difference method. Finally, the stiff matrix and mass matrix are disposed by the diagonal techniques. High accuracy approximation scheme is thus obtained, and simultaneously the computing cost and storage capacity are reduced significantly.%本文给出了三维矢量波动方程的无穷维Hamilton系统形式并提出了一个新的数值逼近格式.基于Gauss-Lobatto-Legendre多项式,建立了该无穷维系统的矢量谱元方法空间离散格式,并得到一个有限维Hamilton系统.进而,利用辛差分方法对该有限维系统进行全离散,以期保持系统的结构和能量.最后,借助于对角化技巧处理刚度矩阵和质量矩阵,在得到高精度逼近格式的同时,大幅降低了计算量和存储量.
Institute of Scientific and Technical Information of China (English)
冯云田; 赵婷婷; 加藤淳; 周伟
2016-01-01
Particles are assumed smooth in classical discrete element modelling,but real particles have random rough surfaces which may influence their mechanical properties.It is necessary therefore to quantitatively improve the conventional discrete element model particles by taking their surface roughness into consideration.In this work,a new random normal contact law is established for particles that have random rough surfaces.The contact law,based on the classic Greenwood and Williamson (GW)model,is derived by both theoretical derivation and numerical simulation.A Newton-Raphson based numerical solution procedure is proposed to obtain the total contact force for a given overlap and a set of rough surface parameters.Some related computational issues key to improve computa-tional efficiency and accuracy are addressed.Instead of a complicated integral expression involved in the GW model, the curve fitted empirical formula of the random contact law retains the closed form and simplicity of the Hertz model,with only one added parameter,σ,the standard deviation of the surface roughness,and therefore can be readily incorporated into the current discrete element modelling framework.%真实颗粒的力学性质会受到其随机粗糙表面的影响，然而在传统离散元模拟中通常假设颗粒具有光滑表面，因此有必要在定量考虑颗粒表面粗糙度的基础上改进离散元的接触模型。本文基于经典 Greenwood-Williamson(GW)模型通过理论分析和数值模拟提出了一种可以考虑颗粒表面粗糙度的法向接触定律；开发了基于 Newton-Raphson迭代的数值计算方法，通过输入颗粒重叠量和一系列表面粗糙系数计算总接触力；讨论了改进计算方法效率和准确性的相关问题。相对于 GW模型中接触关系的复杂积分表示，拟合得到新随机接触定律的表达式具有类似 Hertz定律的简单结构，只包含一个表征颗粒表面粗糙度标准偏差的新增参数，
Groupoids, Discrete Mechanics, and Discrete Variation
Institute of Scientific and Technical Information of China (English)
GUO Jia-Feng; JIA Xiao-Yu; WU Ke; ZHAO Wei-Zhong
2008-01-01
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.
Zhou, Jianqin
2011-01-01
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases.
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Institute of Scientific and Technical Information of China (English)
于瑞江; 汤晓华; 张玉玲
2015-01-01
Based on the discrete element method, using Inventor to establish a three dimensional model of horizontal screw conveyer, to import the model into EDEM software simulation. It was gained by analyzing that when the rotational speed of the screw conveyer and the volumetric fill level was 200 rpm and 20% respectively, transporting a certain mass material consumed power was to minimize; Through simulation obtain the average speed change rule of rice grain and the force situation of screw conveyor, when the volumetric fill level is 20%, 50%, 70%.%基于离散元法，应用Inventor软件建立水平螺旋输送机三维实体模型，将该模型导入EDEM软件进行仿真模拟。分析验证了水平螺旋输送机转速和填充率分别为200r/min和20%时，螺旋输送机输送一定质量物料消耗的功率最小；通过仿真模拟得出填充率为20%、50%、70%时大米颗粒平均速度变化规律以及螺旋输送机受力情况。
Institute of Scientific and Technical Information of China (English)
谭援强; 张浩; 李明军
2011-01-01
According to coupling computational fluid dynamics and computational granular media mechanics method, the motion of abrasive flow in CMP with composite particles was simulated using discrete element method. With PFC3D software, a two-phase flow model that predicted the kinematics and trajectory of the abrasive particles was built herein,two verification simulations were conducted to demonstrate the capability of the current method to solve nano-size two-phase flow problems. Finally, the CMP geometry simulations were conducted, some phenomenon observed in the experiments were explained.%基于耦合计算流体力学和计算散体力学的方法,利用PFC3D软件模拟了复合磨粒抛光液化学机械抛光(CMP)中抛光液固液两相流的流动行为.通过2个数值实验并将其与他人实验数据进行对比,验证了利用PFC3D软件模拟纳米两相流问题的可行性.对CMP过程进行了数值模拟,解释了一些实验中观测到的现象.
Discrete mathematics, discrete physics and numerical methods
Directory of Open Access Journals (Sweden)
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
Dimension Reduction and Discretization in Stochastic Problems by Regression Method
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
1996-01-01
The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ......, Slepian models, Stochastic finite elements.......The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation...
Discrete Wigner function dynamics
Energy Technology Data Exchange (ETDEWEB)
Klimov, A B; Munoz, C [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410, Guadalajara, Jalisco (Mexico)
2005-12-01
We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered.
Institute of Scientific and Technical Information of China (English)
金毅
2016-01-01
Warfare simulation system based on discrete events modeling plays a very important role in the military planning stage. The traceability and analysis of causality is a significant strategy in warfare simulation, which could explore the devel⁃opment of the battle and the causality of it, in order to reveal the sequential relationship from large volumes of data and com⁃plex interaction relationships and then help the researchers to identify certain key objects and events. This paper would first introduce the causal analysis in the field of warfare simulation, and then propose a particular kind of causal analysis, based on the simulation elements of discrete events. This method, known for its universality and practicability, could analyze the causal relationships in warfare simulation.%基于离散事件系统建模与仿真的军事仿真系统在军事筹划阶段扮演着至关重要的作用。因果追溯与分析是军事仿真中重要的技术，它可以在大量的数据与复杂的交互关系中找出时序上的关联关系，帮助研究人员确定作战行动中的一些关键实体或事件，用于探究战争的发展脉络与蕴含其中的因果关系。首先对作战仿真领域的因果追溯分析做了简要介绍，然后提出了一种基于离散事件仿真要素的因果追溯分析方法，这种方法可以分析军事仿真中的因果关系，并且有很高的通用性和良好的实用性。
Institute of Scientific and Technical Information of China (English)
付宏; 吕游; 徐静; 黄山; 于建群
2012-01-01
It needs to establish analysis models of machine parts (boundaries), when use DEM (Discrete Element Method) to analyze the contact action between machine parts and granular materials. There exist irregular surfaces which can not be expressed by the elementary analytic function in the parts' surfaces which contact with granular materials. The AFT (Advancing Front Technique) was used to mesh and discrete irregular surfaces into the triangle planar units,parameters of movement characters and material properties were added in the same time,so the DEM analysis models of irregular surfaces was created. Based on the redevelopment of PRO/E software,the boundary modeling software of irregular surfaces was developed. By application examples,the feasibility of boundary modeling method and the software which based on the AFT was validated,which lays foundations for simulation and analysis of working process for machine parts with complex structure.%在采用离散元法分析机械部件与颗粒材料接触作用时,需要建立机械部件(边界)的离散元法分析模型.分析可知,机械部件中与颗粒材料接触作用的零件表面,存在不能用初等解析函数表达的非规则曲面.为此,采用推进波前法(AFT:Advancing Front Technique)进行非规则曲面网格划分,把非规则曲面离散成三角形平面片的组合,同时添加运动属性和材料特性参数,由此建立非规则曲面边界的离散元法分析模型.在对PRO/E软件进行二次开发的基础上,研制了非规则曲面边界建模软件.通过实例验证,初步证明了基于AFT边界建模方法和软件的可行性,为复杂结构机械部件工作过程的仿真分析奠定了基础.
Institute of Scientific and Technical Information of China (English)
赵学亮; 赫建明; 董高峰; 李腾飞; 吴方华
2012-01-01
Microstructure and micromechanics of granular soils have been of interest to many researchers because of their significant role in the macroscale response. Discrete element method( DEM) is usually simpler, faster, and cheaper than the traditional experimental method and able to obtain some information that is difficult or inaccessible in the experimental method. In this paper, some new developments of the microscale study on granular soil using DEM are briefly reviewed. Some issues in numerical modeling such as density ( mass) scaling and membrane boundary simulation are discussed. The new developments on microstructure study such as particle rotation and displacement and mesoscale void ratio distribution using DEM are analyzed. It is concluded that DEM is a powerful tool that can capture the discrete characteristics of the granular materials.%粒状土的微观结构和微观力学被认为是其宏观力学和体积特性的内在根本因素,近年来得到越来越多的关注和研究.离散单元法作为一种研究颗粒材料的数值模拟计算方法,比试验方法快捷、简便、经济,而且能够容易得到在实验室试验中很难或无法得到的更多重要的微观结构和微观力学的信息,近年来得到越来越多应用.本文介绍了离散单元法对土的微观特性研究的一些最新方法和进展,对数值建模中的一些重要方面如比重(质量)放大、树脂薄膜模拟等方面进行了阐述,对离散单元法在土的微观结构分析(如颗粒旋转、颗粒位移、中尺度孔隙率分布)的一些最新研究作了分析和介绍.分析表明,离散单元法是研究粒状土的微观特性的一个有力工具,可以对土的宏观特性从微观角度得到更好的解释和认识.
Directory of Open Access Journals (Sweden)
Ramiro Acevedo
2013-03-01
Full Text Available The eddy current model is obtained from Maxwell’s equations by neglecting the displacement currents in the Amp`ere-Maxwell’s law and it is commonly used in many problems in sciences, engineering and industry (e.g, in induction heating, electromagnetic braking, and power transformers. The so-called “A, V −A potential formulation” (B´ır´o & Preis [1] is nowadays one of the most accepted formulations to solve the eddy current equations numerically, and B´ır´o & Valli [2] have recently provided its well-posedness and convergence analysis for the time-harmonic eddy current problem. The aim of this paper is to extend the analysis performed by B´ır´o & Valli to the general transient eddy current model. We provide a backward-Euler fully-discrete approximation based on nodal ﬁnite elements and we show that the resulting discrete variational problem is well posed. Furthermore, error estimates that prove optimal convergence are settled.El modelo de corrientes inducidas se obtiene a partir de las ecuaciones de Maxwell, despreciando las corrientes de desplazamiento de la Ley de AmpèreMaxwell. Bíró & Valli realizaron recientemente el análisis de existencia y unicidad de solución y el análisis teórico de convergencia para una de las formulaciones más populares del problema de corrientes inducidas en regimen armónico, conocida como “formulación en potenciales A; V A”. En el presente artículo se extiende el análisis realizado por Bíró & Valli al modelo evolutivo general de corrientes inducidas. Presentamos un esquema completamente discreto para la formulación, basado en una aproximación temporal usando un método de Euler implícito y una aproximación espacial a través del método de elementos ﬁnitos. Además, demostramos que el problema discreto resultante es un problema bien planteado y obtenemos estimaciones del error que muestran convergencia óptima.
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
. The numerical approach allows for a detailed analysis of the material dynamics and shear zone development during progressive shear strain. We demonstrate how the shear zone thickness and dilation increase with the magnitude of the normal stress. The stresses are distributed heterogeneously through the granular...... of the inter-particle contacts parameterizes the model. For validating the numerical approach, the macromechanical behavior of the numerical material is compared to the results from successive laboratory ring-shear experiments. Overall, there is a good agreement between the geotechnical behavior of the real...... granular materials and the numerical results. The materials deform by an elasto-plastic rheology under the applied effective normal stress and horizontal shearing. The peak and ultimate shear strengths depend linearly on the magnitude of the normal stress by the Mohr-Coulomb constitutive relationship...
Discrete element modelling of granular materials
Van Baars, S.
1996-01-01
A new model is developed by the author, which does not use the equations of motion but the equations of equilibrium to describe granular materials. The numerical results show great similarities with reality and can generally be described by an advanced Mohr-Coulomb model. However, many contacts betw
Discrete Element Method for Modeling Penetration
2006-07-01
toughness K,, increases as the rate of applied load is increased. Mindess et al. (1987) conducted experiments on single-edge 24 notched concrete beams loaded...547. Mindess , S., Banthia, N., and Yan, C., "The Fracture Toughness of Concrete under Impact Loading," Cement and Concrete Research, Vol. 17, 1987
Discrete elements for 3D microfluidics
Krisna C. Bhargava; Thompson, Bryant; Malmstadt, Noah
2014-01-01
Microfluidic systems promise to improve the analysis and synthesis of materials, biological or otherwise, by lowering the required volume of fluid samples, offering a tightly controlled fluid-handling environment, and simultaneously integrating various chemical processes. To build these systems, designers depend on microfabrication techniques that restrict them to arranging their designs in two dimensions and completely fabricating their design in a single step. This study introduces modular,...
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elasto-plastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative...... on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring...... to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain....
Seidl, Gerhart
2014-01-01
We present a simple generalization of Noether's theorem for discrete symmetries in relativistic continuum field theories. We calculate explicitly the conserved current for several discrete spacetime and internal symmetries. In addition, we formulate an analogue of the Ward-Takahashi identity for the Noether current associated with a discrete symmetry.
The Pairing Matrix in Discrete Electromagnetism On the Geometry of Discrete de Rham Currents
Auchmann, B
2007-01-01
We introduce pairing matrices on simplicial cell complexes in discrete electromagnetism as a means to avoid the explicit construction of a topologically dual complex. Interestingly, the Finite Element Method with first-order Whitney elements â when it is looked upon from a cell-method perspective â features pairing matrices and thus an implicitly defined dual mesh. We show that the pairing matrix can be used to construct discrete energy products. In this exercise we find that different formalisms lead to equivalent matrix representations. Discrete de Rham currents are an elegant way to subsume these geometrically equivalent but formally distinct ways of defining energy-products.
Cagnoli, Bruno; Piersanti, Antonio
2017-02-01
We have carried out new three-dimensional numerical simulations by using a discrete element method (DEM) to study the mobility of dry granular flows of angular rock fragments. These simulations are relevant for geophysical flows such as rock avalanches and pyroclastic flows. The model is validated by previous laboratory experiments. We confirm that (1) the finer the grain size, the larger the mobility of the center of mass of granular flows; (2) the smaller the flow volume, the larger the mobility of the center of mass of granular flows and (3) the wider the channel, the larger the mobility of the center of mass of granular flows. The grain size effect is due to the fact that finer grain size flows dissipate intrinsically less energy. This volume effect is the opposite of that experienced by the flow fronts. The original contribution of this paper consists of providing a comparison of the mobility of granular flows in six channels with a different cross section each. This results in a new scaling parameter χ that has the product of grain size and the cubic root of flow volume as the numerator and the product of channel width and flow length as the denominator. The linear correlation between the reciprocal of mobility and parameter χ is statistically highly significant. Parameter χ confirms that the mobility of the center of mass of granular flows is an increasing function of the ratio of the number of fragments per unit of flow mass to the total number of fragments in the flow. These are two characteristic numbers of particles whose effect on mobility is scale invariant.
Institute of Scientific and Technical Information of China (English)
宜晨虹; 慕青松; 苗天德
2009-01-01
The discrete element method is used to research the distribution of forces within the two-dimensional granular system under gravity. The force chains among the particles are generated according to the magnitudes of the forces. Then the simulation results are compared with the well-known q-model, a-model and experimental results obtained through the photoelastic test under the same conditions. According to the computational solution, we conclude that the simulation results are similar to the experimental results are some what different from the two probability models. In addition, we also obtained that the probability distribution of the force is very uneven. The probability of the large force decays exponentially and the distribution of the force chains takes on a fraetal character.%用离散元的方法模拟了仅有重力作用的二维颗粒系统内部力的分布情况,并根据力的大小得到颗粒之间的应力链.模拟结果与颗粒介质研究中的两个著名模型q模型和a模型作了对比,并与光弹实验的结果作了比较.对比结果表明,模拟结果与实验相似,而与两个概率模型有一定的差异.另外计算结果还表明,颗粒介质中力大小的概率分布极为不均匀,较大的力概率呈指数衰减,应力链的分布具有分形特征.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
Structure of beef chewing model based on discrete element method%基于离散元法的牛肉咀嚼破碎模型构建
Institute of Scientific and Technical Information of China (English)
王笑丹; 王洪美; 韩云秀; 焦娜; 才英明; 金佳慧; 徐丽萍; 刘爱阳
2016-01-01
Tenderness is one of the most important factors influencing the quality of beef. Traditional evaluation methods have some disadvantages and limitations more or less. In order to predict beef tenderness accurately, conveniently and objectively, in this research, the discrete element method was used to establish the beef chewing model. Beef from the mid-region of longissimus dorsi (LD) was collected from 50 cattle as the samples, in which 30 cattle were used for structuring the beef chewing model, and 20 cattle were prepared for verifying the accuracy. The age of cattle (400-550 kg) was from 30 to 36 months, and the cattle were fattened for more than 6 months. After starving for 24 h, the live cattle were weighed, showered, stunned, killed, and bled blood. The 4 limbs and head of each animal were cut off, and the body of cattle was split into halves, cooled at 4℃for 24 h, and then the carcasses were divided. Each piece of beef was cut into 10 mm × 10 mm × 10 mm sample, but the inter-muscular fat, connective tissues and tendon were deleted. The samples were placed into plastic bags individually in a 75-80℃water bath, and cooked for 15 min until the internal temperature of beef sample reached 70℃. The samples were divided into 3 groups so as to carry out the experiments in triplicate after the samples were cooled to room temperature (20℃). Shear modulus and normal stiffness were detected by Brookfield CT3 texture analyzer (Brookfield Engineering Laboratories, INC. Middleboro Massachusetts, USA). With a two-cycle texture profile analysis (TPA) model (a compression model for normal stiffness) and a TA44 probe (cylinder diameter=4 mm), the size of testing surface of each sample was 10 mm ×10 mm × 10 mm (for normal stiffness). The related parameters settings were: test speed of 0.5 mm/s and deformation quantity of 2.5 mm for shear modulus detection, and test speed of 0.5 mm/s and preload of 2 N for detecting normal stiffness. In addition, density, restitution
Institute of Scientific and Technical Information of China (English)
韩燕龙; 贾富国; 曾勇; 王爱芳
2015-01-01
Granular grinding is one of the most important unit operations used in a wide variety of industries. Examples can be found in the food industry, for instance, rice processing, etc.. The performance of grinding can be characterized by the particle flow process. Thus in order to study the stable flow process of particles during grinding, we must establish a discrete element model (DEM) of granular axial flow in the grinding area between the grinding roller and the screen drum. DEM is a numerical method used for modelling the mechanical behaviour of granular materials. When DEM is used in grinding, the particle motion is controlled by contact models that are governed by physical laws. Using EDEM software, the process of grinding can be simulated and analyzed. The simulation system chooses continuous feeding;after a period of time, it reaches a steady flow. Research results show that the uneven distribution of particle flow density (PFD) is caused by the axial movement difference of particles in the grinding area. The form, flow rate and distribution of granular axial flow are influenced by static friction coeﬃcient difference between particles and screen drum. Axial mean square deviation of single particles in the grinding area is positively correlated with the square of time, which follows a “super” diffusive behavior defined by some studies. By an overall consideration of the grinding area, we find that the axial average velocities increase, however, the average velocities that are synthesized by three-axis velocities gradually decrease along the axial direction. This is because in a different axial position with different PFI, the PFI plays the key role in energy transfer. More energy will be transferred between high PFI particles that may cause high particle velocity. We also find that the fluctuation velocity square of particles presents the trend of first increasing then decreasing and finally increasing along the axial direction. The difference between
Institute of Scientific and Technical Information of China (English)
陈永雄; 梁秀兵; 刘燕; 程江波; 徐滨士
2011-01-01
采用有限元法模拟了高速电弧喷涂枪二维气流场的分布.通过计算比较了收缩型和缩扩型喷管的流场差异,同时分析了不同的丝材夹角、丝交点离喷管出口距离等喷枪结构参数下喷枪气流场行为.结果显示,缩扩型喷管更有利于熔滴的雾化,丝交点离喷管出口距离减小至0、丝夹角为40°时更有利于熔滴的加速.基于以上模拟结果,优化设计了一种新型的高速电弧喷涂枪.喷涂粒子的形貌实验表明,新型喷枪的雾化粒子粒度比原始喷枪更细、分布更均匀.%In order to investigate fracture failure mechanism of asphalt mixture from micro-structure, probability method has been used to present a theoretical formula which develops to convert the aggregate weight gradation into the two-dimension (2D) quantity gradation. Two 2D digital specimens with different thicknesses of asphalt films are generated based on particle generation algorithm. Based on the discrete element method, the fracture process of asphalt mixture beam has been simulated and the effect of asphalt film thickness, cohesive strength of asphalt mastics and adhesive strength between asphalt mastic and aggregate on the fracture failure of asphalt mixture has been also investigated. The results show that the cracking has the tendency to occur in asphalt mastics for asphalt mixture with thick asphalt films and the cohesive strength of asphalt mastics has a great influence on fracture failure of this type mixture. For asphalt mixture with thin films, the early cracking often appears in asphalt mastics and propagation of cracking occurs at the interface between aggregates and mastics. Fracture initiation is dominated by the cohesive strength of asphalt mastics and propagation of cracking is controlled by adhesive strength between asphalt mastic and aggregate for mixture with thin films.
Institute of Scientific and Technical Information of China (English)
朱立平; 袁竹林; 闫亚明; 罗登山; 王宏生; 李斌
2012-01-01
丝状颗粒作为一类长径比较大的非球形颗粒,其传热特性及相关技术广泛应用于工农业生产的诸多领域.但目前颗粒在运动过程中传热问题的研究还很不充分,特别是对于丝状颗粒,更是缺乏有效的数学模型进行描述.从颗粒传热机理出发,提出了一种基于离散单元法的丝状颗粒传热模型,模型中综合考虑了颗粒碰撞(接触)传热、颗粒的内部导热以及颗粒与气体间的对流换热.利用该模型,对固定床中堆积丝状颗粒的热量迁移过程进行了数值模拟,着重比较了各种传热方式对传热过程的影响.研究表明,对流换热对整体传热量的贡献较大.此外,还获得了不同工况下颗粒温度随时间的变化规律.%Filamentous particle is a kind of non-spherical particles with large aspect ratio. It has been widely applied in industrial and agricultural processes. However, the heat transfer phenomenon about particles is not well understood, especially the filamentous particle. In this study, in order to describe the heat transfer process of filamentous particle, a new mathematical model based on the discrete element method was proposed through the analysis of heat transfer mechanisms. The impact heat transfer between particles, the internal heat conduction and the convection heat exchange between gas and particles were considered in this model, and then it was used to numerically study the heat transfer process of filamentous particles in a fixed bed. Comparing the mechanisms with each other, it showed that the convection heat exchange had greater contribution to the total heat transfer. In addition, the simulation results revealed some internal temperature rules in filamentous particles under different operating conditions.
Institute of Scientific and Technical Information of China (English)
杜欣; 曾亚武; 高睿; 颜敬; 曹源
2012-01-01
In order to reveal the effects of particle shape on friction mechanism, frictions among non-viscous particles were decomposed into the macro biting-force and the mesoscopic biting-force. Impact and angle-of-repose (AOR) numerical tests were conducted to study the effects of particle shape on macro biting-force and mesoscopic biting-force by modeling irregular shape particles using discrete element method. The results of numerical tests show that the friction coefficient of irregularly shaped particles is nearly two times its interface friction coefficient, while the friction coefficient of ellipsoid particles is approximately equal to the interface friction coefficient. Meanwhile, different particle shapes endowed the particles with rolling or slipping characteristics, and influence the macro biting-force and the granular friction behavior.%为了揭示颗粒外形对无粘性散体摩擦机理的影响,将无粘性颗粒材料之间的摩擦作用分解为颗粒间宏观咬合和微观咬合摩擦,运用不规则外形颗粒离散元建模方法,进行撞击模拟和自然安息角模拟,研究颗粒外形对微观咬合摩擦和宏观咬合作用的影响.数值计算结果表明,不规则外形颗粒集料摩擦因数近似为接触面摩擦因数的2倍,椭球体集料摩擦因数与接触面摩擦因数近似相等；颗粒外形不同使得颗粒运动状态呈现出滑动或滚动特征,并影响其宏观咬合特性及颗粒集料的摩擦性能.
Finite Discrete Gabor Analysis
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2007-01-01
on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Lee, Taeyoung; McClamroch, N Harris
2007-01-01
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of geometric integration. Geometric integrators are numerical integration methods that preserve geometric properties of continuous systems, such as conservation of the symplectic form, momentum, and energy. They also guarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-body dynamics. In nonlinear control, one typically relies on differential geometric and dynamical systems techniques to prove properties such as stability, controllability, and optimality. More generally, the geometric structure of such systems plays a critical role in the nonlinear analysis of the corresponding control problems. Despite the critical role of geometry and mechanics in the analysis of nonlinear control systems, non...
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Burgin, Mark
2010-01-01
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and television programs. At the same time, continuous models that are in the background of discrete representations use mathematical technology developed for continuous media. The most important example of such a technology is calculus, which is so useful in physics and other sciences. The main goal of this paper is to synthesize continuous features and powerful technology of the classical calculus with the discrete approach of numerical mathematics and computational physics. To do this, we further develop the theory of fuzzy continuous functions and apply this theory to functions defined on discrete sets. The main interest is the classical Intermediate Value theorem. Although the result of this theorem is completely based on continuity, utilization of a relaxed version of contin...
Institute of Scientific and Technical Information of China (English)
李永奎; 孙月铢; 白雪卫
2015-01-01
Mechanical behavior in the densification of biomass material is closely related to pellet quality. In order to explore the forming mechanism of typical biomass material from loose state to consolidation, the discrete element method (DEM) was introduced to investigate the movement and interaction of the milled corn stalk particles in the compacting process, and the verification experiments were carried out to test the effectiveness of the DEM simulation in this study. Firstly, the three-dimensional (3D) particle contact model of corn stalk powder based on the soft-sphere model of DEM was established, and the constraining walls in DEM model were completely consistent with the compressing cavity boundary conditions in geometric shape and dimension of experimental tests conducted in December, 2014; the loading speed in simulation was also set as the same value as the DEM model. Secondly, the diameter range of simulated particles was configured to 0.4-1.0 mm in accordance to the particle size distribution acquired through the screening experiment and calculation, and the generated particles were fully filled into the whole cavity at the original state before the compressing force was loaded. The mechanical parameters of the particles, such as normal stiffness, shear stiffness and friction coefficient between the 2 contact particles, were set to the values generated at random in specific range which was determined according to compacting experimental data. Thirdly, the comparison of compression stress relaxation data between tests and simulation was carried out and the validity of the simulation was verified by the hypothesis test. It was found that the force data with time from the hypothesis tests and DEM simulation followed the similar tendency, and the absolute error was not higher than 100 N in both initial loading stage and 20 seconds after stress relaxation. In the first 20 seconds of stress relaxation course, the values of absolute error were obviously higher
Institute of Scientific and Technical Information of China (English)
董辉; 马一跃; 傅鹤林; 王智超; 陈铖
2015-01-01
The author uses the granular discrete element method to simulate the arbitrary shape stone and calibrate the mesoscopic parameters of gravel soil which was mainly constituted by weathering , unloading ,alluvial ,deluvial ,etc .Calibration is based on indoor triaxial compression experiments meas‐ured data at the same time considering the scale effect of sample .T his paper analyzed the sensitivity of the mesoscopic parameters w hich affection the accumulation of gravel soil macro deformation characteris‐tics through the virtual experiment .Studies have shown that :① The mesoscopic parameters of gravel soils based on indoor experimental calibration relative error is within 5% .② The size of the virtual experiment include model 1(101 mm × 200 mm) and the model 2(300 mm × 600 mm) .The model 2 to mesoscopi parameters calibration has scale effect ,but the relative error controlled within 9% .③ There are nonlinear positive relationships between the coefficient of friction of discrete element particles and the angle of internal friction ,and the shear strength ,and the residual strength .When the friction coefficient increased by 0 .1 ,the peak deviator stress average increased 118 .85 kPa and the residual strength average increased 90 .44 kPa .④ The greater the confining pressure ,the weaker the material dilatancy is ,when the confining pressure is changing betw een 100 kPa~500 kPa ,the dilatancy characteristic value K is obtained from 3 to 6 .The cohesive force of the damaged model nearly increases linearly as confining pressure increases .⑤ The greater the Young’s modulus ,the greater the shear strength of the gravel soil is ,but there is not a linear relationship between them .Moreover ,Young’s modulus does not affect residual strength of material significantly .%采用颗粒离散单元方法，实现任意形状块石的模拟，基于室内试验数据标定滑坡坡体物质的堆（残、坡）积碎石土的细观参数，并考虑试样尺
Compatible Spatial Discretizations for Partial Differential Equations
Energy Technology Data Exchange (ETDEWEB)
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Torus Bifurcation Under Discretization
Institute of Scientific and Technical Information of China (English)
邹永魁; 黄明游
2002-01-01
Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
Aydin, Alhun; Sisman, Altug
2016-03-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic.
Discrete element simulation of mechanical prop erties of wet granular pile%湿颗粒堆力学特性的离散元法模拟研究
Institute of Scientific and Technical Information of China (English)
赵啦啦; 赵跃民; 刘初升; 李珺
2014-01-01
Discrete element method (DEM) simulations for pile-up processes of different particle systems were performed based on linear cohesion contact model. Effects of particle shape and liquid bridge force between wet particles on the piling form were analyzed. The significant central dip profiles of normal force acting on the base surface, normal force and tangential force between particles were predicted. Effects of particle shape and cohesion energy density on the forces on the base surface and inter-particles were described. The results show that particle shape and the liquid bridge force have significant impacts on the piling form. With the increase of the cohesion energy density the angle of repose for each granular pile increases. But the angle of repose of cubical particles is bigger than that of spherical particles under the same condition. Particle shape and the liquid bridge force also significantly affect the change and the maximum amplitude of the forces acting on the base surface and the forces between the particles. The maximum amplitude of the forces increases with the increase of the cohesion energy density, and the value of the maximum force on cubical particles is bigger than that on spherical particles. When the value of cohesion energy density is very large, the mechanical properties of granular piles become more complicated, so that the liquid bridge force has a larger impact on the packing characteristic of particles than the impact on particle shape.%利用基于线性黏聚接触模型的离散元法对不同颗粒系统的堆积过程进行了数值模拟研究，分析了颗粒形状和湿颗粒间液桥力对颗粒堆积形态的影响机理，获得了球形和块状湿颗粒堆基底表面所受的法向力以及堆中颗粒间的法向力和切向力“中心凹陷”式的分布规律，讨论了颗粒形状和黏聚能量密度对基底表面作用力和颗粒间作用力的影响。研究结果表明，颗粒形状和液桥力对颗粒
Institute of Scientific and Technical Information of China (English)
陈俊; 黄晓明
2011-01-01
为了从细观角度深入分析沥青混凝土的断裂机理,根据概率理论,建立了集料质量级配与二维数量级配的关系,并通过计算机随机投放技术生成了具有2种不同沥青膜厚度的沥青混合料二维数字试件;利用离散元方法,模拟了沥青混合料小梁试件的断裂过程,分析了沥青砂浆抗拉强度、砂浆与集料黏结强度和沥青膜厚度对沥青混合料断裂过程的影响.结果表明:对于沥青膜较厚的沥青混合料而言,起裂阶段和扩展阶段的裂纹主要出现在沥青砂浆中,沥青砂浆的抗拉强度是影响混合料断裂的主要因素;当沥青膜较薄时,起裂和扩展阶段的裂纹在沥青砂浆内部和砂浆与集料界面中都有发现,砂浆抗拉强度决定着混合料的破坏应力和应变,砂浆与集料的黏结强度决定着混合料裂纹扩展的速率.%In order to investigate fracture failure mechanism of asphalt mixture from micro-structure, probability method has been used to present a theoretical formula which develops to convert the aggregate weight gradation into the two-dimension (2D) quantity gradation. Two 2D digital specimens with different thicknesses of asphalt films are generated based on particle generation algorithm. Based on the discrete element method, the fracture process of asphalt mixture beam has been simulated and the effect of asphalt film thickness, cohesive strength of asphalt mastics and adhesive strength between asphalt mastic and aggregate on the fracture failure of asphalt mix ture has been also investigated. The results show that the cracking has the tendency to occur in asphalt mastics for asphalt mixture with thick asphalt films and the cohesive strength of asphalt mastics has a great influence on fracture failure of this type mixture. For asphalt mixture with thin films, the early cracking often appears in as phalt mastics and propagation of cracking occurs at the interface between aggregates and mastics
Institute of Scientific and Technical Information of China (English)
蒋明镜; 张望城; 王剑锋
2013-01-01
砂土等散粒体在剪切过程中的能量存储及耗散是其宏观力学响应的深层原因,但因量测难度较大而研究较少.将考虑抗转动的接触模型引入离散元软件PFC2D,基于热力学第一定律建立各种能量量测方法,并在平面应变双轴压缩试验中采用该方法统计密实散粒体在剪切过程中的能量演化规律.采取了4种耗散类型,即滑动-滚动(S-R)、滑动-非滚动(S-NR)、非滑动-滚动(NS-R)和非滑动-非滚动(NS-NR).结果表明:密实散粒体加载时能量耗散以滑动摩擦为主；且小应变加载阶段,外力功主要转化为弹性应变能,但同时也存在均布于试样的耗散能；随着应变的增加,外力功的转化形式逐渐过渡为以耗散能为主,且集中分布在带状区域内；各个加载阶段的摩擦耗散均存在各向异性.%Energy storing and dissipation are the underlying mechanisms of the macromechanical responses of granular materials subjected to shear failure, while they are difficult to measure in laboratory. We implemented a user-defined contact model considering rolling resistance to the commercial software PFC2D, and made a calculable method to count the energy components based on the first law of thermodynamics. Then the energy storing and dissipation through the whole sample are investigated in a series of numerical biaxial compression tests by discrete element method (DEM). Four kinds of friction are adopted, i.e. sliding and rolling (S-R), sliding and non-rolling (S-NR), non-sliding and rolling (NS-R) and non-sliding and non-rolling (NS-NR). The results show that the energy is mainly dissipated in the type of sliding rather than rolling. And at a small biaxial strain, the input energy is mainly stored as elastic energy with a small portion dissipated and the dissipated energy is globally distributed through the whole sample. While a large biaxial strain is achieved, the dissipated energy gradually turns dominant and the majority
Charging behavior in a bell-less blast furnace based on 3D discrete element method%基于三维离散元法的无钟高炉装料行为
Institute of Scientific and Technical Information of China (English)
张建良; 邱家用; 国宏伟; 刘征建; 孙辉; 王广伟; 高征铠
2013-01-01
利用三维离散元法建立了无钟高炉布料模型，分析了料罐、旋转溜槽中的颗粒流动行为以及颗粒离开溜槽后的下落轨迹和料堆形成，可视化再现了装料过程。结果发现：炉料在流动过程中始终存在粒度偏析，料罐排料流为漏斗流，小颗粒由于偏析而倾向于后期排出；溜槽倾角对颗粒流动行为和料堆形成影响较大；溜槽内颗粒流由于溜槽旋转而向侧上部偏离和翻动，小颗粒因靠近壁面而位于料流内侧，大颗粒因聚集在溜槽上部而处在料流外侧，炉料颗粒偏析、偏转翻动和速度分布影响下落轨迹；在炉料下落到料面的堆积过程中，大颗粒易于向炉喉中心和边缘偏析，小颗粒因位于料流内侧和渗透作用而分布在堆尖下方且偏向中心侧。结合激光网格炉内测量技术料流轨迹测量结果，验证了模型的适用性。%A bell-less blast furnace charging model was established by using 3D discrete element method. The flow behavior of particles in the hopper and rotating chute, the falling trajectory and heaping process of particles discharged from the rotating chute were modeled and analyzed by using this model. Consequently, the charging process was reproduced visually. It is found that size segregation is always prevalent throughout the flow process of particles. The discharging flow from the hopper is funnel flow, and small particles tend to be discharged in the later stage due to size segregation. It is proved that the influence of chute inclination angle on the particle behavior and heaping process is very significance. The granular flow in the chute deviates upward to one side and tumbles attributing to rotation. Small particles close to the chute wall surface move to the inside of the stream, while large ones staying at the upper part of the chute flow move to the outside. The falling tra jectory of particles is affected by particle size segregation
Pearls of Discrete Mathematics
Erickson, Martin
2009-01-01
Presents methods for solving counting problems and other types of problems that involve discrete structures. This work illustrates the relationship of these structures to algebra, geometry, number theory and combinatorics. It addresses topics such as information and game theories
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
Institute of Scientific and Technical Information of China (English)
张涛; 刘飞; 赵满全; 刘月琴; 李凤丽; 陈晨; 张勇
2016-01-01
domain of vibration signal is conducted with the MATLAB software. Then the time domain and frequency domain results are taken as input parameters of seed metering device model in discrete element software, and the movement law of maize populations under the condition of vibration is simulated in the field work of no-till planter. Seed suction performance bench test verification is performed with the JPS-12 computer vision test bench and LKD-P type suction electromagnetic vibration table, and the analysis on seed metering performance of air-suction seed metering device is conducted under different operation speed and vibration amplitude. Field vibration signal analysis results show that when the field operation speed of planter increases from 2 to 7 km/h, the frequency of the main vibration power of seed metering device is basically kept at 5, 6 and 7 Hz; the vibration amplitude of the seed metering device shows a linear increase from 2.4 to 7.9 mm. Discrete element method simulation results show that the fitting curve between the maximum speed of corn population in seed room and the forward speed of planter has a fitting determination coefficient (R2) of 0.9671. The fitting straight line between the average speed of corn population and the speed of planter has a fitting determination coefficient (R2) of 0.9325. Bench test results show that the operation speed for good seed metering performance of the air-suction seed metering device is 3-5 km/h, and the good vibration amplitude is 6 mm; the maximum speed range of the population is 0.1203-0.2243 m/s, the population average speed range is 0.0807-0.1413 m/s, the maximum speed range of the population in seed suction area is 0.127-0.26 m/s, and the air-suction seed metering device has a good performance. The results can provide theoretical basis for improving the seed suction performance of air-suction seed metering device of no-tillage planter.%高寒干旱地区免耕地表播种作业时，排种器振动与种群运动
The Discrete Wavelet Transform
1991-06-01
focuses on bringing together two separately motivated implementations of the wavelet transform , the algorithm a trous and Mallat’s multiresolution...decomposition. These algorithms are special cases of a single filter bank structure, the discrete wavelet transform , the behavior of which is governed by...nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, we show that the commonly used Lagrange a trous
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
Discrete Event Simulation Modeling of Radiation Medicine Delivery Methods
Energy Technology Data Exchange (ETDEWEB)
Paul M. Lewis; Dennis I. Serig; Rick Archer
1998-12-31
The primary objective of this work was to evaluate the feasibility of using discrete event simulation (DES) modeling to estimate the effects on system performance of changes in the human, hardware, and software elements of radiation medicine delivery methods.
Binary discrete method of topology optimization
Institute of Scientific and Technical Information of China (English)
MEI Yu-lin; WANG Xiao-ming; CHENG Geng-dong
2007-01-01
The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities. Especially, when material is added to elements, the estimation of element sensitivities is very inaccurate,even their signs are also estimated wrong. In order to overcome the problem, a new incremental sensitivity analysis formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide us a good estimate of the change of the objective function whether material is removed from or added to elements,meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix. As a consequence, a binary discrete method of topology optimization is established, in which each element is assigned either a stiffness value of solid material or a small value indicating no material, and the optimization process can remove material from elements or add material to elements so as to make the objective function decrease. And a main advantage of the method is simple and no need of much mathematics, particularly interesting in engineering application.
Dynamic mesh refinement for discrete models of jet electro-hydrodynamics
Lauricella, Marco; Pisignano, Dario; Succi, Sauro
2015-01-01
Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non constant resolution of the jet representation. We develop a dynamic mesh-refinement method for the numerical study of the electro-hydrodynamic behavior of charged jets using discrete element methods. To this purpose, we import ideas and techniques from the string method originally developed in the framework of free-energy landscape simulations. The mesh-refined discrete element method is demonstrated for the case of electrospinning applications.
Directory of Open Access Journals (Sweden)
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Kondakci, H Esat; Saleh, Bahaa E A
2016-01-01
When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and analytical modeling, we uncover a set of surprising features that characterize discrete speckle in one- and two-dimensional lattices known to exhibit transverse Anderson localization. Firstly, the fingerprint of localization is embedded in the fluctuations of the discrete speckle and is revealed in the narrowing of the spatial coherence function. Secondly, the transverse coherence length (or speckle grain size) is frozen during propagation. Thirdly, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. We take these unique featu...
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Discrete Classical Electromagnetic Fields
De Souza, M M
1997-01-01
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.
CONSTRAINED QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENT
Institute of Scientific and Technical Information of China (English)
Jun Hu; Zhong-ci Shi
2005-01-01
In this paper, we define a new nonconforming quadrilateral finite element based on the nonconforming rotated Q1 element by enforcing a constraint on each element, which has only three degrees of freedom. We investigate the consistency, approximation, superclose property, discrete Green's function and superconvergence of this element. Moreover, we propose a new postprocessing technique and apply it to this element. It is proved that the postprocessed discrete solution is superconvergent under a mild assumption on the mesh.
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Discrete breathers in crystals
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Discrete element simulation of impact disaggregation for wet granule agglomerate%湿颗粒聚团碰撞解聚过程的离散元法模拟∗
Institute of Scientific and Technical Information of China (English)
焦杨; 章新喜; 孔凡成; 刘海顺
2015-01-01
Based on the combination of linear contact model, Coulomb slip contact model and parallel bond contact model, a discret element model (DEM) of wet granule agglomerates with coating structure is constructed. Disaggregation pro-cesses of wet agglomerates in impacting to a horizontal plate are performed by applying particle flow code (PFC). Three failure patterns are obtained corresponding to those in experiment. The variation of velocities and rupture characteristics of liquid bridge in disaggregation process are investigated. Effects of impact velocity, gravity of adhered granules, and rotation of core granule are analyzed. DEM simulations show that there are three disaggregation patterns in the coat-ing structure of agglomerates: impact disaggregation, gravity-impact disaggregation and shear-impact disaggregation, depending on the size of primary particles and the rotation of the core granules. With the enlargement of size, gravity plays an increasingly important role and the impact disaggregation pattern shifts to gravity-impact disaggregation. The rotation of core can generate a shear force to separate the fine and disaggregation pattern to turn to shear-impact disag-gregation. Impacting results in a heterogeneous distribution of granule velocities and a tendency of relative movement in agglomerates. Relative movement will bring about the stretch of liquid bridge between granules. If the maximum separation distance of wet granules exceeds the rupture distance of liquid bridge, disaggregation happens. The ruptures of liquid bridge start from impact point and expand to outward, from bottom to up, from inside to outside in coating agglomeration. It is found that the rupture of liquid bridge needs time for accumulation and goes through three stages termed as slow rupture stage, quick rupture stage and entire rupture stage. With the increase of impact velocity, par-ticle gravity, and rotating speed of core granules, disaggregation processes of wet granule agglomerates
Institute of Scientific and Technical Information of China (English)
刘凡一; 张舰; 李博; 陈军
2016-01-01
In this study, we determined the parameters of wheat required in discrete element method (DEM) simulation by the response surface method. The repose angle is a macroscopic parameter, which is used to describe the friction and flow properties of particle material and widely applied in DEM parameter calibration for it can be measured easily. In this research, the heap of wheat was formed through the bottomless cylinder method and the repose angle was measured using a computer graphic technology. The calibration tests were conducted in laboratory and by simulation using EDEM 2.7.0 software. According to previous research, an acrylic cylinder with an inner diameter of 39 mm and a height of 120 mm was used. The wheat particles were filled into the cylinder using the "rainy method" through a square-opening sieve with 12 mm aperture and lifted with a speed of 0.05 m/s. For DEM simulation, different parameter combination tests were designed. Specifically, the Plackett-Burman test was performed to screen the significant parameters from the 8 selected parameters. It was found that the static friction for wheat-wheat and wheat-acrylic contact and the rolling friction for wheat-wheat contact had a significant effect on the repose angle, while the other 5 parameters' influence was negligible. Then the steepest ascent test was used to determine the optimal value range of the significant parameters. In the steepest ascent test, the 5 non-significant parameters were the mid-value of the corresponding initial region, while the 3 significant parameters increased progressively until the relative errors between the simulated and the test value reached the minimum. Based on the result of the Box-Behnken test, a quadratic polynomial model for the repose angle and the 3 significant parameters was created. The analysis of variance (ANOVA) of the quadratic polynomial model showed that the model was significant and the lack-of-fit was non-significant. This means the model can be used to
Institute of Scientific and Technical Information of China (English)
贾富国; 姚丽娜; 韩燕龙; 王会; 史宇菲; 曾勇; 蒋龙伟
2016-01-01
Humidifying evenly is the key to moisture conditioning technology. The uniformity of moisture content depends on the material distribution uniformity. Material uniform plate is the chief work part for increasing the material uniformity, and it has an immediate influence on the follow-up material processing quality and production efficiency. In order to improve the humidifying uniformity in the process of brown rice moisture conditioning, a new type of plate called curved-surface material uniform plate was designed on the basis of existing technology. Combined with the material movement rule on the cone material uniform plate, the parabola was set as the curved generatrix of curved-surface material uniform plate. One of the characteristics of the curved-surface material uniform plate was that it enhanced the uniformity of the material thickness by controlling the floating velocity of the material and offered a favorable condition for uniform humidification of brown rice, and moreover it couldn’t damage brown rice. In this study, on the basis of the theoretical analysis, the working process of the curved-surface material uniform plate was simulated with the discrete element method (DEM), and it was found that the structure parameters and operating conditions of curved-surface refining plate were the key factors affecting its wok performance through the analysis based on the orthogonal design. DEM is a numerical method used for modelling the mechanical behavior of granular materials. Using the EDEM software, the influence laws of the rotation rate of material uniform plate, the curved-surface form and the feeding rateon the material thickness uniformity were simulated and analyzed. According to the performance evaluation indices of evenly distributing material, the structure of curved-surface material uniform plate was optimized. By the response surface analysis method, the mathematical model between each factor and coefficient of variation was established. The
Discrete calculus methods for counting
Mariconda, Carlo
2016-01-01
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...
Discretized Volumes in Numerical Methods
Antal, Miklós
2007-01-01
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem is sought. We associate a group and a graph to that volume. When the group is symmetry of the boundary value problem under investigation, one can specify the structure of the solution, and find out if there are equispectral volumes of a given type. The second technique uses a complex mapping to transplant the solution from volume to volume and a correction function. Equation for the correction function is given. A simple example demonstrates the feasibility of the suggested method.
Institute of Scientific and Technical Information of China (English)
张江源; 林福泳
2013-01-01
By constructing a discrete base, multi-resolution analysis methods are applied to denoise the noise signal. The proposed method of discrete base can be explicitly represented, and has symmetric characteristics. The calculation is greatly reduced through the cycle matrix inverse matrix method. Comparing different denoising methods, the signal de-noising effect is assessed from two aspects of signal-to-noise ratio (SNR) and mean square error (MSE). Experimental results indicate that this method shows good characteristics in signal denoising aspect relative to wavelet analysis method. Denoising effect is obvious, and can achieve good signal-to-noise ratio and mean square error when discrete base coefficient is near 0. 75.%通过构造离散基,应用多分辨率分析的方法,对噪声信号进行去噪处理.所提出方法的离散基能够显式表示,且具有对称性等特点,通过循环矩阵求逆矩阵的方法,可以使计算量大大降低.对比不同的去噪方法,并分别从信噪比(SNR)和均方误差(MSE)两个方面对信号去噪效果进行评估.实验结果表明:相对小波分析方法而言,该方法在信号去噪方面表现出较好的特性,去噪效果明显,离散基系数在0.75附近达到较好的信噪比及均方误差.
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Ambati, V.R.; Bokhove, Onno
2007-01-01
A space–time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space–time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the
Space-time discontinuous Galerkin discretization of rotating shallow water equations on moving grids
Ambati, V.R.; Bokhove, Onno
2006-01-01
A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the
Dorlas, T. C.; Thomas, E. G. F.
2008-01-01
We construct a genuine Radon measure with values in B(l(2)(Z(d))) on the set of paths in Z(d) representing Feynman's integral for the discrete Laplacian on l(2)(Z(d)), and we prove the Feynman integral formula for the solutions of the Schrodinger equation with Hamiltonian H=-1/2 Delta+ V, where Delt
Bergstra, J.A.; Baeten, J.C.M.
1996-01-01
The axiom system ACP of [BeK84a] was extended with real time features in [BaB91]. Here we proceed to define a discrete time extension of ACP, along the lines of ATP [NiS94]. We present versions based on relative timing and on absolute timing. Both approaches are integrated using parametric timing. T
de Wild Propitius, M.D.F.; Bais, F.A.
1999-01-01
In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
On the ranges of discrete exponentials
Directory of Open Access Journals (Sweden)
Florin Caragiu
2004-01-01
Full Text Available Let a>1 be a fixed integer. We prove that there is no first-order formula ϕ(X in one free variable X, written in the language of rings, such that for any prime p with gcd(a,p=1 the set of all elements in the finite prime field Fp satisfying ϕ coincides with the range of the discrete exponential function t↦at(modp.
Energy Technology Data Exchange (ETDEWEB)
Mugica R, A.; Valle G, E. del [IPN, ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: mugica@esfm.ipn.mx
2003-07-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Discrete Feature Model (DFM) User Documentation
Energy Technology Data Exchange (ETDEWEB)
Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))
2008-06-15
software, the geometry of discrete features and their hydrologic properties are defined as a mesh composed of triangular, finite elements. Hydrologic boundary conditions arc prescribed as a simulation sequence, which permits specification of conditions ranging from simple, steady-state flow to complex situations where both the magnitude and type of boundary conditions may vary over time
Lumped impulses, discrete displacements and a moving load analysis
Kok, A.W.M.
1997-01-01
Finite element models are usually presented as relations between lumped forces and discrete displacements. Mostly finite element models are found by the elaboration of the method of the virtual work - which is a special case of the Galerkin's variational principle -. By application of Galerkin's var
Discrete mathematics with applications
Koshy, Thomas
2003-01-01
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects*...
Brunner, Ilka; Plencner, Daniel
2014-01-01
Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories. In the case of Landau-Ginzburg models only the bulk sector had been studied previously, and we re-derive all known results. We also introduce the notion of `projective matrix factorisations', show how they naturally describe boundary and defect sectors, and we further illustrate the efficiency of the defect-based approach by explicitly computing RR charges. Roughly half of our results are not restricted to Landau-Ginzburg models but hold more generally, for any topological field theory. In particular we prove that for a pivotal bicategory, any two objects of its orbifold completion that have the same base are orbifold equivalent. Equivalently, from any orbifold theory (including those based on nonabelian groups) the original unorbifolded theory can be be obtained by orbifo...
Discrete Variational Optimal Control
Jimenez, Fernando; de Diego, David Martin
2012-01-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.
Discrete Variational Optimal Control
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
Salinelli, Ernesto
2014-01-01
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economic...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Linearity stabilizes discrete breathers
Indian Academy of Sciences (India)
T R Krishna Mohan; Surajit Sen
2011-11-01
The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the Fermi–Pasta–Ulam (FPU) and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Here we study the dynamics of highly localized excitations, or discrete breathers, which are known to be initiated by the quasistatic stretching of bonds between adjacent particles. We show via dynamical simulations that acoustic waves introduced by the harmonic term stabilize the discrete breather by suppressing the breather’s tendency to delocalize and disperse. We conclude that the harmonic term, and hence acoustic waves, are essential for the existence of localized breathers in these systems.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Steerable Discrete Cosine Transform
Fracastoro, Giulia; Fosson, Sophie; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely, a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, an...
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Cortical Neural Computation by Discrete Results Hypothesis
Castejon, Carlos; Nuñez, Angel
2016-01-01
One of the most challenging problems we face in neuroscience is to understand how the cortex performs computations. There is increasing evidence that the power of the cortical processing is produced by populations of neurons forming dynamic neuronal ensembles. Theoretical proposals and multineuronal experimental studies have revealed that ensembles of neurons can form emergent functional units. However, how these ensembles are implicated in cortical computations is still a mystery. Although cell ensembles have been associated with brain rhythms, the functional interaction remains largely unclear. It is still unknown how spatially distributed neuronal activity can be temporally integrated to contribute to cortical computations. A theoretical explanation integrating spatial and temporal aspects of cortical processing is still lacking. In this Hypothesis and Theory article, we propose a new functional theoretical framework to explain the computational roles of these ensembles in cortical processing. We suggest that complex neural computations underlying cortical processing could be temporally discrete and that sensory information would need to be quantized to be computed by the cerebral cortex. Accordingly, we propose that cortical processing is produced by the computation of discrete spatio-temporal functional units that we have called “Discrete Results” (Discrete Results Hypothesis). This hypothesis represents a novel functional mechanism by which information processing is computed in the cortex. Furthermore, we propose that precise dynamic sequences of “Discrete Results” is the mechanism used by the cortex to extract, code, memorize and transmit neural information. The novel “Discrete Results” concept has the ability to match the spatial and temporal aspects of cortical processing. We discuss the possible neural underpinnings of these functional computational units and describe the empirical evidence supporting our hypothesis. We propose that fast
Discrete and continuum modelling of soil cutting
Coetzee, C. J.
2014-12-01
Both continuum and discrete methods are used to investigate the soil cutting process. The Discrete Element Method ( dem) is used for the discrete modelling and the Material-Point Method ( mpm) is used for continuum modelling. M pmis a so-called particle method or meshless finite element method. Standard finite element methods have difficulty in modelling the entire cutting process due to large displacements and deformation of the mesh. The use of meshless methods overcomes this problem. M pm can model large deformations, frictional contact at the soil-tool interface, and dynamic effects (inertia forces). In granular materials the discreteness of the system is often important and rotational degrees of freedom are active, which might require enhanced theoretical approaches like polar continua. In polar continuum theories, the material points are considered to possess orientations. A material point has three degrees-of-freedom for rigid rotations, in addition to the three classic translational degrees-of-freedom. The Cosserat continuum is the most transparent and straightforward extension of the nonpolar (classic) continuum. Two-dimensional dem and mpm (polar and nonpolar) simulations of the cutting problem are compared to experiments. The drag force and flow patterns are compared using cohesionless corn grains as material. The corn macro (continuum) and micro ( dem) properties were obtained from shear and oedometer tests. Results show that the dilatancy angle plays a significant role in the flow of material but has less of an influence on the draft force. Nonpolar mpm is the most accurate in predicting blade forces, blade-soil interface stresses and the position and orientation of shear bands. Polar mpm fails in predicting the orientation of the shear band, but is less sensitive to mesh size and mesh orientation compared to nonpolar mpm. dem simulations show less material dilation than observed during experiments.
A Dynamics for Discrete Quantum Gravity
Gudder, Stan
2013-01-01
This paper is based on the causal set approach to discrete quantum gravity. We first describe a classical sequential growth process (CSGP) in which the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the "completed" universe is given by a path through a discretely growing chain of causets. We then quantize the CSGP by forming a Hilbert space $H$ on the set of paths. The quantum dynamics is governed by a sequence of positive operators $\\rho_n$ on $H$ that satisfy normalization and consistency conditions. The pair $(H,\\brac{\\rho_n})$ is called a quantum sequential growth process (QSGP). We next discuss a concrete realization of a QSGP in terms of a natural quantum action. This gives an amplitude process related to the sum over histories" approach to quantum mechanics. Finally, we briefly discuss a discrete form of Einstein's field equation and speculate how this may be employed to compare the present framework with classical general rela...
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich
2009-12-18
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.
Brauer, Fred; Feng, Zhilan; Castillo-Chavez, Carlos
2010-01-01
The mathematical theory of single outbreak epidemic models really began with the work of Kermack and Mackendrick about decades ago. This gave a simple answer to the long-standing question of why epidemics woould appear suddenly and then disappear just as suddenly without having infected an entire population. Therefore it seemed natural to expect that theoreticians would immediately proceed to expand this mathematical framework both because the need to handle recurrent single infectious disease outbreaks has always been a priority for public health officials and because theoreticians often try to push the limits of exiting theories. However, the expansion of the theory via the inclusion of refined epidemiological classifications or through the incorporation of categories that are essential for the evaluation of intervention strategies, in the context of ongoing epidemic outbreaks, did not materialize. It was the global threat posed by SARS in that caused theoreticians to expand the Kermack-McKendrick single-outbreak framework. Most recently, efforts to connect theoretical work to data have exploded as attempts to deal with the threat of emergent and re-emergent diseases including the most recent H1N1 influenza pandemic, have marched to the forefront of our global priorities. Since data are collected and/or reported over discrete units of time, developing single outbreak models that fit collected data naturally is relevant. In this note, we introduce a discrete-epidemic framework and highlight, through our analyses, the similarities between single-outbreak comparable classical continuous-time epidemic models and the discrete-time models introduced in this note. The emphasis is on comparisons driven by expressions for the final epidemic size.
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
Karpeev, D
2004-01-01
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible w...
Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
Institute of Scientific and Technical Information of China (English)
LUO Xu-Dong; GUO Han-Ying; LI Yu-Qi; WU Ke
2004-01-01
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Poisson hierarchy of discrete strings
Energy Technology Data Exchange (ETDEWEB)
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Finite element analysis for general elastic multi-structures
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.
Investigation into discretization methods of the six-parameter Iwan model
Li, Yikun; Hao, Zhiming; Feng, Jiaquan; Zhang, Dingguo
2017-02-01
Iwan model is widely applied for the purpose of describing nonlinear mechanisms of jointed structures. In this paper, parameter identification procedures of the six-parameter Iwan model based on joint experiments with different preload techniques are performed. Four kinds of discretization methods deduced from stiffness equation of the six-parameter Iwan model are provided, which can be used to discretize the integral-form Iwan model into a sum of finite Jenkins elements. In finite element simulation, the influences of discretization methods and numbers of Jenkins elements on computing accuracy are discussed. Simulation results indicate that a higher accuracy can be obtained with larger numbers of Jenkins elements. It is also shown that compared with other three kinds of discretization methods, the geometric series discretization based on stiffness provides the highest computing accuracy.
Discrete R Symmetries and Anomalies
Michael Dine(Santa Cruz Institute for Particle Physics and Department of Physics, Santa Cruz CA 95064, U.S.A.); Angelo Monteux(Santa Cruz Institute for Particle Physics, University of California Santa Cruz, 1156 High Street, Santa Cruz, U.S.A.)
2012-01-01
We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples...
Steerable Discrete Cosine Transform
Fracastoro, Giulia; Fosson, Sophie M.; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.
Discrete Thermodynamics of Lasers
Zilbergleyt, B
2007-01-01
The paper offers a discrete thermodynamic model of lasers. Laser is an open system; its equilibrium is based on a balance of two thermodynamic forces, one related to the incoming pumping power and another to the emitted light. The basic expression for such equilibrium is a logistic map, graphical solutions to which are pitchfork bifurcation diagrams. As pumping force increases, the relative populations on the ground and lasing branches tend to zero and unity correspondingly. An interesting feature of this model is the line spectrum of the up and down transitions between the branches beyond bifurcation point. Even in a simple case of 2-level laser with only 2 possible transition types (up and down), the spectra look like sets of the line packets, starting well before the population inversion. This effect is an independent confirmation of the Einstein's prohibition on practical realization of 2-level laser. Multilevel lasers may be approached by employing the idea of thermodynamic activity for the emitting atom...
Noyes, H. Pierre; Starson, Scott
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields with the relativistic Wheeler-Feynman action at a distance, allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound.
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P. (Stanford Linear Accelerator Center, Menlo Park, CA (USA)); Starson, S. (STARSON Corp. (USA))
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields'' with the relativistic Wheeler-Feynman action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs.
Discrete Pearson distributions
Energy Technology Data Exchange (ETDEWEB)
Bowman, K.O. [Oak Ridge National Lab., TN (United States); Shenton, L.R. [Georgia Univ., Athens, GA (United States); Kastenbaum, M.A. [Kastenbaum (M.A.), Basye, VA (United States)
1991-11-01
These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Immigration and Prosecutorial Discretion.
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration.
McKenzie, Alan
2016-01-01
The Many Worlds Interpretation (MWI) famously avoids the issue of wave function collapse. Different MWI trees representing the same quantum events can have different topologies, depending upon the observer. However, they are all isomorphic to the group of block universes containing all of the outcomes of all of the events, and so, in that sense, the group of block universes is a more fundamental representation. Different branches of the MWI tree, representing different universes in MWI, ultimately share the same quantum state in a common ancestor branch. This branching topology is incompatible with that of the Minkowski block universe; the resolution is to replace the branches with discrete, parallel block universes, each of which extends from the trunk to the outermost twigs. The number of universes in a branch is proportional to its thickness which, in turn, depends upon the absolute square of the probability amplitude for the state in that branch. Every quantum event may be represented by a kernel of unive...
Thermodynamics of discrete quantum processes
Anders, Janet; Giovannetti, Vittorio
2013-03-01
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Discrete dynamics versus analytic dynamics
DEFF Research Database (Denmark)
Toxværd, Søren
2014-01-01
For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...
Discretization error of Stochastic Integrals
Fukasawa, Masaaki
2010-01-01
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.
Discrete Mathematics and Its Applications
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Discretization and implicit mapping dynamics
Luo, Albert C J
2015-01-01
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics,...
New treatment of breakup continuum in the method of continuum discretized coupled channels
Matsumoto, T; Ogata, K; Iseri, Y; Hiyama, E; Kamimura, M; Yahiro, M
2003-01-01
In the method of continuum discretized coupled channels (CDCC) for treating three-body processes in projectile breakup reactions, the discretization of continuous breakup channels is essential. We propose a practical method of the discretization. The validity of the method is numerically tested and confirmed for two realistic examples, $d+^{58}$Ni scattering at 80 MeV and $^{6}Li+^{40}$Ca scattering at 156 MeV. Calculated elastic and breakup S-matrix elements based on the new method converge as the number of discretized breakup channels is increased. The converged S-matrix element agrees with the exact one which is derived with average (Av) discretization established as an accurate method. The new discretization requires a smaller number of breakup channels than the Av method. The feasibility of the new method for more complicated reactions is also discussed.
International Conference eXtended Discretization MethodS
Benvenuti, Elena
2016-01-01
This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.
Uniform Deterministic Discrete Method for Three Dimensional Systems
Institute of Scientific and Technical Information of China (English)
无
1997-01-01
For radiative direct exchange areas in three dimensional system,the Uniform Deterministic Discrete Method(UDDM) was adopted.The spherical surface dividing method for sending area element and the regular icosahedron for sending volume element can meet with the direct exchange area computation of any kind of zone pairs.The numerical examples of direct exchange area in three dimensional system with nonhomogeneous attenuation coefficients indicated that the UDDM can give very high numercal accuracy.
CutFEM : Discretizing geometry and partial differential equations
Burman, Erik; Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, Andre
2015-01-01
We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.
Discrete Darboux transformation for discrete polynomials of hypergeometric type
Bangerezako, Gaspard
1998-03-01
The Darboux transformation, well known in second-order differential operator theory, is applied to the difference equations satisfied by the discrete hypergeometric polynomials (Charlier, Meixner-Kravchuk, Hahn).
Discrete Averaging Relations for Micro to Macro Transition
Liu, Chenchen; Reina, Celia
2016-05-01
The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in multiscale finite element procedures (FE$^2$). We show in this paper that these averaging relations hold exactly under standard finite element discretizations, even if the stress field is discontinuous across elements and the standard proofs based on the divergence theorem are no longer suitable. The discrete averaging results are derived for the three classical types of boundary conditions (affine displacement, periodic and uniform traction boundary conditions) using the properties of the shape functions and the weak form of the microscopic equilibrium equations. The analytical proofs are further verified numerically through a simple finite element simulation of an irregular representative volume element undergoing large deformations. Furthermore, the proofs are extended to include the effects of body forces and inertia, and the results are consistent with those in the smooth continuum setting. This work provides a solid foundation to apply Hill's averaging relations in multiscale finite element methods without introducing an additional error in the scale transition due to the discretization.
Nambu quantum mechanics on discrete 3-tori
Energy Technology Data Exchange (ETDEWEB)
Axenides, M [National Research Center ' Demokritos' , 15310 Aghia Paraskevi, Athens (Greece); Floratos, E G [Nuclear and Particle Physics Section, University of Athens, 15771 Athens (Greece); Nicolis, S [CNRS-Laboratoire de Mathematiques et Physique Theorique (UMR 6083) Federation Denis Poisson (FR 9164) Universite de Tours ' Francois Rabelais' , Parc Grandmont, 37200 Tours (France)], E-mail: axenides@inp.demokritos.gr, E-mail: mflorato@physics.uoa.gr, E-mail: Stam.Nicolis@lmpt.univ-tours.fr
2009-07-10
We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus T{sub N}{sup 3} represented by elements of the group SL(3,Z{sub N}). These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three-dimensional toroidal phase space and are characterized by invariant vectors a of T{sub N}{sup 3}. We quantize all such flows, which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a. The corresponding maps belong to the little group of a element of SL(3,Z{sub N}), which is an SL(2,Z{sub N}) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps realize the metaplectic representation of SL(3,Z{sub N}) on the discrete group of three-dimensional magnetic translations, i.e. the non-commutative 3-torus with a deformation parameter the Nth root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three-dimensional objects.
The origin of discrete particles
Bastin, T
2009-01-01
This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction
A Joint Criterion for Reachability and Observability of Nonuniformly Sampled Discrete Systems
Fúster-Sabater, Amparo
2010-01-01
A joint characterization of reachability (controllability) and observability (constructibility) for linear SISO nonuniformly sampled discrete systems is presented. The work generalizes to the nonuniform sampling the criterion known for the uniform sampling. Emphasis is on the nonuniform sampling sequence, which is believed to be an additional element for analysis and handling of discrete systems.
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Causal Dynamics of Discrete Surfaces
Directory of Open Access Journals (Sweden)
Pablo Arrighi
2014-03-01
Full Text Available We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
Discrete Event Programming with Simkit
Buss, Arnold
2001-01-01
This paper is a brief introduction to the use of Simkit, a software package for implementing Discrete Event Simulation (DES) models. Simkit is written in Java (for any operating system with Java 2TM ).
Institute of Scientific and Technical Information of China (English)
赵选恒; 董为民; 郑广明
2012-01-01
The classifying mechanism of cone classifying liners was explained, and the classifying effects of the ball mills with several typical cone classifying liners were simulated by the discrete element simulation soil-ware EDEM2.3. The obtained data was analysed, and the cone classifying liner with the best classifying effects---cone classifying liner with dual slopes was identified, which provided theoretical basis for the selection of liners.%阐述了球磨机锥面分级衬板的分级机理,应用离散元仿真软件EDEM2.3,对几种典型的锥面分级衬板对磨球的分级作用进行仿真,并对结果数据进行分析,选出分级效果最佳的锥面分级衬板——双斜度分级衬板,为衬板的选用提供理论依据。
Multiscale expansions in discrete world
Indian Academy of Sciences (India)
Ömer Ünsal; Filiz Taşcan; Mehmet Naci Özer
2014-07-01
In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.
Discrete solitons in graphene metamaterials
Bludov, Yuliy V.; Smirnova, Daria A.; Kivshar, Yuri S.; Peres, N. M. R.; Vasilevskiy, Mikhail
2014-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schr\\"{o}dinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states. Fundação para a Ciência e a Tecnolog...
Discrete solitons in graphene metamaterials
Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.
2015-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Energy Technology Data Exchange (ETDEWEB)
Moulton, J.D.; Ascher, U.M. [Univ. of British Columbia, Vancouver, British Columbia (Canada); Morel, J.E. [Los Alamos National Lab., NM (United States)
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Designing of discrete mechatronic vibrating systems with negative value parameters
Buchacz, Andrzej; Gałęziowski, Damian
2016-10-01
In the paper, the known problem of vibration control, authors expanded for designing of mechatronic discrete systems that contains single or multiply piezoelectric elements connected to external electric networks. Main focus has been given for investigations in relation to damping performance and parameters study, in case of potential practical application. By different configurations of considered mechatronic discrete branched structures with two degrees of freedom, key negative parameters have been identified and investigated in case of vibration control effectiveness. Results have been presented in graphical form of amplitudes and dynamical flexibility functions.
Discrete-element method simulations: from micro to macro scales.
Heyes, D M; Baxter, J; Tüzün, U; Qin, R S
2004-09-15
Many liquid systems encountered in environmental science are often complex mixtures of many components which place severe demands on traditional computational modelling techniques. A meso scale description is required to account adequately for their flow behaviour on the meso and macro scales. Traditional techniques of computational fluid dynamics and molecular simulation are not well suited to tackling these systems, and researchers are increasingly turning to a range of relatively new computational techniques that offer the prospect of addressing the factors relevant to multicomponent multiphase liquids on length- and time-scales between the molecular level and the macro scale. In this category, we discuss the off-lattice techniques of 'smooth particle hydrodynamics' (SPH) and 'dissipative particle dynamics' (DPD), and the grid-based techniques of 'lattice gas' and 'lattice Boltzmann' (LB). We highlight the main conceptual and technical features underpinning these methods, their strengths and weaknesses, and provide a few examples of the applications of these techniques that illustrate their utility.
Extension of silo discharge model based on discrete element method
Energy Technology Data Exchange (ETDEWEB)
Oldal, Istvan; Safranyil, Ferenc [Szent Istvan University, Goedoelloe (Hungary)
2015-09-15
Silos are containers used by almost all fields of industry for storing granular materials and generally classified in two types: mass flow and funnel flow. One of the most important design parameter of these equipment is the discharge rate which depends on the flow mode. There are high numbers of analytical and empirical models used for determine this parameter, however none of them is suitable for both flow modes; moreover the accuracy of mass flow models is not acceptable. Recently a few numerical discharge models are made for certain geometries; but the applicability of these models in case of different flow modes was not examined. Aim of our work is the creation of an experimentally validated numerical discharge model based on others work and examination of this in term of different flow modes. We prove that our modified model is suitable for determine silos discharge rate independently from flow mode.
Wind-Aided Firespread Across Arrays of Discrete Fuel Elements
1990-10-01
Ph.D. thesis, Department of Chemical Engineering. Fredericton , Canada: University of New Brunswick. Fang, J. B., and Steward, F. R. 1969 Flame spread... Fredericton , Canada: University of New Brunswick. Steward, F. R., and Tennankore, K. N. 1981 The measurement of the burning rate of an individual dowel in a...1973 Flame spread through uniform fuel matrices. Report, Fire Science Center. Fredericton , Canada: University of New Brunswick. Steward, F. R
Discrete element modelling of permanent pavement deformation in granular materials
Cai, Wei
2015-01-01
The permanent deformation of a pavement due to vehicle load is one of the important factors affecting the design life as well as the maintenance cost of a pavement. For the purpose of obtaining a cost-effective design, it is advisable to predict the traffic-loadinduced permanent pavement deformation. The permanent deformation in pavements (i.e. rutting) can be classified into three categories, including the wearing of the asphalt layers, compaction, and shear deformations. In the present stud...
Discrete Element study of granular material - Bumpy wall interface behavior
El Cheikh, Khadija; Rémond, Sébastien; Pizette, Patrick; Vanhove, Yannick; Djelal, Chafika
2016-09-01
This paper presents a DEM study of a confined granular material sheared between two parallel bumpy walls. The granular material consists of packed dry spherical particles. The bumpiness is modeled by spheres of a given diameter glued on horizontal planes. Different bumpy surfaces are modeled by varying diameter or concentration of glued spheres. The material is sheared by moving the two bumpy walls at fixed velocity. During shear, the confining pressure applied on each bumpy wall is controlled. The effect of wall bumpiness on the effective friction coefficient and on the granular material behavior at the bumpy walls is reported for various shearing conditions. For given bumpiness and confining pressure that we have studied, it is found that the shear velocity does not affect the shear stress. However, the effective friction coefficient and the behavior of the granular material depend on the bumpiness. When the diameter of the glued spheres is larger than about the average grains diameter of the medium, the latter is uniformly sheared and the effective friction coefficient remains constant. For smaller diameters of the glued spheres, the effective friction coefficient increases with the diameter of glued spheres. The influence of glued spheres concentration is significant only for small glued spheres diameters, typically half of average particle diameter of the granular material. In this case, increasing the concentration of glued spheres leads to a decrease in effective friction coefficient and to shear localization at the interface. For different diameters and concentrations of glued spheres, we show that the effect of bumpiness on the effective friction coefficient can be characterized by the depth of interlocking.
GPU-based discrete element rigid body transport
CSIR Research Space (South Africa)
Govender, Nicolin
2013-08-01
Full Text Available The protection of harbours and coastal infrastructure is of vital importance to South Africa. A major development in the design of packing strategies for breakwaters is numerical modelling, and the use of physics engines and DEM models...
Discrete element simulations and experiments: toward applications for cohesive powders
Imole, Olukayode Isaiah
2014-01-01
Granular materials are omnipresent in nature and widely used in various industries ranging from food and pharmaceutical to agriculture and mining – among others. It has been estimated that about 10% of the world’s energy consumption is used in the processing, storage and transport of granular
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
Directory of Open Access Journals (Sweden)
M. P. Menguc
2011-09-01
Full Text Available We embark on this preliminary study of the suitability of the discrete dipole approximation with surface interaction (DDA-SI method to model electric field scattering from noble metal nano-structures on dielectric substrates. The refractive index of noble metals, particularly due to their high imaginary components, require smaller lattice spacings and are especially sensitive to the shape integrity and the volume of the dipole model. The results of DDA-SI method are validated against those of the well-established finite element method (FEM and the finite difference time domain (FDTD method.
Analysis of Discrete Mittag - Leffler Functions
Directory of Open Access Journals (Sweden)
N. Shobanadevi
2015-03-01
Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.
Coupled 3D discrete-continuum numerical modeling of pile penetration in sand
Institute of Scientific and Technical Information of China (English)
Jian ZHOU; Qi-wei JIAN; Jiao ZHANG; Jian-jun GUO
2012-01-01
A coupled discrete-continuum simulation incorporating a 3D aspect and non-circular particles was performed to analyze soil-pile interactions during pile penetration in sand.A self-developed non-circular particle numerical simulation program was used which considered sand near the pile as interacted particles using a discrete element method; the sand away from the pile was simulated as a continuous medium exhibiting linear elastic behaviors.The domain analyzed was divided into two zones.Contact forces at the interface between the two zones were obtained from a discrete zone and applied to the continuum boundaries as nodal forces,while the interface velocities were obtained from the continuum zone and applied to the discrete boundaries.We show that the coupled discrete-continuum simulation can give a microscopic description of the pile penetration process without losing the discrete nature of the zone concerned,and may significantly improve computational efticiency.
Adjoint Based A Posteriori Analysis of Multiscale Mortar Discretizations with Multinumerics
Tavener, Simon
2013-01-01
In this paper we derive a posteriori error estimates for linear functionals of the solution to an elliptic problem discretized using a multiscale nonoverlapping domain decomposition method. The error estimates are based on the solution of an appropriately defined adjoint problem. We present a general framework that allows us to consider both primal and mixed formulations of the forward and adjoint problems within each subdomain. The primal subdomains are discretized using either an interior penalty discontinuous Galerkin method or a continuous Galerkin method with weakly imposed Dirichlet conditions. The mixed subdomains are discretized using Raviart- Thomas mixed finite elements. The a posteriori error estimate also accounts for the errors due to adjoint-inconsistent subdomain discretizations. The coupling between the subdomain discretizations is achieved via a mortar space. We show that the numerical discretization error can be broken down into subdomain and mortar components which may be used to drive adaptive refinement.Copyright © by SIAM.
Lattice Boltzmann based discrete simulation for gas-solid fluidization
Wang, Limin; Wang, Xiaowei; Ge, Wei
2013-01-01
Discrete particle simulation, a combined approach of computational fluid dynamics and discrete methods such as DEM (Discrete Element Method), SPH (Smoothed Particle Hydrodynamics), PIC (Particle-In-Cell), etc., is becoming a practical tool for exploring lab-scale gas-solid systems owing to the fast development of its parallel computation. However, the gas-solid coupling and the corresponding fluid flow solver remain immature. In this work, we presented a modified lattice Boltzmann approach to consider the effect of both the local solid volume fraction and the local relative velocity between the particles and the fluid, which was different from the traditional volume-averaged Navier-Stokes equations. This approach is combined with a time-driven hard sphere algorithm to simulate the motion of individual particles in which particles interact with each other via hard-sphere collisions but the collision detection and motion of the particle are performed at constant time intervals, and the EMMS (energy minimization...
Correction of Discretization Errors Simulated at Supply Wells.
MacMillan, Gordon J; Schumacher, Jens
2015-01-01
Many hydrogeology problems require predictions of hydraulic heads in a supply well. In most cases, the regional hydraulic response to groundwater withdrawal is best approximated using a numerical model; however, simulated hydraulic heads at supply wells are subject to errors associated with model discretization and well loss. An approach for correcting the simulated head at a pumping node is described here. The approach corrects for errors associated with model discretization and can incorporate the user's knowledge of well loss. The approach is model independent, can be applied to finite difference or finite element models, and allows the numerical model to remain somewhat coarsely discretized and therefore numerically efficient. Because the correction is implemented external to the numerical model, one important benefit of this approach is that a response matrix, reduced model approach can be supported even when nonlinear well loss is considered.
Minisuperspace models of discrete systems
Baytaş, Bekir
2016-01-01
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous configurations and the dynamical building-up and stability of long-range correlations. Different types of homogeneous minisuperspace models are introduced for the system, including one based on condensate states, and shown to capture different aspects of the discrete system. They are evaluated with effective methods and by means of continuum limits, showing good agreement with operator calculations whenever the latter are available. As a possibly quite general result, it is concluded that an analysis of the building-up of long-range correlations in discrete systems requires non-perturbative solutions of the dynamical equations. Some questions related to stability can be analyzed perturbatively, but suggest that matter couplings may be relevant for this question in the context o...
Interference in discrete Wigner functions
Cormick, C; Cormick, Cecilia; Paz, Juan Pablo
2006-01-01
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We consider "cat" states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase-space (including the regions where the two interfering states are localized). This is a generic property which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this...
DISCRETE AND CONTINUUM MODELLING OF GRANULAR FLOW
Institute of Scientific and Technical Information of China (English)
H. P. Zhu; Y. H. WU; A. B. Yu
2005-01-01
This paper analyses three popular methods simulating granular flow at different time and length scales:discrete element method (DEM), averaging method and viscous, elastic-plastic continuum model. The theoretical models of these methods and their applications to hopper flows are discussed. It is shown that DEM is an effective method to study the fundamentals of granular flow at a particle or microscopic scale. By use of the continuum approach, granular flow can also be described at a continuum or macroscopic scale. Macroscopic quantities such as velocity and stress can be obtained by use of such computational method as FEM. However, this approach depends on the constitutive relationship of materials and ignores the effect of microscopic structure of granular flow. The combined approach of DEM and averaging method can overcome this problem. The approach takes into account the discrete nature of granular materials and does not require any global assumption and thus allows a better understanding of the fundamental mechanisms of granular flow. However, it is difficult to adapt this approach to process modelling because of the limited number of particles which can be handled with the present computational capacity, and the difficulty in handling non-spherical particles.Further work is needed to develop an appropriate approach to overcome these problems.
Neutrino mass, mixing and discrete symmetries
Smirnov, Alexei Y.
2013-07-01
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry Gf to different residual symmetries Gl and Gv in the charged lepton and neutrino sectors. In this framework the symmetry group condition has been derived which allows to get relations between the lepton mixing elements immediately without explicit model building. The condition has been applied to different residual neutrino symmetries Gv. For generic (mass independent) Gv = Z2 the condition leads to two relations between the mixing parameters and fixes one column of the mixing matrix. In the case of Gv = Z2 × Z2 the condition fixes the mixing matrix completely. The non-generic (mass spectrum dependent) Gv lead to relations which include mixing angles, neutrino masses and Majorana phases. The symmetries Gl, Gv, Gf are identified which lead to the experimentally observed values of the mixing angles and allow to predict the CP phase.
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
An element by element spectral element method for elastic wave modeling
Institute of Scientific and Technical Information of China (English)
LIN Weijun; WANG Xiuming; ZHANG Hailan
2006-01-01
The spectral element method which combines the advantages of spectral method with those of finite element method,provides an efficient tool in simulating elastic wave equation in complex medium. Based on weak form of elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order Lagrange interpolation, and integration over the element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element technique is introduced in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are presented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and spectral algorithms, this method can be used for complex models, including free surface boundaries and strong heterogeneity.
Isogeometric shell discretizations for flexible multibody dynamics
Energy Technology Data Exchange (ETDEWEB)
Goyal, Anmol, E-mail: goyal@mathematik.uni-kl.de; Doerfel, Michael R., E-mail: michael.doerfel@web.de; Simeon, Bernd, E-mail: simeon@mathematik.uni-kl.de; Vuong, Anh-Vu, E-mail: vuong@mathematik.uni-kl.de [Technische Universitaet Kaiserslautern, Felix Klein Zentrum fuer Mathematik, FB Mathematik (Germany)
2013-08-01
This work aims at including nonlinear elastic shell models in a multibody framework. We focus our attention to Kirchhoff-Love shells and explore the benefits of an isogeometric approach, the latest development in finite element methods, within a multibody system. Isogeometric analysis extends isoparameteric finite elements to more general functions such as B-splines and NURBS (Non-Uniform Rational B-Splines) and works on exact geometry representations even at the coarsest level of discretizations. Using NURBS as basis functions, high regularity requirements of the shell model, which are difficult to achieve with standard finite elements, are easily fulfilled. A particular advantage is the promise of simplifying the mesh generation step, and mesh refinement is easily performed by eliminating the need for communication with the geometry representation in a CAD (Computer-Aided Design) tool. Target applications are wind turbine blades and twist beam rear suspensions. First numerical examples demonstrate an impressive convergence behavior of the isogeometric approach even for a coarse mesh, while offering substantial savings with respect to the number of degrees of freedom.
DISCRETE ROTATIONS AND CELLULAR AUTOMATA
Nouvel, Bertrand
2006-01-01
In a discrete space, such as the set of integer-coordinate points, the modelization of isotropy may lead to noticeable theoretical difficulties. At this time, we do not know any gerometric theory on $\\ZZ^n$ that would be suitable to describe the isotropy the same way it is perceived by Euclidean geometry. With respect to this problematic, our aim is to describe some algorithms that would give to the discrete rotations some properties that would be similar to the properties of the Euclidean ro...
Stable discrete surface light bullets.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-01-22
We analyze spatiotemporal light localization near the edge of a semi-infinite array of weakly coupled nonlinear optical waveguides and demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons, the so-called discrete surface light bullets. We show that their properties are strongly affected by the presence of the surface. To this end the crossover between surface and quasi-bulk bullets is studied by analyzing the families of solitons propagating at different distances from the edge of the waveguide array.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Directory of Open Access Journals (Sweden)
Dayanne Aline de Souza Fidelis
2006-07-01
Full Text Available The space and time discretization of the finite element method was optimized for following application in multicomponent diffusion simulation during Prato cheese salting, a traditional and much consumed foodstuff in Brazil originated from the European Gouda cheese. It was ascertained that the correct choice of the time intervals and mesh is fundamental in applying the method. After optimization the simulated results were in agreement with the experimental and calculated results by the analytical method, showing that the method is a promising tool for simulation of diffusive processes when two solutes are considered, and is also a much less restrictive technique than the analytical method.Neste trabalho foi realizada a otimização da discretização espaço-temporal do método de elementos finitos para sua posterior aplicação na simulação da difusão multicomponente durante a salda de queijo prato, um alimento tradicional e muito consumido no Brasil e similar ao queijo Gouda. Foi verificado que a escolha correta dos intervalos de tempo e da malha é fundamental para a aplicação do método. Após a otimização os resultados simulados concordaram com os experimentais e estimados pelo método analítico. Mostrando que o método é uma ferramenta promissora para a simulação de processos difusivos quando dois solutos são considerados, além de ser uma técnica muito menosrestritiva que o método analítico.