Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures

OpenAIRE

Majidi, Behzad; Taghavi, Seyed Mohammad; Fafard, Mario; Ziegler, Donald P.; Alamdari, Houshang

2016-01-01

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 use...

Discrete elements method of neutral particle transport

International Nuclear Information System (INIS)

Mathews, K.A.

1983-01-01

A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

Science.gov (United States)

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved

Prediction of Fracture Behavior in Rock and Rock-like Materials Using Discrete Element Models

Science.gov (United States)

Katsaga, T.; Young, P.

2009-05-01

The study of fracture initiation and propagation in heterogeneous materials such as rock and rock-like materials are of principal interest in the field of rock mechanics and rock engineering. It is crucial to study and investigate failure prediction and safety measures in civil and mining structures. Our work offers a practical approach to predict fracture behaviour using discrete element models. In this approach, the microstructures of materials are presented through the combination of clusters of bonded particles with different inter-cluster particle and bond properties, and intra-cluster bond properties. The geometry of clusters is transferred from information available from thin sections, computed tomography (CT) images and other visual presentation of the modeled material using customized AutoCAD built-in dialog- based Visual Basic Application. Exact microstructures of the tested sample, including fractures, faults, inclusions and void spaces can be duplicated in the discrete element models. Although the microstructural fabrics of rocks and rock-like structures may have different scale, fracture formation and propagation through these materials are alike and will follow similar mechanics. Synthetic material provides an excellent condition for validating the modelling approaches, as fracture behaviours are known with the well-defined composite's properties. Calibration of the macro-properties of matrix material and inclusions (aggregates), were followed with the overall mechanical material responses calibration by adjusting the interfacial properties. The discrete element model predicted similar fracture propagation features and path as that of the real sample material. The path of the fractures and matrix-inclusion interaction was compared using computed tomography images. Initiation and fracture formation in the model and real material were compared using Acoustic Emission data. Analysing the temporal and spatial evolution of AE events, collected during the

A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

Directory of Open Access Journals (Sweden)

Paul Brocklehurst

2015-01-01

Full Text Available 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 Ca2+ 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.

Calibration of discrete element model parameters: soybeans

Science.gov (United States)

Ghodki, Bhupendra M.; Patel, Manish; Namdeo, Rohit; Carpenter, Gopal

2018-05-01

Discrete element method (DEM) simulations are broadly used to get an insight of flow characteristics of granular materials in complex particulate systems. DEM input parameters for a model are the critical prerequisite for an efficient simulation. Thus, the present investigation aims to determine DEM input parameters for Hertz-Mindlin model using soybeans as a granular material. To achieve this aim, widely acceptable calibration approach was used having standard box-type apparatus. Further, qualitative and quantitative findings such as particle profile, height of kernels retaining the acrylic wall, and angle of repose of experiments and numerical simulations were compared to get the parameters. The calibrated set of DEM input parameters includes the following (a) material properties: particle geometric mean diameter (6.24 mm); spherical shape; particle density (1220 kg m^{-3} ), and (b) interaction parameters such as particle-particle: coefficient of restitution (0.17); coefficient of static friction (0.26); coefficient of rolling friction (0.08), and particle-wall: coefficient of restitution (0.35); coefficient of static friction (0.30); coefficient of rolling friction (0.08). The results may adequately be used to simulate particle scale mechanics (grain commingling, flow/motion, forces, etc) of soybeans in post-harvest machinery and devices.

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

and the reliability of which have been validated. The dynamic modulus of asphalt mixtures were predicted by conducting Discrete Element simulation under dynamic strain control loading. In order to reduce the calculation time, a method based on frequency–temperature superposition principle has been implemented......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....... The ball density effect on the internal stress distribution of the asphalt mixture model has been studied when using this method. Furthermore, the internal stresses under dynamic loading have been studied. The agreement between the predicted and the laboratory test results of the complex modulus shows...

Discrete Element Modeling (DEM) of Triboelectrically Charged Particles: Revised Experiments

Science.gov (United States)

Hogue, Michael D.; Calle, Carlos I.; Curry, D. R.; Weitzman, P. S.

2008-01-01

In a previous work, the addition of basic screened Coulombic electrostatic forces to an existing commercial discrete element modeling (DEM) software was reported. Triboelectric experiments were performed to charge glass spheres rolling on inclined planes of various materials. Charge generation constants and the Q/m ratios for the test materials were calculated from the experimental data and compared to the simulation output of the DEM software. In this paper, we will discuss new values of the charge generation constants calculated from improved experimental procedures and data. Also, planned work to include dielectrophoretic, Van der Waals forces, and advanced mechanical forces into the software will be discussed.

Discrete element modeling of cemented sand and particle crushing at high pressures

OpenAIRE

de Bono, John Patrick

2013-01-01

This project aims to provide an insight into the behaviour of cemented sand under high pressures, and to further the understanding of the role of particle crushing. The discrete element method is used to investigate the micro mechanics of sand and cemented sand in high-pressure triaxial tests and one-dimensional normal compression. Using the software PFC3D, a new triaxial model has been developed, which features an effective flexible membrane that allows free deformation of the specimen ...

Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction

Science.gov (United States)

Kaewunruen, S.; Mirza, O.

2017-10-01

At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.

Three Different Ways of Calibrating Burger's Contact Model for Viscoelastic Model of Asphalt Mixtures by Discrete Element Method

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...

Discrete element modelling of bedload transport

Science.gov (United States)

Loyer, A.; Frey, P.

2011-12-01

Discrete element modelling (DEM) has been widely used in solid mechanics and in granular physics. In this type of modelling, each individual particle is taken into account and intergranular interactions are modelled with simple laws (e.g. Coulomb friction). Gravity and contact forces permit to solve the dynamical behaviour of the system. DEM is interesting to model configurations and access to parameters not directly available in laboratory experimentation, hence the term "numerical experimentations" sometimes used to describe DEM. DEM was used to model bedload transport experiments performed at the particle scale with spherical glass beads in a steep and narrow flume. Bedload is the larger material that is transported on the bed on stream channels. It has a great geomorphic impact. Physical processes ruling bedload transport and more generally coarse-particle/fluid systems are poorly known, arguably because granular interactions have been somewhat neglected. An existing DEM code (PFC3D) already computing granular interactions was used. We implemented basic hydrodynamic forces to model the fluid interactions (buoyancy, drag, lift). The idea was to use the minimum number of ingredients to match the experimental results. Experiments were performed with one-size and two-size mixtures of coarse spherical glass beads entrained by a shallow turbulent and supercritical water flow down a steep channel with a mobile bed. The particle diameters were 4 and 6mm, the channel width 6.5mm (about the same width as the coarser particles) and the channel inclination was typically 10%. The water flow rate and the particle rate were kept constant at the upstream entrance and adjusted to obtain bedload transport equilibrium. Flows were filmed from the side by a high-speed camera. Using image processing algorithms made it possible to determine the position, velocity and trajectory of both smaller and coarser particles. Modelled and experimental particle velocity and concentration depth

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.

Study of normal and shear material properties for viscoelastic model of asphalt mixture by discrete element method

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...

Determining Trajectory of Triboelectrically Charged Particles, Using Discrete Element Modeling

Science.gov (United States)

2008-01-01

The Kennedy Space Center (KSC) Electrostatics and Surface Physics Laboratory is participating in an Innovative Partnership Program (IPP) project with an industry partner to modify a commercial off-the-shelf simulation software product to treat the electrodynamics of particulate systems. Discrete element modeling (DEM) is a numerical technique that can track the dynamics of particle systems. This technique, which was introduced in 1979 for analysis of rock mechanics, was recently refined to include the contact force interaction of particles with arbitrary surfaces and moving machinery. In our work, we endeavor to incorporate electrostatic forces into the DEM calculations to enhance the fidelity of the software and its applicability to (1) particle processes, such as electrophotography, that are greatly affected by electrostatic forces, (2) grain and dust transport, and (3) the study of lunar and Martian regoliths.

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

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.

Finite element discretization of Darcy's equations with pressure dependent porosity

KAUST Repository

Girault, Vivette; Murat, Franç ois; Salgado, Abner

2010-01-01

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

Sensitivity of Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations

Science.gov (United States)

2016-06-12

Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations Venkatesh Babu, Kumar Kulkarni, Sanjay...buried in soil viz., (1) coupled discrete element & particle gas methods (DEM-PGM) and (2) Arbitrary Lagrangian-Eulerian (ALE), are investigated. The...DEM_PGM and identify the limitations/strengths compared to the ALE method. Discrete Element Method (DEM) can model individual particle directly, and

Feeder Type Optimisation for the Plain Flow Discharge Process of an Underground Hopper by Discrete Element Modelling

OpenAIRE

Jan Nečas; Jakub Hlosta; David Žurovec; Martin Žídek; Jiří Rozbroj; Jiří Zegzulka

2017-01-01

This paper describes optimisation of a conveyor from an underground hopper intended for a coal transfer station. The original solution was designed with a chain conveyor encountered operational problems that have limited its continuous operation. The Discrete Element Modeling (DEM) was chosen to optimise the transport. DEM simulations allow device design modifications directly in the 3D CAD model, and then the simulation makes it possible to evaluate whether the adjustment was successful. By...

New formulation of the discrete element method

Science.gov (United States)

Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon

2018-01-01

A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

Discrete element simulation of internal stress in SiCp/aluminum ...

African Journals Online (AJOL)

SiCp / Al-Mg-Si matrix composite was prepared by pressureless Infiltration Process. By discrete element method, microcosmic two-dimensional numerical model of SiCp / Al matrix composites was established and the simulation of the size and distribution of micro-contact pressure and tension was performed from small load ...

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

Fracture Failure of Reinforced Concrete Slabs Subjected to Blast Loading Using the Combined Finite-Discrete Element Method

Directory of Open Access Journals (Sweden)

Z. M. Jaini

Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.

Blocking Mechanism Study of Self-Compacting Concrete Based on Discrete Element Method

Science.gov (United States)

Zhang, Xuan; Li, Zhida; Zhang, Zhihua

2017-11-01

In order to study the influence factors of blocking mechanism of Self-Compaction Concrete (SCC), Roussel’s granular blocking model was verified and extended by establishing the discrete element model of SCC. The influence of different parameters on the filling capacity and blocking mechanism of SCC were also investigated. The results showed that: it was feasible to simulate the blocking mechanism of SCC by using Discrete Element Method (DEM). The passing ability of pebble aggregate was superior to the gravel aggregate and the passing ability of hexahedron particles was bigger than tetrahedron particles, while the tetrahedron particle simulation results were closer to the actual situation. The flow of SCC as another significant factor affected the passing ability that with the flow increased, the passing ability increased. The correction coefficient λ of the steel arrangement (channel section shape) and flow rate γ in the block model were introduced that the value of λ was 0.90-0.95 and the maximum casting rate was 7.8 L/min.

Modelling Dowel Action of Discrete Reinforcing Bars in Cracked Concrete Structures

International Nuclear Information System (INIS)

Kwan, A. K. H.; Ng, P. L.; Lam, J. Y. K.

2010-01-01

Dowel action is one of the component actions for shear force transfer in cracked reinforced concrete. In finite element analysis of concrete structures, the use of discrete representation of reinforcing bars is considered advantageous over the smeared representation due to the relative ease of modelling the bond-slip behaviour. However, there is very limited research on how to simulate the dowel action of discrete reinforcing bars. Herein, a numerical model for dowel action of discrete reinforcing bars crossing cracks in concrete is developed. The model features the derivation of dowel stiffness matrix based on beam-on-elastic-foundation theory and the direct assemblage of dowel stiffness into the concrete element stiffness matrices. The dowel action model is incorporated in a nonlinear finite element programme with secant stiffness formulation. Deep beams tested in the literature are analysed and it is found that the incorporation of dowel action model improves the accuracy of analysis.

Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures.

Science.gov (United States)

Majidi, Behzad; Taghavi, Seyed Mohammad; Fafard, Mario; Ziegler, Donald P; Alamdari, Houshang

2016-05-04

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.

Governing equations of multi-component rigid body-spring discrete element models of reinforced concrete columns

International Nuclear Information System (INIS)

Guan, P B; Tingatinga, E A; Longalong, R E; Saguid, J

2016-01-01

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. (paper)

A new discrete-element approach for the assessment of the seismic resistance of composite reinforced concrete-masonry buildings

International Nuclear Information System (INIS)

Calio, I.; Cannizzaro, F.; Marletta, M.; Panto, B.; D'Amore, E.

2008-01-01

In the present study a new discrete-element approach for the evaluation of the seismic resistance of composite reinforced concrete-masonry structures is presented. In the proposed model, unreinforced masonry panels are modelled by means of two-dimensional discrete-elements, conceived by the authors for modelling masonry structures, whereas the reinforced concrete elements are modelled by lumped plasticity elements interacting with the masonry panels through nonlinear interface elements. The proposed procedure was adopted for the assessment of the seismic response of a case study confined-masonry building which was conceived to be a typical representative of a wide class of residential buildings designed to the requirements of the 1909 issue of the Italian seismic code and widely adopted in the aftermath of the 1908 earthquake for the reconstruction of the cities of Messina and Reggio Calabria

Discrete Feature Model (DFM) User Documentation

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

2008-06-15

This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this

Discrete Feature Model (DFM) User Documentation

International Nuclear Information System (INIS)

Geier, Joel

2008-06-01

This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this software, the

Discrete modelling of drapery systems

Science.gov (United States)

Thoeni, Klaus; Giacomini, Anna

2016-04-01

Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R

Finite element discretization of Darcy's equations with pressure dependent porosity

KAUST Repository

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.

Coupled large eddy simulation and discrete element model of bedload motion

Science.gov (United States)

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

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.

Discrete Element Method for Modeling the Mechanical Behavior of Unsaturated Granular Material

Directory of Open Access Journals (Sweden)

K. Tourani

2016-09-01

Full Text Available Although a significant portion of conditions encountered in geotechnical engineering, for investigating engineering behavior of soil, involves unsaturated soils; the traditional analysis and design approach has been to assume the limiting conditions of soils being either completely dry or completely saturated. In unsaturated soils the capillary force produce attractive forces between particles. Discrete Element Method (DEM is an appropriate tool to consider the capillary effects. The calculations performed in DEM is based on iterative application of Newton’s second law to the particles and force-displacement law at the contacts. In the present study, the behavior of unsaturated soils in pendular regime is simulated utilizing DEM. Triaxial  compression tests were modeled as two-dimensional, considering capillary force effects. Finally, capillary effects on Macro parameters of a simulated granular soil (stress, axial strain, volumetric strain and void ratio and Mohr Coulomb failure criteria parameters were studied.

An implicit finite element method for discrete dynamic fracture

Energy Technology Data Exchange (ETDEWEB)

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

A Discrete Element Method Centrifuge Model of Monopile under Cyclic Lateral Loads

OpenAIRE

Nuo Duan; Yi Pik Cheng

2016-01-01

This paper presents the data of a series of two-dimensional Discrete Element Method (DEM) simulations of a large-diameter rigid monopile subjected to cyclic loading under a high gravitational force. At present, monopile foundations are widely used to support the tall and heavy wind turbines, which are also subjected to significant from wind and wave actions. A safe design must address issues such as rotations and changes in soil stiffness subject to these loadings conditions. Design guidance ...

Comparisons between a high resolution discrete element model and analogue model

Science.gov (United States)

LI, C. S.; Yin, H.; WU, C.; Zhang, J.

2017-12-01

A two-dimensional discrete element model (DEM) with high resolution is constructed to simulate the evolution of thrust wedge and an analogue model (AM) experiment is constructed to compare with the DEM results. This efficient parallel DEM program is written in the C language, and it is useful to solve the complex geological problems. More detailed about fold and thrust belts of DEM can be identified with the help of strain field. With non-rotating and non-tensile assumption, dynamic evolution of DEM is highly consistent with AM. Simulations in different scale can compare with each other by conversion formulas in DEM. Our results show that: (1) The overall evolution of DEM and AM is broadly similar. (2) Shortening is accommodated by in-sequence forward propagation of thrusts. The surface slope of the thrust wedge is within the stable field predicted by critical taper theory. (3) Details of thrust spacing, dip angle and number of thrusts vary between DEM and AM for the shortening experiment, but the characteristics of thrusts are similar on the whole. (4) Dip angles of the forward thrusts increased from foreland (ca. 30°) to the mobile wall (ca. 80°) (5) With shortening, both models had not the obvious volume loss. Instead, the volume basic remained unchanged in the whole extrusion processes. (6) Almost all high strain values are within fold-and-thrust belts in DEM, which allows a direct comparison between the fault zone identified on the DEM deformation field and that in the strain field. (7) The first fault initiates at deep depths and propagate down toward the surface. For the maximal volumetric strain focused on the décollement near the mobile wall, strengthening the material and making it for brittle. (8) With non-tensile particles for DEM, contraction is broadly distributed throughout the model and dilation is hardly any, which also leads to a higher efficient computation. (9) High resolution DEM can to first order successfully reproduce structures observed

Toward the modeling of combustion reactions through discrete element method (DEM) simulations

Science.gov (United States)

Reis, Martina Costa; Alobaid, Falah; Wang, Yongqi

2018-03-01

In this work, the process of combustion of coal particles under turbulent regime in a high-temperature reaction chamber is modeled through 3D discrete element method (DEM) simulations. By assuming the occurrence of interfacial transport phenomena between the gas and solid phases, one investigates the influence of the physicochemical properties of particles on the rates of heterogeneous chemical reactions, as well as the influence of eddies present in the gas phase on the mass transport of reactants toward the coal particles surface. Moreover, by considering a simplistic chemical mechanism for the combustion process, thermochemical and kinetic parameters obtained from the simulations are employed to discuss some phenomenological aspects of the combustion process. In particular, the observed changes in the mass and volume of coal particles during the gasification and combustion steps are discussed by emphasizing the changes in the chemical structure of the coal. In addition to illustrate how DEM simulations can be used in the modeling of consecutive and parallel chemical reactions, this work also shows how heterogeneous and homogeneous chemical reactions become a source of mass and energy for the gas phase.

Adaptive Finite Element-Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre-Existing Fractures

Directory of Open Access Journals (Sweden)

Yongliang Wang

2018-01-01

Full Text Available Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre-existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element-discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre-existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre-existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B-values, Hudson source type plots, and focal spheres.

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

International Nuclear Information System (INIS)

Gerstl, S.A.W.; Zardecki, A.

1985-01-01

Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

Coupling of a continuum ice sheet model and a discrete element calving model using a scientific workflow system

Science.gov (United States)

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

Modeling of brittle-viscous flow using discrete particles

Science.gov (United States)

Thordén Haug, Øystein; Barabasch, Jessica; Virgo, Simon; Souche, Alban; Galland, Olivier; Mair, Karen; Abe, Steffen; Urai, Janos L.

2017-04-01

Many geological processes involve both viscous flow and brittle fractures, e.g. boudinage, folding and magmatic intrusions. Numerical modeling of such viscous-brittle materials poses challenges: one has to account for the discrete fracturing, the continuous viscous flow, the coupling between them, and potential pressure dependence of the flow. The Discrete Element Method (DEM) is a numerical technique, widely used for studying fracture of geomaterials. However, the implementation of viscous fluid flow in discrete element models is not trivial. In this study, we model quasi-viscous fluid flow behavior using Esys-Particle software (Abe et al., 2004). We build on the methodology of Abe and Urai (2012) where a combination of elastic repulsion and dashpot interactions between the discrete particles is implemented. Several benchmarks are presented to illustrate the material properties. Here, we present extensive, systematic material tests to characterize the rheology of quasi-viscous DEM particle packing. We present two tests: a simple shear test and a channel flow test, both in 2D and 3D. In the simple shear tests, simulations were performed in a box, where the upper wall is moved with a constant velocity in the x-direction, causing shear deformation of the particle assemblage. Here, the boundary conditions are periodic on the sides, with constant forces on the upper and lower walls. In the channel flow tests, a piston pushes a sample through a channel by Poisseuille flow. For both setups, we present the resulting stress-strain relationships over a range of material parameters, confining stress and strain rate. Results show power-law dependence between stress and strain rate, with a non-linear dependence on confining force. The material is strain softening under some conditions (which). Additionally, volumetric strain can be dilatant or compactant, depending on porosity, confining pressure and strain rate. Constitutive relations are implemented in a way that limits the

Finite element modelling of the mechanics of discrete carbon nanotubes filled with ZnS and comparison with experimental observations

KAUST Repository

Monteiro, André O.; Da Costa, Pedro M. F. J.; Cachim, Paulo Barreto

2013-01-01

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.

Finite element modelling of the mechanics of discrete carbon nanotubes filled with ZnS and comparison with experimental observations

KAUST Repository

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.

Physical models on discrete space and time

International Nuclear Information System (INIS)

Lorente, M.

1986-01-01

The idea of space and time quantum operators with a discrete spectrum has been proposed frequently since the discovery that some physical quantities exhibit measured values that are multiples of fundamental units. This paper first reviews a number of these physical models. They are: the method of finite elements proposed by Bender et al; the quantum field theory model on discrete space-time proposed by Yamamoto; the finite dimensional quantum mechanics approach proposed by Santhanam et al; the idea of space-time as lattices of n-simplices proposed by Kaplunovsky et al; and the theory of elementary processes proposed by Weizsaecker and his colleagues. The paper then presents a model proposed by the authors and based on the (n+1)-dimensional space-time lattice where fundamental entities interact among themselves 1 to 2n in order to build up a n-dimensional cubic lattice as a ground field where the physical interactions take place. The space-time coordinates are nothing more than the labelling of the ground field and take only discrete values. 11 references

ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF TWO-DIMENSIONAL STRUCTURAL ANALYSIS WITH THE USE OF COMBINED APPLICATION OF FINITE ELEMENT METHOD AND DISCRETE-CONTINUAL FINITE ELEMENT METHOD PART 2: SPECIAL ASPECTS OF FINITE ELEMENT APPROXIMATION

Directory of Open Access Journals (Sweden)

Pavel A. Akimov

2017-12-01

Full Text Available As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM, and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM. In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic variants are available are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.

Finite-element semi-discretization of linearized compressible and resistive MHD

International Nuclear Information System (INIS)

Kerner, W.; Jakoby, A.; Lerbinger, K.

1985-08-01

The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)

Discrete modeling of multiple discontinuities in rock mass using XFEM

OpenAIRE

Das, Kamal C.; Ausas, Roberto Federico; Carol, Ignacio; Rodrigues, Eduardo; Sandeep, Sandra; Vargas, P. E.; Gonzalez, Nubia Aurora; Segura, Josep María; Lakshmikantha, Ramasesha Mookanahallipatna; Mello,, U.

2017-01-01

Modeling of discontinuities (fractures and fault surfaces) is of major importance to assess the geomechanical behavior of oil and gas reservoirs, especially for tight and unconventional reservoirs. Numerical analysis of discrete discontinuities traditionally has been studied using interface element concepts, however more recently there are attempts to use extended finite element method (XFEM). The development of an XFEM tool for geo-mechanical fractures/faults modeling has significant industr...

Novel Discrete Element Method for 3D non-spherical granular particles.

Science.gov (United States)

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.

Periodic Properties of 1D FE Discrete Models in High Frequency Dynamics

Directory of Open Access Journals (Sweden)

A. Żak

2016-01-01

Full Text Available Finite element discrete models of various engineering 1D structures may be considered as structures of certain periodic characteristics. The source of this periodicity comes from the discontinuity of stress/strain field between the elements. This behaviour remains unnoticeable, when low frequency dynamics of these structures is investigated. At high frequency regimes, however, its influence may be strong enough to dominate calculated structural responses distorting or even falsifying them completely. In this paper, certain computational aspects of structural periodicity of 1D FE discrete models are discussed by the authors. In this discussion, the authors focus their attention on an exemplary problem of 1D rod modelled according to the elementary theory.

Cyclic loading tests on ceramic breeder pebble bed by discrete element modeling

Energy Technology Data Exchange (ETDEWEB)

Zhang, Hao [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Guo, Haibing; Shi, Tao [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Ye, Minyou [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Huang, Hongwen, E-mail: hhw@caep.cn [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Li, Zhenghong, E-mail: inpcnyb@sina.com [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); University of Science and Technology of China, Hefei 230027 (China)

2017-05-15

Highlights: • Methods of cyclic loading tests on the pebble beds were developed in DEM. • Size distribution and sphericity of the pebbles were considered for the specimen. • Mechanical responses of the pebble beds under cyclic loading tests were assessed. - Abstract: Complex mechanics and packing instability can be induced by loading operation on ceramic breeder pebble bed for its discrete nature. A numerical approach using discrete element method (DEM) is applied to study the mechanical performance of the ceramic breeder pebble bed under quasi-static and cyclic loads. A preloaded specimen can be made with servo-control mechanism, the quasi-static and dynamic stress-strain performances are studied during the tests. It is found that the normalized normal contact forces under quasi-static loads have the similar distributions, and increase with increasing loads. Furthermore, the relatively low volumetric strain can be absorbed by pebble bed after several loading and unloading cycles, but the peak normal contact force can be extremely high during the first cycle. Cyclic loading with target pressure is recommended for densely packing, irreversible volume reduction gradually increase with cycles, and the normal contact forces decrease with cycles.

Cyclic loading tests on ceramic breeder pebble bed by discrete element modeling

International Nuclear Information System (INIS)

Zhang, Hao; Guo, Haibing; Shi, Tao; Ye, Minyou; Huang, Hongwen; Li, Zhenghong

2017-01-01

Highlights: • Methods of cyclic loading tests on the pebble beds were developed in DEM. • Size distribution and sphericity of the pebbles were considered for the specimen. • Mechanical responses of the pebble beds under cyclic loading tests were assessed. - Abstract: Complex mechanics and packing instability can be induced by loading operation on ceramic breeder pebble bed for its discrete nature. A numerical approach using discrete element method (DEM) is applied to study the mechanical performance of the ceramic breeder pebble bed under quasi-static and cyclic loads. A preloaded specimen can be made with servo-control mechanism, the quasi-static and dynamic stress-strain performances are studied during the tests. It is found that the normalized normal contact forces under quasi-static loads have the similar distributions, and increase with increasing loads. Furthermore, the relatively low volumetric strain can be absorbed by pebble bed after several loading and unloading cycles, but the peak normal contact force can be extremely high during the first cycle. Cyclic loading with target pressure is recommended for densely packing, irreversible volume reduction gradually increase with cycles, and the normal contact forces decrease with cycles.

Discrete Maximum Principle for Higher-Order Finite Elements in 1D

Czech Academy of Sciences Publication Activity Database

Vejchodský, Tomáš; Šolín, Pavel

2007-01-01

Roč. 76, č. 260 (2007), s. 1833-1846 ISSN 0025-5718 R&D Projects: GA ČR GP201/04/P021 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z20760514 Keywords : discrete maximum principle * discrete Grren´s function * higher-order elements Subject RIV: BA - General Mathematics Impact factor: 1.230, year: 2007

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

Science.gov (United States)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

Experimental Investigation and Discrete Element Modelling of Composite Hollow Spheres Subjected to Dynamic Fracture

Directory of Open Access Journals (Sweden)

Arthur Coré

2017-01-01

Full Text Available This paper deals with the characterization and the numerical modelling of the collapse of composite hollow spherical structures developed to absorb energy during high velocity impacts. The structure is composed of hollow spheres (ϕ=2–30 mm made of epoxy resin and mineral powder. First of all, quasi-static and dynamic (v=5 mm·min−1 to v=2 m·s−1 compression tests are conducted at room temperature on a single sphere to study energy dissipation mechanisms. Fracture of the material appears to be predominant. A numerical model based on the discrete element method is investigated to simulate the single sphere crushing. The stress-strain-time relationship of the material based on the Ree-Eyring law is numerically implemented. The DEM modelling takes naturally into account the dynamic fracture and the crack path computed is close to the one observed experimentally in uniaxial compression. Eventually, high velocity impacts (v>100 m·s−1 of a hollow sphere on a rigid surface are conducted with an air cannon. The numerical results are in good agreement with the experimental data and demonstrate the ability of the present model to correctly describe the mechanical behavior of brittle materials at high strain rate.

Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations

Science.gov (United States)

Takizawa, Kenji; Tezduyar, Tayfun E.; Otoguro, Yuto

2018-04-01

Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space-time (ST) computational methods in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection-diffusion equation and the Navier-Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

International Nuclear Information System (INIS)

Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

2011-01-01

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 discretization 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. (author)

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

International Nuclear Information System (INIS)

Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

2010-01-01

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.

A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

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.

Granulation of snow: From tumbler experiments to discrete element simulations

Science.gov (United States)

Steinkogler, Walter; Gaume, Johan; Löwe, Henning; Sovilla, Betty; Lehning, Michael

2015-06-01

It is well known that snow avalanches exhibit granulation phenomena, i.e., the formation of large and apparently stable snow granules during the flow. The size distribution of the granules has an influence on flow behavior which, in turn, affects runout distances and avalanche velocities. The underlying mechanisms of granule formation are notoriously difficult to investigate within large-scale field experiments, due to limitations in the scope for measuring temperatures, velocities, and size distributions. To address this issue we present experiments with a concrete tumbler, which provide an appropriate means to investigate granule formation of snow. In a set of experiments at constant rotation velocity with varying temperatures and water content, we demonstrate that temperature has a major impact on the formation of granules. The experiments showed that granules only formed when the snow temperature exceeded -1∘C. No evolution in the granule size was observed at colder temperatures. Depending on the conditions, different granulation regimes are obtained, which are qualitatively classified according to their persistence and size distribution. The potential of granulation of snow in a tumbler is further demonstrated by showing that generic features of the experiments can be reproduced by cohesive discrete element simulations. The proposed discrete element model mimics the competition between cohesive forces, which promote aggregation, and impact forces, which induce fragmentation, and supports the interpretation of the granule regime classification obtained from the tumbler experiments. Generalizations, implications for flow dynamics, and experimental and model limitations as well as suggestions for future work are discussed.

3D Discrete element approach to the problem on abutment pressure in a gently dipping coal seam

Science.gov (United States)

Klishin, S. V.; Revuzhenko, A. F.

2017-09-01

Using the discrete element method, the authors have carried out 3D implementation of the problem on strength loss in surrounding rock mass in the vicinity of a production heading and on abutment pressure in a gently dripping coal seam. The calculation of forces at the contacts between particles accounts for friction, rolling resistance and viscosity. Between discrete particles modeling coal seam, surrounding rock mass and broken rocks, an elastic connecting element is introduced to allow simulating coherent materials. The paper presents the kinematic patterns of rock mass deformation, stresses in particles and the graph of the abutment pressure behavior in the coal seam.

Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers

Science.gov (United States)

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.

Simulation of hemp fibre bundle and cores using discrete element method

Energy Technology Data Exchange (ETDEWEB)

Al-Amin Sadek, M.; Chen, Y. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Biosystems Engineering; Lague, C. [Ottawa Univ., Ottawa, ON (Canada). Faculty of Engineering; Landry, H. [Prairie Agricultural Machinery Inst., Humboldt, SK (Canada); Peng, Q. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Mechanical and Manufacturing Engineering; Zhong, W. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Textile Sciences

2010-07-01

The mechanical behaviour of hemp fibre and core must be well understood in order to obtain high-grade hemp fibre that is currently in high demand for various industrial applications. Modelling by discrete element method can simulate the mechanical behaviour of such materials. A commercial discrete element software called Particle Flow Code was used in this study. In particular, the 3-dimension (PFC3D) was used to simulate hemp fibre and core. Since the basic PFC3D particles are spherical, the individual virtual hemp fibres were defined as strings of balls held together by PFC3D parallel bonds. The study showed that the virtual fibre is flexible and can bend and break by forces. This reflects the characteristics of hemp fibre. Using the clump logic of PFC3D, the virtual hemp core was defined as a rigid and unbreakable body, which reflect the characteristics of the core. The virtual fibre and core were defined with several microproperties, some of which were previously calibrated. The PFC3D bond properties were calibrated in this study. They included normal and shear stiffness; pb{sub k}n and pb{sub k}s; normal and shear strength; and bond disk radius, R of the virtual fibre. The calibration started with developing a PFC3D model to simulate fibre tensile test. The microproperties of virtual fibre and core were calibrated by running the PFC3D model. Literature data from fibre tensile tests was compared with simulation results.

Basal friction evolution and crevasse distribution during the surge of Basin 3, Austfonna ice-cap - offline coupling between a continuum ice dynamic model and a discrete element model

Science.gov (United States)

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.

Defining the effect of sweep tillage tool cutting edge geometry on tillage forces using 3D discrete element modelling

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

A discrete element model for the influence of surfactants on sedimentation characteristics of magnetorheological fluids

Science.gov (United States)

Son, Kwon Joong

2018-02-01

Hindering particle agglomeration and re-dispersion processes, gravitational sedimentation of suspended particles in magnetorheological (MR) fluids causes inferior performance and controllability of MR fluids in response to a user-specified magnetic field. Thus, suspension stability is one of the principal factors to be considered in synthesizing MR fluids. However, only a few computational studies have been reported so far on the sedimentation characteristics of suspended particles under gravity. In this paper, the settling dynamics of paramagnetic particles suspended in MR fluids was investigated via discrete element method (DEM) simulations. This work focuses particularly on developing accurate fluid-particle and particle-particle interaction models which can account for the influence of stabilizing surfactants on the MR fluid sedimentation. Effect of the stabilizing surfactants on interparticle interactions was incorporated into the derivation of a reliable contact-impact model for DEM computation. Also, the influence of the stabilizing additives on fluid-particle interactions was considered by incorporating Stokes drag with shape and wall correction factors into DEM formulation. The results of simulations performed for model validation purposes showed a good agreement with the published sedimentation measurement data in terms of an initial sedimentation velocity and a final sedimentation ratio.

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.

A parallel Discrete Element Method to model collisions between non-convex particles

Directory of Open Access Journals (Sweden)

Rakotonirina Andriarimina Daniel

2017-01-01

Full Text Available 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.

Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

Science.gov (United States)

Sistaninia, M.; Phillion, A. B.; Drezet, J.-M.; Rappaz, M.

2011-01-01

As a necessary step toward the quantitative prediction of hot tearing defects, a three-dimensional stress-strain simulation based on a combined finite element (FE)/discrete element method (DEM) has been developed that is capable of predicting the mechanical behavior of semisolid metallic alloys during solidification. The solidification model used for generating the initial solid-liquid structure is based on a Voronoi tessellation of randomly distributed nucleation centers and a solute diffusion model for each element of this tessellation. At a given fraction of solid, the deformation is then simulated with the solid grains being modeled using an elastoviscoplastic constitutive law, whereas the remaining liquid layers at grain boundaries are approximated by flexible connectors, each consisting of a spring element and a damper element acting in parallel. The model predictions have been validated against Al-Cu alloy experimental data from the literature. The results show that a combined FE/DEM approach is able to express the overall mechanical behavior of semisolid alloys at the macroscale based on the morphology of the grain structure. For the first time, the localization of strain in the intergranular regions is taken into account. Thus, this approach constitutes an indispensible step towards the development of a comprehensive model of hot tearing.

Newton-type methods for the mixed finite element discretization of some degenerate parabolic equations

NARCIS (Netherlands)

Radu, F.A.; Pop, I.S.; Knabner, P.; Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P.

2006-01-01

In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For

Feeder Type Optimisation for the Plain Flow Discharge Process of an Underground Hopper by Discrete Element Modelling

Directory of Open Access Journals (Sweden)

Jan Nečas

2017-09-01

Full Text Available This paper describes optimisation of a conveyor from an underground hopper intended for a coal transfer station. The original solution was designed with a chain conveyor encountered operational problems that have limited its continuous operation. The Discrete Element Modeling (DEM was chosen to optimise the transport. DEM simulations allow device design modifications directly in the 3D CAD model, and then the simulation makes it possible to evaluate whether the adjustment was successful. By simulating the initial state of coal extraction using a chain conveyor, trouble spots were identified that caused operational failures. The main problem has been the increased resistance during removal of material from the underground hopper. Revealed resistances against material movement were not considered in the original design at all. In the next step, structural modifications of problematic nodes were made. For example, the following changes have been made: reduction of storage space or installation of passive elements into the interior of the underground hopper. These modifications made were not effective enough, so the type of the conveyor was changed from a drag chain conveyor to a belt conveyor. The simulation of the material extraction using a belt conveyor showed a significant reduction in resistance parameters while maintaining the required transport performance.

Predicting the behavior of microfluidic circuits made from discrete elements

Science.gov (United States)

Bhargava, Krisna C.; Thompson, Bryant; Iqbal, Danish; Malmstadt, Noah

2015-10-01

Microfluidic devices can be used to execute a variety of continuous flow analytical and synthetic chemistry protocols with a great degree of precision. The growing availability of additive manufacturing has enabled the design of microfluidic devices with new functionality and complexity. However, these devices are prone to larger manufacturing variation than is typical of those made with micromachining or soft lithography. In this report, we demonstrate a design-for-manufacturing workflow that addresses performance variation at the microfluidic element and circuit level, in context of mass-manufacturing and additive manufacturing. Our approach relies on discrete microfluidic elements that are characterized by their terminal hydraulic resistance and associated tolerance. Network analysis is employed to construct simple analytical design rules for model microfluidic circuits. Monte Carlo analysis is employed at both the individual element and circuit level to establish expected performance metrics for several specific circuit configurations. A protocol based on osmometry is used to experimentally probe mixing behavior in circuits in order to validate these approaches. The overall workflow is applied to two application circuits with immediate use at on the bench-top: series and parallel mixing circuits that are modularly programmable, virtually predictable, highly precise, and operable by hand.

Predicting the behavior of microfluidic circuits made from discrete elements.

Science.gov (United States)

Bhargava, Krisna C; Thompson, Bryant; Iqbal, Danish; Malmstadt, Noah

2015-10-30

Microfluidic devices can be used to execute a variety of continuous flow analytical and synthetic chemistry protocols with a great degree of precision. The growing availability of additive manufacturing has enabled the design of microfluidic devices with new functionality and complexity. However, these devices are prone to larger manufacturing variation than is typical of those made with micromachining or soft lithography. In this report, we demonstrate a design-for-manufacturing workflow that addresses performance variation at the microfluidic element and circuit level, in context of mass-manufacturing and additive manufacturing. Our approach relies on discrete microfluidic elements that are characterized by their terminal hydraulic resistance and associated tolerance. Network analysis is employed to construct simple analytical design rules for model microfluidic circuits. Monte Carlo analysis is employed at both the individual element and circuit level to establish expected performance metrics for several specific circuit configurations. A protocol based on osmometry is used to experimentally probe mixing behavior in circuits in order to validate these approaches. The overall workflow is applied to two application circuits with immediate use at on the bench-top: series and parallel mixing circuits that are modularly programmable, virtually predictable, highly precise, and operable by hand.

IDENTIFYING FRACTURE ORIGIN IN CERAMICS BY COMBINATION OF NONDESTRUCTIVE TESTING AND DISCRETE ELEMENT ANALYSIS

International Nuclear Information System (INIS)

Senapati, Rajeev; Zhang Jianmei

2010-01-01

Advanced ceramic materials have been extensively applied in aerospace, automobile and other industries. However, the reliability of the advanced ceramics is a major concern because of the brittle nature of the materials. In this paper, combination of nondestructive testing and numerical modeling Discrete Element Method is proposed to identify the fracture origin in ceramics. The nondestructive testing--laser scattering technology is first performed on the ceramic components to reveal the machining-induced damage such as cracks and the material-inherent flaws such as voids, then followed by the four point bending test. Discrete Element software package PFC 2D is used to simulate the four point bending test and try to identify where the fractures start. The numerical representation of the ceramic materials is done by generating a densely packed particle system using the specimen genesis procedure and then applying the suitable microparameters to the particle system. Simulation of four point bending test is performed on materials having no defects, materials having manufacturing-induced defects like cracks, and materials having material-inherent flaws like voids. The initiation and propagation of defects is modeled and the mean contact force on the loading ball is also plotted. The simulation prediction results are well in accordance with the nondestructive testing results.

Discrete element method study of fuel relocation and dispersal during loss-of-coolant accidents

International Nuclear Information System (INIS)

Govers, K.; Verwerft, M.

2016-01-01

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. - Highlights: • We performed Discrete Element Methods simulation for fuel relocation and dispersal during LOCA transients. • The approach provides a mechanistic description of these phenomena. • The approach shows the ability of the technique to reproduce experimental observations. • The packing fraction in the balloon is shown to stabilize at 50–60%.

Failure analysis of pebble bed reactors during earthquake by discrete element method

International Nuclear Information System (INIS)

Keppler, Istvan

2013-01-01

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

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.

Analyzing the Mixing Dynamics of an Industrial Batch Bin Blender via Discrete Element Modeling Method

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.

Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain

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Victor Kravets

2016-05-01

Full Text Available Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced. The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.

Finite element analysis of three dimensional crack growth by the use of a boundary element sub model

DEFF Research Database (Denmark)

Lucht, Tore

2009-01-01

A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...

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.

Elements of matrix modeling and computing with Matlab

CERN Document Server

White, Robert E

2006-01-01

As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applicat

Finite element modelling of fibre-reinforced brittle materials

NARCIS (Netherlands)

Kullaa, J.

1997-01-01

The tensile constitutive behaviour of fibre-reinforced brittle materials can be extended to two or three dimensions by using the finite element method with crack models. The three approaches in this study include the smeared and discrete crack concepts and a multi-surface plasticity model. The

A discrete finite element modelling and measurements for powder compaction

International Nuclear Information System (INIS)

Choi, J L; Gethin, D T

2009-01-01

An experimental investigation into friction between powder and a target surface together with numerical modelling of compaction and friction processes at a micro-scale are presented in this paper. The experimental work explores friction mechanisms by using an extended sliding plate apparatus operating at low load while sliding over a long distance. Tests were conducted for copper and 316 steel with variation in loads, surface finish and its orientation. The behaviours of the static and dynamic friction were identified highlighting the important influence of particle size, particle shape, material response and surface topography. The results also highlighted that under light loading the friction coefficient remains at a level lower than that derived from experiments on equipment having a wider dynamic range and this is attributed to the enhanced sensitivity of the measurement equipment. The results also suggest that friction variation with sliding distance is a consequence of damage, rather than presentation of an uncontaminated target sliding surface. The complete experimental cycle was modelled numerically using a combined discrete and finite element scheme enabling exploration of mechanisms that are defined at the particle level. Using compaction as the starting point, a number of simulation factors and process parameters were investigated. Comparisons were made with previously published work, showing reasonable agreement and the simulations were then used to explore the process response to the range of particle scale factors. Models comprising regular packing of round particles exhibited stiff response with high initial density. Models with random packing were explored and were found to reflect trends that are more closely aligned with experimental observation, including rearrangement, followed by compaction under a regime of elastic then plastic deformation. Numerical modelling of the compaction stage was extended to account for the shearing stage of the

Discrete series representations for sl(2|1), Meixner polynomials and oscillator models

International Nuclear Information System (INIS)

Jafarov, E I; Van der Jeugt, J

2012-01-01

We explore a model for a one-dimensional quantum oscillator based on the Lie superalgebra sl(2|1). For this purpose, a class of discrete series representations of sl(2|1) is constructed, each representation characterized by a real number β > 0. In this model, the position and momentum operators of the oscillator are odd elements of sl(2|1) and their expressions involve an arbitrary parameter γ. In each representation, the spectrum of the Hamiltonian is the same as that of a canonical oscillator. The spectrum of a position operator can be continuous or infinite discrete, depending on the value of γ. We determine the position wavefunctions both in the continuous and the discrete case and discuss their properties. In the discrete case, these wavefunctions are given in terms of Meixner polynomials. From the embedding osp(1|2) subset of sl(2|1), it can be seen why the case γ = 1 corresponds to a paraboson oscillator. Consequently, taking the values (β, γ) = (1/2, 1) in the sl(2|1) model yields a canonical oscillator. (paper)

Using the discrete element method to simulate brittle fracture in the indentation of a silica glass with a blunt indenter

International Nuclear Information System (INIS)

Andre, Damien; Iordanoff, Ivan; Charles, Jean-luc; Jebahi, Mohamed; Neauport, Jerome

2013-01-01

The mechanical behavior of materials is usually simulated by a continuous mechanics approach. However, non-continuous phenomena such as multi-fracturing cannot be accurately simulated using a continuous description. The discrete element method (DEM) naturally accounts for discontinuities and is therefore a good alternative to the continuum approach. This work uses a discrete element model based on interaction given by 3D beam model. This model has proved to correctly simulate the elastic properties at the macroscopic scale. The simulation of brittle cracks is now tackled. This goal is attained by computing a failure criterion based on an equivalent hydrostatic stress. This microscopic criterion is then calibrated to fit experimental values of the macroscopic failure stress. Then, the simulation results are compared to experimental results of indentation tests in which a spherical indenter is used to load a silica glass, which is considered to be a perfectly brittle elastic material. (authors)

Discrete-Feature Model Implementation of SDM-Site Forsmark

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

2010-03-15

A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

Discrete-Feature Model Implementation of SDM-Site Forsmark

International Nuclear Information System (INIS)

Geier, Joel

2010-03-01

A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

A discrete element and ray framework for rapid simulation of acoustical dispersion of microscale particulate agglomerations

Science.gov (United States)

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.

Knowledge network model of the energy consumption in discrete manufacturing system

Science.gov (United States)

Xu, Binzi; Wang, Yan; Ji, Zhicheng

2017-07-01

Discrete manufacturing system generates a large amount of data and information because of the development of information technology. Hence, a management mechanism is urgently required. In order to incorporate knowledge generated from manufacturing data and production experience, a knowledge network model of the energy consumption in the discrete manufacturing system was put forward based on knowledge network theory and multi-granularity modular ontology technology. This model could provide a standard representation for concepts, terms and their relationships, which could be understood by both human and computer. Besides, the formal description of energy consumption knowledge elements (ECKEs) in the knowledge network was also given. Finally, an application example was used to verify the feasibility of the proposed method.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

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.

Handbook on modelling for discrete optimization

CERN Document Server

Pitsoulis, Leonidas; Williams, H

2006-01-01

The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...

Crack nucleation in solid materials under external load - simulations with the Discrete Element Method

Directory of Open Access Journals (Sweden)

Klejment Piotr

2018-01-01

Full Text Available Numerical analysis of cracking processes require an appropriate numerical technique. Classical engineering approach to the problem has its roots in the continuum mechanics and is based mainly on the Finite Element Method. This technique allows simulations of both elastic and large deformation processes, so it is very popular in the engineering applications. However, a final effect of cracking - fragmentation of an object at hand can hardly be described by this approach in a numerically efficient way since it requires a solution of a problem of nontrivial evolving in time boundary conditions. We focused our attention on the Discrete Element Method (DEM, which by definition implies “molecular” construction of the matter. The basic idea behind DEM is to represent an investigated body as an assemblage of discrete particles interacting with each other. Breaking interaction bonds between particles induced by external forces imeditelly implies creation/evolution of boundary conditions. In this study we used the DEM approach to simulate cracking process in the three dimensional solid material under external tension. The used numerical model, although higly simplified, can be used to describe behaviour of such materials like thin films, biological tissues, metal coatings, to name a few.

Synchronization Techniques in Parallel Discrete Event Simulation

OpenAIRE

Lindén, Jonatan

2018-01-01

Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...

Symplectic discretization for spectral element solution of Maxwell's equations

International Nuclear Information System (INIS)

Zhao Yanmin; Dai Guidong; Tang Yifa; Liu Qinghuo

2009-01-01

Applying the spectral element method (SEM) based on the Gauss-Lobatto-Legendre (GLL) polynomial to discretize Maxwell's equations, we obtain a Poisson system or a Poisson system with at most a perturbation. For the system, we prove that any symplectic partitioned Runge-Kutta (PRK) method preserves the Poisson structure and its implied symplectic structure. Numerical examples show the high accuracy of SEM and the benefit of conserving energy due to the use of symplectic methods.

Discrete ellipsoidal statistical BGK model and Burnett equations

Science.gov (United States)

Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

2018-06-01

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

A discrete element based simulation framework to investigate particulate spray deposition processes

KAUST Repository

Mukherjee, Debanjan; Zohdi, Tarek I.

2015-01-01

© 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

Modeling of Hydraulic Fracture Propagation at the kISMET Site Using a Fully Coupled 3D Network-Flow and Quasi- Static Discrete Element Model

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.

Modeling 3D PCMI using the Extended Finite Element Method with higher order elements

Energy Technology Data Exchange (ETDEWEB)

Jiang, W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2017-03-31

This report documents the recent development to enable XFEM to work with higher order elements. It also demonstrates the application of higher order (quadratic) elements to both 2D and 3D models of PCMI problems, where discrete fractures in the fuel are represented using XFEM. The modeling results demonstrate the ability of the higher order XFEM to accurately capture the effects of a crack on the response in the vicinity of the intersecting surfaces of cracked fuel and cladding, as well as represent smooth responses in the regions away from the crack.

GPU accelerated Discrete Element Method (DEM) molecular dynamics for conservative, faceted particle simulations

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.

Sound propagation in dry granular materials : discrete element simulations, theory, and experiments

NARCIS (Netherlands)

Mouraille, O.J.P.

2009-01-01

In this study sound wave propagation through different types of dry confined granular systems is studied. With three-dimensional discrete element simulations, theory and experiments, the influence of several micro-scale properties: friction, dissipation, particle rotation, and contact disorder, on

Mathematical Modeling of Contact Problems of Elasticity Theory with Unilateral Discrete Contact

Directory of Open Access Journals (Sweden)

I. V. Stankevich

2015-01-01

Full Text Available Development and operation of modern machinery and latest technology require reliable estimates of the strength characteristics of the critical elements of structures and technological equipment under the impact of high-intensity thermomechanical loading, accompanied, as a rule, by complex contact interaction. Mathematical modeling of stress-strain state of such parts and components in the contact area, based on adequate mathematical models, modern numerical methods and efficient algorithms that implement the direct determination of displacement fields, strains and stresses, is the main tool that allows fast acquisition of data required for the calculations of strength and durability. The paper considers an algorithm for constructing the numerical solution of the contact problem of elasticity theory in relation to the body, which has an obvious one-sided discrete contact interaction with an elastic half-space. The proposed algorithm is specially designed to have a correction of the tangential forces at discrete contact points, allowing us to achieve sufficiently accurate implementation of the adopted law of friction. The algorithm is embedded in a general finite element technology, with which the application code is generated. Numerical study of discrete unilateral contact interaction of an elastic plate and a rigid half-space showed a high efficiency of the developed algorithm and the application code that implements it.

A discrete control model of PLANT

Science.gov (United States)

Mitchell, C. M.

1985-01-01

A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.

Finite element model for heat conduction in jointed rock masses

International Nuclear Information System (INIS)

Gartling, D.K.; Thomas, R.K.

1981-01-01

A computatonal procedure for simulating heat conduction in a fractured rock mass is proposed and illustrated in the present paper. The method makes use of a simple local model for conduction in the vicinity of a single open fracture. The distributions of fractures and fracture properties within the finite element model are based on a statistical representation of geologic field data. Fracture behavior is included in the finite element computation by locating local, discrete fractures at the element integration points

Discrete modeling considerations in multiphase fluid dynamics

International Nuclear Information System (INIS)

Ransom, V.H.; Ramshaw, J.D.

1988-01-01

The modeling of multiphase flows play a fundamental role in light water reactor safety. The main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must be cast into discrete form for a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is potentially hazardous. It may be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a statistical closure problem. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples. 48 refs

Transient, two-dimensional, discrete-element, far-field model for thermal impact analysis of power plant discharges in coastal and offshore regions. Part I. General description of the mathematical model and the results of an application

International Nuclear Information System (INIS)

Eraslan, A.H.

1975-02-01

A far-field mathematical model is presented for numerical simulation of short-time (within tidal cycle) transient, two-dimensional temperature distributions in large coastal and offshore regions resulting from the condenser cooling water discharges of power plants. The Eulerian FLIDE (fluid-in-discrete-element) formulation employs the integral forms of the conservation principles for mass and thermal energy in variable-sized discrete elements that span the specific flow region. The contributions of vertical variations of the velocity components and temperature are rigorously incorporated in the development of depth-averaged, two-dimensional energy transport fluxes by spatially integrating the conservation equations over the enclosure surfaces of the discrete elements. The general mathematical formulation considers completely arbitrary, transient oceanic flow conditions, which include periodic tidal, geostrophic, and wind-induced currents, as locally specified inputs to the model. The thermal impact of a hypothetical, multiunit generating station in a coastal region is analyzed where the oceanic flow conditions are assumed to be strictly periodic tidal currents within any appreciable net drift of sufficient duration to remove the heated effluent. The numerical simulation indicates that the periodic flow conditions cause considerable variations in the temperature distributions during the day and the tidal cycles, which result in severe recirculation and re-entrainment of the heated water between the intakes and the discharges of the different units. This leads to a gradual, long-term increase of the temperatures in the immediate vicinity of the discharge structures and also in the far-field zone. (U.S.)

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.

Space-Time Discrete KPZ Equation

Science.gov (United States)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Discrete Element Simulations and Experiments on the Deformation of Cohesive Powders in a Bi-Axial Box

NARCIS (Netherlands)

Imole, Olukayode Isaiah; Kumar, Nishant; Magnanimo, Vanessa; Luding, Stefan

2012-01-01

We compare element test experiments and simulations on the deformation of frictional, cohesive particles in a bi-axial box. We show that computer simulations with the Discrete Element Method qualitatively reproduce a uniaxial compression element test in the true bi-axial tester. We highlight the

A discrete element model for damage and fracture of geomaterials under fatigue loading

Science.gov (United States)

Gao, Xiaofeng; Koval, Georg; Chazallon, Cyrille

2017-06-01

Failure processes in geomaterials (concrete, asphalt concrete, masonry, etc.) under fatigue loading (repeated moving loads, cycles of temperature, etc.) are responsible for most of the dysfunctions in pavements, brick structures, etc. In the beginning of the lifetime of a structure, the material presents only inner defects (micro cracks, voids, etc.). Due to the effect of the cyclic loading, these small defects tend to grow in size and quantity which damage the material, reducing its stiffness. With a relatively high number of cycles, these growing micro cracks become large cracks, which characterizes the fracture behavior. From a theoretical point of view, both mechanisms are treated differently. Fracture is usually described locally, with the propagation of cracks defined by the energy release rate at the crack tip; damage is usually associated to non-local approaches. In the present work, damage and fracture mechanics are combined in a local discrete element approach.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

Science.gov (United States)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

OpenAIRE

Vescovi, Dalila; Berzi, Diego; Richard, Patrick; Brodu, Nicolas

2014-01-01

International audience; We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed av...

A discrete element model of brittle damages generated by thermal expansion mismatch of heterogeneous media

Directory of Open Access Journals (Sweden)

André Damien

2017-01-01

Full Text Available At the macroscopic scale, such media as rocks or ceramics can be seen as homogeneous continuum. However, at the microscopic scale these materials involve sophisticated micro-structures that mix several phases. Generally, these micro-structures are composed by a large amount of inclusions embedded in a brittle matrix that ensures the cohesion of the structure. These materials generally exhibit complex non linear mechanical behaviors that result from the interactions between the different phases. This paper proposes to study the impact of the diffuse damages that result from the thermal expansion mismatch between the phases in presence. The Discrete Element Method (DEM that naturally take into account discontinuities is proposed to study these phenomena.

Identification of parameters of discrete-continuous models

International Nuclear Information System (INIS)

Cekus, Dawid; Warys, Pawel

2015-01-01

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible

Identification of parameters of discrete-continuous models

Energy Technology Data Exchange (ETDEWEB)

Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)

2015-03-10

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.

Discrete dispersion models and their Tweedie asymptotics

DEFF Research Database (Denmark)

Jørgensen, Bent; Kokonendji, Célestin C.

2016-01-01

The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this ap......The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place...... in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models...... with power variance functions. Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning. The Poisson-Tweedie factorial dispersion models are closed under dilation, which in turn leads to a Poisson...

Discrete dynamic modeling of T cell survival signaling networks

Science.gov (United States)

Zhang, Ranran

2009-03-01

Biochemistry-based frameworks are often not applicable for the modeling of heterogeneous regulatory systems that are sparsely documented in terms of quantitative information. As an alternative, qualitative models assuming a small set of discrete states are gaining acceptance. This talk will present a discrete dynamic model of the signaling network responsible for the survival and long-term competence of cytotoxic T cells in the blood cancer T-LGL leukemia. We integrated the signaling pathways involved in normal T cell activation and the known deregulations of survival signaling in leukemic T-LGL, and formulated the regulation of each network element as a Boolean (logic) rule. Our model suggests that the persistence of two signals is sufficient to reproduce all known deregulations in leukemic T-LGL. It also indicates the nodes whose inactivity is necessary and sufficient for the reversal of the T-LGL state. We have experimentally validated several model predictions, including: (i) Inhibiting PDGF signaling induces apoptosis in leukemic T-LGL. (ii) Sphingosine kinase 1 and NFκB are essential for the long-term survival of T cells in T-LGL leukemia. (iii) T box expressed in T cells (T-bet) is constitutively activated in the T-LGL state. The model has identified potential therapeutic targets for T-LGL leukemia and can be used for generating long-term competent CTL necessary for tumor and cancer vaccine development. The success of this model, and of other discrete dynamic models, suggests that the organization of signaling networks has an determining role in their dynamics. Reference: R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, T. P. Loughran, Jr., Network Model of Survival Signaling in LGL Leukemia, PNAS 105, 16308-16313 (2008).

Boundary Layer Effect on Behavior of Discrete Models.

Science.gov (United States)

Eliáš, Jan

2017-02-10

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.

Hydraulic Fracture Growth in a Layered Formation based on Fracturing Experiments and Discrete Element Modeling

Science.gov (United States)

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.

Towards an integrated numerical simulator for crack-seal vein microstructure: Coupling phase-field with the Discrete Element Method

Science.gov (United States)

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

On discrete models of space-time

International Nuclear Information System (INIS)

Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.

1992-02-01

Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)

Wave-induced stress and breaking of sea ice in a coupled hydrodynamic discrete-element wave-ice model

Science.gov (United States)

Herman, Agnieszka

2017-11-01

In this paper, a coupled sea ice-wave model is developed and used to analyze wave-induced stress and breaking in sea ice for a range of wave and ice conditions. The sea ice module is a discrete-element bonded-particle model, in which ice is represented as cuboid grains floating on the water surface that can be connected to their neighbors by elastic joints. The joints may break if instantaneous stresses acting on them exceed their strength. The wave module is based on an open-source version of the Non-Hydrostatic WAVE model (NHWAVE). The two modules are coupled with proper boundary conditions for pressure and velocity, exchanged at every wave model time step. In the present version, the model operates in two dimensions (one vertical and one horizontal) and is suitable for simulating compact ice in which heave and pitch motion dominates over surge. In a series of simulations with varying sea ice properties and incoming wavelength it is shown that wave-induced stress reaches maximum values at a certain distance from the ice edge. The value of maximum stress depends on both ice properties and characteristics of incoming waves, but, crucially for ice breaking, the location at which the maximum occurs does not change with the incoming wavelength. Consequently, both regular and random (Jonswap spectrum) waves break the ice into floes with almost identical sizes. The width of the zone of broken ice depends on ice strength and wave attenuation rates in the ice.

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

Current density and continuity in discretized models

International Nuclear Information System (INIS)

Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.

Discrete modelling of front propagation in backward piping erosion

Science.gov (United States)

Tran, Duc-Kien; Prime, Noémie; Froiio, Francesco; Callari, Carlo; Vincens, Eric

2017-06-01

A preliminary discrete numerical model of a REV at the front region of an erosion pipe in a cohesive granular soil is briefly presented. The results reported herein refer to a simulation carried out by coupling the Discrete Element Method (DEM) with the Lattice Boltzmann Method (LBM) for the representation of the granular and fluid phases, respectively. The numerical specimen, consisiting of bonded grains, is tested under fully-saturated conditions and increasing pressure difference between the inlet (confined) and the outlet (unconfined) flow regions. The key role of compression arches of force chains that transversely cross the sample and carry most part of the hydrodynamic actions is pointed out. These arches partition the REV into an upstream region that remains almost intact and a downstream region that gradually degrades and is subsequently eroded in the form of a cluster. Eventually, the collapse of the compression arches causes the upstream region to be also eroded, abruptly, as a whole. A complete presentation of the numerical model and of the results of the simulation can be found in [12].

Local discrete symmetries from superstring derived models

International Nuclear Information System (INIS)

Faraggi, A.E.

1996-10-01

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

International Nuclear Information System (INIS)

Ding Qing

2007-01-01

We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

Continuum and discrete approach in modeling biofilm development and structure: a review.

Science.gov (United States)

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

Discrete stochastic analogs of Erlang epidemic models.

Science.gov (United States)

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Discretization-dependent model for weakly connected excitable media

Science.gov (United States)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

New non-structured discretizations for fluid flows with reinforced incompressibility

International Nuclear Information System (INIS)

Heib, S.

2003-01-01

This work deals with the discretization of Stokes and Navier-Stokes equations modeling the flow of incompressible fluids on 2-D or 3-D non-structured meshes. Triangles and tetrahedrons are used for 2-D and 3-D meshes, respectively. The developments and calculations are performed with the code Priceles (fast CEA-EdF industrial platform for large Eddy simulation). This code allows to perform simulations both on structured and non-structured meshes. A finite-volume resolution method is used: a finite difference volume (FDV) method is used for the structured meshes and a finite element volume (FEV) method is used for the non-structured meshes. The finite element used in the beginning of this work has several defects. Starting from this situation, the discretization is improved by adding modifications to this element and the new elements introduced are analyzed theoretically. In parallel to these analyses, the new discretizations are implemented in order to test them numerically and to confirm the theoretical analyses. The first chapter presents the physical and mathematical modeling used in this work. The second chapter treats of the discretization of Stokes equations and presents the FEV resolution method. Chapter 3 presents a first attempt of improvement of this finite element and leads to the proposal of a new element which is presented in details. The problem encountered with the new discretization leads to a modification presented in chapter 4. This new discretization gives all the expected convergence results and sometimes shows super-convergence properties. Chapter 5 deals with the study and discretization of the Navier-Stokes equations. The study of the filtered Navier-Stokes equations, used for large Eddy simulations, requires to give a particular attention to the discretization of the diffusive terms. Then, the convective terms are considered. The effects of the convective terms in the initial discretization and in the improved method are compared. The use of

Simulated evolution of fractures and fracture networks subject to thermal cooling: A coupled discrete element and heat conduction model

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.

A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. I - An extended DKT element for thick-plate bending analysis. II - An extended DKQ element for thick-plate bending analysis

Science.gov (United States)

Katili, Irwan

1993-06-01

A new three-node nine-degree-of-freedom triangular plate bending element is proposed which is valid for the analysis of both thick and thin plates. The element, called the discrete Kirchhoff-Mindlin triangle (DKMT), has a proper rank, passes the patch test for thin and thick plates in an arbitrary mesh, and is free of shear locking. As an extension of the DKMT element, a four-node element with 3 degrees of freedom per node is developed. The element, referred to as DKMQ (discrete Kirchhoff-Mindlin quadrilateral) is found to provide good results for both thin and thick plates without any compatibility problems.

A comparison of the lattice discrete particle method to the finite-element method and the K&C material model for simulating the static and dynamic response of concrete.

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.

Constraining the parameters of the EAP sea ice rheology from satellite observations and discrete element model

Science.gov (United States)

Tsamados, Michel; Heorton, Harry; Feltham, Daniel; Muir, Alan; Baker, Steven

2016-04-01

The new elastic-plastic anisotropic (EAP) rheology that explicitly accounts for the sub-continuum anisotropy of the sea ice cover has been implemented into the latest version of the Los Alamos sea ice model CICE. The EAP rheology is widely used in the climate modeling scientific community (i.e. CPOM stand alone, RASM high resolution regional ice-ocean model, MetOffice fully coupled model). Early results from sensitivity studies (Tsamados et al, 2013) have shown the potential for an improved representation of the observed main sea ice characteristics with a substantial change of the spatial distribution of ice thickness and ice drift relative to model runs with the reference visco-plastic (VP) rheology. The model contains one new prognostic variable, the local structure tensor, which quantifies the degree of anisotropy of the sea ice, and two parameters that set the time scale of the evolution of this tensor. Observations from high resolution satellite SAR imagery as well as numerical simulation results from a discrete element model (DEM, see Wilchinsky, 2010) have shown that these individual floes can organize under external wind and thermal forcing to form an emergent isotropic sea ice state (via thermodynamic healing, thermal cracking) or an anisotropic sea ice state (via Coulombic failure lines due to shear rupture). In this work we use for the first time in the context of sea ice research a mathematical metric, the Tensorial Minkowski functionals (Schroeder-Turk, 2010), to measure quantitatively the degree of anisotropy and alignment of the sea ice at different scales. We apply the methodology on the GlobICE Envisat satellite deformation product (www.globice.info), on a prototype modified version of GlobICE applied on Sentinel-1 Synthetic Aperture Radar (SAR) imagery and on the DEM ice floe aggregates. By comparing these independent measurements of the sea ice anisotropy as well as its temporal evolution against the EAP model we are able to constrain the

Analysis of Tire Tractive Performance on Deformable Terrain by Finite Element-Discrete Element Method

Science.gov (United States)

Nakashima, Hiroshi; Takatsu, Yuzuru

The goal of this study is to develop a practical and fast simulation tool for soil-tire interaction analysis, where finite element method (FEM) and discrete element method (DEM) are coupled together, and which can be realized on a desktop PC. We have extended our formerly proposed dynamic FE-DE method (FE-DEM) to include practical soil-tire system interaction, where not only the vertical sinkage of a tire, but also the travel of a driven tire was considered. Numerical simulation by FE-DEM is stable, and the relationships between variables, such as load-sinkage and sinkage-travel distance, and the gross tractive effort and running resistance characteristics, are obtained. Moreover, the simulation result is accurate enough to predict the maximum drawbar pull for a given tire, once the appropriate parameter values are provided. Therefore, the developed FE-DEM program can be applied with sufficient accuracy to interaction problems in soil-tire systems.

Benders decomposition for discrete material optimization in laminate design with local failure criteria

DEFF Research Database (Denmark)

Munoz, Eduardo; Stolpe, Mathias; Bendsøe, Martin P.

2009-01-01

in any discrete angle optimization design, or material selection problems. The mathematical modeling of this problem is more general than the one of standard topology optimization. When considering only two material candidates with a considerable difference in stiffness, it corresponds exactly...... to a topology optimization problem. The problem is modeled as a discrete design problem coming from a finite element discretization of the continuum problem. This discretization is made of shell or plate elements. For each element (selection domain), only one of the material candidates must be selected...... of the relaxed master problem and the current best compliance (weight) found get close enough with respect to certain tolerance. The method is investigated by computational means, using the finite element method to solve the analysis problems, and a commercial branch and cut method for solving the relaxed master...

Development of a convex polyhedral discrete element simulation framework for NVIDIA Kepler based GPUs

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...

Applications of the discrete element method in mechanical engineering

International Nuclear Information System (INIS)

Fleissner, Florian; Gaugele, Timo; Eberhard, Peter

2007-01-01

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 approximations to vector spin models

Energy Technology Data Exchange (ETDEWEB)

Van Enter, Aernout C D [University of Groningen, Johann Bernoulli Institute of Mathematics and Computing Science, Postbus 407, 9700 AK Groningen (Netherlands); Kuelske, Christof [Ruhr-Universitaet Bochum, Fakultaet fuer Mathematik, D44801 Bochum (Germany); Opoku, Alex A, E-mail: A.C.D.v.Enter@math.rug.nl, E-mail: Christof.Kuelske@ruhr-uni-bochum.de, E-mail: opoku@math.leidenuniv.nl [Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden (Netherlands)

2011-11-25

We strengthen a result from Kuelske and Opoku (2008 Electron. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)

Discrete approximations to vector spin models

International Nuclear Information System (INIS)

Van Enter, Aernout C D; Külske, Christof; Opoku, Alex A

2011-01-01

We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)

An efficient hydro-mechanical model for coupled multi-porosity and discrete fracture porous media

Science.gov (United States)

Yan, Xia; Huang, Zhaoqin; Yao, Jun; Li, Yang; Fan, Dongyan; Zhang, Kai

2018-02-01

In this paper, a numerical model is developed for coupled analysis of deforming fractured porous media with multiscale fractures. In this model, the macro-fractures are modeled explicitly by the embedded discrete fracture model, and the supporting effects of fluid and fillings in these fractures are represented explicitly in the geomechanics model. On the other hand, matrix and micro-fractures are modeled by a multi-porosity model, which aims to accurately describe the transient matrix-fracture fluid exchange process. A stabilized extended finite element method scheme is developed based on the polynomial pressure projection technique to address the displacement oscillation along macro-fracture boundaries. After that, the mixed space discretization and modified fixed stress sequential implicit methods based on non-matching grids are applied to solve the coupling model. Finally, we demonstrate the accuracy and application of the proposed method to capture the coupled hydro-mechanical impacts of multiscale fractures on fractured porous media.

Rigid missiles impact on reinforced concrete structures: analysis by discrete element method

International Nuclear Information System (INIS)

Shiu, W.J.

2008-10-01

The constructions likely to be subjected to some extreme loadings like reactor containment buildings have to be dimensioned accordingly. As a part of study of concrete structures, this thesis focuses on numerical modelling of rigid missile impacts against a rigid reinforced concrete slab. Based on some experiment tests data, an elasto-plastic-damaged constitutive law has been implanted into a discrete element numerical code. To calibrate certain parameters of the numerical model, some quasi static tests have been first simulated. Once the model calibration was done, some missile impact simulation tests have then been carried out. The numerical results are well agree with these provided by French Atomic Energy Agency (Cea) and the French Electrical power Company (EDF) in terms of the trajectory of the missile. We were able to show the need of a constitutive law taking into account the compaction behaviour of the concrete when the predictions of penetration and perforation of a thick slab was demanded. Finally, a parametric study confirmed that the numerical model can be used the way predictive as well as the empirical prediction law, while the first can provide additional significant mechanical description. (author)

Lumped impulses, discrete displacements and a moving load analysis

NARCIS (Netherlands)

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

Boundary element method for modelling creep behaviour

International Nuclear Information System (INIS)

Zarina Masood; Shah Nor Basri; Abdel Majid Hamouda; Prithvi Raj Arora

2002-01-01

A two dimensional initial strain direct boundary element method is proposed to numerically model the creep behaviour. The boundary of the body is discretized into quadratic element and the domain into quadratic quadrilaterals. The variables are also assumed to have a quadratic variation over the elements. The boundary integral equation is solved for each boundary node and assembled into a matrix. This matrix is solved by Gauss elimination with partial pivoting to obtain the variables on the boundary and in the interior. Due to the time-dependent nature of creep, the solution has to be derived over increments of time. Automatic time incrementation technique and backward Euler method for updating the variables are implemented to assure stability and accuracy of results. A flowchart of the solution strategy is also presented. (Author)

Finite Element Method Based Modeling of Resistance Spot-Welded Mild Steel

Directory of Open Access Journals (Sweden)

Miloud Zaoui

Full Text Available Abstract This paper deals with Finite Element refined and simplified models of a mild steel spot-welded specimen, developed and validated based on quasi-static cross-tensile experimental tests. The first model was constructed with a fine discretization of the metal sheet and the spot weld was defined as a special geometric zone of the specimen. This model provided, in combination with experimental tests, the input data for the development of the second model, which was constructed with respect to the mesh size used in the complete car finite element model. This simplified model was developed with coarse shell elements and a spring-type beam element was used to model the spot weld behavior. The global accuracy of the two models was checked by comparing simulated and experimental load-displacement curves and by studying the specimen deformed shapes and the plastic deformation growth in the metal sheets. The obtained results show that both fine and coarse finite element models permit a good prediction of the experimental tests.

The discretized Schroedinger equation and simple models for semiconductor quantum wells

International Nuclear Information System (INIS)

Boykin, Timothy B; Klimeck, Gerhard

2004-01-01

The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

Quadratic Term Structure Models in Discrete Time

OpenAIRE

Marco Realdon

2006-01-01

This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...

Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model

Directory of Open Access Journals (Sweden)

Wang Yueying

2017-08-01

Full Text Available Isolated fractures usually exist in fractured media systems, where the capillary pressure in the fracture is lower than that of the matrix, causing the discrepancy in oil recoveries between fractured and non-fractured porous media. Experiments, analytical solutions and conventional simulation methods based on the continuum model approach are incompetent or insufficient in describing media containing isolated fractures. In this paper, the simulation of the counter-current imbibition in fractured media is based on the discrete-fracture model (DFM. The interlocking or arrangement of matrix and fracture system within the model resembles the traditional discrete fracture network model and the hybrid-mixed-finite-element method is employed to solve the associated equations. The Behbahani experimental data validates our simulation solution for consistency. The simulation results of the fractured media show that the isolated-fractures affect the imbibition in the matrix block. Moreover, the isolated fracture parameters such as fracture length and fracture location influence the trend of the recovery curves. Thus, the counter-current imbibition behavior of media with isolated fractures can be predicted using this method based on the discrete-fracture model.

Discrete Modeling of Early-Life Thermal Fracture in Ceramic Nuclear Fuel

Energy Technology Data Exchange (ETDEWEB)

Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Dolbow, John E. [Duke Univ., Durham, NC (United States); Hales, Jason D. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2015-03-01

Fracturing of ceramic fuel pellets heavily influences performance of light water reactor (LWR) fuel. Early in the life of fuel, starting with the initial power ramp, large thermal gradients cause high tensile hoop and axial stresses in the outer region of the fuel pellets, resulting in the formation of radial and axial cracks. Circumferential cracks form due to thermal gradients that occur when the power is ramped down. These thermal cracks cause the fuel to expand radially, closing the pellet/cladding gap and enhancing the thermal conductance across that gap, while decreasing the effective conductivity of the fuel in directions normal to the cracking. At lower length scales, formation of microcracks is an important contributor to the decrease in bulk thermal conductivity that occurs over the life of the fuel as the burnup increases. Because of the important effects that fracture has on fuel performance, a realistic, physically based fracture modeling capability is essential to predict fuel behavior in a wide variety of normal and abnormal conditions. Modeling fracture within the context of the finite element method, which is based on continuous interpolations of solution variables, has always been challenging because fracture is an inherently discontinuous phenomenon. Work is underway at Idaho National Laboratory to apply two modeling techniques model fracture as a discrete displacement discontinuity to nuclear fuel: The extended finite element method (XFEM), and discrete element method (DEM). XFEM is based on the standard finite element method, but with enhancements to represent discontinuous behavior. DEM represents a solid as a network of particles connected by bonds, which can arbitrarily fail if a fracture criterion is reached. This paper presents initial results applying the aforementioned techniques to model fuel fracturing. This work has initially focused on early life behavior of ceramic LWR fuel. A coupled thermal-mechanical XFEM method that includes

Modelling and real-time simulation of continuous-discrete systems in mechatronics

Energy Technology Data Exchange (ETDEWEB)

Lindow, H. [Rostocker, Magdeburg (Germany)

1996-12-31

This work presents a methodology for simulation and modelling of systems with continuous - discrete dynamics. It derives hybrid discrete event models from Lagrange`s equations of motion. This method combines continuous mechanical, electrical and thermodynamical submodels on one hand with discrete event models an the other hand into a hybrid discrete event model. This straight forward software development avoids numeric overhead.

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 dynamic modeling of cellular signaling networks.

Science.gov (United States)

Albert, Réka; Wang, Rui-Sheng

2009-01-01

Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.

Simulation of quasistatic deformations using discrete rod models

OpenAIRE

Linn, J.; Stephan, T.

2008-01-01

Recently we developed a discrete model of elastic rods with symmetric cross section suitable for a fast simulation of quasistatic deformations [33]. The model is based on Kirchhoff’s geometrically exact theory of rods. Unlike simple models of “mass & spring” type typically used in VR applications, our model provides a proper coupling of bending and torsion. The computational approach comprises a variational formulation combined with a finite difference discretization of the continuum model. A...

Discrete-time rewards model-checked

NARCIS (Netherlands)

Larsen, K.G.; Andova, S.; Niebert, Peter; Hermanns, H.; Katoen, Joost P.

2003-01-01

This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and

Analysis hierarchical model for discrete event systems

Science.gov (United States)

Ciortea, E. M.

2015-11-01

The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.

Discrete element method study of fuel relocation and dispersal during loss-of-coolant accidents

Science.gov (United States)

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.

Modeling discrete time-to-event data

CERN Document Server

Tutz, Gerhard

2016-01-01

This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are expla...

Conforming discretizations of boundary element solutions to the electroencephalography forward problem

Science.gov (United States)

Rahmouni, Lyes; Adrian, Simon B.; Cools, Kristof; Andriulli, Francesco P.

2018-01-01

discretization based on dual boundary elements residing on a suitably defined dual mesh. We devote also a particular attention to implementation-oriented details of our new technique that will allow the rapid incorporation of our finding in one's own EEG forward solution technology. We conclude by showing how the resulting forward EEG problems show favorable properties with respect to previously proposed schemes, and we show their applicability to real-case modeling scenarios obtained from Magnetic Resonance Imaging (MRI) data. xml:lang="fr" Malheureusement, il est également reconnu dans la littérature que leur précision diminue particulièrement lorsque la source de courant est dipolaire et se situe près de la surface du cerveau. Ce défaut constitue une importante limitation, étant donné qu'au cours d'une session d'imagerie EEG à haute résolution, plusieurs solutions du problème direct EEG sont requises, pour lesquelles les sources de courant sont proches ou sur la surface de cerveau. Ce travail présente d'abord une analyse des opérateurs intervenant dans le problème direct et leur discrétisation. Nous montrons que plusieurs discrétisations couramment utilisées ne conviennent que dans un cadre L2, nécessitant que le terme d'expansion soit une fonction de carré intégrable. Dès lors, ces techniques ne sont pas cohérentes avec les propriétés spectrales des opérateurs en termes d'espaces de Sobolev d'ordre fractionnaire. Nous développons ensuite une nouvelle stratégie de discrétisation conforme aux espaces de Sobolev avec des fonctions d'expansion moins régulières, donnant lieu à une nouvelle formulation intégrale. Le solveur résultant présente des propriétés favorables par rapport aux méthodes existantes et réduit sensiblement le recours à un maillage adaptatif et autres stratégies actuellement requises pour améliorer la précision du calcul. Les résultats numériques présentés corroborent les développements théoriques et mettent en �

A discrete-space urban model with environmental amenities

Science.gov (United States)

Liaila Tajibaeva; Robert G. Haight; Stephen Polasky

2008-01-01

This paper analyzes the effects of providing environmental amenities associated with open space in a discrete-space urban model and characterizes optimal provision of open space across a metropolitan area. The discrete-space model assumes distinct neighborhoods in which developable land is homogeneous within a neighborhood but heterogeneous across neighborhoods. Open...

Shale Fracture Analysis using the Combined Finite-Discrete Element Method

Science.gov (United States)

Carey, J. W.; Lei, Z.; Rougier, E.; Knight, E. E.; Viswanathan, H.

2014-12-01

Hydraulic fracturing (hydrofrac) is a successful method used to extract oil and gas from highly carbonate rocks like shale. However, challenges exist for industry experts estimate that for a single $10 million dollar lateral wellbore fracking operation, only 10% of the hydrocarbons contained in the rock are extracted. To better understand how to improve hydrofrac recovery efficiencies and to lower its costs, LANL recently funded the Laboratory Directed Research and Development (LDRD) project: "Discovery Science of Hydraulic Fracturing: Innovative Working Fluids and Their Interactions with Rocks, Fractures, and Hydrocarbons". Under the support of this project, the LDRD modeling team is working with the experimental team to understand fracture initiation and propagation in shale rocks. LANL's hybrid hydro-mechanical (HM) tool, the Hybrid Optimization Software Suite (HOSS), is being used to simulate the complex fracture and fragment processes under a variety of different boundary conditions. HOSS is based on the combined finite-discrete element method (FDEM) and has been proven to be a superior computational tool for multi-fracturing problems. In this work, the comparison of HOSS simulation results to triaxial core flooding experiments will be presented.

Numerical sedimentation particle-size analysis using the Discrete Element Method

Science.gov (United States)

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.

Analysis of a discrete element method and coupling with a compressible fluid flow method

International Nuclear Information System (INIS)

Monasse, L.

2011-01-01

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an un-deformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method. (author) [fr

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues.

Science.gov (United States)

Li, Kewei; Ogden, Ray W; Holzapfel, Gerhard A

2018-01-01

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension-compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost. © 2018 The Author(s).

Evaluation and optimization of footwear comfort parameters using finite element analysis and a discrete optimization algorithm

Science.gov (United States)

Papagiannis, P.; Azariadis, P.; Papanikos, P.

2017-10-01

Footwear is subject to bending and torsion deformations that affect comfort perception. Following review of Finite Element Analysis studies of sole rigidity and comfort, a three-dimensional, linear multi-material finite element sole model for quasi-static bending and torsion simulation, overcoming boundary and optimisation limitations, is described. Common footwear materials properties and boundary conditions from gait biomechanics are used. The use of normalised strain energy for product benchmarking is demonstrated along with comfort level determination through strain energy density stratification. Sensitivity of strain energy against material thickness is greater for bending than for torsion, with results of both deformations showing positive correlation. Optimization for a targeted performance level and given layer thickness is demonstrated with bending simulations sufficing for overall comfort assessment. An algorithm for comfort optimization w.r.t. bending is presented, based on a discrete approach with thickness values set in line with practical manufacturing accuracy. This work illustrates the potential of the developed finite element analysis applications to offer viable and proven aids to modern footwear sole design assessment and optimization.

Current Density and Continuity in Discretized Models

Science.gov (United States)

Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…

Model-Checking Discrete Duration Calculus

DEFF Research Database (Denmark)

Hansen, Michael Reichhardt

1994-01-01

can do model-checking. The subset we consider is expressive enough to formalize the requirements to the gas burner system given by A.P. Ravn (1993); but only for a discrete time domain. Model-checking is done by reducing the correctness problem ℳ|=𝒟 to the inclusion problem of regular...

A self-adaptive finite element approach for simulation of mixed-mode delamination using cohesive zone models

NARCIS (Netherlands)

Samimi, M.; Dommelen, van J.A.W.; Geers, M.G.D.

2011-01-01

Oscillations observed in the load–displacement response of brittle interfaces modeled by cohesive zone elements in a quasi-static finite element framework are artifacts of the discretization. The typical limit points in this oscillatory path can be traced by application of path-following techniques,

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

Science.gov (United States)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

International Nuclear Information System (INIS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

Energy Technology Data Exchange (ETDEWEB)

Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)

2016-05-16

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

Science.gov (United States)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

Science.gov (United States)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

A discrete dislocation–transformation model for austenitic single crystals

International Nuclear Information System (INIS)

Shi, J; Turteltaub, S; Remmers, J J C; Van der Giessen, E

2008-01-01

A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations is developed. The model is intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite is simulated using a plane-strain discrete dislocation model. The phase transformation is modeled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto-transformation problem is solved using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions are specified. The constitutive rules used in discrete dislocation simulations are supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction are analyzed. The simulations indicate that plastic flow reduces the average stress at which transformation begins, but it also reduces the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems can be activated even though transformation would not appear to be favorable based on the average stress. Conversely, the simulations indicate that the plastic hardening behavior is influenced by the reduction in the effective austenitic grain size due to the evolution of transformation. During cyclic simulations, the coupled plasticity

Compensatory neurofuzzy model for discrete data classification in biomedical

Science.gov (United States)

Ceylan, Rahime

2015-03-01

Biomedical data is separated to two main sections: signals and discrete data. So, studies in this area are about biomedical signal classification or biomedical discrete data classification. There are artificial intelligence models which are relevant to classification of ECG, EMG or EEG signals. In same way, in literature, many models exist for classification of discrete data taken as value of samples which can be results of blood analysis or biopsy in medical process. Each algorithm could not achieve high accuracy rate on classification of signal and discrete data. In this study, compensatory neurofuzzy network model is presented for classification of discrete data in biomedical pattern recognition area. The compensatory neurofuzzy network has a hybrid and binary classifier. In this system, the parameters of fuzzy systems are updated by backpropagation algorithm. The realized classifier model is conducted to two benchmark datasets (Wisconsin Breast Cancer dataset and Pima Indian Diabetes dataset). Experimental studies show that compensatory neurofuzzy network model achieved 96.11% accuracy rate in classification of breast cancer dataset and 69.08% accuracy rate was obtained in experiments made on diabetes dataset with only 10 iterations.

A discrete element based simulation framework to investigate particulate spray deposition processes

KAUST Repository

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.

Experiments and discrete element simulation of the dosing of cohesive powders in a simplified geometry

NARCIS (Netherlands)

Imole, Olukayode Isaiah; Krijgsman, Dinant; Weinhart, Thomas; Magnanimo, Vanessa; Chavez Montes, Bruno E.; Ramaioli, Marco; Luding, Stefan

2016-01-01

We perform experiments and discrete element simulations on the dosing of cohesive granular materials in a simplified geometry. The setup is a canister box where the powder is dosed out through the action of a constant-pitch coil feeder connected to a motor. A dosing step consists of a rotation

Statistical and Probabilistic Extensions to Ground Operations' Discrete Event Simulation Modeling

Science.gov (United States)

Trocine, Linda; Cummings, Nicholas H.; Bazzana, Ashley M.; Rychlik, Nathan; LeCroy, Kenneth L.; Cates, Grant R.

2010-01-01

NASA's human exploration initiatives will invest in technologies, public/private partnerships, and infrastructure, paving the way for the expansion of human civilization into the solar system and beyond. As it is has been for the past half century, the Kennedy Space Center will be the embarkation point for humankind's journey into the cosmos. Functioning as a next generation space launch complex, Kennedy's launch pads, integration facilities, processing areas, launch and recovery ranges will bustle with the activities of the world's space transportation providers. In developing this complex, KSC teams work through the potential operational scenarios: conducting trade studies, planning and budgeting for expensive and limited resources, and simulating alternative operational schemes. Numerous tools, among them discrete event simulation (DES), were matured during the Constellation Program to conduct such analyses with the purpose of optimizing the launch complex for maximum efficiency, safety, and flexibility while minimizing life cycle costs. Discrete event simulation is a computer-based modeling technique for complex and dynamic systems where the state of the system changes at discrete points in time and whose inputs may include random variables. DES is used to assess timelines and throughput, and to support operability studies and contingency analyses. It is applicable to any space launch campaign and informs decision-makers of the effects of varying numbers of expensive resources and the impact of off nominal scenarios on measures of performance. In order to develop representative DES models, methods were adopted, exploited, or created to extend traditional uses of DES. The Delphi method was adopted and utilized for task duration estimation. DES software was exploited for probabilistic event variation. A roll-up process was used, which was developed to reuse models and model elements in other less - detailed models. The DES team continues to innovate and expand

Discrete Element Method Simulation of a Boulder Extraction From an Asteroid

Science.gov (United States)

Kulchitsky, Anton K.; Johnson, Jerome B.; Reeves, David M.; Wilkinson, Allen

2014-01-01

The force required to pull 7t and 40t polyhedral boulders from the surface of an asteroid is simulated using the discrete element method considering the effects of microgravity, regolith cohesion and boulder acceleration. The connection between particle surface energy and regolith cohesion is estimated by simulating a cohesion sample tearing test. An optimal constant acceleration is found where the peak net force from inertia and cohesion is a minimum. Peak pulling forces can be further reduced by using linear and quadratic acceleration functions with up to a 40% reduction in force for quadratic acceleration.

Discrete event simulation tool for analysis of qualitative models of continuous processing systems

Science.gov (United States)

Malin, Jane T. (Inventor); Basham, Bryan D. (Inventor); Harris, Richard A. (Inventor)

1990-01-01

An artificial intelligence design and qualitative modeling tool is disclosed for creating computer models and simulating continuous activities, functions, and/or behavior using developed discrete event techniques. Conveniently, the tool is organized in four modules: library design module, model construction module, simulation module, and experimentation and analysis. The library design module supports the building of library knowledge including component classes and elements pertinent to a particular domain of continuous activities, functions, and behavior being modeled. The continuous behavior is defined discretely with respect to invocation statements, effect statements, and time delays. The functionality of the components is defined in terms of variable cluster instances, independent processes, and modes, further defined in terms of mode transition processes and mode dependent processes. Model construction utilizes the hierarchy of libraries and connects them with appropriate relations. The simulation executes a specialized initialization routine and executes events in a manner that includes selective inherency of characteristics through a time and event schema until the event queue in the simulator is emptied. The experimentation and analysis module supports analysis through the generation of appropriate log files and graphics developments and includes the ability of log file comparisons.

Discrete element modeling approach to porosimetry for durability risk estimation of concrete

NARCIS (Netherlands)

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.

Discrete modelling of the electrochemical performance of SOFC electrodes

International Nuclear Information System (INIS)

Schneider, L.C.R.; Martin, C.L.; Bultel, Y.; Bouvard, D.; Siebert, E.

2006-01-01

The composite anode and cathode of solid oxide fuel cells (SOFC) are modelled as sintered mixtures of electrolyte and electrocatalyst particles. A particle packing is first created numerically by the discrete element method (DEM) from a loose packing of 40 000 spherical, monosized, homogeneously mixed, and randomly positioned particles. Once the microstructure is sintered numerically, the effective electrode conductivity is determined by discretization of the particle packing into a resistance network. Each particle contact is characteristic of a bond resistance that depends on contact geometry and particle properties. The network, which typically consists of 120 000 bond resistances in total, is solved using Kirchhoff's current law. Distributions of local current densities and particle potentials are then performed. We investigate how electrode performance depends on parameters such as electrode composition, thickness, density and intrinsic material conductivities that are temperature dependent. The simulations show that the best electrode performance is obtained for compositions close to the percolation threshold of the electronic conductor. Depending on particle conductivities, the electrode performance is a function of its thickness. Additionally, DEM simulations generate useful microstructural information such as: coordination numbers, triple phase boundary length and percolation thresholds

Numerical simulations of granular dynamics: I. Hard-sphere discrete element method and tests

Science.gov (United States)

Richardson, Derek C.; Walsh, Kevin J.; Murdoch, Naomi; Michel, Patrick

2011-03-01

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 centrifuging as a function of rotation rate.

Comparisons of physical experiment and discrete element simulations of sheared granular materials in an annular shear cell

Science.gov (United States)

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.

PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL

DEFF Research Database (Denmark)

Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.

2010-01-01

The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...

Modeling and simulation of discrete event systems

CERN Document Server

Choi, Byoung Kyu

2013-01-01

Computer modeling and simulation (M&S) allows engineers to study and analyze complex systems. Discrete-event system (DES)-M&S is used in modern management, industrial engineering, computer science, and the military. As computer speeds and memory capacity increase, so DES-M&S tools become more powerful and more widely used in solving real-life problems. Based on over 20 years of evolution within a classroom environment, as well as on decades-long experience in developing simulation-based solutions for high-tech industries, Modeling and Simulation of Discrete-Event Systems is the only book on

An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu

2010-07-01

An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)

Dynamic nonlinear interaction of elastic plates on discrete supports

International Nuclear Information System (INIS)

Coutinho, A.L.G.A.; Landau, L.; Lima, E.C.P. de; Ebecken, N.F.F.

1984-01-01

A study on the dynamic nonlinear interaction of elastic plates using the finite element method is presented. The elastic plate is discretized by 4-node isoparametric Mindlin elements. The constitutive relation of the discrete supports can be any nonlinear curve given by pairs of force-displacement points. The nonlinear behaviour is represented by the overlay approach. This model also allows the simulation of a progressive decrease on the supports stiffnesses during load cycles. The dynamic nonlinear incremental movement equations are integrated by the Newmark implicit operator. Two alternatives for the incremental-iterative formulation are compared. The paper ends with a discussion of the advantages and limitations of the presented numerical models. (Author) [pt

ADAM: analysis of discrete models of biological systems using computer algebra.

Science.gov (United States)

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web

Discrete competing risk model with application to modeling bus-motor failure data

International Nuclear Information System (INIS)

Jiang, R.

2010-01-01

Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

A discrete stress-strength interference model based on universal generating function

International Nuclear Information System (INIS)

An Zongwen; Huang Hongzhong; Liu Yu

2008-01-01

Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

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)

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.

Directory of Open Access Journals (Sweden)

Paul Brocklehurst

Full Text Available We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM. Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.

Science.gov (United States)

Brocklehurst, Paul; Ni, Haibo; Zhang, Henggui; Ye, Jianqiao

2017-01-01

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano

Discrete-Slots Models of Visual Working-Memory Response Times

Science.gov (United States)

Donkin, Christopher; Nosofsky, Robert M.; Gold, Jason M.; Shiffrin, Richard M.

2014-01-01

Much recent research has aimed to establish whether visual working memory (WM) is better characterized by a limited number of discrete all-or-none slots or by a continuous sharing of memory resources. To date, however, researchers have not considered the response-time (RT) predictions of discrete-slots versus shared-resources models. To complement the past research in this field, we formalize a family of mixed-state, discrete-slots models for explaining choice and RTs in tasks of visual WM change detection. In the tasks under investigation, a small set of visual items is presented, followed by a test item in 1 of the studied positions for which a change judgment must be made. According to the models, if the studied item in that position is retained in 1 of the discrete slots, then a memory-based evidence-accumulation process determines the choice and the RT; if the studied item in that position is missing, then a guessing-based accumulation process operates. Observed RT distributions are therefore theorized to arise as probabilistic mixtures of the memory-based and guessing distributions. We formalize an analogous set of continuous shared-resources models. The model classes are tested on individual subjects with both qualitative contrasts and quantitative fits to RT-distribution data. The discrete-slots models provide much better qualitative and quantitative accounts of the RT and choice data than do the shared-resources models, although there is some evidence for “slots plus resources” when memory set size is very small. PMID:24015956

Ecological monitoring in a discrete-time prey-predator model.

Science.gov (United States)

Gámez, M; López, I; Rodríguez, C; Varga, Z; Garay, J

2017-09-21

The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

Model of the saltation transport by Discrete Element Method coupled with wind interaction

Directory of Open Access Journals (Sweden)

Oger Luc

2017-01-01

Full Text Available We study the Aeolian saltation transport problem by analysing the collision of incident energetic beads with granular packing. We investigate the collision process for the case where the incident bead and those from the packing have identical mechanical properties. We analyse the features of the consecutive collision process. We used a molecular dynamics method known as DEM (soft Discrete Element Method with 20000 particles (2D. The grains were displayed randomly in a box (250X60. A few incident disks are launched with a constant velocity and angle with high random position to initiate the flow. A wind velocity profile is applied on the flowing zone of the saltation. The velocity profile is obtained by the calculi of the counter-flow due to the local packing fraction induced by the granular flow. We analyse the evolution of the upper surface of the disk packing. In the beginning, the saltation process can be seen as the classical “splash function” in which one bead hits a fully static dense packing. Then, the quasi-fluidized upper layer of the packing creates a completely different behaviour of the “animated splash function”. The dilation of the upper surface due to the previous collisions is responsible for a need of less input energy for launching new ejected disks. This phenomenon permits to maintain a constant granular flow with a “small” wind velocity on the surface of the disk bed.

Cone-beam tomography with discrete data sets

International Nuclear Information System (INIS)

Barrett, H.H.

1994-01-01

Sufficiently conditions for cone-beam data are well known for the case of continuous data collection along a cone-vortex curve with continuous detectors. These continuous conditions are inadequate for real-world data where discrete vertex geometries and discrete detector arrays are used. In this paper we present a theoretical formulation of cone-beam tomography with arbitrary discrete arrays of detectors and vertices. The theory models the imaging system as a linear continuous-to-discrete mapping and represents the continuous object exactly as a Fourier series. The reconstruction problem is posed as the estimation of some subset of the Fourier coefficients. The main goal of the theory is to determine which Fourier coefficients can be reliably determined from the data delivered by a specific discrete design. A fourier component will be well determined by the data if it satisfies two conditions: it makes a strong contribution to the data, and this contribution is relatively independent of the contribution of other Fourier components. To make these considerations precise, we introduce a concept called the cross-talk matrix. A diagonal element of this matrix measures the strength of a Fourier component in the data, while an off-diagonal element quantifies the dependence or aliasing of two different components. (Author)

Study on small-strain behaviours of methane hydrate sandy sediments using discrete element method

Energy Technology Data Exchange (ETDEWEB)

Yu Yanxin; Cheng Yipik [Department of Civil, Environmental and Geomatic Engineering, University College London (UCL), Gower Street, London, WC1E 6BT (United Kingdom); Xu Xiaomin; Soga, Kenichi [Geotechnical and Environmental Research Group, Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ (United Kingdom)

2013-06-18

Methane hydrate bearing soil has attracted increasing interest as a potential energy resource where methane gas can be extracted from dissociating hydrate-bearing sediments. Seismic testing techniques have been applied extensively and in various ways, to detect the presence of hydrates, due to the fact that hydrates increase the stiffness of hydrate-bearing sediments. With the recognition of the limitations of laboratory and field tests, wave propagation modelling using Discrete Element Method (DEM) was conducted in this study in order to provide some particle-scale insights on the hydrate-bearing sandy sediment models with pore-filling and cementation hydrate distributions. The relationship between shear wave velocity and hydrate saturation was established by both DEM simulations and analytical solutions. Obvious differences were observed in the dependence of wave velocity on hydrate saturation for these two cases. From the shear wave velocity measurement and particle-scale analysis, it was found that the small-strain mechanical properties of hydrate-bearing sandy sediments are governed by both the hydrate distribution patterns and hydrate saturation.

Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements.

Science.gov (United States)

Xu, Jason; Guttorp, Peter; Kato-Maeda, Midori; Minin, Vladimir N

2015-12-01

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. © 2015, The International Biometric Society.

Modelling road accident blackspots data with the discrete generalized Pareto distribution.

Science.gov (United States)

Prieto, Faustino; Gómez-Déniz, Emilio; Sarabia, José María

2014-10-01

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed. Copyright © 2014 Elsevier Ltd. All rights reserved.

Discrete element weld model, phase 2

Science.gov (United States)

Prakash, C.; Samonds, M.; Singhal, A. K.

1987-01-01

A numerical method was developed for analyzing the tungsten inert gas (TIG) welding process. The phenomena being modeled include melting under the arc and the flow in the melt under the action of buoyancy, surface tension, and electromagnetic forces. The latter entails the calculation of the electric potential and the computation of electric current and magnetic field therefrom. Melting may occur at a single temperature or over a temperature range, and the electrical and thermal conductivities can be a function of temperature. Results of sample calculations are presented and discussed at length. A major research contribution has been the development of numerical methodology for the calculation of phase change problems in a fixed grid framework. The model has been implemented on CHAM's general purpose computer code PHOENICS. The inputs to the computer model include: geometric parameters, material properties, and weld process parameters.

Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

OpenAIRE

Ochoa-Avendaño, J.; Garzon-Alvarado, D. A.; Linero, Dorian L.; Cerrolaza, M.

2017-01-01

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...

Thermal modelling using discrete vasculature for thermal therapy: a review

Science.gov (United States)

Kok, H.P.; Gellermann, J.; van den Berg, C.A.T.; Stauffer, P.R.; Hand, J.W.; Crezee, J.

2013-01-01

Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality. PMID:23738700

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

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)

Nuclear facility safeguards systems modeling using discrete event simulation

International Nuclear Information System (INIS)

Engi, D.

1977-01-01

The threat of theft or dispersal of special nuclear material at a nuclear facility is treated by studying the temporal relationships between adversaries having authorized access to the facility (insiders) and safeguards system events by using a GASP IV discrete event simulation. The safeguards system events--detection, assessment, delay, communications, and neutralization--are modeled for the general insider adversary strategy which includes degradation of the safeguards system elements followed by an attempt to steal or disperse special nuclear material. The performance measure used in the analysis is the estimated probability of safeguards system success in countering the adversary based upon a predetermined set of adversary actions. An exemplary problem which includes generated results is presented for a hypothetical nuclear facility. The results illustrate representative information that could be utilized by safeguards decision-makers

Discrete element method based scale-up model for material synthesis using ball milling

Science.gov (United States)

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

Modeling of light dynamic cone penetration test - Panda 3 ® in granular material by using 3D Discrete element method

Science.gov (United States)

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.

Modeling discrete and rhythmic movements through motor primitives: a review.

Science.gov (United States)

Degallier, Sarah; Ijspeert, Auke

2010-10-01

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.

An application of a discrete fixed point theorem to the Cournot model

OpenAIRE

Sato, Junichi

2008-01-01

In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.

Comparing the Discrete and Continuous Logistic Models

Science.gov (United States)

Gordon, Sheldon P.

2008-01-01

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

Energy Technology Data Exchange (ETDEWEB)

Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

2008-04-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced 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 first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. 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.

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

International Nuclear Information System (INIS)

Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

2008-01-01

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced 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 first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. 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

Galerkin v. discrete-optimal projection in nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

2015-04-01

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

Modeling the growth and interaction of stylolite networks, using the discrete element method for pressure solution

Science.gov (United States)

Makedonska, N.; Sparks, D. W.; Aharonov, E.

2012-12-01

Pressure solution (also termed chemical compaction) is considered the most important ductile deformation mechanism operating in the Earth's upper crust. This mechanism is a major player in a variety of geological processes, including evolution of sedimentary basins, hydrocarbon reservoirs, aquifers, earthquake recurrence cycles, and fault healing. Pressure solution in massive rocks often localizes into solution seams or stylolites. Field observations of stylolites often show elastic/brittle interactions in regions between pressure solution features, including and shear fractures, veins and pull-apart features. To understand these interactions, we use a grain-scale model based on the Discrete Element Method that allows granular dissolution at stressed contacts between grains. The new model captures both the slow chemical compaction process and the more abrupt brittle fracturing and sliding between grains. We simulate a sample of rock as a collection of particles, each representing either a grain or a unit of rock, bonded to each other with breakable cement. We apply external stresses to this sample, and calculate elastic and frictional interactions between the grains. Dissolution is modeled by an irreversible penetration of contacting grains into each other at a rate that depends on the contact stress and an adjustable rate constant. Experiments have shown that dissolution rates at grain contacts are greatly enhanced when there is a mineralogical contrast. Therefore, we dissolution rate constant can be increased to account for an amount of impurities (e.g. clay in a quartz or calcite sandstone) that can accumulate on dissolving contacts. This approach allows large compaction and shear strains within the rock, while allowing examination of local grain-scale heterogeneity. For example, we will describe the effect of pressure solution on the distribution of contact forces magnitudes and orientations. Contact forces in elastic granular packings are inherently

Video modeling to train staff to implement discrete-trial instruction.

Science.gov (United States)

Catania, Cynthia N; Almeida, Daniel; Liu-Constant, Brian; DiGennaro Reed, Florence D

2009-01-01

Three new direct-service staff participated in a program that used a video model to train target skills needed to conduct a discrete-trial session. Percentage accuracy in completing a discrete-trial teaching session was evaluated using a multiple baseline design across participants. During baseline, performances ranged from a mean of 12% to 63% accuracy. During video modeling, there was an immediate increase in accuracy to a mean of 98%, 85%, and 94% for each participant. Performance during maintenance and generalization probes remained at high levels. Results suggest that video modeling can be an effective technique to train staff to conduct discrete-trial sessions.

Performance analysis of chi models using discrete-time probabilistic reward graphs

NARCIS (Netherlands)

Trcka, N.; Georgievska, S.; Markovski, J.; Andova, S.; Vink, de E.P.

2008-01-01

We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains, full-fledged platform for qualitative and

Discrete element modeling of triggered slip in faults with granular gouge: application to dynamic earthquake triggering

International Nuclear Information System (INIS)

Ferdowsi, B.

2014-01-01

Recent seismological observations based on new, more sensitive instrumentation show that seismic waves radiated from large earthquakes can trigger other earthquakes globally. This phenomenon is called dynamic earthquake triggering and is well-documented for over 30 of the largest earthquakes worldwide. Granular materials are at the core of mature earthquake faults and play a key role in fault triggering by exhibiting a rich nonlinear response to external perturbations. The stick-slip dynamics in sheared granular layers is analogous to the seismic cycle for earthquake fault systems. In this research effort, we characterize the macroscopic scale statistics and the grain-scale mechanisms of triggered slip in sheared granular layers. We model the granular fault gouge using three dimensional discrete element method simulations. The modeled granular system is put into stick-slip dynamics by applying a conning pressure and a shear load. The dynamic triggering is simulated by perturbing the spontaneous stick-slip dynamics using an external vibration applied to the boundary of the layer. The influences of the triggering consist in a frictional weakening during the vibration interval, a clock advance of the next expected large slip event and long term effects in the form of suppression and recovery of the energy released from the granular layer. Our study suggests that above a critical amplitude, vibration causes a significant clock advance of large slip events. We link this clock advance to a major decline in the slipping contact ratio as well as a decrease in shear modulus and weakening of the granular gouge layer. We also observe that shear vibration is less effective in perturbing the stick-slip dynamics of the granular layer. Our study suggests that in order to have an effective triggering, the input vibration must also explore the granular layer at length scales about or less than the average grain size. The energy suppression and the subsequent recovery and increased

Nonparametric Identification and Estimation of Finite Mixture Models of Dynamic Discrete Choices

OpenAIRE

Hiroyuki Kasahara; Katsumi Shimotsu

2006-01-01

In dynamic discrete choice analysis, controlling for unobserved heterogeneity is an important issue, and finite mixture models provide flexible ways to account for unobserved heterogeneity. This paper studies nonparametric identifiability of type probabilities and type-specific component distributions in finite mixture models of dynamic discrete choices. We derive sufficient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in appli...

Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems

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.

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

Phase Chaos and Multistability in the Discrete Kuramoto Model

DEFF Research Database (Denmark)

Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.

2008-01-01

The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...

Discrete event simulation: Modeling simultaneous complications and outcomes

NARCIS (Netherlands)

Quik, E.H.; Feenstra, T.L.; Krabbe, P.F.M.

2012-01-01

OBJECTIVES: To present an effective and elegant model approach to deal with specific characteristics of complex modeling. METHODS: A discrete event simulation (DES) model with multiple complications and multiple outcomes that each can occur simultaneously was developed. In this DES model parameters,

An isogeometric boundary element method for electromagnetic scattering with compatible B-spline discretizations

Science.gov (United States)

Simpson, R. N.; Liu, Z.; Vázquez, R.; Evans, J. A.

2018-06-01

We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-order approximations and crucially provides a direct link with CAD data structures that allows for efficient design workflows. After outlining the construction of div- and curl-conforming B-splines defined over 3D surfaces we describe their use with the electric and magnetic field integral equations using a Galerkin formulation. We use Bézier extraction to accelerate the computation of NURBS and B-spline terms and employ H-matrices to provide accelerated computations and memory reduction for the dense matrices that result from the boundary integral discretization. The method is verified using the well known Mie scattering problem posed over a perfectly electrically conducting sphere and the classic NASA almond problem. Finally, we demonstrate the ability of the approach to handle models with complex geometry directly from CAD without mesh generation.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

Science.gov (United States)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

Dynamic modeling method for infrared smoke based on enhanced discrete phase model

Science.gov (United States)

Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo

2018-03-01

The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.

Discrete fracture modelling for the Stripa tracer validation experiment predictions

International Nuclear Information System (INIS)

Dershowitz, W.; Wallmann, P.

1992-02-01

Groundwater flow and transport through three-dimensional networks of discrete fractures was modeled to predict the recovery of tracer from tracer injection experiments conducted during phase 3 of the Stripa site characterization and validation protect. Predictions were made on the basis of an updated version of the site scale discrete fracture conceptual model used for flow predictions and preliminary transport modelling. In this model, individual fractures were treated as stochastic features described by probability distributions of geometric and hydrologic properties. Fractures were divided into three populations: Fractures in fracture zones near the drift, non-fracture zone fractures within 31 m of the drift, and fractures in fracture zones over 31 meters from the drift axis. Fractures outside fracture zones are not modelled beyond 31 meters from the drift axis. Transport predictions were produced using the FracMan discrete fracture modelling package for each of five tracer experiments. Output was produced in the seven formats specified by the Stripa task force on fracture flow modelling. (au)

Discrete meso-element simulation of the failure behavior of short-fiber composites under dynamic loading

International Nuclear Information System (INIS)

Liu Wenyan; Tang, Z.P.; Liu Yunxin

2000-01-01

In recent years, more attention has been paid to a better understanding of the failure behavior and mechanism of heterogeneous materials at the meso-scale level. In this paper, the crack initiation and development in epoxy composites reinforced with short steel fibers under dynamic loading were simulated and analyzed with the 2D Discrete Meso-Element Dynamic Method. Results show that the damage process depends greatly on the binding property between matrix and fibers

A Discrete Dynamical Model of Signed Partitions

Directory of Open Access Journals (Sweden)

G. Chiaselotti

2013-01-01

Full Text Available We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.

Discrete choice models with multiplicative error terms

DEFF Research Database (Denmark)

Fosgerau, Mogens; Bierlaire, Michel

2009-01-01

The conditional indirect utility of many random utility maximization (RUM) discrete choice models is specified as a sum of an index V depending on observables and an independent random term ε. In general, the universe of RUM consistent models is much larger, even fixing some specification of V due...

Stability analysis of the Euler discretization for SIR epidemic model

International Nuclear Information System (INIS)

Suryanto, Agus

2014-01-01

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart

On the Robustness and Prospects of Adaptive BDDC Methods for Finite Element Discretizations of Elliptic PDEs with High-Contrast Coefficients

KAUST Repository

Zampini, Stefano; Keyes, David E.

2016-01-01

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

Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling

KAUST Repository

Hackett-Jones, Emily J.

2012-04-17

Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.

Symmetries and discretizations of the O(3) nonlinear sigma model

Energy Technology Data Exchange (ETDEWEB)

Flore, Raphael [TPI, Universitaet Jena (Germany)

2011-07-01

Nonlinear sigma models possess many interesting properties like asymptotic freedom, confinement or dynamical mass generation, and hence serve as toy models for QCD and other theories. We derive a formulation of the N=2 supersymmetric extension of the O(3) nonlinear sigma model in terms of constrained field variables. Starting from this formulation, it is discussed how the model can be discretized in a way that maintains as many symmetries of the theory as possible. Finally, recent numerical results related to these discretizations are presented.

On discrete symmetries for a whole Abelian model

International Nuclear Information System (INIS)

Chauca, J.; Doria, R.

2012-01-01

Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {D μ ,X i μ } and the physical basis {G μI }. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {G μI } manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.

Methodology for characterizing modeling and discretization uncertainties in computational simulation

Energy Technology Data Exchange (ETDEWEB)

ALVIN,KENNETH F.; OBERKAMPF,WILLIAM L.; RUTHERFORD,BRIAN M.; DIEGERT,KATHLEEN V.

2000-03-01

This research effort focuses on methodology for quantifying the effects of model uncertainty and discretization error on computational modeling and simulation. The work is directed towards developing methodologies which treat model form assumptions within an overall framework for uncertainty quantification, for the purpose of developing estimates of total prediction uncertainty. The present effort consists of work in three areas: framework development for sources of uncertainty and error in the modeling and simulation process which impact model structure; model uncertainty assessment and propagation through Bayesian inference methods; and discretization error estimation within the context of non-deterministic analysis.

Discrete kink dynamics in hydrogen-bonded chains: The two-component model

DEFF Research Database (Denmark)

Karpan, V.M.; Zolotaryuk, Yaroslav; Christiansen, Peter Leth

2004-01-01

We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton inte......We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion...... chain subject to a substrate with two optical bands), both providing a bistability of the hydrogen-bonded proton. Exact two-component (kink and antikink) discrete solutions for these models are found numerically. We compare the soliton solutions and their properties in both the one- (when the heavy ions...... principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist....

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

Analysis of stochastic effects in Kaldor-type business cycle discrete model

Science.gov (United States)

Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna

2016-07-01

We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.

Which spatial discretization for distributed hydrological models? Proposition of a methodology and illustration for medium to large-scale catchments

Directory of Open Access Journals (Sweden)

J. Dehotin

2008-05-01

Full Text Available Distributed hydrological models are valuable tools to derive distributed estimation of water balance components or to study the impact of land-use or climate change on water resources and water quality. In these models, the choice of an appropriate spatial discretization is a crucial issue. It is obviously linked to the available data, their spatial resolution and the dominant hydrological processes. For a given catchment and a given data set, the "optimal" spatial discretization should be adapted to the modelling objectives, as the latter determine the dominant hydrological processes considered in the modelling. For small catchments, landscape heterogeneity can be represented explicitly, whereas for large catchments such fine representation is not feasible and simplification is needed. The question is thus: is it possible to design a flexible methodology to represent landscape heterogeneity efficiently, according to the problem to be solved? This methodology should allow a controlled and objective trade-off between available data, the scale of the dominant water cycle components and the modelling objectives.

In this paper, we propose a general methodology for such catchment discretization. It is based on the use of nested discretizations. The first level of discretization is composed of the sub-catchments, organised by the river network topology. The sub-catchment variability can be described using a second level of discretizations, which is called hydro-landscape units. This level of discretization is only performed if it is consistent with the modelling objectives, the active hydrological processes and data availability. The hydro-landscapes take into account different geophysical factors such as topography, land-use, pedology, but also suitable hydrological discontinuities such as ditches, hedges, dams, etc. For numerical reasons these hydro-landscapes can be further subdivided into smaller elements that will constitute the

Differential-discrete mathematical model of two phase flow heat exchanger

International Nuclear Information System (INIS)

Debeljkovic, D.Lj.; Zitek, Pavel; Simeunovic, G.; Inard, Christian

2007-01-01

A dynamic thermal-hydraulic mathematical model of evaporator dynamics of a once - through sub critical steam generator is derived and presented. This model allows the investigation of evaporator dynamics including its transients responses. The evaporator was considered as a part of three-section (economizer, evaporator and super-heater) model with time varying phase boundaries and is described by a set of linearized discrete - difference equations which, with some other algebraic equations, constitutes a closed system of equations possible for exact computer solution. This model has been derived upon the fundamental equations of mass, energy and momentum balance. For the first time, a discrete differential approach has been applied in order to investigate such complex, two phase processes. Namely, this approach allows one to escape from the model of this process usually described by a set of partial differential equations and enables one, using this method, to simulate evaporators dynamics in an extraordinarily simple way. In current literature this approach is sometimes called physical discretization. (author)

Pellet Cladding Mechanical Interaction Modeling Using the Extended Finite Element Method

Energy Technology Data Exchange (ETDEWEB)

Spencer, Benjamin W.; Jiang, Wen; Dolbow, John E.; Peco, Christian

2016-09-01

As a brittle material, the ceramic UO2 used as light water reactor fuel experiences significant fracturing throughout its life, beginning with the first rise to power of fresh fuel. This has multiple effects on the thermal and mechanical response of the fuel/cladding system. One such effect that is particularly important is that when there is mechanical contact between the fuel and cladding, cracks that extending from the outer surface of the fuel into the volume of the fuel cause elevated stresses in the adjacent cladding, which can potentially lead to cladding failure. Modeling the thermal and mechanical response of the cladding in the vicinity of these surface-breaking cracks in the fuel can provide important insights into this behavior to help avoid operating conditions that could lead to cladding failure. Such modeling has traditionally been done in the context of finite-element-based fuel performance analysis by modifying the fuel mesh to introduce discrete cracks. While this approach is effective in capturing the important behavior at the fuel/cladding interface, there are multiple drawbacks to explicitly incorporating the cracks in the finite element mesh. Because the cracks are incorporated in the original mesh, the mesh must be modified for cracks of specified location and depth, so it is difficult to account for crack propagation and the formation of new cracks at other locations. The extended finite element method (XFEM) has emerged in recent years as a powerful method to represent arbitrary, evolving, discrete discontinuities within the context of the finite element method. Development work is underway by the authors to implement XFEM in the BISON fuel performance code, and this capability has previously been demonstrated in simulations of fracture propagation in ceramic nuclear fuel. These preliminary demonstrations have included only the fuel, and excluded the cladding for simplicity. This paper presents initial results of efforts to apply XFEM to

The compaction of a random distribution of metal cylinders by the discrete element method

DEFF Research Database (Denmark)

Redanz, Pia; Fleck, N. A.

2001-01-01

-linear springs. The initial packing of the particles is generated by the ballistic deposition method. Salient micromechanical features of closed die and isostatic powder compaction are elucidated for both frictionless and sticking contacts. It is found that substantial rearrangement of frictionless particles......The cold compaction of a 2D random distribution of metal circular cylinders has been investigated numerically by the discrete element method. Each cylindrical particle is located by a node at its centre and the plastic indentation of the contacts between neighbouring particles is represented by non...

Model-based Quantile Regression for Discrete Data

KAUST Repository

Padellini, Tullia

2018-04-10

Quantile regression is a class of methods voted to the modelling of conditional quantiles. In a Bayesian framework quantile regression has typically been carried out exploiting the Asymmetric Laplace Distribution as a working likelihood. Despite the fact that this leads to a proper posterior for the regression coefficients, the resulting posterior variance is however affected by an unidentifiable parameter, hence any inferential procedure beside point estimation is unreliable. We propose a model-based approach for quantile regression that considers quantiles of the generating distribution directly, and thus allows for a proper uncertainty quantification. We then create a link between quantile regression and generalised linear models by mapping the quantiles to the parameter of the response variable, and we exploit it to fit the model with R-INLA. We extend it also in the case of discrete responses, where there is no 1-to-1 relationship between quantiles and distribution\\'s parameter, by introducing continuous generalisations of the most common discrete variables (Poisson, Binomial and Negative Binomial) to be exploited in the fitting.

Failure diagnosis using discrete event models

International Nuclear Information System (INIS)

Sampath, M.; Sengupta, R.; Lafortune, S.; Teneketzis, D.; Sinnamohideen, K.

1994-01-01

We propose a Discrete Event Systems (DES) approach to the failure diagnosis problem. We present a methodology for modeling physical systems in a DES framework. We discuss the notion of diagnosability and present the construction procedure of the diagnoser. Finally, we illustrate our approach using a Heating, Ventilation and Air Conditioning (HVAC) system

Discrete time duration models with group-level heterogeneity

DEFF Research Database (Denmark)

Frederiksen, Anders; Honoré, Bo; Hu, Loujia

2007-01-01

Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration...

Straightened cervical lordosis causes stress concentration: a finite element model study

Energy Technology Data Exchange (ETDEWEB)

Wei, Wei; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue [Hangzhou Red Cross Hospital, Hangzhou, Zhejiang, (China); Liao, Shenhui [School of Information Science and Engineering, Central South University, Changsha, Hunan (China)

2013-03-15

In this study, we propose a finite element analysis of the complete cervical spine with straightened and normal physiological curvature by using a specially designed modelling system. An accurate finite element model is established to recommend plausible approaches to treatment of cervical spondylosis through the finite element analysis results. There are few reports of biomechanics influence of the straightened cervical curve. It is difficult to measure internal responses of cervical spine directly. However, the finite element method has been reported to have the capability to quantify both external and internal responses to mechanical loading, such as the strain and stress distribution of spinal components. We choose a subject with a straightened cervical spine from whom to collect the CT scan data, which formed the basis of the finite element analysis. By using a specially designed modelling system, a high quality finite element model of the complete cervical spine with straightened curvature was generated, which was then mapped to reconstruct a normal physiological curvature model by a volumetric mesh deformation method based on discrete differential properties. Then, the same boundary conditions were applied to do a comparison. The result demonstrated that the active movement range of straightened cervical spine decreased by 24–33 %, but the stress increased by 5–95 %. The stress was concentrated at the facet joint cartilage, uncovertebral joint and the disk. The results suggest that cervical lordosis may have a direct impact on cervical spondylosis treatment. These results may be useful for clinical treatment of cervical spondylosis with straightened curvature.

Straightened cervical lordosis causes stress concentration: a finite element model study

International Nuclear Information System (INIS)

Wei, Wei; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue; Liao, Shenhui

2013-01-01

In this study, we propose a finite element analysis of the complete cervical spine with straightened and normal physiological curvature by using a specially designed modelling system. An accurate finite element model is established to recommend plausible approaches to treatment of cervical spondylosis through the finite element analysis results. There are few reports of biomechanics influence of the straightened cervical curve. It is difficult to measure internal responses of cervical spine directly. However, the finite element method has been reported to have the capability to quantify both external and internal responses to mechanical loading, such as the strain and stress distribution of spinal components. We choose a subject with a straightened cervical spine from whom to collect the CT scan data, which formed the basis of the finite element analysis. By using a specially designed modelling system, a high quality finite element model of the complete cervical spine with straightened curvature was generated, which was then mapped to reconstruct a normal physiological curvature model by a volumetric mesh deformation method based on discrete differential properties. Then, the same boundary conditions were applied to do a comparison. The result demonstrated that the active movement range of straightened cervical spine decreased by 24–33 %, but the stress increased by 5–95 %. The stress was concentrated at the facet joint cartilage, uncovertebral joint and the disk. The results suggest that cervical lordosis may have a direct impact on cervical spondylosis treatment. These results may be useful for clinical treatment of cervical spondylosis with straightened curvature.

Finite Element Model for Nonlinear Analysis of Reinforced Concrete Beams and Plane Frames

Directory of Open Access Journals (Sweden)

R.S.B. STRAMANDINOLI

Full Text Available Abstract In this work, a two-dimensional finite element (FE model for physical and geometric nonlinear analysis of reinforced concrete beams and plane frames, developed by the authors, is presented. The FE model is based on the Euler-Bernoulli Beam Theory, in which shear deformations are neglected. The bar elements have three nodes with a total of seven degrees of freedom. Three Gauss-points are utilized for the element integration, with the element section discretized into layers at each Gauss point (Fiber Model. It is assumed that concrete and reinforcing bars are perfectly bonded, and each section layer is assumed to be under a uniaxial stress-state. Nonlinear constitutive laws are utilized for both concrete and reinforcing steel layers, and a refined tension-stiffening model, developed by the authors, is included. The Total Lagrangean Formulation is adopted for geometric nonlinear consideration and several methods can be utilized to achieve equilibrium convergence of the nonlinear equations. The developed model is implemented into a computer program named ANEST/CA, which is validated by comparison with some tests on RC beams and plane frames, showing an excellent correlation between numerical and experimental results.

Rich dynamics of discrete delay ecological models

International Nuclear Information System (INIS)

Peng Mingshu

2005-01-01

We study multiple bifurcations and chaotic behavior of a discrete delay ecological model. New form of chaos for the 2-D map is observed: the combination of potential period doubling and reverse period-doubling leads to cascading bubbles

Coupled distinct element-finite element numerical modelling of fluid circulation in deforming sedimentary basins.

Science.gov (United States)

Hindle, D.; Malz, A.; Donndorf, S.; Kley, J.; Kopp, H.

2012-04-01

We develop a coupled numerical model for fluid flow in deforming sedimentary basins. We combine a distinct element method for large deformations of crustal materials, with a finite element method for fluid flow according to a diffusion type equation. The key question in such a model is how to simulate evolving permeabilities due to upper and possibly middle crustal deformation, and the coupled issue of how localisation of deformation in faults and shear zones is itself influenced by fluid flow and fluid pressure and vice versa. Currently our knowledge of these issues is restricted, even sketchy. There are a number of hypotheses, based partly on geological and isotope geochemical observations, such as "seismic pumping" models, and fluid induced weak décollement models for thrust sheet transport which have gained quite wide acceptance. Observations around thrusts at the present day have also often been interpreted as showing deformation induced permeability. However, combining all the physics of these processes into a numerical simulation is a complicated task given the ranges of, in particular time scales of the processes we infer to be operating based on our various observations. We start this task by using an elastic fracture relationship between normal stresses across distinct element contacts (which we consider to be the equivalent of discrete, sliding fractures) and their openness and hence their transmissivity. This relates the mechanical state of the distinct element system to a discrete permeability field. Further than that, the geometry of the mechanical system is used to provide boundary conditions for fluid flow in a diffusion equation which also incorporates the permeability field. The next question we address is how to achieve a feedback between fluid pressures and deformation. We try two approaches: one treats pore space in the DEM as real, and calculates the force exerted locally by fluids and adds this to the force balance of the model; another

Sensitivity analysis of a coupled hydro-mechanical paleo-climate model of density-dependent groundwater flow in discretely fractured crystalline rock

International Nuclear Information System (INIS)

Normani, S.D.; Sykes, J.F.

2011-01-01

A high resolution three-dimensional sub-regional scale (104 km 2 ) density-dependent, discretely fractured groundwater flow model with hydro-mechanical coupling and pseudo-permafrost was developed from a larger 5734 km 2 regional-scale groundwater flow model of a Canadian Shield setting. The objective of the work is to determine the sensitivity of modelled groundwater system evolution to the hydro-mechanical parameters. The discrete fracture dual continuum numerical model FRAC3DVS-OPG was used for all simulations. A discrete fracture network model delineated from surface features was superimposed onto an approximate 790 000 element domain mesh with approximately 850 000 nodes. Orthogonal fracture faces (between adjacent finite element grid blocks) were used to best represent the irregular discrete fracture zone network. Interconnectivity of the permeable fracture zones is an important pathway for the possible migration and subsequent reduction in groundwater and contaminant residence times. The crystalline rock matrix between these structural discontinuities was assigned mechanical and flow properties characteristic of those reported for the Canadian Shield. The variation of total dissolved solids with depth was assigned using literature data for the Canadian Shield. Performance measures for the sensitivity analysis include equivalent freshwater heads, environmental heads, linear velocities, and depth of penetration by conservative non-decaying tracers released at the surface. A 121 000 year North American continental scale paleo-climate simulation was applied to the domain with ice-sheet histories estimated by the University of Toronto Glacial Systems Model (UofT GSM). Hydro-mechanical coupling between the rock matrix and the pore fluid, due to the ice sheet normal stress, was included in the simulations. The flow model included the influence of vertical strain and assumed that areal loads were homogeneous. Permafrost depth was applied as a permeability reduction

A Discrete Model for Color Naming

Science.gov (United States)

Menegaz, G.; Le Troter, A.; Sequeira, J.; Boi, J. M.

2006-12-01

The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1). Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2), and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.

Models for the discrete berth allocation problem: A computational comparison

DEFF Research Database (Denmark)

Buhrkal, Katja Frederik; Zuglian, Sara; Røpke, Stefan

2011-01-01

In this paper we consider the problem of allocating arriving ships to discrete berth locations at container terminals. This problem is recognized as one of the most important processes for any container terminal. We review and describe three main models of the discrete dynamic berth allocation...

Models for the Discrete Berth Allocation Problem: A Computational Comparison

DEFF Research Database (Denmark)

Buhrkal, Katja; Zuglian, Sara; Røpke, Stefan

In this paper we consider the problem of allocating arriving ships to discrete berth locations at container terminals. This problem is recognized as one of the most important processes for any container terminal. We review and describe the three main models of the discrete dynamic berth allocation...

Discrete element method modeling of the triboelectric charging of polyethylene particles: Can particle size distribution and segregation reduce the charging?

International Nuclear Information System (INIS)

Konopka, Ladislav; Kosek, Juraj

2015-01-01

Polyethylene particles of various sizes are present in industrial gas-dispersion reactors and downstream processing units. The contact of the particles with a device wall as well as the mutual particle collisions cause electrons on the particle surface to redistribute in the system. The undesirable triboelectric charging results in several operational problems and safety risks in industrial systems, for example in the fluidized-bed polymerization reactor. We studied the charging of polyethylene particles caused by the particle-particle interactions in gas. Our model employs the Discrete Element Method (DEM) describing the particle dynamics and incorporates the ‘Trapped Electron Approach’ as the physical basis for the considered charging mechanism. The model predicts the particle charge distribution for systems with various particle size distributions and various level of segregation. Simulation results are in a qualitative agreement with experimental observations of similar particulate systems specifically in two aspects: 1) Big particles tend to gain positive charge and small particles the negative one. 2) The wider the particle size distribution is, the more pronounced is the charging process. Our results suggest that not only the size distribution, but also the effect of the spatial segregation of the polyethylene particles significantly influence the resulting charge distribution ‘generated’ in the system. The level of particle segregation as well as the particle size distribution of polyethylene particles can be in practice adjusted by the choice of supported catalysts, by the conditions in the fluidized-bed polymerization reactor and by the fluid dynamics. We also attempt to predict how the reactor temperature affects the triboelectric charging of particles. (paper)

Estimation of friction loss under forced flow pulsations in a channel with discrete roughness elements

Science.gov (United States)

Davletshin, I. A.; Dushina, O. A.; Mikheev, N. I.; Kolchin, S. A.

2017-11-01

The pulsating flow in a circular channel with semicircular annular ribs as discrete roughness elements has been studied experimentally. Air flow under atmospheric conditions at the channel inlet has been considered. Steady and pulsating air flow has been studied under different frequencies and amplitudes of forced pulsations generated by periodic blockage of the channel cross section by a rotating flap. Flow resistance in pulsating regimes has been estimated from the average static pressure drop. The resistance values attained twice the steady flow ones.

Systemic characterization and evaluation of particle packings as initial sets for discrete element simulations

Science.gov (United States)

Morfa, Carlos Recarey; Cortés, Lucía Argüelles; Farias, Márcio Muniz de; Morales, Irvin Pablo Pérez; Valera, Roberto Roselló; Oñate, Eugenio

2018-07-01

A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.

Systemic characterization and evaluation of particle packings as initial sets for discrete element simulations

Science.gov (United States)

Morfa, Carlos Recarey; Cortés, Lucía Argüelles; Farias, Márcio Muniz de; Morales, Irvin Pablo Pérez; Valera, Roberto Roselló; Oñate, Eugenio

2017-10-01

A methodology that comprises several characterization properties for particle packings is proposed in this paper. The methodology takes into account factors such as dimension and shape of particles, space occupation, homogeneity, connectivity and isotropy, among others. This classification and integration of several properties allows to carry out a characterization process to systemically evaluate the particle packings in order to guarantee the quality of the initial meshes in discrete element simulations, in both the micro- and the macroscales. Several new properties were created, and improvements in existing ones are presented. Properties from other disciplines were adapted to be used in the evaluation of particle systems. The methodology allows to easily characterize media at the level of the microscale (continuous geometries—steels, rocks microstructures, etc., and discrete geometries) and the macroscale. A global, systemic and integral system for characterizing and evaluating particle sets, based on fuzzy logic, is presented. Such system allows researchers to have a unique evaluation criterion based on the aim of their research. Examples of applications are shown.

Features and validation of discrete element method for simulating pebble flow in reactor core

International Nuclear Information System (INIS)

Xu Yong; Li Yanjie

2005-01-01

The core of a High-Temperature Gas-cooled Reactor (HTGR) is composed of big number of fuel pebbles, their kinetic behaviors are of great importance in estimating the path and residence time of individual pebble, the evolution of the mixing zone for the assessment of the efficiency of a reactor. Numerical method is highlighted in modern reactor design. In view of granular flow, the Discrete Element Model based on contact mechanics of spheres was briefly described. Two typical examples were presented to show the capability of the DEM method. The former is piling with glass/steel spheres, which provides validated evidences that the simulated angles of repose are in good coincidence with the experimental results. The later is particle discharge in a flat- bottomed silo, which shows the effects of material modulus and demonstrates several features. The two examples show the DEM method enables to predict the behaviors, such as the evolution of pebble profiles, streamlines etc., and provides sufficient information for pebble flow analysis and core design. In order to predict the cyclic pebble flow in a HTGR core precisely and efficiently, both model and code improvement are needed, together with rational specification of physical properties with proper measuring techniques. Strategic and methodological considerations were also discussed. (authors)

Modeling commodity salam contract between two parties for discrete and continuous time series

Science.gov (United States)

Hisham, Azie Farhani Badrol; Jaffar, Maheran Mohd

2017-08-01

In order for Islamic finance to remain competitive as the conventional, there needs a new development of Islamic compliance product such as Islamic derivative that can be used to manage the risk. However, under syariah principles and regulations, all financial instruments must not be conflicting with five syariah elements which are riba (interest paid), rishwah (corruption), gharar (uncertainty or unnecessary risk), maysir (speculation or gambling) and jahl (taking advantage of the counterparty's ignorance). This study has proposed a traditional Islamic contract namely salam that can be built as an Islamic derivative product. Although a lot of studies has been done on discussing and proposing the implementation of salam contract as the Islamic product however they are more into qualitative and law issues. Since there is lack of quantitative study of salam contract being developed, this study introduces mathematical models that can value the appropriate salam price for a commodity salam contract between two parties. In modeling the commodity salam contract, this study has modified the existing conventional derivative model and come out with some adjustments to comply with syariah rules and regulations. The cost of carry model has been chosen as the foundation to develop the commodity salam model between two parties for discrete and continuous time series. However, the conventional time value of money results from the concept of interest that is prohibited in Islam. Therefore, this study has adopted the idea of Islamic time value of money which is known as the positive time preference, in modeling the commodity salam contract between two parties for discrete and continuous time series.

Discrete analysis of clay layer tensile strength

International Nuclear Information System (INIS)

Le, T.N.H.; Ple, O.; Villard, P.; Gourc, J.P.

2010-01-01

The Discrete Element Method is used to investigate the tensile behaviour and cracks mechanisms of a clay material submitted to bending loading. It is the case of compacted clay liners in landfill cap cover application. Such as the soil tested in this study is plastic clay, the distinct elements model was calibrated with previous data results by taking into account cohesive properties. Various contact and cohesion laws are tested to show that the numerical model is able to reproduce the failure mechanism. Numerical results are extending to simulate a landfill cap cover and comparing to experimental large scale field bending tests achieved in a real site of storage. (authors)

Discrete Model Reference Adaptive Control System for Automatic Profiling Machine

Directory of Open Access Journals (Sweden)

Peng Song

2012-01-01

Full Text Available Automatic profiling machine is a movement system that has a high degree of parameter variation and high frequency of transient process, and it requires an accurate control in time. In this paper, the discrete model reference adaptive control system of automatic profiling machine is discussed. Firstly, the model of automatic profiling machine is presented according to the parameters of DC motor. Then the design of the discrete model reference adaptive control is proposed, and the control rules are proven. The results of simulation show that adaptive control system has favorable dynamic performances.

Optimization of Operations Resources via Discrete Event Simulation Modeling

Science.gov (United States)

Joshi, B.; Morris, D.; White, N.; Unal, R.

1996-01-01

The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.

Continuous limit of discrete systems with long-range interaction

International Nuclear Information System (INIS)

Tarasov, Vasily E

2006-01-01

Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class

Discrete fracture modelling of the Finnsjoen rock mass. Phase 1: Feasibility study

International Nuclear Information System (INIS)

Geier, J.E.; Axelsson, C.L.

1991-03-01

The geometry and properties of discrete fractures are expected to control local heterogeneity in flow and solute transport within crystalline rock in the Finnsjoen area. The present report describes the first phase of a discrete-fracture modelling study, the goal of which is to develop stochastic-continuum and hydrologic properties. In the first phase of this study, the FracMan discrete fracture modelling package was used to analyse discrete fracture geometrical and hyrological data. Constant-pressure packer tests were analysed using fractional dimensional methods to estimate effective transmissivities and flow dimension for the packer test intervals. Discrete fracture data on orientation, size, shape, and location were combined with hydrologic data to develop a preliminary conceptual model for the conductive fractures at the site. The variability of fracture properties was expressed in the model by probability distributions. The preliminary conceptual model was used to simulate three-dimensional populations of conductive fractures in 25 m and 50 m cubes of rock. Transient packer tests were simulated in these fracture populations, and the simulated results were used to validate the preliminary conceptual model. The calibrated model was used to estimate the components of effective conductivity tensors for the rock by simulating steady-state groundwater flow through the cubes in three orthogonal directions. Monte Carlo stochastic simulations were performed for alternative realizations of the conceptual model. The number of simulations was insufficient to give a quantitative prediction of the effective conductivity heterogeneity and anisotropy on the scales of the cubes. However, the results give preliminary, rough estimates of these properties, and provide a demonstration of how the discrete-fracture network concept can be applied to derive data that is necessary for stochastic continuum and channel network modelling. (authors)

Finite element modeling of tornado missile impact on reinforced concrete wall panels

International Nuclear Information System (INIS)

Zhang, Y.; Vallabhan, C.V.G.; McDonald, J.R.

1993-01-01

This paper describes a finite element model for the impact of large tornado-generated missiles with reinforced concrete wall panels. The analysis predicts the dynamic response of a wall panel when impacted by a missile with a large contact area such as an automobile. Quadratic finite elements are used to discretize the domain of the wall panel. Fundamental assumptions are based on the Mindlin and the related Reinsser plate theories. An 'embedded' model is employed to account for the reinforcing bars. The nonlinear behavior of concrete and steel bars are analyzed by means of time-dependent constitutive relationships. A model is proposed to describe the initial and subsequent yield surfaces of concrete material, which avoids underestimation of the effect of high hydrostatic stresses on the yielding behavior of concrete. Ottosen's four-parameter failure criterion is used to define the failure surface of concrete. A crack monitoring algorithm accounts for post-cracking and post-crushing behavior of concrete. Explicit time step integration of nonlinear dynamic equations are carried out using the finite element discretization of a concrete wall panel. As a practical application of the analysis technique, the contact failure pressure for a particular panel geometry can be calculated. The contact failure pressure and the elapsed time to failure after missile contact define a rectangular or triangular impulse loading to produce failure of the panel. Since automobile crashes are known to produce triangular impulse loads, the two pulses (failure and impact) can be compared to determine if a particular impact will fail the panels. Thus, a particular concrete panel can be analyzed to determine if it will fail under a postulated missile impact

Application of network methods for understanding evolutionary dynamics in discrete habitats.

Science.gov (United States)

Greenbaum, Gili; Fefferman, Nina H

2017-06-01

In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.

Modeling discrete competitive facility location

CERN Document Server

Karakitsiou, Athanasia

2015-01-01

This book presents an up-to-date review of modeling and optimization approaches for location problems along with a new bi-level programming methodology which captures the effect of competition of both producers and customers on facility location decisions. While many optimization approaches simplify location problems by assuming decision making in isolation, this monograph focuses on models which take into account the competitive environment in which such decisions are made. New insights in modeling, algorithmic and theoretical possibilities are opened by this approach and new applications are possible. Competition on equal term plus competition between market leader and followers are considered in this study, consequently bi-level optimization methodology is emphasized and further developed. This book provides insights regarding modeling complexity and algorithmic approaches to discrete competitive location problems. In traditional location modeling, assignment of customer demands to supply sources are made ...

On the relationship of steady states of continuous and discrete models arising from biology.

Science.gov (United States)

Veliz-Cuba, Alan; Arthur, Joseph; Hochstetler, Laura; Klomps, Victoria; Korpi, Erikka

2012-12-01

For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

Science.gov (United States)

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

Directory of Open Access Journals (Sweden)

Zhenhua Hu

2013-01-01

Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

A Discrete Model for Color Naming

Directory of Open Access Journals (Sweden)

J. M. Boi

2007-01-01

Full Text Available The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1. Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2, and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.

A fast iterative model for discrete velocity calculations on triangular grids

International Nuclear Information System (INIS)

Szalmas, Lajos; Valougeorgis, Dimitris

2010-01-01

A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime.

Discrete gradient methods for solving variational image regularisation models

International Nuclear Information System (INIS)

Grimm, V; McLachlan, Robert I; McLaren, David I; Quispel, G R W; Schönlieb, C-B

2017-01-01

Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting. (paper)

Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.

Science.gov (United States)

van den Driessche, P; Yakubu, Abdul-Aziz

2018-04-12

We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].

Discretization model for nonlinear dynamic analysis of three dimensional structures

International Nuclear Information System (INIS)

Hayashi, Y.

1982-12-01

A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt

Investigation of discrete-fracture network conceptual model uncertainty at Forsmark

International Nuclear Information System (INIS)

Geier, Joel

2011-04-01

In the present work a discrete fracture model has been further developed and implemented using the latest SKB site investigation data. The model can be used for analysing the fracture network and to model flow through the rock in Forsmark. The aim has been to study uncertainties in the hydrological discrete fracture network (DFN) for the repository model. More specifically the objective has been to study to which extent available data limits uncertainties in the DFN model and how data that can be obtained in future underground work can further limit these uncertainties. Moreover, the effects on deposition hole utilisation and placement have been investigated as well as the effects on the flow to deposition holes

Efficiency determination of an electrostatic lunar dust collector by discrete element method

Science.gov (United States)

Afshar-Mohajer, Nima; Wu, Chang-Yu; Sorloaica-Hickman, Nicoleta

2012-07-01

Lunar grains become charged by the sun's radiation in the tenuous atmosphere of the moon. This leads to lunar dust levitation and particle deposition which often create serious problems in the costly system deployed in lunar exploration. In this study, an electrostatic lunar dust collector (ELDC) is proposed to address the issue and the discrete element method (DEM) is used to investigate the effects of electrical particle-particle interactions, non-uniformity of the electrostatic field, and characteristics of the ELDC. The simulations on 20-μm-sized lunar particles reveal the electrical particle-particle interactions of the dust particles within the ELDC plates require 29% higher electrostatic field strength than that without the interactions for 100% collection efficiency. For the given ELDC geometry, consideration of non-uniformity of the electrostatic field along with electrical interactions between particles on the same ELDC geometry leads to a higher requirement of ˜3.5 kV/m to ensure 100% particle collection. Notably, such an electrostatic field is about 103 times less than required for electrodynamic self-cleaning methods. Finally, it is shown for a "half-size" system that the DEM model predicts greater collection efficiency than the Eulerian-based model at all voltages less than required for 100% efficiency. Halving the ELDC dimensions boosts the particle concentration inside the ELDC, as well as the resulting field strength for a given voltage. Though a lunar photovoltaic system was the subject, the results of this study are useful for evaluation of any system for collecting charged particles in other high vacuum environment using an electrostatic field.

From discrete-time models to continuous-time, asynchronous modeling of financial markets

NARCIS (Netherlands)

Boer, Katalin; Kaymak, Uzay; Spiering, Jaap

2007-01-01

Most agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modeling of financial markets. We study the behavior of a learning market maker in a market with information

From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets

NARCIS (Netherlands)

K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)

2006-01-01

textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with

Integrable discretizations for the short-wave model of the Camassa-Holm equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

Science.gov (United States)

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

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

Dynamic mortar finite element method for modeling of shear rupture on frictional rough surfaces

Science.gov (United States)

Tal, Yuval; Hager, Bradford H.

2017-09-01

This paper presents a mortar-based finite element formulation for modeling the dynamics of shear rupture on rough interfaces governed by slip-weakening and rate and state (RS) friction laws, focusing on the dynamics of earthquakes. The method utilizes the dual Lagrange multipliers and the primal-dual active set strategy concepts, together with a consistent discretization and linearization of the contact forces and constraints, and the friction laws to obtain a semi-smooth Newton method. The discretization of the RS friction law involves a procedure to condense out the state variables, thus eliminating the addition of another set of unknowns into the system. Several numerical examples of shear rupture on frictional rough interfaces demonstrate the efficiency of the method and examine the effects of the different time discretization schemes on the convergence, energy conservation, and the time evolution of shear traction and slip rate.

Discrete Discriminant analysis based on tree-structured graphical models

DEFF Research Database (Denmark)

Perez de la Cruz, Gonzalo; Eslava, Guillermina

The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant a...... analysis based on tree{structured graphical models is a simple nonlinear method competitive with, and sometimes superior to, other well{known linear methods like those assuming mutual independence between variables and linear logistic regression.......The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant...

Powering stochastic reliability models by discrete event simulation

DEFF Research Database (Denmark)

Kozine, Igor; Wang, Xiaoyun

2012-01-01

it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...

Anyons in discrete gauge theories with Chern-Simons terms

International Nuclear Information System (INIS)

Bais, F.A.; Driel, P. van; Wild Propitius, M. de

1993-01-01

A gauge theory with a discrete group H in (2+1)-dimensional space-time is known to describe (non-abelian) anyons. We study the effect of adding a Chern-Simons term to such a theory. As in a previous paper, we emphasize the algebraic structure underlying a discrete H gauge theory, namely the Hopf algebra D(H). For H≅Z N , we argue on physical grounds that a Chern-Simons term in the action leads to a non-trivial 3-cocycle on D(H). Accordingly, the physically inequivalent models are labeled by the elements of the cohomology group H 3 (H, U(1)). It depends periodically on the coefficient of the Chern-Simons term which model is realized. This establishes a relation with the discrete topological field theories of Dijkgraaf and Witten. We extrapolate these results to non-abelian H, and work out the representative example H≅anti D 2 . (orig.)

Mechanics of a crushable pebble assembly using discrete element method

International Nuclear Information System (INIS)

Annabattula, R.K.; Gan, Y.; Zhao, S.; Kamlah, M.

2012-01-01

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 (ε 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 (η) of the assembly.

Collective Robotic Assembly of Discrete Lattice Elements (CRADLE)

Data.gov (United States)

National Aeronautics and Space Administration — CRADLE seeks to address this need through a novel application of an integrated robot-structure-material system based on discrete lattice construction using task...

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

Science.gov (United States)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

3D airborne EM modeling based on the spectral-element time-domain (SETD) method

Science.gov (United States)

Cao, X.; Yin, C.; Huang, X.; Liu, Y.; Zhang, B., Sr.; Cai, J.; Liu, L.

2017-12-01

In the field of 3D airborne electromagnetic (AEM) modeling, both finite-difference time-domain (FDTD) method and finite-element time-domain (FETD) method have limitations that FDTD method depends too much on the grids and time steps, while FETD requires large number of grids for complex structures. We propose a time-domain spectral-element (SETD) method based on GLL interpolation basis functions for spatial discretization and Backward Euler (BE) technique for time discretization. The spectral-element method is based on a weighted residual technique with polynomials as vector basis functions. It can contribute to an accurate result by increasing the order of polynomials and suppressing spurious solution. BE method is a stable tine discretization technique that has no limitation on time steps and can guarantee a higher accuracy during the iteration process. To minimize the non-zero number of sparse matrix and obtain a diagonal mass matrix, we apply the reduced order integral technique. A direct solver with its speed independent of the condition number is adopted for quickly solving the large-scale sparse linear equations system. To check the accuracy of our SETD algorithm, we compare our results with semi-analytical solutions for a three-layered earth model within the time lapse 10-6-10-2s for different physical meshes and SE orders. The results show that the relative errors for magnetic field B and magnetic induction are both around 3-5%. Further we calculate AEM responses for an AEM system over a 3D earth model in Figure 1. From numerical experiments for both 1D and 3D model, we draw the conclusions that: 1) SETD can deliver an accurate results for both dB/dt and B; 2) increasing SE order improves the modeling accuracy for early to middle time channels when the EM field diffuses fast so the high-order SE can model the detailed variation; 3) at very late time channels, increasing SE order has little improvement on modeling accuracy, but the time interval plays

Final Report for DOE grant DE-FG02-07ER64432 "New Grid and Discretization Technologies for Ocean and Ice Simulations"

Energy Technology Data Exchange (ETDEWEB)

Gunzburger, Max

2013-03-12

The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

Convergence of discrete Aubry–Mather model in the continuous limit

Science.gov (United States)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

A discrete element method study on the evolution of thermomechanics of a pebble bed experiencing pebble failure

Energy Technology Data Exchange (ETDEWEB)

Van Lew, Jon T., E-mail: jtvanlew@fusion.ucla.edu; Ying, Alice; Abdou, Mohamed

2014-10-15

The discrete element method (DEM) is used to study the thermal effects of pebble failure in an ensemble of lithium ceramic spheres. Some pebbles crushing in a large system is unavoidable and this study provides correlations between the extent of pebble failure and the reduction in effective thermal conductivity of the bed. In the model, we homogeneously induced failure and applied nuclear heating until dynamic and thermal steady-state. Conduction between pebbles and from pebbles to the boundary is the only mode of heat transfer presently modeled. The effective thermal conductivity was found to decrease rapidly as a function of the percent of failed pebbles in the bed. It was found that the dominant contributor to the reduction was the drop in inter-particle forces as pebbles fail; implying the extent of failure induced may not occur in real pebble beds. The results are meant to assist designers in the fusion energy community who are planning to use packed beds of ceramic pebbles. The evolution away from experimentally measured thermomechanical properties as pebbles fail is necessary for proper operation of fusion reactors.

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

1995-01-01

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....

A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil

Science.gov (United States)

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.

Discrete port-Hamiltonian systems

NARCIS (Netherlands)

Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

2006-01-01

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

A finite element model for the quench front evolution problem

International Nuclear Information System (INIS)

Folescu, J.; Galeao, A.C.N.R.; Carmo, E.G.D. do.

1985-01-01

A model for the rewetting problem associated with the loss of coolant accident in a PWR reactor is proposed. A variational formulation for the time-dependent heat conduction problem on fuel rod cladding is used, and appropriate boundary conditions are assumed in order to simulate the thermal interaction between the fuel rod cladding and the fluid. A numerical procedure which uses the finite element method for the spatial discretization and a Crank-Nicolson-like method for the step-by-step integration is developed. Some numerical results are presented showing the quench front evolution and its stationary profile. (Author) [pt

Discrete Element Modeling of the Mobilization of Coarse Gravel Beds by Finer Gravel Particles

Science.gov (United States)

Hill, K. M.; Tan, D.

2012-12-01

Recent research has shown that the addition of fine gravel particles to a coarse bed will mobilize the coarser bed, and that the effect is sufficiently strong that a pulse of fine gravel particles can mobilize an impacted coarser bed. Recent flume experiments have demonstrated that the degree of bed mobilization by finer particles is primarily dependent on the particle size ratio of the coarse and fine particles, rather than absolute size of either particle, provided both particles are sufficiently large. However, the mechanism behind the mobilization is not understood. It has previously been proposed that the mechanism is driven by a combination of geometric effects and hydraulic effects. For example, it has been argued that smaller particles fill in gaps along the bed, resulting in a smoother bed over which the larger particles are less likely to be disentrained and a reduced near-bed flow velocity and subsequent increased drag on protruding particles. Altered near-bed turbulence has also been cited as playing an important role. We perform simulations using the discrete element method with one-way fluid-solid coupling to conduct simulations of mobilization of a gravel bed by fine gravel particles. By independently and artificially controlling average and fluctuating velocity profiles, we systematically investigate the relative role that may be played by particle-particle interactions, average near-bed velocity profiles, and near-bed turbulence statistics. The simulations indicate that the relative importance of these mechanisms changes with the degree of mobilization of the bed. For higher bed mobility similar to bed sheets, particle-particle interactions, plays a significant role in an apparent rheology in the bed sheets, not unlike that observed in a dense granular flow of particles of different sizes. For conditions closer to a critical shear stress for bedload transport, the near-bed velocity profiles and turbulence statistics become increasingly important.

Three-dimensional discrete element method simulation of core disking

Science.gov (United States)

Wu, Shunchuan; Wu, Haoyan; Kemeny, John

2018-04-01

The phenomenon of core disking is commonly seen in deep drilling of highly stressed regions in the Earth's crust. Given its close relationship with the in situ stress state, the presence and features of core disking can be used to interpret the stresses when traditional in situ stress measuring techniques are not available. The core disking process was simulated in this paper using the three-dimensional discrete element method software PFC3D (particle flow code). In particular, PFC3D is used to examine the evolution of fracture initiation, propagation and coalescence associated with core disking under various stress states. In this paper, four unresolved problems concerning core disking are investigated with a series of numerical simulations. These simulations also provide some verification of existing results by other researchers: (1) Core disking occurs when the maximum principal stress is about 6.5 times the tensile strength. (2) For most stress situations, core disking occurs from the outer surface, except for the thrust faulting stress regime, where the fractures were found to initiate from the inner part. (3) The anisotropy of the two horizontal principal stresses has an effect on the core disking morphology. (4) The thickness of core disk has a positive relationship with radial stress and a negative relationship with axial stresses.

Analysis of a block Gauss-Seidel iterative method for a finite element discretization of the neutron transport equation

International Nuclear Information System (INIS)

Lorence, L.J. Jr.; Martin, W.R.; Luskin, M.

1985-01-01

We prove the convergence of a finite element discretization of the neutron transport equation. The iterative solution of the resulting linear system by a block Gauss-Seidel method is also analyzed. This procedure is shown to require less storage than the direct solution by Gaussian elimination, and an estimate for the rate of convergence is used to show that fewer arithmetic operations are required

On a discrete version of the CP 1 sigma model and surfaces immersed in R3

International Nuclear Information System (INIS)

Grundland, A M; Levi, D; Martina, L

2003-01-01

We present a discretization of the CP 1 sigma model. We show that the discrete CP 1 sigma model is described by a nonlinear partial second-order difference equation with rational nonlinearity. To derive discrete surfaces immersed in three-dimensional Euclidean space a 'complex' lattice is introduced. The so-obtained surfaces are characterized in terms of the quadrilateral cross-ratio of four surface points. In this way we prove that all surfaces associated with the discrete CP 1 sigma model are of constant mean curvature. An explicit example of such discrete surfaces is constructed

Discrete Event Simulation Model of the Polaris 2.1 Gamma Ray Imaging Radiation Detection Device

Science.gov (United States)

2016-06-01

release; distribution is unlimited DISCRETE EVENT SIMULATION MODEL OF THE POLARIS 2.1 GAMMA RAY IMAGING RADIATION DETECTION DEVICE by Andres T...ONLY (Leave blank) 2. REPORT DATE June 2016 3. REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE DISCRETE EVENT SIMULATION MODEL...modeled. The platform, Simkit, was utilized to create a discrete event simulation (DES) model of the Polaris. After carefully constructing the DES

SR 97 - Alternative models project. Discrete fracture network modelling for performance assessment of Aberg

International Nuclear Information System (INIS)

Dershowitz, B.; Eiben, T.; Follin, S.; Andersson, Johan

1999-08-01

As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL -1 ]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT -1 ]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and statistical

SR 97 - Alternative models project. Discrete fracture network modelling for performance assessment of Aberg

Energy Technology Data Exchange (ETDEWEB)

Dershowitz, B.; Eiben, T. [Golder Associates Inc., Seattle (United States); Follin, S.; Andersson, Johan [Golder Grundteknik KB, Stockholm (Sweden)

1999-08-01

As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL{sup -1}]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT{sup -1}]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and

Integrating Continuous-Time and Discrete-Event Concepts in Process Modelling, Simulation and Control

NARCIS (Netherlands)

Beek, van D.A.; Gordijn, S.H.F.; Rooda, J.E.; Ertas, A.

1995-01-01

Currently, modelling of systems in the process industry requires the use of different specification languages for the specification of the discrete-event and continuous-time subsystems. In this way, models are restricted to individual subsystems of either a continuous-time or discrete-event nature.

Stable cycling in discrete-time genetic models.

OpenAIRE

Hastings, A

1981-01-01

Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.

Stable cycling in discrete-time genetic models.

Science.gov (United States)

Hastings, A

1981-11-01

Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.

Finite Element Based Lagrangian Vortex Dynamics Model for Wind Turbine Aerodynamics

International Nuclear Information System (INIS)

McWilliam, Michael K; Crawford, Curran

2014-01-01

This paper presents a novel aerodynamic model based on Lagrangian Vortex Dynamics (LVD) formulated using a Finite Element (FE) approach. The advantage of LVD is improved fidelity over Blade Element Momentum Theory (BEMT) while being faster than Numerical Navier-Stokes Models (NNSM) in either primitive or velocity-vorticity formulations. The model improves on conventional LVD in three ways. First, the model is based on an error minimization formulation that can be solved with fast root finding algorithms. In addition to improving accuracy, this eliminates the intrinsic numerical instability of conventional relaxed wake simulations. The method has further advantages in optimization and aero-elastic simulations for two reasons. The root finding algorithm can solve the aerodynamic and structural equations simultaneously, avoiding Gauss-Seidel iteration for compatibility constraints. The second is that the formulation allows for an analytical definition for sensitivity calculations. The second improvement comes from a new discretization scheme based on an FE formulation and numerical quadrature that decouples the spatial, influencing and temporal meshes. The shape for each trailing filament uses basis functions (interpolating splines) that allow for both local polynomial order and element size refinement. A completely independent scheme distributes the influencing (vorticity) elements along the basis functions. This allows for concentrated elements in the near wake for accuracy and progressively less in the far-wake for efficiency. Finally the third improvement is the use of a far-wake model based on semi-infinite vortex cylinders where the radius and strength are related to the wake state. The error-based FE formulation allows the transition to the far wake to occur across a fixed plane

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities

Science.gov (United States)

Bauer, Daniel J.; Curran, Patrick J.

2004-01-01

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model,…

Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method

KAUST Repository

Efendiev, Yalchin R.

2015-06-05

In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.

Understanding the discrete element method simulation of non-spherical particles for granular and multi-body systems

CERN Document Server

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

Discrete Model for the Structure and Strength of Cementitious Materials

Science.gov (United States)

Balopoulos, Victor D.; Archontas, Nikolaos; Pantazopoulou, Stavroula J.

2017-12-01

Cementitious materials are characterized by brittle behavior in direct tension and by transverse dilatation (due to microcracking) under compression. Microcracking causes increasingly larger transverse strains and a phenomenological Poisson's ratio that gradually increases to about ν =0.5 and beyond, at the limit point in compression. This behavior is due to the underlying structure of cementitious pastes which is simulated here with a discrete physical model. The computational model is generic, assembled from a statistically generated, continuous network of flaky dendrites consisting of cement hydrates that emanate from partially hydrated cement grains. In the actual amorphous material, the dendrites constitute the solid phase of the cement gel and interconnect to provide the strength and stiffness against load. The idealized dendrite solid is loaded in compression and tension to compute values for strength and Poisson's effects. Parametric studies are conducted, to calibrate the statistical parameters of the discrete model with the physical and mechanical characteristics of the material, so that the familiar experimental trends may be reproduced. The model provides a framework for the study of the mechanical behavior of the material under various states of stress and strain and can be used to model the effects of additives (e.g., fibers) that may be explicitly simulated in the discrete structure.

A Model Stitching Architecture for Continuous Full Flight-Envelope Simulation of Fixed-Wing Aircraft and Rotorcraft from Discrete Point Linear Models

Science.gov (United States)

2016-04-01

AND ROTORCRAFT FROM DISCRETE -POINT LINEAR MODELS Eric L. Tobias and Mark B. Tischler Aviation Development Directorate Aviation and Missile...Stitching Architecture for Continuous Full Flight-Envelope Simulation of Fixed-Wing Aircraft and Rotorcraft from Discrete -Point Linear Models 5...of discrete -point linear models and trim data. The model stitching simulation architecture is applicable to any aircraft configuration readily

Dynamics of breathers in discrete nonlinear Schrodinger models

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge

1998-01-01

We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...

Exact solutions for some discrete models of the Boltzmann equation

International Nuclear Information System (INIS)

Cabannes, H.; Hong Tiem, D.

1987-01-01

For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models [fr

Element Verification and Comparison in Sierra/Solid Mechanics Problems

Energy Technology Data Exchange (ETDEWEB)

Ohashi, Yuki; Roth, William

2016-05-01

The goal of this project was to study the effects of element selection on the Sierra/SM solutions to five common solid mechanics problems. A total of nine element formulations were used for each problem. The models were run multiple times with varying spatial and temporal discretization in order to ensure convergence. The first four problems have been compared to analytical solutions, and all numerical results were found to be sufficiently accurate. The penetration problem was found to have a high mesh dependence in terms of element type, mesh discretization, and meshing scheme. Also, the time to solution is shown for each problem in order to facilitate element selection when computer resources are limited.

An embedded crack in a constant strain triangle utilizing extended finite element concepts

DEFF Research Database (Denmark)

Olesen, J.F.; Poulsen, P.N.

2013-01-01

This paper revisits the formulation of the CST element with an embedded discrete crack taking advantage of the direct formulations developed within the framework of the extended finite element method, XFEM. The result is a simple element for modeling cohesive fracture processes in quasi-brittle m......This paper revisits the formulation of the CST element with an embedded discrete crack taking advantage of the direct formulations developed within the framework of the extended finite element method, XFEM. The result is a simple element for modeling cohesive fracture processes in quasi......-element discontinuity of displacements. The formulation is based on a variational principle of virtual work involving only the interpolation of displacements. The good performance of the element is demonstrated through the comparison with three benchmark tests in which a single crack is propagated: The center cracked...

Use of Structure-from-Motion Photogrammetry Technique to model Danxia red bed landform slope stability by discrete element modeling - case study at Mt. Langshan, Hunan Province, China

Science.gov (United States)

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-time modelling of musical instruments

International Nuclear Information System (INIS)

Vaelimaeki, Vesa; Pakarinen, Jyri; Erkut, Cumhur; Karjalainen, Matti

2006-01-01

This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass-spring, modal, wave digital, finite difference, digital waveguide and source-filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed

Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

Science.gov (United States)

Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

2018-06-01

We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

Optimization and Openmp Parallelization of a Discrete Element Code for Convex Polyhedra on Multi-Core Machines

Science.gov (United States)

Chen, Jian; Matuttis, Hans-Georg

2013-02-01

We report our experiences with the optimization and parallelization of a discrete element code for convex polyhedra on multi-core machines and introduce a novel variant of the sort-and-sweep neighborhood algorithm. While in theory the whole code in itself parallelizes ideally, in practice the results on different architectures with different compilers and performance measurement tools depend very much on the particle number and optimization of the code. After difficulties with the interpretation of the data for speedup and efficiency are overcome, respectable parallelization speedups could be obtained.

Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

Science.gov (United States)

Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.

2014-05-01

We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

International Nuclear Information System (INIS)

Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.

2014-01-01

We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature

Discrete mathematics in the high school curriculum

NARCIS (Netherlands)

Anderson, I.; Asch, van A.G.; van Lint, J.H.

2004-01-01

In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various

Low Reynolds number steady state flow through a branching network of rigid vessels: II. A finite element mixture model

NARCIS (Netherlands)

Huyghe, J.M.R.J.; Oomens, C.W.J.; Campen, van D.H.; Heethaar, R.M.

1989-01-01

This research aims at formulating and verifying a finite element mixture formulation for blood perfusion. The equations derived in a companion paper [3] are discretized according to the Galerkin method. A flow experiment in a rigid model of a vascular tree of about 500 vessels is performed in order

HIGHLY-ACCURATE MODEL ORDER REDUCTION TECHNIQUE ON A DISCRETE DOMAIN

Directory of Open Access Journals (Sweden)

L. D. Ribeiro

2015-09-01

Full Text Available AbstractIn this work, we present a highly-accurate technique of model order reduction applied to staged processes. The proposed method reduces the dimension of the original system based on null values of moment-weighted sums of heat and mass balance residuals on real stages. To compute these sums of weighted residuals, a discrete form of Gauss-Lobatto quadrature was developed, allowing a high degree of accuracy in these calculations. The locations where the residuals are cancelled vary with time and operating conditions, characterizing a desirable adaptive nature of this technique. Balances related to upstream and downstream devices (such as condenser, reboiler, and feed tray of a distillation column are considered as boundary conditions of the corresponding difference-differential equations system. The chosen number of moments is the dimension of the reduced model being much lower than the dimension of the complete model and does not depend on the size of the original model. Scaling of the discrete independent variable related with the stages was crucial for the computational implementation of the proposed method, avoiding accumulation of round-off errors present even in low-degree polynomial approximations in the original discrete variable. Dynamical simulations of distillation columns were carried out to check the performance of the proposed model order reduction technique. The obtained results show the superiority of the proposed procedure in comparison with the orthogonal collocation method.

Multicomponent mass transport model: theory and numerical implementation (discrete-parcel-random-walk version)

International Nuclear Information System (INIS)

Ahlstrom, S.W.; Foote, H.P.; Arnett, R.C.; Cole, C.R.; Serne, R.J.

1977-05-01

The Multicomponent Mass Transfer (MMT) Model is a generic computer code, currently in its third generation, that was developed to predict the movement of radiocontaminants in the saturated and unsaturated sediments of the Hanford Site. This model was designed to use the water movement patterns produced by the unsaturated and saturated flow models coupled with dispersion and soil-waste reaction submodels to predict contaminant transport. This report documents the theorical foundation and the numerical solution procedure of the current (third) generation of the MMT Model. The present model simulates mass transport processes using an analog referred to as the Discrete-Parcel-Random-Walk (DPRW) algorithm. The basic concepts of this solution technique are described and the advantages and disadvantages of the DPRW scheme are discussed in relation to more conventional numerical techniques such as the finite-difference and finite-element methods. Verification of the numerical algorithm is demonstrated by comparing model results with known closed-form solutions. A brief error and sensitivity analysis of the algorithm with respect to numerical parameters is also presented. A simulation of the tritium plume beneath the Hanford Site is included to illustrate the use of the model in a typical application. 32 figs

Modelling a reliability system governed by discrete phase-type distributions

International Nuclear Information System (INIS)

Ruiz-Castro, Juan Eloy; Perez-Ocon, Rafael; Fernandez-Villodre, Gemma

2008-01-01

We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab

Modelling a reliability system governed by discrete phase-type distributions

Energy Technology Data Exchange (ETDEWEB)

Ruiz-Castro, Juan Eloy [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)], E-mail: jeloy@ugr.es; Perez-Ocon, Rafael [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)], E-mail: rperezo@ugr.es; Fernandez-Villodre, Gemma [Departamento de Estadistica e Investigacion Operativa, Universidad de Granada, 18071 Granada (Spain)

2008-11-15

We present an n-system with one online unit and the others in cold standby. There is a repairman. When the online fails it goes to repair, and instantaneously a standby unit becomes the online one. The operational and repair times follow discrete phase-type distributions. Given that any discrete distribution defined on the positive integers is a discrete phase-type distribution, the system can be considered a general one. A model with unlimited number of units is considered for approximating a system with a great number of units. We show that the process that governs the system is a quasi-birth-and-death process. For this system, performance reliability measures; the up and down periods, and the involved costs are calculated in a matrix and algorithmic form. We show that the discrete case is not a trivial case of the continuous one. The results given in this paper have been implemented computationally with Matlab.

Nonparametric volatility density estimation for discrete time models

NARCIS (Netherlands)

Es, van Bert; Spreij, P.J.C.; Zanten, van J.H.

2005-01-01

We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared process is proposed

Discrete element method (DEM) simulations of stratified sampling during solid dosage form manufacturing.

Science.gov (United States)

Hancock, Bruno C; Ketterhagen, William R

2011-10-14

Discrete element model (DEM) simulations of the discharge of powders from hoppers under gravity were analyzed to provide estimates of dosage form content uniformity during the manufacture of solid dosage forms (tablets and capsules). For a system that exhibits moderate segregation the effects of sample size, number, and location within the batch were determined. The various sampling approaches were compared to current best-practices for sampling described in the Product Quality Research Institute (PQRI) Blend Uniformity Working Group (BUWG) guidelines. Sampling uniformly across the discharge process gave the most accurate results with respect to identifying segregation trends. Sigmoidal sampling (as recommended in the PQRI BUWG guidelines) tended to overestimate potential segregation issues, whereas truncated sampling (common in industrial practice) tended to underestimate them. The size of the sample had a major effect on the absolute potency RSD. The number of sampling locations (10 vs. 20) had very little effect on the trends in the data, and the number of samples analyzed at each location (1 vs. 3 vs. 7) had only a small effect for the sampling conditions examined. The results of this work provide greater understanding of the effect of different sampling approaches on the measured content uniformity of real dosage forms, and can help to guide the choice of appropriate sampling protocols. Copyright © 2011 Elsevier B.V. All rights reserved.

A flat triangular shell element with Loof nodes

DEFF Research Database (Denmark)

Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat...... triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiences are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal...

Discrete Analysis of Damage and Shear Banding in Argillaceous Rocks

Science.gov (United States)

Dinç, Özge; Scholtès, Luc

2018-05-01

A discrete approach is proposed to study damage and failure processes taking place in argillaceous rocks which present a transversely isotropic behavior. More precisely, a dedicated discrete element method is utilized to provide a micromechanical description of the mechanisms involved. The purpose of the study is twofold: (1) presenting a three-dimensional discrete element model able to simulate the anisotropic macro-mechanical behavior of the Callovo-Oxfordian claystone as a particular case of argillaceous rocks; (2) studying how progressive failure develops in such material. Material anisotropy is explicitly taken into account in the numerical model through the introduction of weakness planes distributed at the interparticle scale following predefined orientation and intensity. Simulations of compression tests under plane-strain and triaxial conditions are performed to clarify the development of damage and the appearance of shear bands through micromechanical analyses. The overall mechanical behavior and shear banding patterns predicted by the numerical model are in good agreement with respect to experimental observations. Both tensile and shear microcracks emerging from the modeling also present characteristics compatible with microstructural observations. The numerical results confirm that the global failure of argillaceous rocks is well correlated with the mechanisms taking place at the local scale. Specifically, strain localization is shown to directly result from shear microcracking developing with a preferential orientation distribution related to the orientation of the shear band. In addition, localization events presenting characteristics similar to shear bands are observed from the early stages of the loading and might thus be considered as precursors of strain localization.

Discrete Symmetries and Models of Flavour Mixing

International Nuclear Information System (INIS)

King, Stephen F

2015-01-01

In this talk we shall give an overview of the role of discrete symmetries, including both CP and family symmetry, in constructing unified models of quark and lepton (including especially neutrino) masses and mixing. Various different approaches to model building will be described, denoted as direct, semi-direct and indirect, and the pros and cons of each approach discussed. Particular examples based on Δ(6n 2 ) will be discussed and an A to Z of Flavour with Pati-Salam will be presented. (paper)

Network Science Research Laboratory (NSRL) Discrete Event Toolkit

Science.gov (United States)

2016-01-01

ARL-TR-7579 ● JAN 2016 US Army Research Laboratory Network Science Research Laboratory (NSRL) Discrete Event Toolkit by...Laboratory (NSRL) Discrete Event Toolkit by Theron Trout and Andrew J Toth Computational and Information Sciences Directorate, ARL...Research Laboratory (NSRL) Discrete Event Toolkit 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Theron Trout

Structure of the discrete Dirac vacuum in the sigma + omega model

International Nuclear Information System (INIS)

Miller, L.D.

1989-01-01

The sigma + omega model potentials imply that any moderate to large nucleus should have thousands of discrete negative-energy nucleon states. Theoretical predictions of structure in this discrete island of the nuclear Dirac sea are presented in this paper. This structure is related to the spectral functions that will emerge in high energy electron- and hardon-induced reactions on nuclei. These high-energy reaction studies should supplement our understanding of the saturation mechanism of the sigma + omega model. They could also identify the threshold for observable quantum chromo-dynamics (QCD) effects in nuclei

Investigation into macroscopic and microscopic behaviors of wet granular soils using discrete element method and X-ray computed tomography

Science.gov (United States)

Than, Vinh-Du; Tang, Anh-Minh; Roux, Jean-Noël; Pereira, Jean-Michel; Aimedieu, Patrick; Bornert, Michel

2017-06-01

We present an investigation into macroscopic and microscopic behaviors of wet granular soils using the discrete element method (DEM) and the X-ray Computed Tomography (XRCT) observations. The specimens are first prepared in very loose states, with frictional spherical grains in the presence of a small amount of an interstitial liquid. Experimental oedometric tests are carried out with small glass beads, while DEM simulations implement a model of spherical grains joined by menisci. Both in experiments and in simulations, loose configurations with solid fraction as low as 0.30 are prepared under low stress, and undergo a gradual collapse in compression, until the solid fraction of cohesionless bead packs (0.58 to 0.6) is obtained. In the XRCT tests, four 3D tomography images corresponding to different typical stages of the compression curve are used to characterize the microstructure.

Simulating subduction zone earthquakes using discrete element method: a window into elusive source processes

Science.gov (United States)

Blank, D. G.; Morgan, J.

2017-12-01

Large earthquakes that occur on convergent plate margin interfaces have the potential to cause widespread damage and loss of life. Recent observations reveal that a wide range of different slip behaviors take place along these megathrust faults, which demonstrate both their complexity, and our limited understanding of fault processes and their controls. Numerical modeling provides us with a useful tool that we can use to simulate earthquakes and related slip events, and to make direct observations and correlations among properties and parameters that might control them. Further analysis of these phenomena can lead to a more complete understanding of the underlying mechanisms that accompany the nucleation of large earthquakes, and what might trigger them. In this study, we use the discrete element method (DEM) to create numerical analogs to subduction megathrusts with heterogeneous fault friction. Displacement boundary conditions are applied in order to simulate tectonic loading, which in turn, induces slip along the fault. A wide range of slip behaviors are observed, ranging from creep to stick slip. We are able to characterize slip events by duration, stress drop, rupture area, and slip magnitude, and to correlate the relationships among these quantities. These characterizations allow us to develop a catalog of rupture events both spatially and temporally, for comparison with slip processes on natural faults.

Discrete element simulation of charging and mixed layer formation in the ironmaking blast furnace

Science.gov (United States)

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.

Customized Finite Element Modelling of the Human Cornea.

Directory of Open Access Journals (Sweden)

Irene Simonini

Full Text Available To construct patient-specific solid models of human cornea from ocular topographer data, to increase the accuracy of the biomechanical and optical estimate of the changes in refractive power and stress caused by photorefractive keratectomy (PRK.Corneal elevation maps of five human eyes were taken with a rotating Scheimpflug camera combined with a Placido disk before and after refractive surgery. Patient-specific solid models were created and discretized in finite elements to estimate the corneal strain and stress fields in preoperative and postoperative configurations and derive the refractive parameters of the cornea.Patient-specific geometrical models of the cornea allow for the creation of personalized refractive maps at different levels of IOP. Thinned postoperative corneas show a higher stress gradient across the thickness and higher sensitivity of all geometrical and refractive parameters to the fluctuation of the IOP.Patient-specific numerical models of the cornea can provide accurate quantitative information on the refractive properties of the cornea under different levels of IOP and describe the change of the stress state of the cornea due to refractive surgery (PRK. Patient-specific models can be used as indicators of feasibility before performing the surgery.

Selection and storage of perceptual groups is constrained by a discrete resource in working memory.

Science.gov (United States)

Anderson, David E; Vogel, Edward K; Awh, Edward

2013-06-01

Perceptual grouping can lead observers to perceive a multielement scene as a smaller number of hierarchical units. Past work has shown that grouping enables more elements to be stored in visual working memory (WM). Although this may appear to contradict so-called discrete resource models that argue for fixed item limits in WM storage, it is also possible that grouping reduces the effective number of "items" in the display. To test this hypothesis, we examined how mnemonic resolution declined as the number of items to be stored increased. Discrete resource models predict that precision will reach a stable plateau at relatively early set sizes, because no further items can be stored once putative item limits are exceeded. Thus, we examined whether the precision by set size function was bilinear when storage was enhanced via perceptual grouping. In line with the hypothesis that each perceptual group counted as a single "item," precision still reached a clear plateau at a set size determined by the number of stored groups. Moreover, the maximum number of elements stored was doubled, and electrophysiological measures showed that selection and storage-related neural responses were the same for a single element and a multielement perceptual group. Thus, perceptual grouping allows more elements to be held in working memory while storage is still constrained by a discrete item limit.

Quasi-one-dimensional scattering in a discrete model

DEFF Research Database (Denmark)

Valiente, Manuel; Mølmer, Klaus

2011-01-01

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero...

Theoretical aspects of the internal element connectivity parameterization approach for topology optimization

DEFF Research Database (Denmark)

Yoon, Gil Ho; Kim, Y.Y.; Langelaar, M.

2008-01-01

The internal element connectivity parameterization (I-ECP) method is an alternative approach to overcome numerical instabilities associated with low-stiffness element states in non-linear problems. In I-ECP, elements are connected by zero-length links while their link stiffness values are varied....... Therefore, it is important to interpolate link stiffness properly to obtain stably converging results. The main objective of this work is two-fold (1) the investigation of the relationship between the link stiffness and the stiffness of a domain-discretizing patch by using a discrete model and a homogenized...

Modeling biological tissue growth: discrete to continuum representations.

Science.gov (United States)

Hywood, Jack D; Hackett-Jones, Emily J; Landman, Kerry A

2013-09-01

There is much interest in building deterministic continuum models from discrete agent-based models governed by local stochastic rules where an agent represents a biological cell. In developmental biology, cells are able to move and undergo cell division on and within growing tissues. A growing tissue is itself made up of cells which undergo cell division, thereby providing a significant transport mechanism for other cells within it. We develop a discrete agent-based model where domain agents represent tissue cells. Each agent has the ability to undergo a proliferation event whereby an additional domain agent is incorporated into the lattice. If a probability distribution describes the waiting times between proliferation events for an individual agent, then the total length of the domain is a random variable. The average behavior of these stochastically proliferating agents defining the growing lattice is determined in terms of a Fokker-Planck equation, with an advection and diffusion term. The diffusion term differs from the one obtained Landman and Binder [J. Theor. Biol. 259, 541 (2009)] when the rate of growth of the domain is specified, but the choice of agents is random. This discrepancy is reconciled by determining a discrete-time master equation for this process and an associated asymmetric nonexclusion random walk, together with consideration of synchronous and asynchronous updating schemes. All theoretical results are confirmed with numerical simulations. This study furthers our understanding of the relationship between agent-based rules, their implementation, and their associated partial differential equations. Since tissue growth is a significant cellular transport mechanism during embryonic growth, it is important to use the correct partial differential equation description when combining with other cellular functions.

The role of the Stripa phase 3 project in the development of practical discrete fracture modelling technology

International Nuclear Information System (INIS)

Dershowitz, W.S.

1994-01-01

The Stripa project has played a major role in developing discrete fracture analysis from a theoretical research topic to a practical repository evaluation tool. The Site Characterization and Validation (SCV) program positively answered questions regarding: (1) the validation of discrete fracture models, (2) the feasibility of collecting data for discrete fracture models, (3) the ability of discrete fracture models to simulate flow in a rock volume of approximately 10 6 cubic meters using modest computing resources, and (4) the ability to model transport in discrete fractures. The SCV program also made progress on such continuing issues as the importance of in-plane fracture heterogeneity and coupled effects. (author). 16 refs., 2 tabs., 6 figs

Coupled Hybrid Continuum-Discrete Model of Tumor Angiogenesis and Growth.

Directory of Open Access Journals (Sweden)

Jie Lyu

Full Text Available The processes governing tumor growth and angiogenesis are codependent. To study the relationship between them, we proposed a coupled hybrid continuum-discrete model. In this model, tumor cells, their microenvironment (extracellular matrixes, matrix-degrading enzymes, and tumor angiogenic factors, and their network of blood vessels, described by a series of discrete points, were considered. The results of numerical simulation reveal the process of tumor growth and the change in microenvironment from avascular to vascular stage, indicating that the network of blood vessels develops gradually as the tumor grows. Our findings also reveal that a tumor is divided into three regions: necrotic, semi-necrotic, and well-vascularized. The results agree well with the previous relevant studies and physiological facts, and this model represents a platform for further investigations of tumor therapy.

Equilibrium and nonequilibrium attractors for a discrete, selection-migration model

Science.gov (United States)

James F. Selgrade; James H. Roberds

2003-01-01

This study presents a discrete-time model for the effects of selection and immigration on the demographic and genetic compositions of a population. Under biologically reasonable conditions, it is shown that the model always has an equilibrium. Although equilibria for similar models without migration must have real eigenvalues, for this selection-migration model we...

Finite elements of nonlinear continua

CERN Document Server

Oden, John Tinsley

1972-01-01

Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

On the Robustness and Prospects of Adaptive BDDC Methods for Finite Element Discretizations of Elliptic PDEs with High-Contrast Coefficients

KAUST Repository

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

International Conference eXtended Discretization MethodS

CERN Document Server

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.

Applied discrete-time queues

CERN Document Server

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...

Discrete control systems

CERN Document Server

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...

Mittag-Leffler function for discrete fractional modelling

Directory of Open Access Journals (Sweden)

Guo-Cheng Wu

2016-01-01

Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.

Local and global dynamics of Ramsey model: From continuous to discrete time.

Science.gov (United States)

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Multiscale Modeling of Blood Flow: Coupling Finite Elements with Smoothed Dissipative Particle Dynamics

KAUST Repository

Moreno Chaparro, Nicolas; Vignal, Philippe; Li, Jun; Calo, Victor M.

2013-01-01

A variational multi scale approach to model blood flow through arteries is proposed. A finite element discretization to represent the coarse scales (macro size), is coupled to smoothed dissipative particle dynamics that captures the fine scale features (micro scale). Blood is assumed to be incompressible, and flow is described through the Navier Stokes equation. The proposed cou- pling is tested with two benchmark problems, in fully coupled systems. Further refinements of the model can be incorporated in order to explicitly include blood constituents and non-Newtonian behavior. The suggested algorithm can be used with any particle-based method able to solve the Navier-Stokes equation.

Multiscale Modeling of Blood Flow: Coupling Finite Elements with Smoothed Dissipative Particle Dynamics

KAUST Repository

Moreno Chaparro, Nicolas

2013-06-01

A variational multi scale approach to model blood flow through arteries is proposed. A finite element discretization to represent the coarse scales (macro size), is coupled to smoothed dissipative particle dynamics that captures the fine scale features (micro scale). Blood is assumed to be incompressible, and flow is described through the Navier Stokes equation. The proposed cou- pling is tested with two benchmark problems, in fully coupled systems. Further refinements of the model can be incorporated in order to explicitly include blood constituents and non-Newtonian behavior. The suggested algorithm can be used with any particle-based method able to solve the Navier-Stokes equation.

Proposal for element size and time increment selection guideline by 3-D finite element method for elastic waves propagation analysis

International Nuclear Information System (INIS)

Ishida, Hitoshi; Meshii, Toshiyuki

2008-01-01

This paper proposes a guideline for selection of element size and time increment by 3-D finite element method, which is applied to elastic wave propagation analysis for a long distance of a large structure. An element size and a time increment are determined by quantitative evaluation of strain, which must be 0 on the analysis model with a uniform motion, caused by spatial and time discretization. (author)

Limit sets for the discrete spectrum of complex Jacobi matrices

International Nuclear Information System (INIS)

Golinskii, L B; Egorova, I E

2005-01-01

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schroedinger operators with complex potential on a half-axis.

A mass and energy conserving spectral element atmospheric dynamical core on the cubed-sphere grid

International Nuclear Information System (INIS)

Taylor, M A; Edwards, J; Thomas, S; Nair, R

2007-01-01

We present results from a conservative formulation of the spectral element method applied to global atmospheric circulation modeling. Exact local conservation of both mass and energy is obtained via a new compatible formulation of the spectral element method. Compatibility insures that the key integral property of the divergence and gradient operators required to show conservation also hold in discrete form. The spectral element method is used on a cubed-sphere grid to discretize the horizontal directions on the sphere. It can be coupled to any conservative vertical/radial discretization. The accuracy and conservation properties of the method are illustrated using a baroclinic instability test case

Unstructured grids and an element based conservative approach for a black-oil reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Nogueira, Regis Lopes; Fernandes, Bruno Ramon Batista [Federal University of Ceara, Fortaleza, CE (Brazil). Dept. of Chemical Engineering; Araujo, Andre Luiz de Souza [Federal Institution of Education, Science and Technology of Ceara - IFCE, Fortaleza (Brazil). Industry Department], e-mail: andre@ifce.edu.br; Marcondes, Francisco [Federal University of Ceara, Fortaleza, CE (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br

2010-07-01

Unstructured meshes presented one upgrade in modeling the main important features of the reservoir such as discrete fractures, faults, and irregular boundaries. From several methodologies available, the Element based Finite Volume Method (EbFVM), in conjunction with unstructured meshes, is one methodology that deserves large attention. In this approach, the reservoir, for 2D domains, is discretized using a mixed two-dimensional mesh using quadrilateral and triangle elements. After the initial step of discretization, each element is divided into sub-elements and the mass balance for each component is developed for each sub-element. The equations for each control-volume using a cell vertex construction are formulated through the contribution of different neighboured elements. This paper presents an investigation of an element-based approach using the black-oil model based on pressure and global mass fractions. In this approach, even when all gas phase is dissolved in oil phase the global mass fraction of gas will be different from zero. Therefore, no additional numerical procedure is necessary in order to treat the gas phase appear/disappearance. In this paper the above mentioned approach is applied to multiphase flows involving oil, gas, and water. The mass balance equations in terms of global mass fraction of oil, gas and water are discretized through the EbFVM and linearized by the Newton's method. The results are presented in terms of volumetric rates of oil, gas, and water and phase saturations. (author)

Discrete integrable systems and deformations of associative algebras

International Nuclear Information System (INIS)

Konopelchenko, B G

2009-01-01

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.

Simplified CFD model of coolant channels typical of a plate-type fuel element: an exhaustive verification of the simulations

Energy Technology Data Exchange (ETDEWEB)

Mantecón, Javier González; Mattar Neto, Miguel, E-mail: javier.mantecon@ipen.br, E-mail: mmattar@ipen.br [Instituto de Pesquisas Energéticas e Nucleares (IPEN/CNEN-SP), São Paulo, SP (Brazil)

2017-07-01

The use of parallel plate-type fuel assemblies is common in nuclear research reactors. One of the main problems of this fuel element configuration is the hydraulic instability of the plates caused by the high flow velocities. The current work is focused on the hydrodynamic characterization of coolant channels typical of a flat-plate fuel element, using a numerical model developed with the commercial code ANSYS CFX. Numerical results are compared to accurate analytical solutions, considering two turbulence models and three different fluid meshes. For this study, the results demonstrated that the most suitable turbulence model is the k-ε model. The discretization error is estimated using the Grid Convergence Index method. Despite its simplicity, this model generates precise flow predictions. (author)

Simplified CFD model of coolant channels typical of a plate-type fuel element: an exhaustive verification of the simulations

International Nuclear Information System (INIS)

Mantecón, Javier González; Mattar Neto, Miguel

2017-01-01

The use of parallel plate-type fuel assemblies is common in nuclear research reactors. One of the main problems of this fuel element configuration is the hydraulic instability of the plates caused by the high flow velocities. The current work is focused on the hydrodynamic characterization of coolant channels typical of a flat-plate fuel element, using a numerical model developed with the commercial code ANSYS CFX. Numerical results are compared to accurate analytical solutions, considering two turbulence models and three different fluid meshes. For this study, the results demonstrated that the most suitable turbulence model is the k-ε model. The discretization error is estimated using the Grid Convergence Index method. Despite its simplicity, this model generates precise flow predictions. (author)

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

Energy Technology Data Exchange (ETDEWEB)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.

Spectral-element Method for 3D Marine Controlled-source EM Modeling

Science.gov (United States)

Liu, L.; Yin, C.; Zhang, B., Sr.; Liu, Y.; Qiu, C.; Huang, X.; Zhu, J.

2017-12-01

As one of the predrill reservoir appraisal methods, marine controlled-source EM (MCSEM) has been widely used in mapping oil reservoirs to reduce risk of deep water exploration. With the technical development of MCSEM, the need for improved forward modeling tools has become evident. We introduce in this paper spectral element method (SEM) for 3D MCSEM modeling. It combines the flexibility of finite-element and high accuracy of spectral method. We use Galerkin weighted residual method to discretize the vector Helmholtz equation, where the curl-conforming Gauss-Lobatto-Chebyshev (GLC) polynomials are chosen as vector basis functions. As a kind of high-order complete orthogonal polynomials, the GLC have the characteristic of exponential convergence. This helps derive the matrix elements analytically and improves the modeling accuracy. Numerical 1D models using SEM with different orders show that SEM method delivers accurate results. With increasing SEM orders, the modeling accuracy improves largely. Further we compare our SEM with finite-difference (FD) method for a 3D reservoir model (Figure 1). The results show that SEM method is more effective than FD method. Only when the mesh is fine enough, can FD achieve the same accuracy of SEM. Therefore, to obtain the same precision, SEM greatly reduces the degrees of freedom and cost. Numerical experiments with different models (not shown here) demonstrate that SEM is an efficient and effective tool for MSCEM modeling that has significant advantages over traditional numerical methods.This research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900).

Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems

Directory of Open Access Journals (Sweden)

Chellaboina Vijaysekhar

2005-01-01

Full Text Available We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.

A parametric model order reduction technique for poroelastic finite element models.

Science.gov (United States)

Lappano, Ettore; Polanz, Markus; Desmet, Wim; Mundo, Domenico

2017-10-01

This research presents a parametric model order reduction approach for vibro-acoustic problems in the frequency domain of systems containing poroelastic materials (PEM). The method is applied to the Finite Element (FE) discretization of the weak u-p integral formulation based on the Biot-Allard theory and makes use of reduced basis (RB) methods typically employed for parametric problems. The parametric reduction is obtained rewriting the Biot-Allard FE equations for poroelastic materials using an affine representation of the frequency (therefore allowing for RB methods) and projecting the frequency-dependent PEM system on a global reduced order basis generated with the proper orthogonal decomposition instead of standard modal approaches. This has proven to be better suited to describe the nonlinear frequency dependence and the strong coupling introduced by damping. The methodology presented is tested on two three-dimensional systems: in the first experiment, the surface impedance of a PEM layer sample is calculated and compared with results of the literature; in the second, the reduced order model of a multilayer system coupled to an air cavity is assessed and the results are compared to those of the reference FE model.

The problem with time in mixed continuous/discrete time modelling

NARCIS (Netherlands)

Rovers, K.C.; Kuper, Jan; Smit, Gerardus Johannes Maria

The design of cyber-physical systems requires the use of mixed continuous time and discrete time models. Current modelling tools have problems with time transformations (such as a time delay) or multi-rate systems. We will present a novel approach that implements signals as functions of time,

A Discrete Model for HIV Infection with Distributed Delay

Directory of Open Access Journals (Sweden)

Brahim EL Boukari

2014-01-01

Full Text Available We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.

A Discrete Numerical Scheme of Modified Leslie-Gower With Harvesting Model

Directory of Open Access Journals (Sweden)

Riski Nur Istiqomah Dinnullah

2018-05-01

Full Text Available Recently, exploitation of biological resources and the harvesting of two populations or more are widely practiced, such as fishery or foresty. The simplest way to describe the interaction of two species is by using predator prey model, that is one species feeds on another. The Leslie-Gower predator prey model has been studied in many works. In this paper, we use Euler method to discretisize the modified Leslie-Gower with harvesting model. The model consists of two simultanious predator prey equations. We show numerically that this discrete numerical scheme model is dynamically consistent with its continuous model only for relatively small step-size. By using computer simulation software, we show that equlibrium points can be stable, saddles, and unstable. It is shown that the numerical simulations not only illustrate the results, but also show the rich dynamics behaviors of the discrete system.

Desktop Modeling and Simulation: Parsimonious, yet Effective Discrete-Event Simulation Analysis

Science.gov (United States)

Bradley, James R.

2012-01-01

This paper evaluates how quickly students can be trained to construct useful discrete-event simulation models using Excel The typical supply chain used by many large national retailers is described, and an Excel-based simulation model is constructed of it The set of programming and simulation skills required for development of that model are then determined we conclude that six hours of training are required to teach the skills to MBA students . The simulation presented here contains all fundamental functionallty of a simulation model, and so our result holds for any discrete-event simulation model. We argue therefore that Industry workers with the same technical skill set as students having completed one year in an MBA program can be quickly trained to construct simulation models. This result gives credence to the efficacy of Desktop Modeling and Simulation whereby simulation analyses can be quickly developed, run, and analyzed with widely available software, namely Excel.

Discrete Hamiltonian evolution and quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

A finite element-based algorithm for rubbing induced vibration prediction in rotors

Science.gov (United States)

Behzad, Mehdi; Alvandi, Mehdi; Mba, David; Jamali, Jalil

2013-10-01

In this paper, an algorithm is developed for more realistic investigation of rotor-to-stator rubbing vibration, based on finite element theory with unilateral contact and friction conditions. To model the rotor, cross sections are assumed to be radially rigid. A finite element discretization based on traditional beam theories which sufficiently accounts for axial and transversal flexibility of the rotor is used. A general finite element discretization model considering inertial and viscoelastic characteristics of the stator is used for modeling the stator. Therefore, for contact analysis, only the boundary of the stator is discretized. The contact problem is defined as the contact between the circular rigid cross section of the rotor and “nodes” of the stator only. Next, Gap function and contact conditions are described for the contact problem. Two finite element models of the rotor and the stator are coupled via the Lagrange multipliers method in order to obtain the constrained equation of motion. A case study of the partial rubbing is simulated using the algorithm. The synchronous and subsynchronous responses of the partial rubbing are obtained for different rotational speeds. In addition, a sensitivity analysis is carried out with respect to the initial clearance, the stator stiffness, the damping parameter, and the coefficient of friction. There is a good agreement between the result of this research and the experimental result in the literature.

A collocation--Galerkin finite element model of cardiac action potential propagation.

Science.gov (United States)

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

Quadratic Finite Element Method for 1D Deterministic Transport

International Nuclear Information System (INIS)

Tolar, D R Jr.; Ferguson, J M

2004-01-01

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms

Family of columns isospectral to gravity-loaded columns with tip force: A discrete approach

Science.gov (United States)

Ramachandran, Nirmal; Ganguli, Ranjan

2018-06-01

A discrete model is introduced to analyze transverse vibration of straight, clamped-free (CF) columns of variable cross-sectional geometry under the influence of gravity and a constant axial force at the tip. The discrete model is used to determine critical combinations of loading parameters - a gravity parameter and a tip force parameter - that cause onset of dynamic instability in the CF column. A methodology, based on matrix-factorization, is described to transform the discrete model into a family of models corresponding to weightless and unloaded clamped-free (WUCF) columns, each with a transverse vibration spectrum isospectral to the original model. Characteristics of models in this isospectral family are dependent on three transformation parameters. A procedure is discussed to convert the isospectral discrete model description into geometric description of realistic columns i.e. from the discrete model, we construct isospectral WUCF columns with rectangular cross-sections varying in width and depth. As part of numerical studies to demonstrate efficacy of techniques presented, frequency parameters of a uniform column and three types of tapered CF columns under different combinations of loading parameters are obtained from the discrete model. Critical combinations of these parameters for a typical tapered column are derived. These results match with published results. Example CF columns, under arbitrarily-chosen combinations of loading parameters are considered and for each combination, isospectral WUCF columns are constructed. Role of transformation parameters in determining characteristics of isospectral columns is discussed and optimum values are deduced. Natural frequencies of these WUCF columns computed using Finite Element Method (FEM) match well with those of the given gravity-loaded CF column with tip force, hence confirming isospectrality.

Basic problems solving for two-dimensional discrete 3 × 4 order hidden markov model

International Nuclear Information System (INIS)

Wang, Guo-gang; Gan, Zong-liang; Tang, Gui-jin; Cui, Zi-guan; Zhu, Xiu-chang

2016-01-01

A novel model is proposed to overcome the shortages of the classical hypothesis of the two-dimensional discrete hidden Markov model. In the proposed model, the state transition probability depends on not only immediate horizontal and vertical states but also on immediate diagonal state, and the observation symbol probability depends on not only current state but also on immediate horizontal, vertical and diagonal states. This paper defines the structure of the model, and studies the three basic problems of the model, including probability calculation, path backtracking and parameters estimation. By exploiting the idea that the sequences of states on rows or columns of the model can be seen as states of a one-dimensional discrete 1 × 2 order hidden Markov model, several algorithms solving the three questions are theoretically derived. Simulation results further demonstrate the performance of the algorithms. Compared with the two-dimensional discrete hidden Markov model, there are more statistical characteristics in the structure of the proposed model, therefore the proposed model theoretically can more accurately describe some practical problems.

Fixed Points in Discrete Models for Regulatory Genetic Networks