Distinct element method

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

Min KB, Jing L, 2003, Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method, Int J Rock Mech Min Sci. 40(6) 795-816. 

Jiang, Y.J., Li, B. and Yamashita, YJ. 2009. Simulation of cracking near a large underground cavern in a discontinuous rock mass using the expanded distinct element method. International Journal of Rock Mechanics Mining Sciences 46 97-106. 

Hydro-mechanical coupling in fractured rock mass is an important issue for many rock mechanics and hydrogeology apphcations (Rutqvist Stephansson 2003). Various numerical methods, i.e. distinct element method (DEM), finite element method (FEM), finite difference method (FDM), etc, are widely used to simulate and analyze the rock hydro-mechanical coupling behaviors. UDEC is DEM software and can be used for modeling the hydro-mechanical coupling behavior of fractured rock masses. 

Tao, L.J. et al. 2000. Modelling of ground water flow in jointed rock masses with distinct element method. Journal of China Coal Society 25(01) 1-4. 

Parisi, D.R. Masson, S. Martinez, J. (2004) Partitioned distinct element method simulation of granular flow within industrial silos. Journal of Engineering Mechanics-ASCE 130, 771-779. 

The mixing and flow patterns of gravitational dry particulate flows in continuous mixer tubes with helical, Kenics-type [1] static mixer elements have been simulated by the distinct element method (DEM) under steady state conditions. In the particular system the subsequent mixer elements were twisted in opposite direction a mixing element twisted clockwise is followed by an element twisted counter-clockwise and so on. A state diagram that gives a general relationship between the mass flow rate and the solids volume fraction in the mixer tube was determined for various construction parameters. 

The development of computers in terms of operational speed and storage capacity made possible to model the particulate systems by the distinct element method (DEM). Using this method the particle trajectories, the particle-particle, and particle-wall interactions are considered separately for each particle. Thus, the bulk mechanical behaviour of the system is related to the properties of single particles. DEM can provide basic information on the particulate system including its microscopic structure, the inter-particle and particle-wall Wees, particle velocities, etc. 

Papantonopoulos C, Psycharis IN, Papastamatiou DY, Lemos JV, Mouzakis H (2002) Numerical prediction of the earthquake response of classical columns using the distinct element method. Earthquake Eng Struct Dyn 31 1699-1717... 

Zhou HS, Flamant G, Gauthier D, Flitris Y Simulation of coal combustion in a bubbling fluidized bed by distinct element method, Chem Eng Res Des 81 1144—1149, 2003. 

Extruder, simulation, solids conveying, distinct element method... 

The abundance of a trace element is often too small to be accurately quantihed using conventional analytical methods such as ion chromatography or mass spectrometry. It is possible, however, to precisely determine very low concentrations of a constituent by measuring its radioactive decay properties. In order to understand how U-Th series radionuclides can provide such low-level tracer information, a brief review of the basic principles of radioactive decay and the application of these radionuclides as geochronological tools is useful. " The U-Th decay series together consist of 36 radionuclides that are isotopes (same atomic number, Z, different atomic mass, M) of 10 distinct elements (Figure 1). Some of these are very short-lived (tj j 1 -nd are thus not directly useful as marine tracers. It is the other radioisotopes with half-lives greater than 1 day that are most useful and are the focus of this chapter. 

A good analytical resource is not cheap. It often has significant ongoing capital requirements for the provision of up to date instruments. It is therefore very important that only those distinctive elements and core competencies are retained within the company. This might well be a particular expertise in a chromatographic method or some advanced methods of mass spectrometry, without which the research could not continue. 

The finite element method, as applied to an engineering structure, consists of dividing the structure into distinct nonoverlaping regions known as elements the elements are connected at a discrete number of points along the periphery, known as nodal points. For each element the stiffness matrix and load vector are calculated, by assembling the calculated stiffness matrix and load vector of the elements, one obtains the overall stiffness and vector of the system or structure the resulting simultaneous equations for the unknown displacement components of the structure (unknown nodal variables) are solved and the stress components are evaluated for the elements. 

The mechanical response of systems of distinct particles is often adequately described by Newton s laws, which constitute the bases of classical mechanics (36) (see sect. The Discrete Element Method ). However, additional concepts are needed for deformable matter, such as stress and strain, which will be described here (37). We will focus on solid materials, but remark that the same principles are also valid for fluids (in which case the field is usually referred to as computational fluid dynamics). 

Insofar as robots are designed to replace human effort partly or completely, their applications can be considered the latest alternative to automatic methods of analysis. Although some workers regard them as a part of batch methods, there are sufficient distinctive elements to treat them as a separate category. 

Now, suppose we apply the transformations to the distinct one-electron integrals and add up the results to generate a one-electron matrix. The result is a one-electron matrix with the correct symmetry but the elements are all doubled-, a matrix of 2hij. It is easy to see why this doubling has occurred the result of applying the symmetry operations to the distinct elements does not result in a disjoint set of new elements-, repetitions occur as they do in the list of transformed orbitals. Of course, these repetitions must occur mth the molecular symmetry-, if hn occurs twice, so must 22 and In our case both hn and hi2 occur twice but this need not be so in general there will be a characteristic number of repetitions of each of the symmetry-distinct matrix elements. Thus the method is clear, we must... 

An example of the use of the finite-element method for the prediction of wave-induced seafloor movement was presented by Kraft and Watkins (1976). In the use of the finite-element method three distinct ways of quantifying the initial stability of slopes have been developed. The first two methods utilize element calculations in which the slope is modeled as a series of individual elements (Seed, 1966). The first method uses a calculated F.S. for each element. By contrast the second method is based on an evaluation of the potential strain experienced by each element. The third method involves predicting the overall resulting permanent deformations. 

Before considering methods of noise control, it is important to remember that the noise at any point may be due to more than one source and that additionally it may be aggravated by noise reflected from walls (reverberant noise) as well as the noise radiated directly from the source. With any noise problems there are the three distinct elements shown in Figure 20.9 -source, path and receiver. 

TTie aerogel carbons are already mentioned in Section 3.4.18 and have seen development studies in terms of their abilities to act as catalyst support materials. Since these carbons are synthesized from monomeric materials, eatalytic elements can be introduced within resultant carbons as distinct from methods of deposition from the liquid phase or by vapor deposition on to an already prepared carbon. Moreno-Castilla and Maldonado-H6dar (2005)... 

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