The behavior of adaptive bone-remodeling simulation models

The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely.\ud \ud It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur.\ud \ud It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing; denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process.\ud \ud It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization

Fast and stable method for simulating quantum electron dynamics

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several computational techniques such as Suzuki's exponential product, Cayley's form, the finite differential method and an operator named adhesive operator. This method conserves the norm of the wavefunction, manages periodic conditions and adaptive mesh refinement technique, and is suitable for vector- and parallel-type supercomputers. Applying this method to some simple electron dynamics, we confirmed the efficiency and accuracy of the method for simulating fast time-dependent quantum phenomena.Comment: 10 pages, 35 eps figure

Characterization and Simulation of Discrete Fracture Networks in Unconventional Shale Reservoirs

Fracture characterization and simulation of complex fracture networks are investigated with the emphasis on better and faster approaches to generate fractures by conforming to available data resources, and on accurate, robust, and efficient techniques to grid and discretize complex fracture networks. Three fracture characterization techniques such as fractal-based, microseismic-constrained, and outcrop-based are presented. Natural fractures are generated either stochastically from fractal-based theory, or constrained by microseismic information, or from outcrop maps. Hydraulic fractures are computed from a fast proxy model for fracture propagation that incooperates material balance and lab-measured conductivity data. Then, optimization-based unstructured gridding and discretization technique is developed to handle complex fracture networks with extensively fracture clustering, nonorthogonal and low-angle fracture intersections, and nonuniform fracture aperture distributions. Moreover, through fracture simulation, sensitivity analysis of natural fracture related parameters, nonuniform fracture aperture, and unstructured gridding related parameters on well production performance are investigated, which are followed by well testing behaviors and CO2 EOR of complex fracture networks. This work presents an integrated workflow to model discrete fractures in unconventional shale reservoirs, together with detailed illustrations of each critical component using both synthetic and field application examples

An approach to investigate surface roughness influence on non-lubricated and lubricated contacts by means of the finite element analysis = Ein Ansatz zur Untersuchung der Oberflächenrauheiteinflüsse bei geschmierten und trockenen Kontakten mittels der Finite Elemente Methode

Present thesis develops a numerical analysis framework to investigate the mixed lubricated contacts of two rough surfaces by means of the finite element method. A verification has been done to check the convergence of the microscopic mixed lubrication model. Parameter study done for the mixed lubrication model displays the contact stresses and temperatures and shows which parameter had the most influence on the friction behavior

Natural Parameterization

The objective of this project has been to develop an approach for imitating physical objects with an underlying stochastic variation. The key assumption is that a set of “natural parameters” can be extracted by a new subdivision algorithm so they reflect what is called the object’s “geometric DNA”. A case study on one hundred wheat grain crosssections (Triticum aestivum) showed that it was possible to extract thirty-six such parameters and to reuse them for Monte Carlo simulation of “new” stochastic phantoms which possessthe same stochastic behavior as the “original” cross-sections