Finite Element Analysis of 2 Immediate Loading Systems in Edentulous Mandible: Rigid and Semirigid Splinting of Implants

Purpose: The objective of this study was to evaluate the stress on the cortical bone around single body dental implants supporting mandibular complete fixed denture with rigid (Neopronto System-Neodent) or semirigid splinting system (Barra Distal System-Neodent). Methods and Materials: Stress levels on several system components were analyzed through finite element analysis. Focusing on stress concentration at cortical bone around single body dental implants supporting mandibular complete fixed dentures with rigid ( Neopronto System-Neodent) or semirigid splinting system ( Barra Distal System-Neodent), after axial and oblique occlusal loading simulation, applied in the last cantilever element. Results: The results showed that semirigid implant splinting generated lower von Mises stress in the cortical bone under axial loading. Rigid implant splinting generated higher von Mises stress in the cortical bone under oblique loading. Conclusion: It was concluded that the use of a semirigid system for rehabilitation of edentulous mandibles by means of immediate implant-supported fixed complete denture is recommended, because it reduces stress concentration in the cortical bone. As a consequence, bone level is better preserved, and implant survival is improved. Nevertheless, for both situations the cortical bone integrity was protected, because the maximum stress level findings were lower than those pointed in the literature as being harmful. The maximum stress limit for cortical bone (167 MPa) represents the threshold between plastic and elastic state for a given material. Because any force is applied to an object, and there is no deformation, we can conclude that the elastic threshold was not surpassed, keeping its structural integrity. If the force is higher than the plastic threshold, the object will suffer permanent deformation. In cortical bone, this represents the beginning of bone resorption and/or remodeling processes, which, according to our simulated loading, would not occur. ( Implant Dent 2010; 19:39-49)

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

An atomistic simulation of solid state sintering using Monte Carlo methods

This paper presents results on the simulation of the solid state sintering of copper wires using Monte Carlo techniques based on elements of lattice theory and cellular automata. The initial structure is superimposed onto a triangular, two-dimensional lattice, where each lattice site corresponds to either an atom or vacancy. The number of vacancies varies with the simulation temperature, while a cluster of vacancies is a pore. To simulate sintering, lattice sites are picked at random and reoriented in terms of an atomistic model governing mass transport. The probability that an atom has sufficient energy to jump to a vacant lattice site is related to the jump frequency, and hence the diffusion coefficient, while the probability that an atomic jump will be accepted is related to the change in energy of the system as a result of the jump, as determined by the change in the number of nearest neighbours. The jump frequency is also used to relate model time, measured in Monte Carlo Steps, to the actual sintering time. The model incorporates bulk, grain boundary and surface diffusion terms and includes vacancy annihilation on the grain boundaries. The predictions of the model were found to be consistent with experimental data, both in terms of the microstructural evolution and in terms of the sintering time. (C) 2002 Elsevier Science B.V. All rights reserved.

Finite Horizon Learning

Incorporating adaptive learning into macroeconomics requires assumptions about how agents incorporate their forecasts into their decision-making. We develop a theory of bounded rationality that we call finite-horizon learning. This approach generalizes the two existing benchmarks in the literature: Eulerequation learning, which assumes that consumption decisions are made to satisfy the one-step-ahead perceived Euler equation; and infinite-horizon learning, in which consumption today is determined optimally from an infinite-horizon optimization problem with given beliefs. In our approach, agents hold a finite forecasting/planning horizon. We find for the Ramsey model that the unique rational expectations equilibrium is E-stable at all horizons. However, transitional dynamics can differ significantly depending upon the horizon.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

Continuum bound states as surface states of a finite periodic system

We discuss the relation between continuum bound states (CBSs) localized on a defect, and surface states of a finite periodic system. We model an experiment of Capasso et al. [F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S-N. G. Chu, and A. Y. Cho, Nature (London) 358, 565 (1992)] using the transfer-matrix method. We compute the rate for intrasubband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.

Delta(1232) isobar excitations and the ground state of nuclei

The influence of Delta isobar components on the ground-state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations and binding energies, are evaluated employing the framework of the coupled-cluster theory. It is demonstrated that the effect of isobar configurations depends in a rather sensitive way on the model used for the baryon-baryon interaction. As examples for realistic baryon-baryon interactions with explicit inclusion of isobar channels we use the local (V28) and nonlocal meson-exchange potentials (Bonn2000) but also a model recently developed by the Salamanca group, which is based on a quark picture. The differences obtained for the nuclear observables are related to the treatment of the interaction, the pi-exchange contributions in particular, at high momentum transfers.

Escape over a potential barrier driven by colored noise: Large but finite correlation times

The recent theory of Tsironis and Grigolini for the mean first-passage time from one metastable state to another of a bistable potential for long correlation times of the noise is extended to large but finite correlation times.

First-passage times for a marginal state driven by colored noise

The dynamical process through a marginal state (saddle point) driven by colored noise is studied. For small correlation time of the noise, the mean first-passage time and its variance are calculated using standard methods. When the correlation time of the noise is finite or large, an alternative approach, based on simple physical arguments, is proposed. It will allow us to study also the passage times of an unstable state. The theoretical predictions are tested satisfactorily by the use of computer simulations.

Fluctuations in finite systems: fluctuations in fluids in thermocapillary motion

We compute nonequilibrium correlation functions about the stationary state in which the fluid moves as a consequence of tangential stresses on the liquid surface, related to a varying surface tension (thermocapillary motion). The nature of the stationary state makes it necessary to take into account that the system is finite. We then extend a previous analysis on fluctuations about simple stationary states to include some effects related to the finite size of the sample.

Nonlinear Finite Element Study of Piles in Integral Abutment Bridges, HR-227, Part 2, 1982

The highway departments of the states which use integral abutments in bridge design were contacted in order to study the extent of integral abutment use in skewed bridges and to survey the different guidelines used for analysis and design of integral abutments in skewed bridges. The variation in design assumptions and pile orientations among the various states in their approach to the use of integral abutments on skewed bridges is discussed. The problems associated with the treatment of the approach slab, backfill, and pile cap, and the reason for using different pile orientations are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure previously developed by the authors was modified and used to study the influence of different factors on behavior of piles in integral abutment bridges. An idealized integral abutment was introduced by assuming that the pile is rigidly cast into the pile cap and that the approach slab offers no resistance to lateral thermal expansion. Passive soil and shear resistance of the cap are neglected in design. A 40-foot H pile (HP 10 X 42) in six typical Iowa soils was analyzed for fully restrained pile head and pinned pile head. According to numerical results, the maximum safe length for fully restrained pile head is one-half the maximum safe length for pinned pile head. If the pile head is partially restrained, the maximum safe length will lie between the two limits. The numerical results from an investigation of the effect of predrilled oversized holes indicate that if the length of the predrilled oversized hole is at least 4 feet below the ground, the vertical load-carrying capacity of the H pile is only reduced by 10 percent for 4 inches of lateral displacement in very stiff clay. With no predrilled oversized hole, the pile failed before the 4-inch lateral displacement was reached. Thus, the maximum safe lengths for integral abutment bridges may be increased by predrilling. Four different typical Iowa layered soils were selected and used in this investigation. In certain situations, compacted soil (> 50 blow count in standard penetration tests) is used as fill on top of natural soil. The numerical results showed that the critical conditions will depend on the length of the compacted soil. If the length of the compacted soil exceeds 4 feet, the failure mechanism for the pile is similar to one in a layer of very stiff clay. That is, the vertical load-carrying capacity of the H pile will be greatly reduced as the specified lateral displacement increases.

Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices

Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.