Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

Finite Element Analysis and Optimization of a Single-Axis Acoustic Levitator

A finite element analysis and a parametric optimization of single-axis acoustic levitators are presented. The finite element method is used to simulate a levitator consisting of a Langevin ultrasonic transducer with a plane radiating surface and a plane reflector. The transducer electrical impedance, the transducer face displacement, and the acoustic radiation potential that acts on small spheres are determined by the finite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a fiber-optic vibration sensor. The numerical acoustic radiation potential is verified experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reflector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reflector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W.

Coarse-grid higher order finite-difference time-domain algorithm with low dispersion errors

Higher order (2,4) FDTD schemes used for numerical solutions of Maxwell`s equations are focused on diminishing the truncation errors caused by the Taylor series expansion of the spatial derivatives. These schemes use a larger computational stencil, which generally makes use of the two constant coefficients, C-1 and C-2, for the four-point central-difference operators. In this paper we propose a novel way to diminish these truncation errors, in order to obtain more accurate numerical solutions of Maxwell`s equations. For such purpose, we present a method to individually optimize the pair of coefficients, C-1 and C-2, based on any desired grid size resolution and size of time step. Particularly, we are interested in using coarser grid discretizations to be able to simulate electrically large domains. The results of our optimization algorithm show a significant reduction in dispersion error and numerical anisotropy for all modeled grid size resolutions. Numerical simulations of free-space propagation verifies the very promising theoretical results. The model is also shown to perform well in more complex, realistic scenarios.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Modeling technique for honeycomb FRP deck bridges via finite elements

Honeycomb structures have been used in different engineering fields. In civil engineering, honeycomb fiber-reinforced polymer (FRP) structures have been used as bridge decks to rehabilitate highway bridges in the United States. In this work, a simplified finite-element modeling technique for honeycomb FRP bridge decks is presented. The motivation is the combination of the complex geometry of honeycomb FRP decks and computational limits, which may prevent modeling of these decks in detail. The results from static and modal analyses indicate that the proposed modeling technique provides a viable tool for modeling the complex geometry of honeycomb FRP bridge decks. The modeling of other bridge components (e.g., steel girders, steel guardrails, deck-to-girder connections, and pier supports) is also presented in this work.

Three-Dimensional Stress Distribution in the Human Periodontal Ligament in Masticatory, Parafunctional, and Trauma Loads: Finite Element Analysis

Background: The presence of the periodontal ligament (PDL) makes it possible to absorb and distribute loads produced during masticatory function and other tooth contacts into the alveolar process via the alveolar bone proper. However, several factors affect the integrity of periodontal structures causing the destruction of the connective matrix and cells, the loss of fibrous attachment, and the resorption of alveolar bone. Methods: The purpose of this study was to evaluate the stress distribution by finite element analysis in a PDL in three-dimensional models of the upper central incisor under three different load conditions: 100 N occlusal loading at 45 degrees (model 1: masticatory load); 500 N at the incisal edge at 45 degrees (model 2: parafunctional habit); and 800 N at the buccal surface at 90 degrees (model 3: trauma case). The models were built from computed tomography scans. Results: The stress distribution was quite different among the models. The most significant values (harmful) of tensile and compressive stresses were observed in models 2 and 3, with similarly distinct patterns of stress distributions along the PDL. Tensile stresses were observed along the internal and external aspects of the PDL, mostly at the cervical and middle thirds. Conclusions: The stress generation in these models may affect the integrity of periodontal structures. A better understanding of the biomechanical behavior of the PDL under physiologic and traumatic loading conditions might enhance the understanding of the biologic reaction of the PDL in health and disease. J Periodontol 2009;80:1859-1867.

Three Dimensional Finite Element Analyses of Oral Structures by Computerized Tomography

Our aim was to document the benefits of three dimensional finite element model generations from computed tomography data as well as the realistic creation of all oral structures in a patient. The stresses resulting from the applied load in our study did not exceed the structure limitations, suggesting a clinically acceptable physiological condition.

Pair correlations in a finite-temperature 1D Bose gas

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature “fermionization” through the measurement of the rates of two-body inelastic processes, such as photoassociation.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

p-cresol as a reversible acylium ion scavenger in solid-phase peptide synthesis

In this work we have defined the nature of the p-cresol and p-thiocresol adducts generated from acylium ions during HF cleavage, following contemporary Boc/benzyl solid-phase peptide synthesis. Contrary to the results in previous reports, we found that both p-cresol and p-thiocresol predominantly form. aryl esters under typical cleavage conditions. Initially we investigated a number of small peptides containing either a single glutamate residue or a C-terminal long-chain amino acid which allowed us to unambiguously characterize the scavenged side products. Whereas, the p-cresol esters are stable at 0 degrees C they rearrange irreversibly at higher temperatures (5-20 degrees C) to form aryl ketones. By contrast, p-thiocresol esters do not undergo a Fries rearrangement but readily undergo further additions of p-thiocresol to form ketenebisthioacetals and trithio ortho esters, even at low temperatures. Importantly, we found by LC/MS and FT-ICR MS analysis that peptides containing p-cresol esters at glutamyl side chains are susceptible to amidation and fragmentation reactions at these sites during standard mild base workup procedures. The significance of these side reactions was further demonstrated in the synthesis of neutrophil immobilization factor, a 26-residue peptide, containing four glutamic acid residues. The side reactions were largely avoided by mild hydrogen peroxide-catalyzed hydrolysis which converted the p-cresol adducts to the free carboxylic acids in near quantitative yield. The choice of p-cresol as a reversible acylium ion scavenger when coupled with the simple workup conditions described is broadly applicable to Boc/benzyl peptide synthesis and will significantly enhance the quality of peptides produced.

Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

Groups with exponent six

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent sis using substantial computations which we explain.

Formal derivation of finite state machines for class testing

Previous work on generating state machines for the purpose of class testing has not been formally based. There has also been work on deriving state machines from formal specifications for testing non-object-oriented software. We build on this work by presenting a method for deriving a state machine for testing purposes from a formal specification of the class under test. We also show how the resulting state machine can be used as the basis for a test suite developed and executed using an existing framework for class testing. To derive the state machine, we identify the states and possible interactions of the operations of the class under test. The Test Template Framework is used to formally derive the states from the Object-Z specification of the class under test. The transitions of the finite state machine are calculated from the derived states and the class's operations. The formally derived finite state machine is transformed to a ClassBench testgraph, which is used as input to the ClassBench framework to test a C++ implementation of the class. The method is illustrated using a simple bounded queue example.

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

Friedmanniella spumicola sp nov and Friedmanniella capsulata sp nov from activated sludge foam: Gram-positive cocci that grow in aggregates of repeating groups of cocci

Two Gram-positive, non-motile, non-spore-forming, strictly aerobic, pigmented cocci, strains Ben 107(T) and Ben 108(T), growing in aggregates were isolated from activated sludge samples by micromanipulation. Both possessed the rare type A3 gamma' peptidoglycan. Major menaquinones of strain Ben 107(T) were MK-9(H-4) and MK-7(H-2), and the main cellular fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). In strain Ben 108(T), MK-9(H-4), MK-9(H-2) and MK-7(H-4) were the menaquinones and again the main fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). Polar lipids in both strains consisted of phosphatidyl inositol, phosphatidyl glycerol and diphosphatidyl glycerol with two other unidentified glycolipids and phospholipids also present in both. These data, together with the 16S rDNA sequence data, suggest that strain Ben 107(T) belongs to the genus Friedmanniella which presently includes a single recently described species, Friedmanniella antarctica. Although the taxonomic status of strain Ben 108(T) is far less certain, on the basis of its 16S rRNA sequence it is also adjudged to be best placed in the genus Friedmanniella, The chemotaxonomic characteristics and DNA-DNA hybridization data support the view that Ben 107(T) and Ben 108(T) are novel species of the genus Friedmanniella. Hence, it is proposed that strain Ben 107(T) (=ACM 5121(T)) is named as Friedmanniella spumicola sp. nov. and strain Ben 108(T) (=ACM 5120(T)) as Friedmanniella capsulata sp. nov.