Acoustic Propagation over Periodic and Quasi-Period Rough Surfaces Proceedings

Numerical techniques such as the Boundary Element Method, Finite Element Method and Finite Difference Time Domain have been used widely to investigate plane and curved wave-front scattering by rough surfaces. For certain shapes of roughness elements (cylinders, semi-cylinders and ellipsoids) there are semi-analytical alternatives. Here, we present a theory for multiple scattering by cylinders on a hard surface to investigate effects due to different roughness shape, the effects of vacancies and variation of roughness element size on the excess attenuation due to a periodically rough surfaces.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Rapid solution of finite element equations on locally refined grids by multi-level methods /

"UILU-ENG 80 1712."

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Trace-element and phosphorus contents in sediment associated with Cretaceous oceanic anoxic events

ABSTRACT : During my SNSF-funded Ph.D. thesis project, I studied the evolution of redox conditions and organic-carbon preservation in the western Tethyan realm during three major positive excursions in the Cretaceous δ13C record, corresponding to the Valanginian, Early Aptian and Late Cenomanian. These periods were characterized by important global environmental and climate change, which was associated with perturbations in the carbon cycle. For the period of the Valanginian δ13C excursion, total organic carbon (TOC) contents and the quality of preserved organic matter are typical of oxic pelagic settings in the western Tethys. This is confirmed by the absence of major excursions in the stratigraphic distribution of RSTE during the δ13C shift. Published TOC data from other parts of the Valanginian oceans indicate that dys- to anaerobic zones were restricted to marginal seas within the Atlantic and Southern Ocean, and to the Pacific. Phosphorus (P) and mineralogical contents suggest a stepwise climatic evolution during the Valanginian, with a humid and warm climate prior to the δ13C shift leading to an increase in continental runoff. During the δ13C shift, a decrease in detrital input and P contents suggests a change in the climate towards more and conditions. During the early Aptian oceanic anoxic event (OAE 1a), a general increase followed by a rapid decrease in P contents suggests enhanced nutrient input at the beginning of OAE 1a. The return to lower values during OAE 1 a, associated with an increase in RSTE contents, may have been related to the weakened capacity to retain P in the sedimentary reservoir due to bottom-water oxygen depletion. In basinal settings, the RSTE distribution indicates well-developed anoxic conditions during OAE la, whereas in the shallower-water environments, conditions were oxic to suboxic, rather than anoxic. Furthermore, in the deeper part of the Tethys, two distinct enrichments have been observed, indicating fluctuations in the intensity of water column anoxia during the δ73C excursion. We also studied the effect of the end-Cenomanian oceanic anoxic event (OAE 2) on an expanded section in the Chrummflueschlucht (E of Euthal, Ct Switzerland). The goal here was to identify paleoceanographic and paleoenvironmental conditions during OAE 2 in this part of the northern Tethyan margin. The results show that this section is one of the most complete sections for the Cenomanian-Turonian boundary interval known from the Helvetic realm, despite a small hiatus between sediments corresponding to peaks 1 and 2 in the δ13C record. The evolution of P contents points to an increase in the input of this nutrient at the onset of OAE 2. The trends in RSTE contents show, however, that this part of the Helvetic realm was not affected by a strong depletion in oxygen conditions during OAE 2, despite its hemipelagic position. A further goal of this project was to submit the samples to a total extraction method (a combined HF/HNO3/HCI acid digestion) and compare the results obtained by the partial HNO3 acid extraction in order to standardize the analytical prócedures in the extraction of RSTE. The obtained results for samples of OAE 1 a suggest that RSTE trends using the partial HNO3 digestion are very comparable to those obtained by the total digestion method and subsequently normalized with regards to AI contents. RÉSUMÉ : Durant ce projet de thèse, financé par le Swiss National Science Funding (SNSF), j'ai étudié l'évolution des conditions redox et de la préservation de carbone organique dans le domnaine ouesttéthysien pendant trois excursions majeures du δ13C au Crétacé correspondant au Valanginien, à l'Aptien inférieur et à la limite Cénomanien-Turonien. Ces périodes sont caractérisées par des changements climatiques et environnementaux globaux associés à des perturbations dans le cylce du carbone. Pour L'excursion positive en δ13C du Valanginien, les analyses du carbone organique total (COT) et les observations palynologiques du domaine téthysien ont présenté des indications d'environnement pélagique relativementbienoxygéné. L'absence d'enrichissements en éléments traces sensibles aux conditions redox (TE) pendant l'excursion positive en δ13C confirme ces interprétations. Les données publiées de COT dans d'autres partie du globe indiquent cependant l'existence de conditions dys- à anaérobiques dans certains bassins restreints de l'Atlantique, l'Océan Austral et du Pacifique. L'évolution du phosphore (P) et la composition minéralogique des sédiments semblent indiquer un climat relativement chaud et humide avant l'excursion en δ13C entraînant une augmentation de l'altération continentale. Pendant le shift isotopique, une diminution des apports détritiques et du P suggèrent une transition vers des conditions plus arides. À l'Aptien Inférieur, le début de l'événement anoxique (OAE 1a) est marqué par une augmentation générale du P dans les sédiments indiquant une augmentation du niveau trophique à la base de l'excursion isotopique. Durant l'événement anoxique, les sédiments sont relativement appauvris en P. Cette diminution rapide associée à des enrichissements en TE est probablement liée à une remobilisation plus importante du P lors de la mise en place de conditions anoxiques dans les eaux de fond. Dans les environnements de bassin, le comportement des TE (enrichissements bien marqués) attestent de conditions réductrices bien marquées alors que dans les environnements moins profonds, les conditions semblent plutôt oxiques à dysoxiques. De plus, deux niveaux d'enrichissement en TE ont été observés dans la partie plus profonde de la Téthys, indiquant des fluctuations assez rapides dans l'intensité de l'anoxie de la colonne d'eau. Nous avons ensuite étudié les effets de l'événement anoxique de la fin du Cenomanien (OAE 2) dans un basin marginal de la marge nord de la Téthys avec la coupe de Chrummflueschlucht (à l'est de Euthal, Ct Schwyz). Les résultats ont montré que cette coupe présente un des enregistrements sédimentaires des plus complets de l'OAE 2 dans le domaine helvétique malgré un hiatus entre le pic 1 et 2 de l'excursion en δ13C. L'évolution du P montre une augmentation au début de l'OAE 2. Cependant, la distribution des TE indique que cette région n'a pas été affectée par des conditions réductrices trop importantes. Un second aspect de ce travail a été l'étude des différentes méthodes sur l'analyse de la distribution des TE. Des échantillons de l'OAE 1a ont été soumis à deux types d'extractions, l'une dite «totale » (attaque combinée d'acides HF/HNO3/HCI) et l'autre dite partielle » (HNO3). Les résultats obtenus suggèrent que les courbes de tendances des TE acquises par extraction partielle sont semblables à celle obtenues par extraction totale et normalisées par l'AI.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Impedance boundary conditions for pseudo-spectral time-domain methods in room acoustics

The pseudo-spectral time-domain (PSTD) method is an alternative time-marching method to classicalleapfrog finite difference schemes in the simulation of wave-like propagating phenomena. It is basedon the fundamentals of the Fourier transform to compute the spatial derivatives of hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acoustics simulations. However, one of the first issues to be solved consists on modeling wallabsorption. Unfortunately, there are no references in the technical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals to overcome this problem are presented, validated and compared to analytical solutions in different scenarios.

Impedance boundary conditions for pseudo-spectral time-domain methods in room acoustics

The Pseudo-Spectral Time Domain (PSTD) method is an alternative time-marching method to classical leapfrog finite difference schemes inthe simulation of wave-like propagating phenomena. It is based on the fundamentals of the Fourier transform to compute the spatial derivativesof hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acousticssimulations. However, one of the first issues to be solved consists on modeling wall absorption. Unfortunately, there are no references in thetechnical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals toovercome this problem are presented, validated and compared to analytical solutions in different scenarios.

Stable isotope and trace element stratigraphy across the Permian-Triassic transition: A redefinition of the boundary in the Velebit Mountain, Croatia

Stable isotopes of carbonates (delta(13)C(carb), delta(18)O(carb)), organic matter (delta(13)C(org), delta(15)N(org)) and major, trace and rare earth element (REE) compositions of marine carbonate rocks of Late Permian to Early Triassic age were used to establish the position of the Permian-Triassic boundary (PTB) at two continuous sections in the Velebit Mountain, Croatia. The chosen sections - Rizvanusa and Brezimenjaca - are composed of two lithostratigraphic units, the Upper Permian Transitional Dolomite and the overlying Sandy Dolomite. The contact between these units, characterized by the erosional features and sudden occurrence of ooids and siliciclastic grains, was previously considered as the chronostratigraphic PTB. The Sandy Dolomite is characterized by high content of non-carbonate material (up to similar to 30 wt.% insoluble residue), originated from erosion of the uplifted hinterland. A relatively rich assemblage of Permian fossils (including Geinitzina, Globivalvulina, Hemigordius, bioclasts of gastropods, ostracods and brachiopods) was found for the first time in Sandy Dolomite, 5 m above the lithologic boundary in the Rizvanusa section. A rather abrupt negative delta(13)C(carb) excursion in both sections appears in rocks showing no recognizable facies change within the Sandy Dolomite, -2 parts per thousand at Rizvanusa and -1.2 parts per thousand at Brezimenjaca, 11 m and 0.2 m above the lithologic contact, respectively. This level within the lower part of the Sandy Dolomite is proposed as the chemostratigraphic PTB. In the Rizvanusa section, the delta(13)C(org) values decline gradually from similar to-25 parts per thousand in the Upper Permian to similar to-29 parts per thousand in the Lower Triassic. The first negative delta(13)C(org) excursion occurs above the lithologic contact, within the uppermost Permian deposits, and appears to be related to the input of terrigenous material. The release of isotopically light microbial soil-biomass into the shallow-marine water may explain this sudden decrease of delta(13)C(org) values below the PTB. This would support the hypothesis that in the western Tethyan realm the land extinction, triggering a sudden drop of woody vegetation and related land erosion, preceded the marine extinction. The relatively low delta(15)N(org) values at the Permian-Triassic (P-Tr) transition level, close to approximate to 0 parts per thousand, and a secondary negative delta(13)C(org) excursion of -0.5 parts per thousand point to significant terrestrial input and primary contribution of cyanobacteria. The profiles of the concentrations of redox-sensitive elements (Ce, Mn, Fe, V), biogenic or biogenic-scavenged elements (P, Ba, Zn, V), Ce/Ce* values, and normalized trace elements, including Ba/Al, Ba/Fe, Ti/Al, Al/(Al + Fe + Mn) and Mn/Ti show clear excursions at the Transitional Dolomite-Sandy Dolomite lithologic boundary and the chemostratigraphic P-Tr boundary. The stratigraphic variations indicate a major regression phase marking the lithologic boundary, transgressive phases in the latest Permian and a gradual change into shallow/stagnant anoxic marine environment towards the P-Tr boundary level and during the earliest Triassic. (C) 2010 Elsevier B.V. All rights reserved.

New methods for controlling twin configurations and characterizing twin boundaries in 5M Ni-Mn-Ga for the development of applications

Traditional methods for studying the magnetic shape memory (MSM) alloys Ni-Mn-Ga include subjecting the entire sample to a uniform magnetic field or completely actuating the sample mechanically. These methods have produced significant results in characterizing the MSM effect, the properties of Ni-Mn-Ga and have pioneered the development of applications from this material. Twin boundaries and their configuration within a Ni-Mn-Ga sample are a key component in the magnetic shape memory effect. Applications that are developed require an understanding of twin boundary characteristics and, more importantly, the ability to predictably control them. Twins have such a critical role that the twinning stress of a Ni-Mn-Ga crystal is the defining characteristic that indicates its quality and significant research has been conducted to minimize this property. This dissertation reports a decrease in the twinning stress, predictably controlling the twin configuration and characterizing the dynamics of twin boundaries. A reduction of the twinning stress is demonstrated by the discovery of Type II twins within Ni-Mn-Ga which have as little as 10% of the twinning stress of traditional Type I twins. Furthermore, new methods of actuating a Ni-Mn-Ga element using localized unidirectional or bidirectional magnetic fields were developed that can predictably control the twin configuration in a localized area of a Ni-Mn-Ga element. This method of controlling the local twin configuration was used in the characterization of twin boundary dynamics. Using a localized magnetic pulse, the velocity and acceleration of a single twin boundary were measured to be 82.5 m/s and 2.9 × 107 m/s2, and the time needed for the twin boundary to nucleate and begin moving was less than 2.8 μs. Using a bidirectional magnetic field from a diametrically magnetized cylindrical magnet, a highly reproducible and controllable local twin configuration was created in a Ni-Mn-Ga element which is the fundamental pumping mechanism in the MSM micropump that has been co-invented and extensively characterized by the author.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.