The pressures and impact forces acting on a hull while experiencing bow wave slamming is analyzed using Vorus' Impact Theory. The theory extends the hydrodynamic analysis of planing hulls from simple wedges to irregular shapes using a Boundary Element Method. A Fortran-based code developed by the Author is used to analyze hullforms. Linear strip theory is used to extend the analysis over a three dimensional hull. Post-processing of output data gives hull pressure distributions at different time steps and is visually presentable. Impact pressure, Impact force, Planing, Wave slamming, Bow impact, Vorus' theory, Boundary Element Method, Linear strip theory

The objectives of this research were 1) to investigate the effects of hydrodemolition treatment timing on chloride concentration profiles in concrete bridge decks for depths of concrete removal below the top mat of reinforcing steel and 2) to investigate factors that influence the occurrence of blow-throughs in concrete bridge decks when hydrodemolition is used. The research results are intended to provide engineers with guidance about the latest timing of hydrodemolition that can maintain a chloride concentration level below 2.0 lb of chloride per cubic yard of concrete at the levels of both the top and bottom mats of reinforcing steel, as well as about conditions that may indicate a higher probability of blow-through during hydrodemolition. The scope of this research included a questionnaire survey of hydrodemolition companies to summarize common practices in the field, numerical modeling of chloride concentration to investigate hydrodemolition treatment timing on typical Utah bridge decks, and structural analysis to investigate factors that influence the occurrence of blow-throughs during hydrodemolition. While some survey respondents indicated that certain parameters vary, the responses are valuable for understanding typical practices and were used to design the numerical experiments. The numerical modeling generated chloride concentration profiles through a 75-year service life given a specific original cover depth (OCD), treatment time, and surface treatment usage. The results indicate that, when a surface treatment is used, the concentration at either the top or bottom mat of reinforcing steel does not reach or exceed 2.0 lb of chloride per cubic yard of concrete after hydrodemolition during the 75 years of simulated bridge deck service life. The results also indicate that, when a surface treatment is not used, the chloride concentration at the top mat of reinforcement exceeds 2.0 lb of chloride per cubic yard of concrete within 10, 15, and 20 years for OCD values of 2.0, 2.5, and 3.0 in., respectively. The numerical experiments generated results in terms of the main effect of each input variable on the occurrence of blow-throughs and interactions among selected input variables. For each analysis, blow-through can be expected when the calculated factor of safety is less than 1.0. The factor of safety significantly increases with increasing values of transverse rebar spacing and concrete compressive strength and decreasing values of depth of removal below the bottom of the top reinforcing mat, orifice size, and water pressure within the ranges of these parameters investigated in this experimentation. The factor of safety is relatively insensitive to jet angle. For both case studies evaluated in this research, the blow-through analysis correctly predicted a high or low potential for blow-through on the given deck.

We consider the Cauchy problem for the focusing energy critical NLS with inverse square potential. The energy of the solution, which consists of the kinetic energy and potential energy, is conserved for all time. Due to the focusing nature, solution with arbitrary energy may exhibit various behaviors: it could exist globally and scatter like a free evolution, persist like a solitary wave, blow up at finite time, or even have mixed behaviors. Our goal in this thesis is to fully characterize the solution when the energy is below or at the level of the energy of the ground state solution $W_a$. Our main result contains two parts. First, we prove that when the energy and kinetic energy of the initial data are less than those of the ground state solution, the solution exists globally and scatters. Second, we show a rigidity result at the level of ground state solution. We prove that among all solutions with the same energy as the ground state solution, there are only two (up to symmetries) solutions $W_a^+, W_a^-$ that are exponential close to $W_a$ and serve as the threshold of scattering and blow-up. All solutions with the same energy will blow up both forward and backward in time if they go beyond the upper threshold $W_a^+$; all solutions with the same energy will scatter both forward and backward in time if they fall below the lower threshold $W_a^-$. In the case of NLS with no potential, this type of results was first obtained by Kenig-Merle \cite{R: Kenig focusing} and Duyckaerts-Merle \cite{R: D Merle}. However, as the potential has the same scaling as $\Delta$, one can not expect to extend their results in a simple perturbative way. We develop crucial spectral estimates for the operator $-\Delta+a/|x|^2$, we also rely heavily on the recent understanding of the operator $-\Delta+a/|x|^2$ in \cite{R: Harmonic inverse KMVZZ}.

This thesis contributes towards the maximal-in-time well-posedness theory of three nonlinear dispersive partial differential equations (PDEs). We are interested in questions that extend beyond the usual well-posedness theory: what is the ultimate fate of solutions? How does Hamiltonian structure influence PDE dynamics? How does randomness, within the PDE or the initial data, interact with well-posedness of the Cauchy problem? The first topic of this thesis is the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of surface water waves. We prove a mass concentration property for H^1-solutions, analogous to the one known for the L^2-critical nonlinear Schrodinger equation. We also prove a mass concentration result for L^2-solutions. The second topic of this thesis is the invariance of the Gibbs measure for the (gauge transformed) periodic quartic KdV equation. The Gibbs measure is a probability measure supported on H^s for s<1/2, and local solutions to the quartic KdV cannot be obtained below H^{1/2} by using the standard fixed point method. We exhibit nonlinear smoothing when the initial data are randomized, and establish almost sure local well-posedness for the (gauge transformed) quartic KdV below H^{1/2}. Then, using the invariance of the Gibbs measure for the finite-dimensional system of ODEs given by projection onto the first N>0 modes of the trigonometric basis, we extend the local solutions of the (gauge transformed) quartic KdV to global solutions, and prove the invariance of the Gibbs measure under the flow. Inverting the gauge, we establish almost sure global well-posedness of the (ungauged) periodic quartic KdV below H^{1/2}. The third topic of this thesis is well-posedness of the stochastic KdV-Burgers equation. This equation is studied as a toy model for the stochastic Burgers equation, which appears in the description of a randomly growing interface. We are interested in rigorously proving the invariance of white noise for the stochastic KdV-Burgers equation. This thesis provides a result in this direction: after smoothing the additive noise (by a fractional derivative), we establish (almost sure) local well-posedness of the stochastic KdV-Burgers equation with white noise as initial data. We also prove a global well-posedness result under an additional smoothing of the noise.

A first goal of this thesis is to contribute to the knowledge of cohomological properties of non-standard multigraded modules. In particular we study the Hilbert function of a non-standard multigraded module, the asymptotic depth of the homogeneous components of a multigraded module and the asymptotic depth of the Veronese modules. To reach our purposes, we generalize some cohomological invariants to the non-standard multigraded case and we study properties on the vanishing of local cohomology modules. In particular we study the generalized depth of a multigraded module.In chapters 2, 3 and 4, we consider multigraded rings S, finitely generated over the local ring S0 by elements of degrees g1,.,gr with gi=(g1i,.,gii,.,0) non-negative integral vectors and gii not zero for i=1,.,r. In Chapter 2, we prove that the Hilbert function of a multigraded S-module is quasi-polynomial in a cone of N^r. Moreover the Grothendieck-Serre formula is satisfied in our situation as well.In Chapter 3, using the quasi-polynomial behavior of the Hilbert function of the Koszul homology modules of a multigraded S-module M with respect to a system of generators of the maximal ideal of S0, we can prove that the depth of the homogeneous components of M is constant for degrees in a subnet of a cone of N^r defined by g1,.,gr. In some cases we can assure constant depth in all the cone. By considering the multigraded blow-up algebras associated to ideals I1,.,Ir in a Noetherian local ring (R,m), we can prove that the depth of R/I1^n1.Ir^nr is constant for n1,.,nr large enough.In Chapter 4, we study the depth of (a,b)-Veronese modules for a, b large enough. In particular we prove that in almost-standard case (i.e. the degrees of the generators are positive multiples of the canonical basis) with S0 a quotient of a regular local ring, this depth is constant for a, b in some regions of N^r. To reach this result we need a previous study about Veronese modules and about the vanishing of local cohomology modules. In particular we prove that, in the moregeneral case, if S0 is a quotient of a regular local ring, the generalized depth is invariant by taking Veronese transforms. Moreover in the almost-standard case the generalized depth coincides with the index of finite graduation of the local cohomology modules with respect to the homogeneous maximal ideal.A second goal of the thesis is the study of the depth of blow-up algebras associated to an ideal. In Chapter 5 we obtain refined versions of some conjectures on the depth of the associated graded ring of an ideal. By using certain non-standard bigraded structures, the integers that appear in Guerrieri's Conjecture and in Wang's Conjecture can be interpreted as a multiplicities of some bigraded modules. In particular we have given an answer to the question formulated by A. Guerrieri and C. Huneke in 1993. We have proved that given an m-primary ideal I in a Cohen-Macaulay local ring (R,m) of dimension d>0 with minimal reduction J, assuming that the lengths of the homogeneous components of the Valabrega-Valla module of I and J are less than or equal to 1, then the depth of the associated graded ring of I is greater than or equal to d-2.Finally, in Chapter 6, the study of the Hilbert function of certain submodules of the bigraded modules studied before, allows us to prove some cases in which the Hilbert function of an m-primary ideal in a one-dimensional Cohen-Macaulay local ring is non-decreasing. / CATALÀ: TÍTOL DE LA TESI: "Estructures Multigraduades i la Profunditat d'Àlgebres de Blow-up"TEXT DEL RESUM:Un primer objectiu d'aquesta tesi és contribuir al coneixement de propietats cohomològiques de mòduls multigraduats no-estàndard. En particular estudiem la funció de Hilbert d'un mòdul multigraduat no-estàndard, la profunditat asimptòtica de les components homogènies d'un mòdul multigraduat i la profunditat asimptòtica dels mòduls de Veronese. Per a això, generalitzem alguns invariants cohomològics en el cas multigraduat no-estàndard i estudiem propietats d'anul·lació de mòduls de cohomologia local. En particular estudiem la profunditat generalitzada d'un mòdul multigraduat.En els capítols 2, 3 i 4, considerem anells multigraduats S finitament generats sobre l'anell local S0 per elements de graus g1,...,gr amb gi=(g1i,...,gii,...,0) vectors enters no-negatius i gii no nul per a i=1,...,r. Al Capítol 2, demostrem que la funció de Hilbert d'un S-mòdul multigraduat és quasi-polinòmica en un con de N^r. A més es satisfà la fórmula de Grothendieck-Serre en la nostra situació.Al Capítol 3, utilitzant el comportament quasi-polinòmic de la funció de Hilbert dels mòduls d'homologia de Koszul d'un S-mòdul M multigraduat respecte d'un sistema de generadors de l'ideal maximal de S0, podem demostrar que la profunditat de les components homogènies de M és constant per a graus en una subxarxa d'un con de N^r definit per g1,...,gr. En alguns casos es pot assegurar profunditat constant en tot un con. Considerant els anells de blow-up multigraduats associats a ideals I1,...,Ir en un anell local Noetherià (R,m), podem demostrar que la profunditat de R/I1^n1...Ir^nr és constant per a n1,...,nr prou grans.Al Capítol 4, estudiem la profunditat dels mòduls de (a,b)-Veronese per a a,b prou grans. En particular demostrem que en el cas quasi-estàndard (i.e. amb generadors de graus múltiples positius de la base canònica) amb S0 quocient d'un anell local regular, aquesta profunditat és constant per a a,b en certes regions de N^r. Per arribar a aquest resultat ens cal un estudi previ dels mòduls de Veronese i de l'anul·lació de mòduls de cohomologia local. En particular demostrem que, en el cas més general, si S0 és quocient d'un anell local regular, la profunditat generalitzada és invariant per transformacions Veronese. A més en el cas quasi-estàndard la profunditat generalitzada coincideix amb l'índex de graduació finita dels mòduls de cohomologia local respecte de l'ideal homogeni maximal.Un segon objectiu de la tesi és l'estudi de la profunditat de les àlgebres de blow-up associades a un ideal. Al Capítol 5 s'obtenen versions refinades de conjectures sobre la profunditat de l'anell graduat associat a un ideal. Utilitzant algunes estructures bigraduades no-estàndard, es poden interpretar els enters que apareixen a la Conjectura de Guerrieri i a la Conjectura de Wang com a multiplicitats de mòduls bigraduats. En particular hem pogut donar resposta a una pregunta formulada per A. Guerrieri i C. Huneke al 1993. Hem demostrat que donat un ideal I m-primari en un anell local (R,m) Cohen-Macaulay de dimensió d>0 amb reducció minimal J, suposant que les longituds de les components homogènies del mòdul de Valabrega-Valla de I i J siguin menors o iguals que 1, aleshores la profunditat de l'anell graduat associat a I és major o igual que d-2.Finalment, al Capítol 6, l'estudi de la funció de Hilbert de certs submòduls dels mòduls bigraduats estudiats anteriorment, permet provar alguns casos en què la funció de Hilbert d'un ideal m-primari en un anell local Cohen-Macaulay de dimensió 1, és no decreixent.

No description available.

Diffusion in bulk has been well studied and our understanding may be said to be adequate if not complete. Similarly, surface diffusion has been investigated by a number of workers and a fair understanding of it has emerged. When guest particles are confined within the micropores of solids such as zeolites, the resulting phase is neither bulk nor an adsorbed phase but something in between. Properties of such a phase have not been understood sufficiently. Such phase found within these porous solids display rich variety in their property. In part, such a variety arises from the large number of factors that determine their properties. Present thesis attempts to study the relationship of some of these factors, viz., the pore size and the disorder in the pore sizes, the sorbate sizes, the role of orienta-tional motion, the inhomogeneities in temperature etc. to diffusion of the guest molecules in porous solids. Chapter 1 gives a brief overview of the literature and the present understanding in the field of diffusion of spherical atoms and small molecules in microporous materials with special attention to zeolites.,The discussion is focussed on the experimental, theoretical and computer simulation results reported in the last few years. In chapter 2 an analytic expression is derived for the diffusion coefficient of a sorbate in a crystalline porous solid with bottlenecks. This is done by assuming a situation of quasiequi-Hbrium and by applying some elementary results of kinetic theory of gases. The diffusion coefficients obtained from the analytic expression is found to agree well with the molecular dynamics results. Further, it is found to reproduce the diffusion anomaly and its temperature dependence for different zeolites such as Y, A and p. The present calculations provide a strong theoretical support for the levitation effect obtained so far purely from molecular dynamics calculations. The computational effort involved in evaluating the derived expression is at least an order of magnitude less as compared to the molecular dynamics simulations. Levitation effect is found to exist in crystalline porous solids, irrespective of the geometry and topology of the void network of the host - the zeolite. Does levitation effect exist in non-crystalline porous solids where a distribution of pore sizes is seen instead of a single size? Chapter 3 attempts to answer this question via detailed molecular dynamics simulations on zeolite Y whose perfectly crystalline pore structure has been modified by introducing disorder. A normal distribution characterized by its width <TQ of 12-ring window diameters has been generated. Investigation of motion of spherical sorbates within such a disordered host suggests that levitation effect persists although the intensity of the anomalous peak is reduced compared to crystalline faujasite. Further, there is a breakdown of the linear relationship between the self-diffusivity D and 1 /^ where a99 is the sorbate diameter in the disordered host. Comparison of similarity between the effect of temperature and that of disorder are discussed. Chapter 4 investigates the role of orientation on diffusion of methane in zeolite NaCaA during intercage and intracage migration. In this work, diffusion of a five site model of methane within porous zeolite A has been investigated by molecular dynamics simulation. Methane exhibits interesting orientational preference during its passage through the 8-membered window, the rate determining step for overall diffusion: (2+2) (or scissor) orientation is preferred to (1+3) (or inverted umbrella) orientation. This suggests strong translational-orientational coupling. This is supported by ab initio mixed basis calculations thereby suggesting that the results are not a consequence of the classical potential employed. Partial freezing of certain rotational degrees of freedom is observed during the passage of methane through the 8-ring window. Intracage motion of methane shows that methane performs a rolling motion rather than a sliding motion within the supercage. In Chapter 5, diffusion of methane and neopentane through the pores of zeolite NaY has been investigated by means of molecular dynamics simulation. Intercage motion consisting of diffusion through 12-ring window of zeolite NaY is seen to occur with strong orientational preference for (2+2) orientation in the case of neopentane but not methane. Comparison of the result with methane diffusion through the 8-ring window of zeolite NaCaA reported in chapter 4 suggests that such a preferential orientation is a typical characteristic of systems whose levitation parameter is close to unity. Temperature dependence of translational-orientational coupling during the passage through the bottleneck has been obtained. As seen earlier, partial freezing of certain rotational degrees of freedom also exists. Little or no freezing is observed around the molecular axis of symmetry parallel to the vector, ft, perpendicular to the window plane since it does the orientation of the molecule with respect to fi. Analysis of intracage motion suggests existence of rolling motion in preference to sliding motion both in methane and neopentane. It is suggested that globular molecules show a predominance of rolling motion in comparison to anisotropic molecules such as benzene. Chapter 6 reports results from molecular dynamics(MD) simulations and its comparison to the quasi-elastic neutron scattering (QENS) measurements of the diffusion of propane, NaY zeolite, at different temperatures and at a relatively high loading. The contributions to S(Q, cu) from ballistic and diffusive motions are analysed. The self-diffusivity D has been calculated from mean squared displacement (MSD) as well as from the dynamic structure factor (S(Q,cu)) computed from the MD simulation. Both the values are consistent with each other. Also, they are in reasonable agreement with the experimental QENS results. The MD results indicate a fixed jump length diffusion process, whereas, the QENS data fits well to a jump diffusion model with a Gaussian distribution of jump lengths. Diffusion is often accompanied by a reaction or sorption which in turn can induce temperature inhomogeneities. In chapter 7 Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported for the presence of a hot zone presumed to be created by a reaction. Our simulations show that the presence of localized hot regions can alter both the kinetic and transport properties such as diffusion. An enhancement in diffusion coefficient is seen in the presence of a local hot spot. Further, the enhancement of the diffusion constant is greater for systems with larger barrier height, a surprising result that may be of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot or cold zone in addition to that which normally exists between them via concentration. Chapter 8 explores the possibility of exploiting a judicial combination of levitation effect and blow-torch effect for the separation of mixtures. In this study, Monte Carlo simulations have been carried out for three different binary mixtures in zeolite NaCaA with hot spot placed just before the position of the window along one direction. The binary mixture consisting of two types of particles both of which are from the linear regime does not separate well while the separation achieved of the mixture with one component from the linear regime and another from the anomalous regime is excellent. The separation factors obtained in the case of the latter mixture is more than an order of magnitude larger than that of the conventional separation methods. In the case of Ne-Ar mixture in NaCaA also, where Ne is in the linear regime and Ar is in the anomalous regime, the separation attained is excellent. These results suggest that a combination of levitation and blow-torch effects can be used to obtain extraordinary separation. Here the levitation effect specifies the sign and the magnitude of the energy barrier. The blow-torch drives the component in positive or negative direction depending on the energy barrier of the guest species. An appendix describes an additional but unrelated work carried out: a Monte Carlo study of the orthorhombic(fJ), monoclinic(ct) and liquid phases of toluene in the isobaric isothermal ensemble employing variable shape simulation cell. The structure has been characterized in terms of the radial distribution functions and orientational correlation functions. The transition from the orthorhombic low temperature (3-phase to the high temperature monoclinic cc-phase has been successfully simulated. The transition is first order and lies between 140 and 145K in agreement with experiment. The reverse transition from the a-to the (3-phase does not take place in agreement with experiment. The liquid phase density and the heat of vapourization are in good agreement with the experimental values.

Plusieurs problèmes d'optimisation liés à la théorie du transport optimal, concernant aussi des critères de concentration, sont étudiés. Il s'agit, pour ce qui est des primiers chapitres, de la minimization de fonctionnelles definies sur les mesures marginales du porblème de transport, en demandant que l'une soit concentrée et l'autre diffusée, alors que les deux doivent être proche au sense du transport de masse. D'autres chapitres portent sur des modèles différentes qui considèrent la concentration des parcours suivis par les particules lors du mouvement, en donnant des effets de congestion ou branchement. Plusieurs problèmes font apparaître des structures de dimension 1 (reseaux, supports rectifiables de mesures vectorielles, ensemble sous contraintes de longueur...) et leur régularité (blow-up) est étudiée dans les deux derniers chapitres. Les modèles viennent dans la majorité des cas de possibles applications à la planification urbaine, la biologie (arbres, feuilles et système sanguin), la géophysique (bassins fluviaux) et la mécanique des fluides. La thèse a été écrite sous la direction du Prof. Buttazzo et soutenue à l'Ecole Normale Supérieure de Pise.

Hydraulic bulge forming has been used as a method to determine the properties of sheet metal alloys in biaxial stretching at room temperature. Gas-pressure bulge forming alleviates the issues of using hydraulic fluids when the tests are conducted at high temperatures (above 200°C). Testing a sheet metal alloy by gas-pressure blow-forming (GPBF) under controlled temperature and pressure conditions requires an accurate and reliable mechanism that delivers repeatable results. It was the purpose of this work to design and implement such an instrument. This instrument should deliver real-time data for material displacement during forming, which can then be used to better understand material plastic response and formability. Four different subsystems within this mechanism must interact, but also have enough independence for analysis and for assembly purposes. The combined sub-systems produced a GPBF apparatus capable of forming a sheet aluminum alloy AA5182 with a thickness of 1.5 mm into a dome with a height nearly equal to its radius under a constant gas pressure as low as 40 psi at 450°C. This GPBF apparatus produced, for the first time, in-situ data for dome peak displacement during gas-pressure bulge forming of AA5182 sheet at 450°C. / text

Ramsey Theorem, in the most simple form, states that if we are given a positive integer l, there exists a minimal integer r(l), called the Ramsey number, such any partition of the edges of K_r(l) into two sets, i.e. a 2-coloring, yields a copy of K_l contained entirely in one of the partitioned sets, i.e. a monochromatic copy of Kl. We prove an extension of Ramsey's Theorem, in the more general form, by replacing complete graphs by multipartite graphs in both senses, as the partitioned set and as the desired monochromatic graph. More formally, given integers l and k, there exists an integer p(m) such that any 2-coloring of the edges of the complete multipartite graph K_p(m);r(k) yields a monochromatic copy of K_m;k . The tools that are used to prove this result are the Szemeredi Regularity Lemma and the Blow Up Lemma. A full proof of the Regularity Lemma is given. The Blow-Up Lemma is merely stated, but other graph embedding results are given. It is also shown that certain embedding conditions on classes of graphs, namely (f , ?) -embeddability, provides a method to bound the order of the multipartite Ramsey numbers on the graphs. This provides a method to prove that a large class of graphs, including trees, graphs of bounded degree, and planar graphs, has a linear bound, in terms of the number of vertices, on the multipartite Ramsey number.