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## Otimização de forma de cascas via deformação livre de forma baseado em NURBS; Shape optimization of shell via free-form deformation NURBSbased

Espath, Luis Felipe da Rosa
Tipo: Dissertação Formato: application/pdf
POR
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Neste trabalho buscou-se consolidar a união entre três áreas do conhecimento: a parametrização de curvas e superfícies do tipo B-spline racionais não-uniformes (NURBS), a otimização matemática e a análise estrutural por elementos finitos. A união destas três áreas é realizada neste trabalho através da otimização de formas de cascas, devido ao fato de que as características mecânicas dos materiais devem refletir-se na forma da estrutura e sua distribuição de espessura expressando um máximo desempenho. Estas variáveis, forma e distribuição de espessura, possuem um rol dominante nos projetos de engenharia, já que mínimas quantidades de materiais, uma frequência específica, um estado puro de tensões de membrana são típicos objetivos de projeto. Neste contexto, obter a forma e a distribuição de espessura adequadas são conceitos intrínsecos à otimização estrutural. Portanto, implementaram-se técnicas para modificar a geometria de cascas, sem perder a parametrização, sem a necessidade de gerar uma nova malha de elementos finitos ao se modificar a forma e ainda ter controle sobre a distorção da malha para evitar erros numéricos inaceitáveis. A modificação de forma é fomentada pelo código de otimização...

## Mathematical Models of Rigid Solid Objects

Requicha, Aristides A.G.
Fonte: University of Rochester. Production Automation Project Publicador: University of Rochester. Production Automation Project
Tipo: Relatório
ENG
Relevância na Pesquisa
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Computational models of solid objects are potentially useful in a variety of scientific and engineering fields, and in particular in the field of design and manufacturing automation for the mechanical industries. In recent years a multitude of modelling systems have been implemented both by research laboratories and commercial vendors, but little attention has been paid to the fundamental theoretical issues in geometric modelling. This has led to severe difficulties in assessing current and proposed systems, and in distinguishing essential capabilities and limitations from user conveniences and efficiency considerations. This paper seeks a sharp mathematical characterization of "rigid solids" in a manner that is suitable for studies in design and production automation. It draws heavily on established results in modern geometry and topology. Relevant results scattered throughout the mathematical literature are placed in a coherent framework and presented in a form accessible to engineers and computer scientists. A companion paper is devoted to a discussion of representational issues in the contest set forth by this paper.

## Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

DUFOUR, Jean-Marie; TAREK, Jouini
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 267450 bytes; application/pdf
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In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.

## Mathematical models of cell migration and self-organization in embryogenesis

DI COSTANZO, EZIO
EN
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In this thesis we deal with mathematical models and numerical simulations for cell migration and self-organization in embryogenesis. The part of biology which studies the formation and development of the embryo from fertilization until birth is called embryology. Morphogenesis is then the part of embryology which is concerned with the development of patterns and forms. It is well known that although morphogenesis processes are controlled at the genetic scale, genes themselves cannot create the pattern. In general a series of biological mechanisms of self-organization intervene during the early development and the formation of particular biological structures can not be anticipated solely by genetic information. This needs to be taken into account in the choice of a suitable mathematical formulation of such phenomena. Two main main topics will be investigated: we will analyze and mathematically model the self-organizing cell migration in the morphogenesis of the lateral line in the zebrafish (Danio rerio); in a second part, starting from this model, we will propose, and will study both from the analytical and the numerical point of view, a mathematical model of collective motion under only alignment and chemotaxis effects. The present thesis is organized in four chapters. In Chapter 1 we will introduce biological elements about the morphogenetic process occurring in the development of the lateral line in a zebrafish. After a first discussion on the lateral line system and on its fundamental relevance in the current scientific research...

## Exterior and evolutionary skew-symmetric differential forms and their role in mathematical physics

Petrova, L. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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At present the theory of skew-symmetric exterior differential forms has been developed. The closed exterior forms possess the invariant properties that are of great importance. The operators of the exterior form theory lie at the basis of the differential and integral operators of the field theory. However, the theory of exterior forms, being invariant one, does not answer the questions related to the evolutionary processes. In the work the readers are introduced to the skew-symmetric differential forms that possess evolutionary properties. They were called evolutionary ones. The radical distinction between the evolutionary forms and the exterior ones consists in the fact that the exterior forms are defined on manifolds with closed metric forms, whereas the evolutionary forms are defined on manifolds with unclosed metric forms. The mathematical apparatus of exterior and evolutionary forms allows description of discrete transitions, quantum steps, evolutionary processes, generation of various structures. These are radically new possibilities of the mathematical physics. A role of exterior and evolutionary forms in the mathematical physics is conditioned by the fact that they reflect properties of the conservation laws and allow elucidate a mechanism of evolutionary processes in material media...

## Pair and Impar, Even and Odd Form Fields and Electromagnetism

da Rocha, Roldao; Rodrigues Jr, Waldyr A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In this paper after reviewing the Schouten and de Rham definition of impair and pair differential form fields (not to be confused with differential form fields of even and odd grades) we prove that in a relativistic spacetime it is possible (despite claims in contrary) to coherently formulate electromagnetism (and we believe any other physical theory) using only pair form fields or, if one wishes, using pair and impair form fields together, in an appropriate way. Those two distinct descriptions involve only a mathematical choice and do not seem to lead to any observable physical consequence if due care is taken. Moreover, we show in details that a formulation of electromagnetic theory in the Clifford bundle formalism of differential forms where the two Maxwell equations of the so called free metric approach becomes a single equation is compatible with both formulations of electromagnetism just mentioned above. Moreover we derive directly from Maxwell equation the density of force (coupling of the electromagnetic field with the charge current) that is a postulate in the free metric approach to electromagnetism. We recall also a formulation of the engineering version of Maxwell equations using electric and magnetic fields as objects of the same nature...

## Supplementary balance laws and the entropy principle

Preston, Serge
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In this work we study the mathematical aspects of the development in the continuum thermodynamics known as the "Entropy Principle". It started with the pioneering works of B.Coleman, W.Noll and I. Muller in 60th of XX cent. and got its further development mostly in the works of G. Boillat, I-Shis Liu and T.Ruggeri. "Entropy Principle" combines in itself the structural requirement on the form of balance laws of the thermodynamical system (denote such system $(\mathcal{C})$) and on the entropy balance law with the convexity condition of the entropy density. First of these requirements has pure mathematical form defining so called "supplementary balance laws" (shortly SBL) associated with the original balance system. Vector space of SBL can be considered as a kind of natural "closure" of the original balance system. This space includes the original balance laws, the entropy balance, the balance laws corresponding to the symmetries of the balance system and some other balance equations. We consider the case of Rational Extended Thermodynamics where densities, fluxes and sources of the balance equations do not depend on the derivatives of physical fields $y^i$. We present the basic structures of RET: Lagrange-Liu equations,"main fields"...

## Unified Form Language: A domain-specific language for weak formulations of partial differential equations

Alnaes, Martin S.; Logg, Anders; Oelgaard, Kristian B.; Rognes, Marie E.; Wells, Garth N.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies for multi-field problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted.; Comment: To appear in ACM Transactions on Mathematical Software

## Energy and electromagnetism of a differential form

Navarro, J.; Sancho, J. B.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Let X be a smooth manifold of dimension 1+n endowed with a lorentzian metric g, and let T be the electromagnetic energy tensor associated to a 2-form F. In this paper we characterize this tensor T as the only 2-covariant natural tensor associated to a lorentzian metric and a 2-form that is independent of the unit of scale and satisfies certain condition on its divergence. This characterization is motivated on physical grounds, and can be used to justify the Einstein-Maxwell field equations. More generally, we characterize in a similar manner the energy tensor associated to a differential form of arbitrary order k. Finally, we develop a generalized theory of electromagnetism where charged particles are not punctual, but of an arbitrary fixed dimension p. In this theory, the electromagnetic field F is a differential form of order 2+p and its electromagnetic energy tensor is precisely the energy tensor associated to F.; Comment: 28 pages. Referee's suggestions added. To appear in Journal of Mathematical Physics

## First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-form

Hansen, Markus; Strobl, Thomas
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant algebroid structures by closed 4-forms H. The presentation is kept pedagogical and accessible to physicists as well as to mathematicians, explaining in detail in particular the interplay of field transformations in a sigma model with the type of geometrical structures induced on a target. In fact, as we also show, even if one does not know the mathematical concept of a Courant algebroid, the study of a rather general class of 3-dimensional sigma models leads one to that notion by itself. Courant algebroids became of relevance for mathematical physics lately from several perspectives - like for example by means of using generalized complex structures in String Theory. One may expect that their twisting by the curvature H of some 3-form Ramond-Ramond gauge field will become of relevance as well.; Comment: 25 pages, invited contribution to the Wolfgang Kummer memorial volume

## Skew-symmetric forms: On integrability of equations of mathematical physics

Petrova, L. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived from these equations. Such a relation connects the differential of state functional and the skew-symmetric form. This relation proves to be nonidentical, and this fact points to the nonintegrability of the equations. In this case a solution to the equations is a functional, which depends on the commutator of skew-symmetric form that appears to be unclosed. However, under realization of the conditions of degenerate transformations, from the nonidentical relation it follows the identical one on some structure. This points out to the local integrability and realization of a generalized solution. In doing so, in addition to the exterior forms, the skew-symmetric forms, which, in contrast to exterior forms, are defined on nonintegrable manifolds (such as tangent manifolds of differential equations, Lagrangian manifolds and so on), were used. In the present paper, the partial differential equations, which describe any processes, the systems of differential equations of mechanics and physics of continuous medium and field theory equations are analyzed.; Comment: 8 pages...

## On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Fauser, Bertfried; Ablamowicz, Rafal
Tipo: Artigo de Revista Científica
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35.81%
Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <-> \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1...

## Assumptions and Axioms: Mathematical Structures to Describe the Physics of Rigid Bodies

Butler, Philip H.; Gresnigt, Niels G.; Renaud, Peter F.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational and rotational properties of such rigid bodies. Nearly all elementary and advanced texts make physical assumptions that are subtly different from ours, and as a result we develop a mathematical description that is subtly different from the standard mathematical structure. Using the homogeneity and isotropy of space, we investigate the translational and rotational features of rigid bodies in two and three dimensions. We find that the concept of rigid bodies and the concept of the homogeneity of space are intrinsically linked. The geometric study of rotations of rigid objects leads to a geometric product relationship for lines and vectors. By requiring this product to be both associative and to satisfy Pythagoras' theorem, we obtain a choice of Clifford algebras. We extend our arguments from space to include time. By assuming that ct=l and rewriting this in Lorentz invariant form as c^2t^2-x^2-y^2-z^2=0 we obtain a generalization of Pythagoras to spacetime. This leads us directly to establishing that the Clifford algebra CL(1...

## Reduction formula of form factors for the integrable spin-s XXZ chains and application to the correlation functions

Deguchi, Tetsuo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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For the integrable spin-s XXZ chain we express explicitly any given spin-$s$ form factor in terms of a sum over the scalar products of the spin-1/2 operators. Here they are given by the operator-valued matrix elements of the monodromy matrix of the spin-1/2 XXZ spin chain. In the paper we call an arbitrary matrix element of a local operator between two Bethe eigenstates a form factor of the operator. We derive all important formulas of the fusion method in detail. We thus revise the derivation of the higher-spin XXZ form factors given in a previous paper. The revised method has several interesting applications in mathematical physics. For instance, we express the spin-$s$ XXZ correlation function of an arbitrary entry at zero temperature in terms of a sum of multiple integrals.; Comment: 41 pages, no figures

## On the Integrated Form of the BBGKY Hierarchy for Hard Spheres

Spohn, Herbert
Tipo: Artigo de Revista Científica
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In my book Large Scale Dynamics of Interacting Particles'' [S] I refer to an unpublished note from early 1985 on the BBGKY hierarchy for hard spheres. My main point there was to provide a direct probabilistic proof for the time-integrated version of the hierarchy. Over recent years there has been repeated interest in this derivation, which encourages me to make my note public. I decided to leave it in its original form including likely inaccuracies. The work of R. Illner and M. Pulvirenti [IP] appeared in September 1985, see also the book by C. Cercignani, R. Illner, and M. Pulvirenti [CIP], who prove the same result using special flow representation and methods from the theory of differential operators. [S] H. Spohn, Large Scale Dynamics of Interacting Particles, Texts and Monographs in Physics, Springer-Verlag, Heidelberg, 1991. [IP] R. Illner and M. Pulvirenti, A derivation of the BBGKY-hierarchy for hard sphere particle systems, Transport Theory and Stat. Phys. \textbf{16}, 997--1012 (1987), preprint DM-388-IR, September 1985. [CIP] C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Applied Mathematical Sciences \textbf{106}, Springer-Verlag, New York, 1994.

## General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids

Grutzmann, Melchior; Strobl, Thomas
Tipo: Artigo de Revista Científica
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Starting with minimal requirements from the physical experience with higher gauge theories, i.e. gauge theories for a tower of differential forms of different form degrees, we discover that all the structural identities governing such theories can be concisely recombined into a so-called Q-structure or, equivalently, a Lie infinity algebroid. This has many technical and conceptual advantages: Complicated higher bundles become just bundles in the category of Q-manifolds in this approach (the many structural identities being encoded in the one operator Q squaring to zero), gauge transformations are generated by internal vertical automorphisms in these bundles and even for a relatively intricate field content the gauge algebra can be determined in some lines only and is given by the so-called derived bracket construction. This article aims equally at mathematicians and theoretical physicists; each more physical section is followed by a purely mathematical one. While the considerations are valid for arbitrary highest form-degree p, we pay particular attention to p=2, i.e. 1- and 2-form gauge fields coupled non-linearly to scalar fields (0-form fields). The structural identities of the coupled system correspond to a Lie 2-algebroid in this case and we provide different axiomatic descriptions of those...

## A new mathematical representation of Game Theory, I

Wu, Jinshan
Tipo: Artigo de Revista Científica
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In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to define their inner product so as to form them as a Hilbert space, and then form a Hilbert space of system state. Basic ideas, concepts and formulas in Game Theory have been reexpressed in such a space of system state. This space provides more possible strategies than traditional classical game and traditional quantum game. So besides those two games, more games have been defined in different strategy spaces. All the games have been unified in the new representation and their relation has been discussed. General Nash Equilibrium for all the games has been proposed but without a general proof of the existence. Besides the theoretical description, ideas and technics from Statistical Physics, such as Kinetics Equation and Thermal Equilibrium can be easily incorporated into Game Theory through such a representation. This incorporation gives an endogenous method for refinement of Equilibrium State and some hits to simplify the calculation of Equilibrium State. The more privileges of this new representation depends on further application on more theoretical and real games. Here...

## Analysis of the equations of mathematical physics and foundations of field theories with the help of skew-symmetric differential forms

Petrova, L. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of mathematical physics, the relation between mathematical physics and field theory, to understand the mechanism of evolutionary processes that develop in material media and lead to emergency of physical structures forming physical fields. This discloses a physical meaning of such concepts like "conservation laws", "postulates" and "causality" and gives answers to many principal questions of mathematical physics and general field theory. In present paper, beside the exterior forms, the skew-symmetric differential forms, whose basis (in contrast to the exterior forms) are deforming manifolds, are used. Mathematical apparatus of such differential forms(which were named evolutionary ones) includes nontraditional elements like nonidentical relations and degenerate transformations and this enables one to describe discrete transitions, quantum steps, evolutionary processes, and generation of various structures.; Comment: 36 pages

## Equivalence of Two Mathematical Forms for the Bound Angular Momentum of the Electromagnetic Field

Stewart, Andrew
Fonte: Taylor & Francis Group Publicador: Taylor & Francis Group
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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It is shown that the mathematical form obtained in a recent paper for the angular momentum of the electromagnetic field in the vicinity of electric charge is equivalent to another form obtained previously.

## On the Structure of Rationality in the Thought and Invention or Creation of Physical Theories; On the Structure of Rationality in the Thought and Invention or Creation of Physical Theories

Paty, Michel; Equipe Rehseis – Laboratoire Sphere (Science, Philosophie, Histoire, Recherche et Enseignement) UMR 7219 CNRS et Université Paris 7 – Diderot
Fonte: Federal University of Santa Catarina – UFSC Publicador: Federal University of Santa Catarina – UFSC
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; Formato: application/pdf