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Добірка наукової літератури з теми "Variational critical problems"

Автор: Grafiati
Опубліковано: 10 березня 2023

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Статті в журналах з теми "Variational critical problems"

1

Ambrosetti, Antonio. "Critical points and nonlinear variational problems." Mémoires de la Société mathématique de France 1 (1992): 1–139. http://dx.doi.org/10.24033/msmf.362.

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2

Prigozhin, Leonid. "Variational inequalities in critical-state problems." Physica D: Nonlinear Phenomena 197, no. 3-4 (October 2004): 197–210. http://dx.doi.org/10.1016/j.physd.2004.07.001.

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3

Ambrosetti, A., J. Garcia Azorero, and I. Peral. "Elliptic Variational Problems in RN with Critical Growth." Journal of Differential Equations 168, no. 1 (November 2000): 10–32. http://dx.doi.org/10.1006/jdeq.2000.3875.

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4

Ghoussoub, Nassif, and Frédéric Robert. "Hardy-singular boundary mass and Sobolev-critical variational problems." Analysis & PDE 10, no. 5 (July 1, 2017): 1017–79. http://dx.doi.org/10.2140/apde.2017.10.1017.

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5

Chow, Shui-Nee, and Reiner Lauterbach. "A bifurcation theorem for critical points of variational problems." Nonlinear Analysis: Theory, Methods & Applications 12, no. 1 (January 1988): 51–61. http://dx.doi.org/10.1016/0362-546x(88)90012-0.

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6

Prigozhin, L. "On the Bean critical-state model in superconductivity." European Journal of Applied Mathematics 7, no. 3 (June 1996): 237–47. http://dx.doi.org/10.1017/s0956792500002333.

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We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.
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7

Leonardi, Salvatore, and Nikolaos S. Papageorgiou. "On a class of critical Robin problems." Forum Mathematicum 32, no. 1 (January 1, 2020): 95–109. http://dx.doi.org/10.1515/forum-2019-0160.

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AbstractWe consider a nonlinear parametric Robin problem. In the reaction, there are two terms, one critical and the other locally defined. Using cut-off techniques, together with variational tools and critical groups, we show that, for all small values of the parameter, the problem has at least three nontrivial smooth solutions all with sign information, which converge to zero in {C^{1}(\bar{\Omega})} as the parameter {\lambda\to 0^{+}}.
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8

Alves, C. O., Ana Maria Bertone, and J. V. Goncalves. "A Variational Approach to Discontinuous Problems with Critical Sobolev Exponents." Journal of Mathematical Analysis and Applications 265, no. 1 (January 2002): 103–27. http://dx.doi.org/10.1006/jmaa.2001.7698.

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9

Béhi, Droh Arsène, and Assohoun Adjé. "A Variational Method for Multivalued Boundary Value Problems." Abstract and Applied Analysis 2020 (January 21, 2020): 1–8. http://dx.doi.org/10.1155/2020/8463263.

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In this paper, we investigate the existence of solution for differential systems involving a ϕ−Laplacian operator which incorporates as a special case the well-known p−Laplacian operator. In this purpose, we use a variational method which relies on Szulkin’s critical point theory. We obtain the existence of solution when the corresponding Euler–Lagrange functional is coercive.
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10

Piccione, Paolo, and Daniel V. Tausk. "Lagrangian and Hamiltonian formalism for constrained variational problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 6 (December 2002): 1417–37. http://dx.doi.org/10.1017/s0308210500002183.

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We consider solutions of Lagrangian variational problems with linear constraints on the derivative. More precisely, given a smooth distribution D ⊂ TM on M and a time-dependent Lagrangian L defined on D, we consider an action functional L defined on the set ΩPQ(M, D) of horizontal curves in M connecting two fixed submanifolds P, Q ⊂ M. Under suitable assumptions, the set ΩPQ(M, D) has the structure of a smooth Banach manifold and we can thus study the critical points of L. If the Lagrangian L satisfies an appropriate hyper-regularity condition, we associate to it a degenerate Hamiltonian H on TM* using a general notion of Legendre transform for maps on vector bundles. We prove that the solutions of the Hamilton equations of H are precisely the critical points of L. In the particular case where L is given by the quadratic form corresponding to a positive-definite metric on D, we obtain the well-known characterization of the normal geodesics in sub-Riemannian geometry (see [8]). By adding a potential energy term to L, we obtain again the equations of motion for the Vakonomic mechanics with non-holonomic constraints (see [6]).
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Дисертації з теми "Variational critical problems"

1

Fiscella, A. "VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/245334.

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My thesis deals with nonlinear elliptic problems involving a non-local integrodifferential operator of fractional type. Our main results concern the existence of weak solutions for these problems and they are obtained using variational and topological methods.
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2

Maad, Sara. "Critical point theory with applications to semilinear problems without compactness." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1557-2/.

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3

König, Tobias [Verfasser], and Rupert [Akademischer Betreuer] Frank. "Symmetry, uniqueness and blow-up in some elliptic variational problems with critical exponent / Tobias König ; Betreuer: Rupert Frank." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2020. http://d-nb.info/1215499914/34.

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4

Souza, Diego Ferraz de. "Concentration-compactness principle and applications to nonlocal elliptic problems." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9308.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The main goal of this work is to analyze concentration-compactness principles for fractional Sobolev spaces based on the concentration compactness principle of P.-L. Lions and in the pro le decomposition for weak convergence in Hilbert spaces due to K. Tintarev and K.-H Fieseler. As application, we address questions on compactness of the associated energy functional to the following nonlocal elliptic problems, $' ''''''&' ''''''% p qsu fpx; uq in RN; p qsu 􀀀 apxqu fpx; uq in RN; $&% p qsu 􀀀 V pxqu 􀀀 Kpxq u fpx; uq 􀀀 gpx; uq in R3; p q Kpxqu2 in R3; where 0   s   1; 0     1; 2 􀀀 4s ¥ 3; ¡ 0 and Kpxq ¥ 0 belongs to a suitable Lebesgue space. We obtain existence results for a wide class of possible singular potentials apxq; not necessarily bounded away from zero and for oscillatory nonlinearities in both subcritical and critical growth range that may not satisfy the Ambrosetti-Rabinowitz condition.
O objetivo principal deste trabalho é analisar princípios de concentração de compacidade para espaços de Sobolev fracionários baseados na concentração de compacidade de P.-L. Lions e no per l de decomposição para convergência fraca em espaços de Hilbert devido a K. Tintarev e K.-H Fieseler. Como aplicação, abordamos questões sobre a compacidade do funcional energia associado aos seguintes problems elípticos não locais, $' ''''''&' ''''''% p qsu fpx; uq em RN; p qsu 􀀀 apxqu fpx; uq em RN; $&% p qsu 􀀀 V pxqu 􀀀 Kpxq u fpx; uq 􀀀 gpx; uq em R3; p q Kpxqu2 em R3; onde 0   s   1; 0     1; 2 􀀀 4s ¥ 3; ¡ 0 e Kpxq ¥ 0 pertence a um espaço de Lebesgue adequado. Obtemos resultados de existência para uma vasta classe de potenciais apxq possivelmente singulares, não necessariamente limitados por baixo por uma constante positiva e para não linearidades oscilatórias em ambos os crescimentos subcríticos e críticos que podem não satisfazer a condição de Ambrosetti-Rabinowitz.
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Freitas, Luciana Roze de. "Existência e multiplicidade de soluções para uma classe de problemas quasilineares com crescimento crítico exponencial." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18012011-145302/.

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Neste trabalho, mostramos a existência e multiplicidade de soluções para a seguinte classe de equações elípticas quasilineares { - \'DELTA IND. \'NÜ\' POT. \'upsilon\' + \'|\'upsilon\'| POT. \'NÜ\' - 2 \'upsilon\' = f(x, u), \'upsilon\' \'DIFERENTE\' 0, \'upsilon\' \'PERTENCE A >>: Nu + jujN2 u = f(x; u); x 2 ; u 6= 0; u 2 W1;N( ); onde e um domnio em RN, N 2, N e o operador N-Laplaciano e f e uma func~ao que possui um crescimento crtico exponencial. Para obter nossos resultados utilizamos o Princpio Variacional de Ekeland, Teorema do Passo da Montanha, Categoria de Lusternik- Schnirelman, Ac~ao de Grupo e tecnicas baseadas na Teoria do G^enero. Palavras chaves: Problemas elpticos quasilineares, Metodo Variacional, N-Laplaciano, crescimento crtico exponencial, Princpio Variacional de Ekeland, Categoria de Lusternik- Schnirelman, Desigualdade de Trudinger-Moser
In this work, we show the existence and multiplicity of solutions for the following class of quasilinear elliptic equations { - \'DELTA\' IND. \'NÜ\' \'upsilon\'\' + |\'upsilon\'| POT. \'NÜ\' - 2 = f(x, \'upsilon\'), x \"IT BELONGS\' \'OMEGA\', \'upsilon\' \'DIFFERENT\' 0, \'upsilon\' \'IT BELONGS\' W POT. 1, \'NÜ\' ( OMEGA), where \'OMEGA\' is a domain in \' R POT. \'NÜ\' > OR = 2, \'DELTA\' IND. \'NÜ\' is the N-Laplacian operator and f is a function with exponential critical growth. To obtain our results we utilize the Ekeland Variational Principle, the Mountain Pass Theorem, Lusternik-Schnirelman of Category, Group Action and techniques based on Genus Theory
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6

Guimarães, Angelo. "Existência e multiplicidade de soluções de problemas elípticos com termo semilinear côncavo-convexo." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/6901.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work we study existence and multiplicity of weak solutions for the eliptic problem with semilinear concave convex term, in a limited domain of a N-dimensional euclidean space. If we take f=0 and σ=1 we have a problem homogeneous with critical Sobolev exponent in which we use the Mountain Pass Theorem to find existence of a solution when pNeste trabalho estudaremos existência e multiplicidade de soluções fracas do problema elíptico com termo semilinear côncavo-convexo, em um domínio limitado de um espaço euclidiano de dimensão N. Ao tomarmos f=0 e σ=1 temos um problema homogêneo com expoente crítico de Sobolev em que utilizamos o Teorema do Passo da Montanha para encontrar existência de uma solução quando p
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7

Milbers, Zoja. "Eigenvalue Problem for the 1-Laplace Operator." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1238150433158-43544.

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We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations
Wir betrachten das zum 1-Laplace-Operator gehörige Eigenwertproblem. Wir definieren höhere Eigenlösungen mittels weak slope und weisen die Existenz einer Folge von Eigenlösungen nach, indem wir die nichtglatte Theorie kritischer Punkte anwenden. Zusätzlich leiten wir eine neue notwendige Bedingung für den ersten Eigenwert des 1-Laplace-Operators mittels innerer Variationen her
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Abreu, Rafael dos Reis 1983. "Soluções ground state para algumas classes de problemas elípticos." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305901.

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Orientador: Marcelo da Silva Montenegro
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho, tratamos de resultados de existência de soluções ground state para algumas classes de problemas elípticos sobre espaços euclidianos ou sobre domínios exteriores. Nos casos em que consideramos um domínio exterior, consideramos a condição de fronteira de Dirichlet ou de Neumann. O fato de se considerar domínios não limitados naturalmente implica em algumas dificuldades como, por exemplo, a falta de compacidade. Quando isso ocorre, em geral, a condição Palais-Smale não é válida. Para contornar esta e outras dificuldades, usamos o Teorema do Passo da Montanha sem condição Palais-Smale, Lema de Lions e Teorema de Vitali. Em nosso estudo, utilizamos métodos variacionais explorando diversas técnicas para a obtenção de pontos críticos de funcionais associados a cada problema. Pontos críticos não nulos de cada funcional são soluções de seu respectivo problema
Abstract: In this work, we deal with existence of ground state solutions for some classes of elliptic problems on Euclidean spaces or on exterior domains. In cases where we consider an exterior domain, we consider the Dirichlet boundary condition or the Neumann boundary condition. Elliptic problems involving unbounded domains naturally have some difficulties, por example, the lack of compactness. When it occurs, in general, the Palais-Smale condition is not valid. To overcome this difficulty and others, we use the Mountain Pass Theorem without Palais-Smale condition, results due to Lions and the Vitali's Theorem. In our study, we use variational methods exploring techniques to obtain critical points of functionals related to each problem. Nonzero critical points of each functional are solutions of its respective problem
Doutorado
Matematica
Doutor em Matemática
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9

Almeida, Samuel Oliveira de. "Soluções para problemas elípticos envolvendo o expoente crítico de Sobolev." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1468.

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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho estudamos a existência de soluções para problemas elípticos envolvendo o expoente crítico de Sobolev. Primeiramente, investigamos a existência de soluções para um problema superlinear do tipo Ambrosetti-Prodi com ressonância em 1, onde 1 é o primeiro autovalor de (−Δ,1 0 (Ω)). Além disso, estudamos resultados de multiplicidade para uma classe de equações elípticas críticas relacionadas com o problema de Brézis-Nirenberg, com condição de contorno de Neumann sobre a bola.
In this work we study the existence of solutions for elliptic problems involving critical Sobolev exponent. Firstly we investigate the existence of solutions for an Ambrosetti-Prodi type superlinear problem with resonance at 1 , where 1 is the first eigenvalue of (−Δ,1 0 (Ω)). Besides, we study multiplicity results for a class of critical elliptic equations related to the Brézis-Nirenberg problem with Neumann boundary condition on a ball.
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Felix, Diego Dias. "Sobre uma classe de problemas elípticos envolvendo o crescimento do tipo Trudinger-Moser." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9263.

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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
In this work, we study a class of quasilinear elliptic problem involving nonlinearities with subcritical polynomial growth, subcritical exponential growth and critical exponential growth. Our main focus is to treat nonlinearities which do not satisfy the condition of super-quadratic of Ambrosetti-Rabinowitz. Our main tool is the Mountain Pass Theorem with the Cerami condition.
Neste trabalho, estudamos uma classe de problemas elípticos quase lineares envolvendo não linearidades com crescimento polinomial subcrítico, exponencial subcrítico e exponencial crítico. Nosso foco principal é tratar não linearidades que não satisfazem a condição de superquadraticidade de Ambrosetti-Rabinowitz. A nossa ferramenta é o Teorema do Passo da Montanha com a condição de Cerami.
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Книги з теми "Variational critical problems"

1

Ambrosetti, A. Critical points and nonlinear variational problems. Paris, France: Société mathématique de France, 1992.

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2

Bartsch, Thomas. Topological methods for variational problems with symmetries. Berlin: Springer-Verlag, 1993.

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3

Bahri, A. Critical points at infinity in some variational problems. Harlow: Longman Scientific & Technical, 1989.

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4

Critical points at infinity in some variational problems. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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5

1944-, Ekeland I., Szulkin Andrzej, and NATO Advanced Study Institute, eds. Minimax results of L[j]usternik-Schnirelman type and applications: Part 2 of the proceedings of the NATO ASI "variational methods in nonlinear problems". Montréal, Québec, Canada: Presses de l'Université de Montréal, 1989.

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6

1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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7

Ontario. Esquisse de cours 12e année: Sciences de l'activité physique pse4u cours préuniversitaire. Vanier, Ont: CFORP, 2002.

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8

Ontario. Esquisse de cours 12e année: Technologie de l'information en affaires btx4e cours préemploi. Vanier, Ont: CFORP, 2002.

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9

Ontario. Esquisse de cours 12e année: Études informatiques ics4m cours préuniversitaire. Vanier, Ont: CFORP, 2002.

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10

Ontario. Esquisse de cours 12e année: Mathématiques de la technologie au collège mct4c cours précollégial. Vanier, Ont: CFORP, 2002.

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Частини книг з теми "Variational critical problems"

1

Precup, Radu. "Compression–Expansion Critical Point Theorems in Conical Shells." In Nonlinear Analysis and Variational Problems, 135–45. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0158-3_12.

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2

Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Variational Principles and Critical Point Theory." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 97–139. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_5.

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Conti, M., and R. Lucchetti. "The Minimax Approach to the Critical Point Theory." In Recent Developments in Well-Posed Variational Problems, 29–76. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8472-2_2.

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4

Bartsch, Thomas. "Category, genus and critical point theory with symmetries." In Topological Methods for Variational Problems with Symmetries, 8–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0073861.

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5

Hebey, Emmanuel. "Bubbles over Bubbles: A C 0-theory for the Blow-up of Second Order Elliptic Equations of Critical Sobolev Growth." In Variational Problems in Riemannian Geometry, 3–17. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7968-2_1.

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6

Reichel, Wolfgang. "2. Uniqueness of critical points (I)." In Uniqueness Theorems for Variational Problems by the Method of Transformation Groups, 9–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40915-1_2.

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Reichel, Wolfgang. "3. Uniqueness of critical points (II)." In Uniqueness Theorems for Variational Problems by the Method of Transformation Groups, 27–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40915-1_3.

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8

del Pino, M., P. Felmer, and M. Musso. "Spike Patterns in the Super-Critical Bahri—Coron Problem." In Variational and Topological Methods in the Study of Nonlinear Phenomena, 89–103. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0081-9_7.

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9

Goodman, David C. "Population-Based Measures of Newborn Care Variation: A Critical Piece of Improving Perinatal Outcomes." In The Problem of Practice Variation in Newborn Medicine, 73–86. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94655-5_7.

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Zhong, Ziyuan, Yuchi Tian, and Baishakhi Ray. "Understanding Local Robustness of Deep Neural Networks under Natural Variations." In Fundamental Approaches to Software Engineering, 313–37. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71500-7_16.

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AbstractDeep Neural Networks (DNNs) are being deployed in a wide range of settings today, from safety-critical applications like autonomous driving to commercial applications involving image classifications. However, recent research has shown that DNNs can be brittle to even slight variations of the input data. Therefore, rigorous testing of DNNs has gained widespread attention.While DNN robustness under norm-bound perturbation got significant attention over the past few years, our knowledge is still limited when natural variants of the input images come. These natural variants, e.g., a rotated or a rainy version of the original input, are especially concerning as they can occur naturally in the field without any active adversary and may lead to undesirable consequences. Thus, it is important to identify the inputs whose small variations may lead to erroneous DNN behaviors. The very few studies that looked at DNN’s robustness under natural variants, however, focus on estimating the overall robustness of DNNs across all the test data rather than localizing such error-producing points. This work aims to bridge this gap.To this end, we study the local per-input robustness properties of the DNNs and leverage those properties to build a white-box (DeepRobust-W) and a black-box (DeepRobust-B) tool to automatically identify the non-robust points. Our evaluation of these methods on three DNN models spanning three widely used image classification datasets shows that they are effective in flagging points of poor robustness. In particular, DeepRobust-W and DeepRobust-B are able to achieve an F1 score of up to 91.4% and 99.1%, respectively. We further show that DeepRobust-W can be applied to a regression problem in a domain beyond image classification. Our evaluation on three self-driving car models demonstrates that DeepRobust-W is effective in identifying points of poor robustness with F1 score up to 78.9%.
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Тези доповідей конференцій з теми "Variational critical problems"

1

Reichel, Wolfgang. "Supercritical variational problems with unique critical points." In Proceedings of the 4th European Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777201_0024.

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2

Rosen, David W., Wei Chen, Stewart Coulter, and Srinivas Vadde. "Goal-Directed Geometry: Beyond Parametric and Variational Geometry CAD Technologies." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0084.

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Abstract Improved computer-aided design tools can significantly impact designer productivity. The ability to formulate and solve “What if” questions is critical in early design stages. In this paper, a new computational framework for preliminary design, called Goal-Directed Geometry, is presented that provides such an exploratory environment for early stages. Tools for parametric geometry, variational modeling, and feature-based design are combined with a multiobjective optimization code to provide robust support for parametric design problems, where parameter values are desired that best meet a set of goals and constraints. Geometric and engineering models of a design are combined into a multiobjective optimization formulation called a Compromise Decision Support Problem, which can be solved by the existing package DSIDES (Decision Support In the Design of Engineering Systems). A prototype CAD system is under development that integrates DSIDES, a geometric modeler, and variational, parametric, and feature capabilities. The system aids a designer in evaluating competing alternatives, common during preliminary design, and in answering “What if” types of questions. Two examples illustrate the use of Goal-Directed Geometry in formulating and solving parametric design problems involving engineering and geometric constraints and goals.
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3

Goun, A. A., and O. K. Sliva. "Time Optimal Transfer Function of a Mechanism in the Presence of Dissipative Forces." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-61907.

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A variety of optimization problems in theoretical mechanics are related to the problem of finding the quickest operating mechanism among all possible mechanisms. Let us consider a mechanical system with one degree of freedom consisting of leading and lagging links with masses M1 and M2 respectively. Source of mechanical energy is attached to the leading link and its potential energy is known as a function of the position of the leading link. Positions of the leading - x and lagging links - y are related through the position function. Now the optimization problem can be formulated in the following way: find the position function such that the lagging link is transferred from initial to the final position in the shortest time. The analytic solution for this problem for the case when dissipative forces can be neglected was found using variational calculus method. In the case when dissipative forces can be described as viscous friction the problem can be solved using iterative methods. The differential equation that describes the stationary point of these iterations was obtained. The dependence of the optimal position function on the magnitude of friction is analyzed. In the case when dissipative forces are of the dry friction type the approach based on the variational calculus fails. We were able to find the optimal position function problem using Maximum Principle. New qualitative features of the solution arising due to dry friction are discussed. Approaches developed in this paper can be generalized for a variety of mechanisms where the operating time is critical.
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4

Goun, A. A., O. K. Sliva, and Vyacheslav Murzin. "Time Optimal Transfer Function of a Mechanism." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58384.

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Анотація:
A variety of optimization problems in theoretical mechanics are related to the problem of finding the quickest operating mechanism among all possible mechanisms. It can be formulated in the following way. Let us consider a mechanical system with one degree of freedom consisting of leading and lagging links with masses M1 and M2 respectively. Source of mechanical energy is attached to the leading link and its potential energy is known as a function of the position of the leading link. Positions of the leading - x and lagging links - y are related through the position function. Now the optimization problem can be formulated in the following way: find the position function such that the lagging link is transferred from initial position to the final position in the shortest time. We have obtained an analytic solution to this problem using variational calculus methods in the case then dissipative forces acting on the system can be neglected. We have shown that this problem is analogous to the classical brachistochtone problem. The qualitative feature of this result is that the optical mechanical system tends to accelerate the leading link first in order to maximize the power being extracted from the mechanical energy source. Analytical solution is applied for the optimization of the fast acting electric switch design. Leading link load and operating time reductions with the use of the optimal transfer function is demonstrated. This approach can be generalized for a variety of mechanisms where the operating time is critical.
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5

White, Joshua A., and Ronaldo I. Borja. "Stabilized Finite Element Methods for Coupled Solid-Deformation/Fluid-Flow in Porous Geomaterials." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66524.

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We present a finite element formulation for saturated and partially saturated porous geomaterials undergoing elastoplastic deformations. The deforming body is treated as a multiphase continuum, and the governing mass and momentum balance equations are solved in a fully coupled manner. The constitutive behavior of the solid is based on a critical state plasticity model that explicitly accounts for the effect of capillary pressures on the geometry of the yield surface in the partially saturated regime. It is well known, however, that mixed formulations of the type examined here may lead to unstable approximations unless the spaces chosen for the pressure and displacement interpolations satisfy stringent stability restrictions. Failure to choose stable combinations typically leads to non-physical pressure oscillations and poor convergence behavior upon mesh refinement. Unfortunately, many seemingly natural combinations—including equal-order interpolations—do not satisfy the necessary requirements. In this work, we instead employ a stabilized formulation, based on a relatively minor modification of the variational equations, which allows us to circumvent these restrictions and employ equal-order mixed elements. We demonstrate the appealing features of this approach with several boundary value problems taken from geotechnical applications, including modeling strain localization and failure initiation in variably saturated slopes.
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6

Lo¨o¨f, Johan, Lars Lindkvist, and Rikard So¨derberg. "Optimizing Locator Position to Maximize Robustness in Critical Product Dimensions." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86598.

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The way parts are located in relation to each other or in fixtures is critical for how geometrical variation will propagate and cause variation in critical product dimensions. Therefore, more emphasis should be put on this activity in early design phases in order to avoid assembly and production problems later on. In earlier literature, locator positions have been defined using optimization to reach a robust locating scheme. This implies that the total robustness of a part is optimized by placing the locators in an optimal way. Sometimes there are areas on parts that are more sensitive to variation than others. Therefore, this paper suggests an approach for optimizing the positions of locators in a locating scheme to maximize robustness in defined critical dimensions. A formulation of an optimization problem is presented, and an algorithm solving this in a heuristic approach is developed. Finally, this algorithm is applied on an industrial example.
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7

Garstecki, Andrzej, and Witold Kakol. "Structural Sensitivity Analysis in Eigenvalue Problems Using Finite Strip Method." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0150.

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Abstract Structural Sensitivity Analysis is performed using the direct differentiation method for buckling and free vibration problems of prismatic thin-walled structures employing the Finite Strip Method. The sensitivity of eigenvalues (critical stresses and free frequencies) with respect to variation of thickness of plate members and with respect to shape-type variations is considered. The differentiation is carried out employing analytical and semi-analytical methods. Numerical examples illustrate the sensitivity of thin-walled plates stiffened with ribs and thin-walled beams. The examples also serve for discussion of numerical efficiency and accuracy of the presented methods.
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8

Park, Jong Sang, and Kyung K. Choi. "Design Sensitivity Analysis and Optimization of Nonlinear Structural Systems With Critical Loads." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0067.

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Abstract A continuum formulation for design sensitivity analysis of critical loads is developed for nonlinear structural systems that are subjected to conservative loading. Both geometric and material nonlinear effects are considered. Sizing design variables such as cross-sectional areas of beam or truss design components and thicknesses of plate or membrane design components, together with their shape design variables, are treated. A continuum approach is used to obtain design sensitivity expressions in integral form. For shape design sensitivity analysis, the material derivative concept and domain method are used to find variations of the critical load due to variations in shape of the physical domain. The total Lagrangian formulation for incremental equilibrium equation and one-point linearized eigenvalue problems are utilized. A numerical method is presented to evaluate continuum design sensitivity expressions using analysis results of established finite element codes. It is found that no adjoint system is necessary for design sensitivity analysis of the critical load. Numerical results show the proposed method for design sensitivity of critical loads is accurate for both sizing and shape design variables. A numerical procedure for optimal design of nonlinear structural systems is presented, using the proposed continuum design sensitivity analysis method. An optimal design problem with a stability constraint is solved.
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9

Lo¨o¨f, Johan, and Rikard So¨derberg. "Top-Down Decomposition of Multi-Product Requirements Onto Locator Tolerances." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43453.

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The tolerance allocation problem consists of choosing tolerances on dimensions of a complex assembly so that they combine into an ‘optimal state’ while fulfilling certain requirements on an allowed variation. This optimal state often coincides with the minimum manufacturing cost of the product. Sometimes it is balanced with an artificial cost that the deviation from target induces on the quality of the product. This paper suggests a multiobjective formulation of the tolerance allocation problem to automatically decompose requirements for an allowed variation on a set of critical product dimensions. This formulation is demonstrated using a rear lamp on a car with multiple requirements on allowed variation. In this case only the tolerances on locators that locates the lamp on the body are considered. The paper also reviews a selection of work that has been made on solving tolerance allocation problems.
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10

Dykman, M. I., G. P. Golubev, V. P. Golubchenko, D. G. Luchinsky, S. V. Tsuprikov, and A. L. Velikovich. "Fluctuational Transitions and Critical Phenomena in a Noise-Driven Optically Bistable Device." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.ndd440.

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Fluctuational transitions between the stable states of a passive optically bistable device have been observed and investigated theoretically and experimentally in the absence of spatial effects (for a lumped-parameter system). The problem of calculation of transition probabilities in dynamical systems driven by weak Gaussian noise has been reduced to logarithmic accuracy to a variational problem which is solved for some types of colored noise. The procedure of the experimental determination of the transition probabilities from the data on transmitted intensity is proposed for the case of a broad-band noise in the intensity of incident radiation. The onset of an extremely narrow peak in the power spectrum of the system in the range of the kinetic phase transition is revealed.
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Звіти організацій з теми "Variational critical problems"

1

Komba, Aneth, and Richard Shukia. An Analysis of the Basic Education Curriculum in Tanzania: The Integration, Scope, and Sequence of 21st Century Skills. Research on Improving Systems of Education (RISE), February 2023. http://dx.doi.org/10.35489/bsg-rise-wp_2023/129.

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Анотація:
This study generated evidence on whether or not the basic education curriculum is geared towards developing problem-solving, collaboration, creativity, and critical thinking skills among those who graduate from the basic education system. It was informed by a mixed methodology research approach. The data were collected using interviews and documentary review. The findings reveal that the intention to promote 21st century skills through the basic education system in Tanzania is clear, as it is stated in various policy documents, including the Education for Self-Reliance philosophy, the 2014 Education and Training Policy and the National Curriculum Framework for Basic and Teacher Education. Furthermore, these skills are clearly reflected in every curriculum and syllabus document, yet those who graduate from the basic and advanced secondary levels are claimed to lack these skills. This suggests a variation between the enacted and the intended curriculum. We conclude that certain system elements are weak, and hence threaten the effective implementation of the curriculum. These weak system elements include limited finance, a teacher shortage, and the lack of a teacher continuous professional development programme. This research suggests that due consideration should be given to provision of the resources required for the successful implementation of the curriculum. These include, allocation of sufficient funds, the employment of more teachers and the provision of regular continuous professional development for teachers as a way to strengthen the system elements that we identified.
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2

Peitz, David, and Naomi Reibold. White-tailed deer monitoring at Arkansas Post National Memorial, Arkansas: 2005–2020 trend report. Edited by Tani Hubbard. National Park Service, April 2021. http://dx.doi.org/10.36967/nrr-2285087.

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Анотація:
From 16 years (2005–2020) of monitoring trends in white-tailed deer within a defined survey area of Arkansas Post National Memorial, we have been able to demonstrate both population declines and recoveries. The adjusted count of deer had a seven-fold increase between 2007 and 2011 following a two-year decline and a three-fold increase between 2017 and 2019 following a six-year decline. Overall, the deer population has declined slightly, averaging a 0.5% reduction in herd size annually. The number of deer in the survey area ranged from 16.77 ± 21.26 (mean + 95% CI) individuals/km2 in 2007 to 118.95 ± 39.03 individuals/km2 in 2011. The amount of visible area surveyed each year varied between 0.25 and 0.47 km2 (coefficient of variation = 16.47%). If the white-tailed deer population becomes too large, this poses several problems for Arkansas Post National Memorial. First, it adds a level of complexity to implementing active natural resource management critical to preventing the cultural landscapes of Arkansas Post National Memorial from changing into something that has little resemblance to the historical character of the park. Deer deferentially browse native vegetation over exotic vegetation, thus promoting the spread of exotic species, and the success of tree planting can be curtailed by heavy deer browsing. Second, controlling deer related disease, some of which can affect domestic livestock and human health in and around the park, becomes increasingly difficult when there are more deer. Third, as additional ancillary data suggests, the largely unreported and costly deer-vehicle collisions in and around Arkansas Post National Memorial have the potential to increase if the deer populations grow.
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3

Heitman, Joshua L., Alon Ben-Gal, Thomas J. Sauer, Nurit Agam, and John Havlin. Separating Components of Evapotranspiration to Improve Efficiency in Vineyard Water Management. United States Department of Agriculture, March 2014. http://dx.doi.org/10.32747/2014.7594386.bard.

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Vineyards are found on six of seven continents, producing a crop of high economic value with much historic and cultural significance. Because of the wide range of conditions under which grapes are grown, management approaches are highly varied and must be adapted to local climatic constraints. Research has been conducted in the traditionally prominent grape growing regions of Europe, Australia, and the western USA, but far less information is available to guide production under more extreme growing conditions. The overarching goal of this project was to improve understanding of vineyard water management related to the critical inter-row zone. Experiments were conducted in moist temperate (North Carolina, USA) and arid (Negev, Israel) regions in order to address inter-row water use under high and low water availability conditions. Specific objectives were to: i) calibrate and verify a modeling technique to identify components of evapotranspiration (ET) in temperate and semiarid vineyard systems, ii) evaluate and refine strategies for excess water removal in vineyards for moist temperate regions of the Southeastern USA, and iii) evaluate and refine strategies for water conservation in vineyards for semi-arid regions of Israel. Several new measurement and modeling techniques were adapted and assessed in order to partition ET between favorable transpiration by the grapes and potentially detrimental water use within the vineyard inter-row. A micro Bowen ratio measurement system was developed to quantify ET from inter-rows. The approach was successful at the NC site, providing strong correlation with standard measurement approaches and adding capability for continuous, non-destructive measurement within a relatively small footprint. The environmental conditions in the Negev site were found to limit the applicability of the technique. Technical issues are yet to be solved to make this technique sufficiently robust. The HYDRUS 2D/3D modeling package was also adapted using data obtained in a series of intense field campaigns at the Negev site. The adapted model was able to account for spatial variation in surface boundary conditions, created by diurnal canopy shading, in order to accurately calculate the contribution of interrow evaporation (E) as a component of system ET. Experiments evaluated common practices in the southeastern USA: inter-row cover crops purported to reduce water availability and thereby favorably reduce grapevine vegetative growth; and southern Israel: drip irrigation applied to produce a high value crop with maximum water use efficiency. Results from the NC site indicated that water use by the cover crop contributed a significant portion of vineyard ET (up to 93% in May), but that with ample rainfall typical to the region, cover crop water use did little to limit water availability for the grape vines. A potential consequence, however, was elevated below canopy humidity owing to the increased inter-row evapotranspiration associated with the cover crops. This creates increased potential for fungal disease occurrence, which is a common problem in the region. Analysis from the Negev site reveals that, on average, E accounts for about10% of the total vineyard ET in an isolated dripirrigated vineyard. The proportion of ET contributed by E increased from May until just before harvest in July, which could be explained primarily by changes in weather conditions. While non-productive water loss as E is relatively small, experiments indicate that further improvements in irrigation efficiency may be possible by considering diurnal shading effects on below canopy potential ET. Overall, research provided both scientific and practical outcomes including new measurement and modeling techniques, and new insights for humid and arid vineyard systems. Research techniques developed through the project will be useful for other agricultural systems, and the successful synergistic cooperation amongst the research team offers opportunity for future collaboration.
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