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Relevant bibliographies by topics / Hyperbolic derivative

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Academic literature on the topic 'Hyperbolic derivative'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Hyperbolic derivative"

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JIANG, MIAOHUA. "Differentiating potential functions of SRB measures on hyperbolic attractors." Ergodic Theory and Dynamical Systems 32, no. 4 (June 10, 2011): 1350–69. http://dx.doi.org/10.1017/s0143385711000241.

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AbstractThe derivation of Ruelle’s derivative formula of the SRB measure depends largely on the calculation of the derivative of the unstable Jacobian. Although Ruelle’s derivative formula is correct, the proofs in the original paper and its corrigendum are not complete. In this paper, we re-visit the differentiation process of the unstable Jacobian and provide a complete derivation of its derivative formula. Our approach is to extend the volume form provided by the SRB measure on local unstable manifolds to a system of Hölder continuous local Riemannian metrics on the manifold so that under this system of local metrics, the unstable Jacobian becomes differentiable with respect to the base point and its derivative with respect to the map can be obtained by the chain rule.

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Eriksson, Sirkka-Liisa, and Heikki Orelma. "Quaternionic k-Hyperbolic Derivative." Complex Analysis and Operator Theory 11, no. 5 (December 30, 2016): 1193–204. http://dx.doi.org/10.1007/s11785-016-0630-8.

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Ford, G. W., and R. F. O'Connell. "Derivative of the hyperbolic cotangent." Nature 380, no. 6570 (March 1996): 113–14. http://dx.doi.org/10.1038/380113b0.

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HOMBURG, ALE JAN. "Piecewise smooth interval maps with non-vanishing derivative." Ergodic Theory and Dynamical Systems 20, no. 3 (June 2000): 749–73. http://dx.doi.org/10.1017/s0143385700000407.

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We consider the dynamics of piecewise smooth interval maps $f$ with a nowhere vanishing derivative. We show that if $f$ is not infinitely renormalizable, then all its periodic orbits of sufficiently high period are hyperbolic repelling. If, in addition all periodic orbits of $f$ are hyperbolic, then $f$ has at most finitely many periodic attractors and there is a hyperbolic expansion outside the basins of these periodic attractors. In particular, if $f$ is not infinitely renormalizable and all its periodic orbits are hyperbolic repelling, then some iterate of $f$ is expanding. In this case, $f$ admits an absolutely continuous invariant probability measure.

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Kwon, E. G. "Fractional integration and the hyperbolic derivative." Bulletin of the Australian Mathematical Society 38, no. 3 (December 1988): 357–64. http://dx.doi.org/10.1017/s0004972700027714.

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We improve S. Yamashita's hyperbolic version of the well-known Hardy-Littlewood theorem. Let f be holomorphic and bounded by one in the unit disc D. If (f#)p has a harmonic mojorant in D for some p, p > 0, then so does σ(f)q for all q, 0 < q < ∞. Here

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Renegar, James. "Hyperbolic Programs, and Their Derivative Relaxations." Foundations of Computational Mathematics 6, no. 1 (January 5, 2006): 59–79. http://dx.doi.org/10.1007/s10208-004-0136-z.

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Birman, Graciela S., and Abraham A. Ungar. "The Hyperbolic Derivative in the Poincaré Ball Model of Hyperbolic Geometry." Journal of Mathematical Analysis and Applications 254, no. 1 (February 2001): 321–33. http://dx.doi.org/10.1006/jmaa.2000.7280.

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Wu, Nan. "On characteristic of bounded analytic functions involving hyperbolic derivative." Mathematica Slovaca 68, no. 4 (August 28, 2018): 811–22. http://dx.doi.org/10.1515/ms-2017-0147.

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Abstract In this article, we give the Nevanlinna type hyperbolic characteristics in simply connected domains and angular domains and the Tsuji type hyperbolic characteristics for bounded analytic functions for the first time. The first fundamental theorems are also established concerning hyperbolic derivative for bounded analytic functions in simply connected domains and angular domains. This is a continuous work of Makhmutov [3].

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Aydın, Ömer Lütfü, Ozcan Bektas, Aydın Büyüksaraç, and Hüseyin Yılmaz. "3D Modeling and Tectonic Interpretation of the Erzincan Basin (Turkey) using Potential Field Data." Earth Sciences Research Journal 23, no. 1 (January 1, 2019): 57–66. http://dx.doi.org/10.15446/esrj.v23n1.71090.

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Erzincan Basin was investigated using gravity data within the scope of this study. It is also aimed to reveal the discontinuities in the work area as well as the buried discontinuities. Boundary determination filters and analysis of the structure of the data and its connection are revealed and clear information is obtained. Gravity anomalies were applied with an upward continuation method for 0.25, 0.50, 0.75 and 1 km levels. Total Horizontal Derivative (THD) filter, Analytical Signal (AS) filter, Tilt Angle Derivative (Tilt) filter, Total Horizontal Derivative (THDR) filter, Theta Angle Derivative (Cos ɵ) filter, Hyperbolic Tilt Angle Derivative (HTAD) were applied to upward continued data. The discontinuities in the region and the boundaries of the geological structure were revealed. Tilt and Theta Angle derivatives yield the best results from the applied derivative based filters. The obtained data were compared with the existing surface geology and the compatibility between the formations was checked. New discontinuities were found in addition to the discontinuities determined from surface observations in the light of the obtained results. Erzincan Basin was modeled in three dimensions using gravity data of the study area. As a result of modeling, Erzincan Basin has been determined to have an average thickness of 7 km.Total Horizontal Derivative (THD) filter, Analytical Signal (AS) filter, Tilt Angle Derivative (TAd) filter, Total Horizontal Derivative (THDR) filter, Teta Angle Derivative (Cos ɵ) filter, Hyperbolic Tilt Angle Derivative (HTAD) were applied to upward continued data. The discontinuities in the region and the boundaries of the geological structure were revealed. Tilt and Theta angle derivatives yield the best results from the applied derivative based filters. The obtained data were compared with the existing surface geology and the compatibility between the formations was checked. New discontinuities were found in addition to the discontinuities determined from surface observations in the light of the obtained results. Erzincan basin is modeled in three dimensions using gravity data of the study area. As a result of modeling, Erzincan Basin has been determined to have an average thickness of 7 km.

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Ding, Hengfei, and Changpin Li. "Numerical Algorithms for the Fractional Diffusion-Wave Equation with Reaction Term." Abstract and Applied Analysis 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/493406.

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Two numerical algorithms are derived to compute the fractional diffusion-wave equation with a reaction term. Firstly, using the relations between Caputo and Riemann-Liouville derivatives, we get two equivalent forms of the original equation, where we approximate Riemann-Liouville derivative by a second-order difference scheme. Secondly, for second-order derivative in space dimension, we construct a fourth-order difference scheme in terms of the hyperbolic-trigonometric spline function. The stability analysis of the derived numerical methods is given by means of the fractional Fourier method. Finally, an illustrative example is presented to show that the numerical results are in good agreement with the theoretical analysis.

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Dissertations / Theses on the topic "Hyperbolic derivative"

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Ashu, Tom A. Ashu. "Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747.

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Köllermeier, Julian [Verfasser], Manuel [Akademischer Betreuer] Torrilhon, and Ruo [Akademischer Betreuer] Li. "Derivation and numerical solution of hyperbolic moment equations for rarefied gas flows / Julian Köllermeier ; Manuel Torrilhon, Ruo Li." Aachen : Universitätsbibliothek der RWTH Aachen, 2017. http://d-nb.info/1162499559/34.

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Ferreira, Daiane Gonçalves 1988. "Métodos de otimização de terceira ordem." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306029.

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Orientadores: Margarida Pinheiro Mello, Maria Aparecida Diniz Ehrhardt
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Métodos de Otimização de terceira ordem, embora de longa tradição, eram considerados, até passado recente, impraticáveis, devido à taxa com que o esforço computacional cresce em função da dimensão do problema. Avanços no desenvolvimento de estruturas de dados, rotinas que trabalham com estas estruturas e a exploração da esparsidade de grande parte dos problemas encontrados na prática já permitem implementações destes métodos que podem torná-los competitivos com métodos de segunda ordem. O objeto desta dissertação é a apresentação do método de Halley, um método de terceira ordem, sua implementação em MATLAB e a realização de testes computacionais, visando uma comparação empírica de sua eficiência frente ao método de Newton, o método de segunda ordem mais empregado na atualidade
Abstract: Higher order optimization methods, though of long-standing tradition, until recently have been deemed impractical, due to the rate of increase of the computational effort as a function of the size of the problem. Advances in the development of data structures, routines that work with these structures and the use of the sparsity of a vast range of practical problems have led to implementations of these methods that are competitive with second order methods. The object of this dissertation is the study of Halley's method, a thirdorder method, the development of a MATLAB implementation thereof and its testing, aiming at an empirical comparison of its efficiency against that of Newton's method, the second-order method most widely used today
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada

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Marcou, Alice. "Interactions d’ondes et de bord." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14267/document.

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Tout d'abord, des ondes de surface, solutions de problèmes aux limites hyperboliques non linéaires, sont étudiées : on construit une solution BKW sous forme de développement infini en puissance de epsilon. On le justifie rigoureusement, en construisant une solution exacte, qui admet ce développement asymptotique. On montre que la solution n'est pas nécessairement purement localisée sur la frontière, même lorsque le terme source l'est ; l'exemple d'un cas particulier de l'élasticité est traité. Ensuite, on étudie la réflexion d'ondes non linéaires discontinues, pour des problèmes aux limites hyperboliques, faiblement bien posés, ni fortement stables, ni fortement instables. On étudie comment les singularités d'une solution striée sont réfléchies lorsque la solution atteint la frontière. On prouve des estimations striées et en normes infinies. On montre qu'une discontinuité du gradient de la solution à travers un hyperplan peut être réfléchie en une discontinuité de la solution elle-même
We first study surface waves, solutions of hyperbolic nonlinear boundary value problems. We construct BKW solutions in the weakly nonlinear regime with infinite expansion in powers of ε. We rigorously justify this expansion,constructing exact solutions, which admit the asymptotic expansions. We also show that the solution is not necessarily localized at the order O(ε∞) in the interior, even if the data are ; a particular case of elasticity is studied: we prove that fast oscillatory elastic surface waves can produce non trivial internal non oscillatory displacements.Afterwards, we study the reflection of non linear discontinuous waves, for weakly well-posed hyperbolic boundary value problems, satisfying the (WR) condition, which has been introduced in [1, 12], that is in a case where the IBVP is neither strongly stable, nor strongly unstable. We study how the singularities of a striated solution are reflected when the solution hits the boundary. We prove striated estimates and L∞ estimates and observe the loss of one derivative: we show that a discontinuityof the gradient of the solution across an hyperplane can be reflected in a discontinuity across an hyperplane of the solution itself

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Pérgola, Gabriel Campos. "Seguro contra risco de downside de uma carteira: uma proposta híbrida frequentista-Bayesiana com uso de derivativos." reponame:Repositório Institucional do FGV, 2013. http://hdl.handle.net/10438/10468.

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Portfolio insurance allows a manager to limit downside risk while allowing participation in upside markets. The purpose of this dissertation is to introduce a framework to portfolio insurance optimization from a hybrid frequentist-Bayesian approach. We obtain the joint distribution of regular returns from a frequentist statistical method, once the outliers have been identified and removed from the data sample. The joint distribution of extreme returns, in its turn, is modelled by a Bayesian network, whose topology reflects the events that can significantly impact the portfolio performance. Once we link the regular and extreme distributions of returns, we simulate future scenarios for the portfolio value. The insurance subportfolio is then optimized by the Differential Evolution algorithm. We show the framework in a step by step example for a long portfolio including stocks participating in the Bovespa Index (Ibovespa), using market data from 2008 to 2012.
Seguros de carteiras proporcionam aos gestores limitar o risco de downside sem renunciar a movimentos de upside. Nesta dissertação, propomos um arcabouço de otimização de seguro de carteira a partir de um modelo híbrido frequentista-Bayesiano com uso de derivativos. Obtemos a distribuição conjunta de retornos regulares através de uma abordagem estatística frequentista, uma vez removidos os outliers da amostra. A distribuição conjunta dos retornos extremos, por sua vez, é modelada através de Redes Bayesianas, cuja topologia contempla os eventos que o gestor considera crítico ao desempenho da carteira. Unindo as distribuições de retornos regulares e extremos, simulamos cenários futuros para a carteira. O seguro é, então, otimizado através do algoritmo Evolução Diferencial. Mostramos uma aplicação passo a passo para uma carteira comprada em ações do Ibovespa, utilizando dados de mercado entre 2008 e 2012.

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Fino, Ahmad. "Contributions aux problèmes d'évolution." Phd thesis, Université de La Rochelle, 2010. http://tel.archives-ouvertes.fr/tel-00437141.

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Dans cette thèse, nous nous intéressons à l'étude de trois équations aux dérivées partielles et d'évolution non-locales en espace et en temps. Les solutions de ces trois solutions peuvent exploser en temps fini. Dans une première partie de cette thèse, nous considérons l'équation de la chaleur nonlinéaire avec une puissance fractionnaire du laplacien, et obtenons notamment que, dans le cas d'exposant sur-critique, le comportement asymptotique de la solution lorsque $t\rightarrow+\infty$ est déterminé par le terme de diffusion anormale. D'autre part, dans le cas d'exposant sous-critique, l'effet du terme non-linéaire domine. Dans une deuxième partie, nous étudions une équation parabolique avec le laplacien fractionnaire et un terme non-linéaire et non-local en temps. On montre que la solution est globale dans le cas sur-critique pour toute donnée initiale ayant une mesure assez petite, tandis que dans le cas sous-critique, on montre que la solution explose en temps fini $T_{\max}>0$ pour toute condition initiale positive et non-triviale. Dans ce dernier cas, on cherche le comportement de la norme $L^1$ de la solution en précisant le taux d'explosion lorsque $t$ s'approche du temps d'explosion $T_{\max}.$ Nous cherchons encore les conditions nécessaires à l'existence locale et globale de la solution. Une toisième partie est consacré à une généralisation de la deuxième partie au cas de systèmes $2\times 2$ avec le laplacien ordinaire. On étudie l'existence locale de la solution ainsi qu'un résultat sur l'explosion de la solution avec les mêmes propriétés étudiées dans le troisième chapitre. Dans la dernière partie, nous étudions une équation hyperbolique dans $\mathbb{R}^N,$ pour tout $N\geq2,$ avec un terme non-linéaire non-local en temps. Nous obtenons un résultat d'existence locale de la solution sous des conditions restrictives sur les données initiales, la dimension de l'espace et les exposants du terme non-linéaire. De plus on obtient, sous certaines conditions sur les exposants, que la solution explose en temps fini, pour toute condition initiale ayant de moyenne strictement positive.

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Dannawi, Ihab. "Contributions aux équations d'évolutions non locales en espace-temps." Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS007/document.

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Dans cette thèse, nous nous intéressons à l'étude de quatre équations d'évolution non-locales. Les solutions de ces quatre équations peuvent exploser en temps fini. Dans la théorie des équations d'évolution non-linéaires, une solution est qualifiée de globale si elle est définie pour tout temps positif. Au contraire, si une solution existe seulement sur un intervalle de temps [0; T) borné, elle est dite locale. Dans ce dernier cas et quand le temps maximal d'existence est relié à une alternative d'explosion, on dit aussi que la solution explose en temps fini. Dans un premier travail, nous considérons l'équation de Schrödinger non-linéaire avec une puissance fractionnaire du laplacien, et nous obtenons l'explosion de la solution en temps fini Tmax > 0 pour toute condition initiale positive et non-triviale dans le cas d'exposant sous-critique. Ensuite, nous étudions une équation des ondes amorties avec un potentiel d'espace-temps et un terme non-linéaire et non-local en temps. Nous obtenons un résultat d'existence locale d'une solution dans l'espace d'énergie sous des conditions restrictives sur les données initiales, la dimension de l'espace et la croissance du terme non-linéaire. De plus, nous obtenons l'explosion de la solution en temps fini pour toute condition initiale de moyenne strictement positive. De plus, nous étudions un problème de Cauchy pour l'équation d'évolution avec un p- Laplacien avec une non linéarité non-locale en temps. Dans ce cadre, nous nous intéressons à l'étude de l'existence locale d'une solution de cette équation ainsi qu'un résultat de non-existence de solution globale. Finalement, nous étudions l'intervalle maximal d'existence des solutions de l'équation des milieux poreux avec un terme non-linéaire non-local en temps
In this thesis, we study four non-local evolution equations. The solutions of these four equations can blow up in finite time. In the theory of nonlinear evolution equations, a solution is qualified as global if it isdefined for any time. Otherwise, if a solution exists only on a bounded interval [0; T), it is called local solution. In this case and when the maximum time of existence is related to a blow up alternative, we say that the solution blows up in finite time. First, we consider the nonlinear Schröodinger equation with a fractional power of the Laplacien operator, and we get a blow up result in finite time Tmax > 0 for any non-trivial non-negative initial condition in the case of sub-critical exponent. Next, we study a damped wave equation with a space-time potential and a non-local in time non-linear term. We obtain a result of local existence of a solution in the energy space under some restrictions on the initial data, the dimension of the space and the growth of nonlinear term. Additionally, we get a blow up result of the solution in finite time for any initial condition positive on average. In addition, we study a Cauchy problem for the evolution p-Laplacien equation with nonlinear memory. We study the local existence of a solution of this equation as well as a result of non-existence of global solution. Finally, we study the maximum interval of existence of solutions of the porous medium equation with a nonlinear non-local in time term

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Arman, Andrii. "Generalizations of Ahlfors lemma and boundary behavior of analytic functions." 2013. http://hdl.handle.net/1993/22095.

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In this thesis we will consider and investigate the properties of analytic functions via their behavior near the boundary of the domain on which they are defined. To do that we introduce the notion of the hyperbolic distortion and the hyperbolic derivative. Classical results state that the hyperbolic derivative is bounded from above by 1, and we will consider the case when it is bounded from below by some positive constant. Boundedness from below of the hyperbolic derivative implies some nice properties of the function near the boundary. For instance Krauss & all in 2007 proved that, if the function is defined on a domain bounded by analytic curve, then boundedness from below of the hyperbolic derivative implies that the function has an analytic continuation across the boundary. We extend this result for the domains with slightly more general boundary, namely for smooth Jordan domains, and get that in this case the function and its derivative will have only continuous extensions to the boundary.

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Prause, Karsten [Verfasser]. "The generalized hyperbolic model: estimation, financial derivatives, and risk measures / vorgelegt von Karsten Prause." 1999. http://d-nb.info/961152192/34.

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Book chapters on the topic "Hyperbolic derivative"

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Toro, E. F., and C. E. Castro. "The Derivative Riemann Problem for the Baer–Nunziato Equations." In Hyperbolic Problems: Theory, Numerics, Applications, 1045–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75712-2_111.

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Courtès, Clémentine. "Convergence for PDEs with an Arbitrary Odd Order Spatial Derivative Term." In Theory, Numerics and Applications of Hyperbolic Problems I, 413–25. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91545-6_32.

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Baribeau, Line. "Hyperbolic Derivatives Determine a Function Uniquely." In Blaschke Products and Their Applications, 187–92. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4614-5341-3_10.

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Bechouche, Philippe, Norbert J. Mauser, and Sigmund Selberg. "Derivation of Schrödinger Poisson as the Non-relativistic Limit of Klein-Gordon Maxwell." In Hyperbolic Problems: Theory, Numerics, Applications, 357–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55711-8_32.

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Eberlein, Ernst, and Karsten Prause. "The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures." In Springer Finance, 245–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-12429-1_12.

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Brenier, Yann. "On the Derivation of Newtonian Gravitation from the Brownian Agitation of a Regular Lattice." In Theory, Numerics and Applications of Hyperbolic Problems I, 227–35. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91545-6_18.

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Kostant, B., and Shlomo Sternberg. "The Schwartzian Derivative and the Conformal Geometry of the Lorentz Hyperboloid." In Quantum Theories and Geometry, 113–25. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3055-1_7.

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Colombini, Ferruccio, Daniele Del Santo, and Francesco Fanelli. "No Loss of Derivatives for Hyperbolic Operators with Zygmund-Continuous Coefficients in Time." In Springer INdAM Series, 127–48. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61346-4_6.

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Alexeyeva, L. A., and G. K. Zakir’yanova. "Generalized Functions Method for Solving Nonstationary Boundary Value Problems for Strictly Hyperbolic Systems with Second-Order Derivatives." In Trends in Mathematics, 3–11. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-48812-7_1.

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Rasulov, Mahir, Zafer Aslan, Bahaddin Sinsoysal, and Hakan Bal. "The D’Alembert Type Solution of the Cauchy Problem for the Homogeneous with Respect to Fourth Order Derivatives for Hyperbolic Equation." In Computational Science and Its Applications – ICCSA 2017, 726–34. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62407-5_54.

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Conference papers on the topic "Hyperbolic derivative"

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Rasekh, Ehsan, Iman Rasekh, and Mohammad Eshghi. "PWL approximation of hyperbolic tangent and the first derivative for VLSI implementation." In 2010 IEEE 23rd Canadian Conference on Electrical and Computer Engineering - CCECE 2010. IEEE, 2010. http://dx.doi.org/10.1109/ccece.2010.5575239.

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Kholodov, Alexander S., and Yaroslav A. Kholodov. "Computational Models on Graphs for the Nonlinear Hyperbolic System of Equations." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2580.

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The problems in the form of nonlinear partial derivative equations on graphs (nets, trees) arise in different applications. As the examples of such models we can name the circulatory and respiratory systems of the human body, the model of heavy traffic in the big cities, the model of flood water and pollution propagation in the large river systems, the model of bar structures and frames behavior under the different impacts, the model of the intensive information flows in the computer networks and others.

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Berdyshev, Abdumauvlen S., Erkinjon T. Karimov, and Nazgul S. Akhtaeva. "On a boundary-value problem for the parabolic-hyperbolic equation with the fractional derivative and the sewing condition of the integral form." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893817.

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Cagan, Jonathan, and Thomas R. Kurfess. "Optimal Tolerance Allocation Over Multiple Manufacturing Alternatives." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0162.

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Abstract We introduce a methodology for concurrent design that considers the allocation of tolerances and manufacturing processes for minimum cost. Cost is approximated as a hyperbolic function over tolerance, and worst-case stack-up tolerance is assumed. Two simulated annealing techniques are introduced to solve the optimization problem. The first assumes independent, unordered, manufacturing processes and uses a Monte-Carlo simulation; the second assumes well known individual process cost functions which can be manipulated to create a single continuous function of cost versus tolerance with discontinuous derivatives solved with a continuous simulated annealing algorithm. An example utilizing a system of friction wheels over the manufacturing processes of turning, grinding, and saw cutting bar stock demonstrates excellent results.

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Hosaka, Tomoyuki, Taisuke Sugii, Eiji Ishii, Kazuhiro Oryoji, and Yoshihiro Sukegawa. "Application of Hyperbolic Tangent Approximation Model to Gasoline Direct Injection Engine Simulation." In ASME 2017 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icef2017-3538.

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The improved fuel economy and low pollutant emissions are highly demanded for internal combustion engines. Gasoline Direct Injection (GDI) engine is the one of promising devices for highly efficient engine. However, GDI engines generally tend to emit more Particulate Matter (PM) than Port Fuel Injection (PFI) engine because the fuel sprayed from the injector can easily attach to the wall, which is the major origin of PM. Therefore, the precise analysis of the fuel/air mixture formation and the prediction of emissions are required. From the view of industrial use, Computational Fluid Dynamics (CFD) becomes a necessary tool for the various analyses including the fuel/air mixture formation, spray attachment on the cylinder wall, the in-cylinder turbulence formation, the combustion and emission etc. In our previous study, the flow and spray simulation in internal combustion engine has been conducted using OpenFOAM®, the open-source CFD toolbox. Since the engine involves the dynamic motion such as valve and piston, the morphing and mapping approach was employed. Furthermore, by virtue of open-source code, we have developed the methodology of the hybrid simulation from the internal nozzle flow to the fuel/air mixture in order to take into account detailed breakup process nearby injector nozzle. We expand the above research to the combustion simulation. For the combustion model, the Hyperbolic Tangent Approximation (HTA) model is adopted. The HTA model has a simple form of equation and one can easily implement; moreover, the HTA model has the following features: 1. capability of both laminar and turbulent flow, 2. the clearness of analytical derivation based on the functional approximation of the reaction progress variable distribution in a one-dimensional laminar flame. In the current study, the premixed flame is studied on a gasoline combustion engine. The simulations for in-cylinder engine are conducted with different Air/Fuel (A/F) ratio conditions, and the results are compared with the experimental results. The in-cylinder pressure agrees well with experimental results and the validity of the current methodology is confirmed.

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Haque, Mohammad Shafinul, and Calvin M. Stewart. "Modeling the Creep Deformation, Damage, and Rupture of Hastelloy X Using MPC Omega, Theta, and Sin-Hyperbolic Models." In ASME 2016 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/pvp2016-63029.

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Combined cycle power plants components such as steam pipe work, pressure vessels, boilers, heat exchangers, and gas turbine disks, etc. are exposed to elevated temperature and pressure operation conditions for longer durations. Components may fail within the elastic limit due to a time dependent deformation and damage mechanism called creep. Creep prediction models are used to determine the state of these components and to schedule optimum inspection, maintenance, and replacement intervals. In this study, the deformation, damage, and life of Hastelloy X is characterized using three recently developed models; the Omega, Theta projection, and Sin-hyperbolic models. An analysis is performed to compare the models in terms of accuracy, assumptions, constant identification techniques, flexibility in use, and limitations. The influence that final creep strain has on Theta and Omega model is discussed. Sixteen tests were performed at four different configurations of stress (2.1–36.5 ksi) and temperature (1200–1800°F). In the experimental data, Hastelloy X does not exhibit the primary stage. In this study, the secondary and tertiary creep stages are modeled. Creep deformation and rupture life data is used to optimize the constants for the three models. Predictions using these models are compared with experimental data. It is found that the novel Sin-hyperbolic model better fits the experimental data, and is easier to apply. The Omega model predicts longer life than the Sinh and the Theta Projection model. The rupture life prediction of the Theta projection model is the worst due to dependence on the critical creep strain rate. It is observed that the Hastelloy X final creep strain depends on stress and temperature; this leads to a less accurate critical creep strain rate prediction resulting in inaccurate rupture life predictions for the Theta projection model. The analytical damage of the Omega model exhibits a linear evolution with time while the Sinh model show a more realistic elliptical creep damage evolution with time. A process to determine the constants of all the models is clearly described. The dependence of the trajectory of the creep curves with respect to the constants is discussed in detail. An analytical derivation of each model is provided. Predictions of these three models show that the Sinh model produces a better creep deformation curve by normalizing the experimental creep strain rate data. It is found that overall the Sinh model offers more flexibility, prediction accuracy, and is easier to apply.

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Xie, Weidong, and Mudasir Ahmad. "Inverse Derivation of Constants for the Constitutive Equation and Fatigue Model of Pb-Free Solder Joints Based on Experiment Results, Finite Element Simulation and Virtual Optimization Methodology." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87734.

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Solder joint reliability of Pb-free ball grid array (BGA) components, one of the most commonly used microelectronic devices, is one of the major concerns in product development and qualification. Accelerated Thermal Cycling (ATC) testing, though very time consuming and costly, remains the most prevalent means to evaluate solder joint reliability under certain end-use conditions. Wherever the test results are not readily available, a fine-tuned and well-benchmarked modeling methodology is of significance in producing quick-turn judgments and risk assessments to expedite product development. The two most critical elements in simulating solder joint reliability are 1) the solder constitutive equations, which describe the solder creep behavior under different working conditions, and 2) the fatigue model which ties the damage index from finite element modeling together with the experimental results. In this study, a novel approach has been explored in which the constants of the constitutive equation and fatigue model for Sn-based Pb-free solder joints were derived inversely based on ATC results of a ceramic BGA test vehicle. In order to cover the typical end-use conditions of the targeted products, the test vehicle was assembled onto PCBs with two different thicknesses and then thermal cycled under three different temperature profiles. The basic idea was that all of the constants, both for the constitutive equation and the fatigue life prediction model, were initially given as a range. Then by utilizing modeFrontier®, a multi-objective optimization software, the finite-element model was coupled with the virtual optimization algorithm to derive simultaneously all the constants that yielded the best fatigue life predictions compared to the test results. To simplify the problem without compromising the generality, a hyperbolic sine creep constitutive equation and Coffin-Manson fatigue model were selected in the analysis. There were a total of 6 constants to be determined; the initial ranges of the constants were defined by fitting the creep experimental data for a variety of Sn-based solder materials. Available in other publications, the selected solder materials cover a wide range of both Ag and Cu content which therefore represent the typical behavior of the most commonly adopted solder materials by the industry. To reduce the computational cost and enable fast convergence of multiple-generation iterations required by the multiple objective optimization algorithms, a very-well benchmarked submodel has been employed. Furthermore, by utilizing ANSYS® high performance computing (HPC) capability and cloud computing, the computational time was reduced significantly. An overall good correlation was achieved between the fatigue life prediction using the constants derived by this approach and the test characteristic life.

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