Готові списки джерел за темами / Equation-free approach

Добірка наукової літератури з теми "Equation-free approach"

Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 29 січня 2023

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Статті в журналах з теми "Equation-free approach"

Dongbin Xiu, I. G. Kevrekidis, and R. Ghanem. "An Equation-Free, Multiscale Approach to Uncertainty Quantification." Computing in Science and Engineering 7, no. 3 (May 2005): 16–23. http://dx.doi.org/10.1109/mcse.2005.46.

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Williams, Matthew O., Joshua L. Proctor, and J. Nathan Kutz. "Modeling disease transmission near eradication: An equation free approach." Physica D: Nonlinear Phenomena 290 (January 2015): 44–56. http://dx.doi.org/10.1016/j.physd.2014.09.006.

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Bold, Katherine A., Yu Zou, Ioannis G. Kevrekidis, and Michael A. Henson. "An equation-free approach to analyzing heterogeneous cell population dynamics." Journal of Mathematical Biology 55, no. 3 (April 11, 2007): 331–52. http://dx.doi.org/10.1007/s00285-007-0086-6.

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Chen, C. S., A. S. Muleshkov, M. A. Golberg, and R. M. M. Mattheij. "A mesh-free approach to solving the axisymmetric Poisson's equation." Numerical Methods for Partial Differential Equations 21, no. 2 (2005): 349–67. http://dx.doi.org/10.1002/num.20040.

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Francken, P., and C. J. Joachain. "Multiphoton Free-Free Transitions in Stochastic Laser Fields: The Kubo-Anderson Master Equation Approach." Europhysics Letters (EPL) 9, no. 6 (July 15, 1989): 517–22. http://dx.doi.org/10.1209/0295-5075/9/6/004.

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McDONALD, N. R. "Generalised Hele-Shaw flow: A Schwarz function approach." European Journal of Applied Mathematics 22, no. 6 (May 16, 2011): 517–32. http://dx.doi.org/10.1017/s0956792511000210.

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An equation governing the evolution of a Hele-Shaw free boundary flow in the presence of an arbitrary external potential – generalised Hele-Shaw flow – is derived in terms of the Schwarz functiong(z,t) of the free boundary. This generalises the well-known equation ∂g/∂t= 2∂w/∂z, wherewis the complex potential, which has been successfully employed in constructing many exact solutions in the absence of external potentials. The new equation is used to re-derive some known explicit solutions for equilibrium and time-dependent free boundary flows in the presence of external potentials, including those with singular potential fields, uniform gravity and centrifugal forces. Some new solutions are also constructed that variously describe equilibrium flows with higher order hydrodynamic singularities in the presence of electric point sources and an unsteady solution describing bubbles under the combined influence of strain and centrifugal potential.

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Jarzynski, C. "Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach." Physical Review E 56, no. 5 (November 1, 1997): 5018–35. http://dx.doi.org/10.1103/physreve.56.5018.

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Zou, Y., I. G. Kevrekidis, and D. Armbruster. "Multiscale analysis of re-entrant production lines: An equation-free approach." Physica A: Statistical Mechanics and its Applications 363, no. 1 (April 2006): 1–13. http://dx.doi.org/10.1016/j.physa.2006.01.043.

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A. Bold, Katherine, Karthikeyan Rajendran, Balázs Ráth, and Ioannis G. Kevrekidis. "An equation-free approach to coarse-graining the dynamics of networks." Journal of Computational Dynamics 1, no. 1 (2014): 111–34. http://dx.doi.org/10.3934/jcd.2014.1.111.

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Huang, Dong-mei, Guo-liang Zou, and L. W. Zhang. "Numerical Approximation of Nonlinear Klein-Gordon Equation Using an Element-Free Approach." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/548905.

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Numerical approximation of nonlinear Klein-Gordon (KG) equation with quadratic and cubic nonlinearity is performed using the element-free improved moving least squares Ritz (IMLS-Ritz) method. A regular arrangement of nodes is employed in this study for the numerical integration to compute the system equation. A functional formulation for the KG equation is established and discretized by the Ritz minimization procedure. Newmark’s integration scheme combined with an iterative technique is applied to the resulting nonlinear system equations. The effectiveness and efficiency of the IMLS-Ritz method for the KG equation have been testified through convergence analyses and comparison study between the present results and the exact solutions.

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Дисертації з теми "Equation-free approach"

Han, Sukho Brown D. Scott. "The impact analysis of structural change in Korean agriculture with respect to the Korean-United States free trade agreement dynamic simultaneous equation model approach /." Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/6969.

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Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 26, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Scott Brown. Includes bibliographical references.

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Dyrssen, Hannah. "Valuation and Optimal Strategies in Markets Experiencing Shocks." Doctoral thesis, Uppsala universitet, Tillämpad matematik och statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-316578.

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This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on. The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices. The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique. Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.

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Khabir, Mohmed Hassan Mohmed. "Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_7416_1320395978.

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Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can be exercised only on the expiration date, and American options which can be exercised on or before the expiration date. American options are much harder to deal with than European ones. The reason being the optimal exercise policy of these options which led to free boundary problems. Ever since the seminal work of Black and Scholes [J. Pol. Econ. 81(3) (1973), 637-659], the differential equation approach in pricing options has attracted many researchers. Recently, numerical singular perturbation techniques have been used extensively for solving many differential equation models of sciences and engineering. In this thesis, we explore some of those methods which are based on spline approximations to solve the option pricing problems. We show a systematic construction and analysis of these methods to solve some European option problems and then extend the approach to solve problems of pricing American options as well as some exotic options. Proposed methods are analyzed for stability and convergence. Thorough numerical results are presented and compared with those seen in the literature.

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Alotaibi, Hammad Mayoof M. "Developing multiscale methodologies for computational fluid mechanics." Thesis, 2017. http://hdl.handle.net/2440/114544.

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The development of multiscale computational methods is a key research area in mathematics, physics, engineering and computer science. Engineers and scientists often perform detailed microscale computational simulations of a large scale complicated spatio-temporal system. For most problems of practical interest, there are two major complications in simulating the dynamical behaviour on large macroscopic space-time scales. The first is the often prohibitive computational cost when only a microscopic model is available. The second complication is the memory constraints which often make the simulation over the whole domain of interest infeasible. To overcome these obstacles, the equation-free approach was proposed by Keverkidis and colleagues in 2000. This approach is a multiscale method for capturing the behaviour on large scales of some complicated systems using only relatively small bursts of the microscale models. The patch dynamics scheme was proposed as an essential component of the equation-free framework. The patch scheme promises a great saving in computation time by predicting the macroscopic dynamics using detailed microscopic computation only on relatively small widely distributed patches of the spatial domain. This thesis provides mathematical analysis and computational simulation of some basic atom dynamics on small patches. The most significant novel result of this research is that patches with microscale periodic boundary conditions can be used to efficiently predict macroscale properties of interest. This result is important because microscale computations are often easiest with microscale periodic boundary conditions. As a major test of the approach, we analyse, implement and evaluate such a scheme for a computationally intensive atomistic simulation. Chapter 1 of this dissertation introduces the challenge of multiscale problems and highlights some recent developments of multiscale methods for complex systems. Chapter 2 explores atomistic simulations in three-dimensional space. The microscale atomistic simulator is used to predict a macroscale temperature field. This is achieved by performing atomistic simulation on a small triply-periodic patch. The method uses locally averaged properties over small space-time scales to advance and predict relatively large space scale dynamics. Our ultimate aim for this chapter is to explore the macroscopic properties of a system through atomistic simulation in small periodic patches, but as a pilot study this thesis only considers one small patch coupled over the macroscale to boundaries. The computation is implemented only on the periodic patch, while over most of the domain we interpolate in order to predict the macroscale temperature. The thesis develops appropriate control terms to the microscale action regions of the patch. The control is applied to the left and right action regions surrounding a core region. A proportional controller dependent upon the relatively distant boundaries enables reasonably accurate macroscale predictions. The analysis and computational simulations indicate that this innovative patch scheme empowers computation of large scale simulations of microscale systems. Chapter 3 analyses the case of a one-dimensional microscale diffusion system in a single microscale patch to predict the macroscale dynamics over a comparatively large spatial region. The nature of the solutions of the patch scheme is explored when operating with time-varying boundary conditions that mimic coupling with neighbouring, dynamically varying patches. The patch eigenfunctions and their adjoints form a biorthogonal basis to determine the spectral coefficients in formal series solutions. We also explore this patch scheme with time delays in the communication of boundary values. This models a patch when information from the neighbouring patches is subject to communication delays. The delayed patch scheme prediction is compared with a scheme without delays to delineate when such delays are significant. Chapter 4 analyses diffusion dynamics on multiple coupled patches. Centre manifold theory supports the patch scheme. The patch coupling conditions are standard Lagrange interpolation from the macroscale values at the centre of surrounding patches to the boundaries of each patch. The results of this chapter demonstrate the feasibility of the microscale patch scheme to model diffusion over large spatial scales. Chapter 5 extends the analysis to one-dimensional microscale advection-diffusion dynamics in a single patch and for multiple patches. Eigenvalue analysis suggests that a slow manifold exists on the macroscale. Computer algebra constructs the slow manifold model for the advection-diffusion dynamics. The long-time dynamics behaviour of numerical solutions on one patch is compared with the prediction of the slow manifold. Comparisons among the patch dynamics scheme, the microscale model over the complete domain, and published experimental data determines regimes where the patch dynamics accurately predicts the large scale advection-diffusion dynamics.
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2017.

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Kordilla, Jannes. "Flow and transport in saturated and unsaturated fractured porous media: Development of particle-based modeling approaches." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0023-9901-9.

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Das Ziel der vorliegenden Arbeit ist die Entwicklung von partikelbasierenden Strömungs- und Transportmodellen zur Charakterisierung von kleinskaligen Strömungsprozessen in gesättigten und ungesättigten Poren- und Kluftsystemen. Aufgrund der unzureichenden Prozessbeschreibung von ungesättigter Strömung in Doppelkontinuummodellen mittels der Richardsgleichung und van Genuchten Parametern werden innovative Methoden präsentiert um die zugrunde liegenden hochdynamischen Strömungs- und Transportprozesse zu erfassen. Die Simulation von Strömung und Transport in ungesättigten geklüfteten Aquiferen bildet immer noch ein höchst anspruchsvolles Aufgabenfeld aufgrund von skalenübergreifenden Diskontinuitäten, welche oftmals die Definition eines globalen repräsentativen Einheitsvolumens nicht zulassen. Des Weiteren können die hydraulischen Eigenschaften und potentiellen Parameterräume von geklüfteten Aquiferen oftmals nur durch integrale Ansätze, wie z.B. Pump- und Slugtests, Zeitreihenanalysen von Quellschüttungen und Tracertests ermittelt werden. Doppelkontinuummodelle bieten hierfür einen ausgewogenen Ansatz hinsichtlich der erforderlichen Felddaten und der resultierenden prädiktiven Modellqualität. Der erste Teil dieser Arbeit evaluiert den Doppelkontinuumansatz, welcher die Simulation von Strömung mittels der Richardsgleichung und van Genuchten Parametern in zwei, durch einen linearen Austauschterm gekoppelten, Kontinua ermöglicht. Ganglinien von Karstquellen weisen eine charakteristischen steilen Abfall nach Niederschlagsereignissen auf, der durch das Modell erfolgreich reproduziert werden kann. Das Röhrensystem bildet die hydraulische Brücke zur Karstquelle und nimmt potentialabhängige Wassermengen des geklüfteten Matrixsystems auf. Um die Simulation von schneller Grundwasserinfiltration durch das Röhrenkontinuum innerhalb der ungesättigten Zone zu vermeiden wurde die entsprechende Randbedingung an die untere Grenze des Kontinuums gesetzt. Ein genereller Nachteil des Doppelkontinuumsansatz ist die potentielle Mehrdeutigkeit von Modellergebnissen. Der duale Parameterraum in Kombination mit schwierig zu ermittelnden Parametern, führt zur Existenz von mehr als einem kalibrierten Modell, wie durch mehrdimensionale Sensitivitätsanalysen aufgezeigt wird. Insbesondere in Karstaquiferen bilden Diskontinuitäten, wie z.B. Lösungsdolinen, Klüfte und Störungssysteme, bevorzugte hydraulische Elemente für schnelle vertikale Grundwasserneubildungsprozesse, die oftmals nicht durch volumeneffektive Modellansätze erfasst werden können. Der Hauptteil dieser Arbeit befasst sich daher mit der Entwicklung von zwei Smoothed Particle Hydrodynamics (SPH) Modellen um ein adäquates numerisches Werkzeug zur partikelbasierenden Simulation von kleinskaligen Strömungen mit freien Oberflächen und Transportprozessen bereitzustellen. SPH Modelle ermöglichen eine Eulersche Beschreibung eines Strömungsfelds auf Basis der Navier-Stokes Gleichung und Partikelbewegung mittels klassischer Newtonscher Mechanik. Der gitterlose Modellansatz ermöglicht flexible Simulationen von hochdynamischen Phasengrenzen in ungesättigten Klüften und Porenräumen. Das erste SPH Modell wird eingesetzt um durch Oberflächenspannung dominierte Tropfen- und Filmströmungen auf glatten und rauhen Kluftoberflächen zu simulieren. Charakteristische dimensionslose Kennzahlen werden über einen weiten Bereich von Benetzungswinkeln und Reynoldszahlen bestimmt. Modellergebnisse weisen einen hervorragende Übereinstimmung mit dimensionslosen Skalierungsfunktionen auf und kritische Kontaktwinkel folgen der zu erwartenden Entnetzungsdynamik. Die Entstehung von adsorbierten Filmen auf trockenen Oberflächen wird für einen breiten Parameterraum bestimmt. Des Weiteren wird der Einfluss von befeuchteten Oberflächen auf die Geschwindigkeitszunahme von Tropfenströmung aufgezeigt und so die Bedeutung der Koexistenz verschiedener Strömungsmodi gezeigt. Der Effekt von Oberflächenrauhigkeit auf Tropfenströmung wird für verschiedene Rauhigkeiten ermittelt und eine deutliche Geschwindigkeitsabnahme demonstriert. Um die makroskopische Kontinuumsbeschreibung der Navier-Stokes Gleichung und atomistische Effekte eines klassischen Partikelsystems der statistischen Mechanik zu kombinieren wurde ein zweites mesoskopisches SPH Modell entwickelt. Diese neue Diskretisation der vollständig gekoppelten Landau-Lifshitz-Navier-Stokes und Advektions- Diffusionsgleichung ermöglicht die Simulation von Strömung und Transport bei gleichzeitiger Berücksichtigung von Fluktuationsdynamiken, welche sich korrekt der Systemskala anpassen. Die Verbindung von klassischer Fickscher Diffusion und thermodynamischen Fluktuationen wird hierbei durch einen effektiven Diffusionskoeffizienten beschrieben. Numerische Experimente zeigen die Präzision des Modells. Grenzflächen zwischen zwei Fluiden unterschiedlicher Konzentration weisen eine korrekte Wellenzahldivergenz entsprechend aktuellen Laborergebnissen auf.

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Книги з теми "Equation-free approach"

E, Brewe David, United States. National Aeronautics and Space Administration., and United States. Army Aviation Research and Technology Activity., eds. A system-approach to the elastohydrodynamic lubrication point-contact problem. [Washington, D.C.?]: NASA, 1991.

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Sherwood, Dennis, and Paul Dalby. Chemical equilibrium and chemical kinetics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782957.003.0014.

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Building on the previous chapter, this chapter examines gas phase chemical equilibrium, and the equilibrium constant. This chapter takes a rigorous, yet very clear, ‘first principles’ approach, expressing the total Gibbs free energy of a reaction mixture at any time as the sum of the instantaneous Gibbs free energies of each component, as expressed in terms of the extent-of-reaction. The equilibrium reaction mixture is then defined as the point at which the total system Gibbs free energy is a minimum, from which concepts such as the equilibrium constant emerge. The chapter also explores the temperature dependence of equilibrium, this being one example of Le Chatelier’s principle. Finally, the chapter links thermodynamics to chemical kinetics by showing how the equilibrium constant is the ratio of the forward and backward rate constants. We also introduce the Arrhenius equation, closing with a discussion of the overall effect of temperature on chemical equilibrium.

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Частини книг з теми "Equation-free approach"

Yoshida, Norio, and Fumio Hirata. "Statistical Mechanical Integral Equation Approach to Reveal the Solvation Effect on Hydrolysis Free Energy of ATP and Its Analogue." In The Role of Water in ATP Hydrolysis Energy Transduction by Protein Machinery, 69–85. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-8459-1_5.

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Bandrauk, André, and HuiZhong Lu. "Singularity-free methods for the time-dependent Schrödinger equation for nonlinear molecules in intense laser fields—A non-perturbative approach." In CRM Proceedings and Lecture Notes, 1–14. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/crmp/041/01.

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WANG, RUIWEN, JIANG ZHU, ZHENDONG LUO, and I. M. NAVON. "AN EQUATION-FREE, REDUCED-ORDER MODELING APPROACH TO TROPICAL PACIFIC SIMULATION." In Advances in Geosciences, 1–16. World Scientific Publishing Company, 2009. http://dx.doi.org/10.1142/9789812836168_0001.

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MÖLLER, J., O. RUNBORG, P. G. KEVREKIDIS, K. LUST, and I. G. KEVREKIDIS. "EQUATION-FREE, EFFECTIVE COMPUTATION FOR DISCRETE SYSTEMS: A TIME STEPPER BASED APPROACH." In World Scientific Series on Nonlinear Science Series B, 279–300. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774569_0015.

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Chong, Song-Ho, and Fumio Hirata. "Non-linear effects in the free energy profile of electron transfer reaction: An integral equation approach." In Studies in Physical and Theoretical Chemistry, 345–48. Elsevier, 1995. http://dx.doi.org/10.1016/s0167-6881(06)80806-2.

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Mussardo, Giuseppe. "Transfer Matrix of the Two-dimensional Ising Model." In Statistical Field Theory, 211–34. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0006.

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This chapter deals with the exact solution of the two-dimensional Ising model as it is achieved through the transfer matrix formalism. It discusses the crucial role played by the commutative properties of the transfer matrices, which lead to a functional equation for their eigenvalues. The exact free energy of the Ising model and its critical point can be identified by means of the lowest eigenvalue. The chapter covers Baxter's approach, the Yang–Baxter equation and its relation to the Boltzmann weights, the R-matrix, and discusses activity away from the critical point, the six-vertex model, as well as functional equations and symmetries.

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Björk, Tomas. "Optimal Stopping Theory and American Options." In Arbitrage Theory in Continuous Time, 376–96. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198851615.003.0028.

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In this chapter we present the dynamic programming approach to optimal stopping problems. We start by presenting the discrete time theory, deriving the relevant Bellman equation. We present the Snell envelope and prove the Snell Envelope Theorem. For Markovian models we explore the connection to alpha-excessive functions. The continuous time theory is presented by deriving the free boundary value problem connected to the stopping problem, and we also derive the associated system of variational inequalities. American options are discussed in some detail.

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Steel, Duncan G. "Free Particle, Wave Packet and Dynamics, Quantum Dots, Defects and Traps." In Introduction to Quantum Nanotechnology, 32–56. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895073.003.0003.

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This chapter continues with a study of the time independent Schrödinger equation and seeks to contrast the quantum behavior of a free particle with that of a particle localized in a potential quantum well. A free particle can exist over all space or can be localized in a wave package. The wave packet is a coherent superposition of the plane waves that make up the wave function that localizes the particle because of constructive and destructive interference. The wave packet spreads out in time because the waves leading to constructive interference get out of phase. In Chapter 2, the particle was localized by a quadratic potential energy. Here, the potentials are described as piecewise constant. The approach is based on assuming a one-dimensional space, x, which is relevant to many problems in the laboratory. The solution is easily generalized to higher dimensions (x-y or x-y-z), but the physics remains the same. The objective is to understand the shape of the eigenfunctions in space and to be able to relate this to the probability density of locating the particle, as well as understanding the relevance of these systems to today’s technology.

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Yury, Yanilkin, Shmelev Vladimir, and Kolobyanin Vadim. "A Monotonic Method of Split Particles." In Recent Advances on Numerical Simulations [Working Title]. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.97044.

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The problem of correct calculation of the motion of a multicomponent (multimaterial) medium is the most serious problem for Lagrangian–Eulerian and Eulerian techniques, especially in multicomponent cells in the vicinity of interfaces. There are two main approaches to solving the advection equation for a multicomponent medium. The first approach is based on the identification of interfaces and determining their position at each time step by the concentration field. In this case, the interface can be explicitly distinguished or reconstructed by the concentration field. The latter algorithm is the basis of widely used methods such as VOF. The second approach involves the use of the particle or marker method. In this case, the material fluxes of substances are determined by the particles with which certain masses of substances bind. Both approaches have their own advantages and drawbacks. The advantages of the particle method consist in the Lagrangian representation of particles and the possibility of” drawbacks. The main disadvantage of the particle method is the strong non-monotonicity of the solution caused by the discrete transfer of mass and mass-related quantities from cell to cell. This paper describes a particle method that is free of this drawback. Monotonization of the particle method is performed by spliting the particles so that the volume of matter flowing out of the cell corresponds to the volume calculated according to standard schemes of Lagrangian–Eulerian and Eulerian methods. In order not to generate an infinite chain of spliting, further split particles are re-united when certain conditions are met. The method is developed for modeling 2D and 3D gas-dynamic flows with accompanying processes, in which it is necessary to preserve the history of the process at Lagrangian points.

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"Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms— an intrinsic approach." In Free and Moving Boundaries, 281–98. Chapman and Hall/CRC, 2007. http://dx.doi.org/10.1201/9781420011159-17.

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Тези доповідей конференцій з теми "Equation-free approach"

Maji, Supriyo, and Pradip Mandal. "A Fast Equation Free Iterative Approach to Analog Circuit Sizing." In 2012 25th International Conference on VLSI Design. IEEE, 2012. http://dx.doi.org/10.1109/vlsid.2012.99.

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Mathelin, Lionel, Luc Pastur, and Olivier Le Maitre. "An adaptive compressed-sensing equation-free approach for closed-loop nonlinear control." In 6th AIAA Theoretical Fluid Mechanics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2011. http://dx.doi.org/10.2514/6.2011-4015.

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Ostertag, Eric. "Steady-state error-free RST-controller design: A double diophantine equation approach." In 1999 European Control Conference (ECC). IEEE, 1999. http://dx.doi.org/10.23919/ecc.1999.7099758.

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Iannelli, Andrea, Urban Fasel, Nivethan Yogarajah, and Roy S. Smith. "A Balanced Mode Decomposition Approach for Equation-Free Reduced-Order Modeling of LPV Aeroservoelastic Systems." In AIAA Scitech 2021 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-1796.

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Wang, Dadong, and Yanbao Ma. "A Novel Approach for Lattice Boltzmann Modeling of Energy Transport." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89661.

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It is well known that Fourier law breaks down for the prediction of heat conduction in nano-scale, where the length scale is comparable to the mean free path of energy carriers. Over the past decade, Boltzmann transport equation (BTE) has been used to predict thermal transport in dielectrics and semiconductors at micro-scale and nano-scale. In this work, a new modified gray model is obtained from BTE. The implicit lattice Boltzmann method (LBM) is developed to simulate the thermal transport process. Based on the new model, we can derive Guyer-Krumhansl equation. Transient heat conduction through a thin nano-film and hotspot self-heating in sub-micron transistors are examined. The numerical results are compared with those provided by Fourier, Cattaneo, and Guyer-Krumhansl equation.

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Elmegaard, Michael, Jan Ru¨bel, Mizuho Inagaki, Atsushi Kawamoto, and Jens Starke. "Equation-Free Continuation of Maximal Vibration Amplitudes in a Nonlinear Rotor-Bearing Model of a Turbocharger." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87339.

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Mechanical systems are typically described with finite element models resulting in high-dimensional dynamical systems. The high-dimensional space excludes the application of certain investigation methods like numerical continuation and bifurcation analysis to investigate the dynamical behaviour and its parameter dependence. Nevertheless, the dynamical behaviour usually lives on a low-dimensional manifold but typically no closed equations are available for the macroscopic quantities of interest. Therefore, an equation-free approach is suggested here to analyse and investigate the vibration behaviour of nonlinear rotating machinery. This allows then in the next step to optimize the rotor design specifications to reduce unbalance vibrations of a rotor-bearing system with nonlinear factors like the oil film dynamics. As an example we provide a simple model of a passenger car turbocharger where we investigate how the maximal vibration amplitude of the rotor depends on the viscosity of the oil used in the bearings.

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Tan, Chin A., and Bongsu Kang. "A Wave Approach for the Free Vibration Analysis of Axially Loaded, Rotating Timoshenko Shaft Systems." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0544.

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Abstract A systematic approach for the free vibration analysis of a rotating Timoshenko shaft system subjected to axial forces is presented in this paper. The system has multiple point discontinuities such as elastic supports, rotor masses, and cross-sectional changes. Wave reflection and transmission matrices are employed to characterize the wave motions between the sub-spans of the shaft system. These matrices are combined with the field transfer matrices expressed in wave forms to obtain the characteristic equation in a straight-forward manner. The solutions are exact since effects of attenuating wave components are included in the formulation. The wave propagation-based matrix algebra leads to recursive algorithms which are suitable for computer coding. Three examples are presented to illustrate the numerical procedure.

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Rojas, Nicola´s, and Federico Thomas. "A Coordinate-Free Approach to Tracing the Coupler Curves of Pin-Jointed Linkages." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48147.

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In general, high-order coupler curves of plane mechanisms cannot be properly traced by standard predictor-corrector algorithms due to drifting problems and the presence of singularities. Instead of focusing on finding better algorithms for tracing curves, a simple coordinate-free method that first traces these curves in a distance space and then maps them onto the mechanism workspace is proposed. Tracing a coupler curve in the proposed distance space is much simpler because (a) the equation of this curve in this space can be straightforwardly obtained from a sequence of bilaterations; and (b) the curve in this space naturally decomposes into branches in which the signs of the oriented areas of the triangles involved in the aforementioned bilaterations remain constant. A surjective mapping permits to map the thus traced curves onto the workspace of the mechanism. The advantages of this two-step method are exemplified by tracing the coupler curves of a double butterfly linkage, curves that can reach order 48.

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Innocenti, C., and V. Parenti-Castelli. "Forward Kinematics of the General 6-6 Fully Parallel Mechanism: An Exhaustive Numerical Approach via a Mono-Dimensional-Search Algorithm." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0257.

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Abstract A new numerical method for the solution of the direct position analysis of the six d.o.f. fully parallel mechanism with general geometry, often referred to as generalized Stewart platform mechanism, is presented. The main feature of the method, making it attractive with respect to the methods available in the literature, is the ability to find out all the real solutions of the direct position analysis. The effectiveness of the new algorithm relies upon the solution of only one equation in one unknown. That equation is strictly representative of the problem, i.e., it is free from extraneous roots and every solution of the direct position analysis entails the existence of a root for the equation. A case study is reported.

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Li, Chen, and Hong Zhaobin. "Robust Control of Coordinated Motion for Free-Floating Space Flexible Manipulator by Singular Perturbation Approach." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86159.

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The robust control of coordinated motion and active vibration control for free-floating space flexible manipulator with an attitude-controlled base are studied. The dynamic equations of the system are developed by using the Lagrangian assumed modes methods, it is verified that the dynamic equation can be linearly dependent on a group of inertial parameters. Based on the results and under the assumption of two-time scale, singular perturbation model of the space flexible manipulator system is obtained. The fast subsystem controller will damp out the vibration of the flexible link using optimal Linear Quadratic Regulator (LQR) method. The slow subsystem robust controller dominates the trajectory tracking of coordinated motion. In particular, the control scheme doesn’t require measuring the position, velocity nor acceleration of the base. The numerical simulation is carried out, which confirms the controller proposed is feasible and effective.

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