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Relevant bibliographies by topics / Differential equations. Bipartite graphs

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Academic literature on the topic 'Differential equations. Bipartite graphs'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Differential equations. Bipartite graphs"

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Yoshimura, H. "A graph-theoretic approach to sparse matrix inversion for implicit differential algebraic equations." Mechanical Sciences 4, no. 1 (June 6, 2013): 243–50. http://dx.doi.org/10.5194/ms-4-243-2013.

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Abstract. In this paper, we propose an efficient numerical scheme to compute sparse matrix inversions for Implicit Differential Algebraic Equations of large-scale nonlinear mechanical systems. We first formulate mechanical systems with constraints by Dirac structures and associated Lagrangian systems. Second, we show how to allocate input-output relations to the variables in kinematical and dynamical relations appearing in DAEs by introducing an oriented bipartite graph. Then, we also show that the matrix inversion of Jacobian matrix associated to the kinematical and dynamical relations can be carried out by using the input-output relations and we explain solvability of the sparse Jacobian matrix inversion by using the bipartite graph. Finally, we propose an efficient symbolic generation algorithm to compute the sparse matrix inversion of the Jacobian matrix, and we demonstrate the validity in numerical efficiency by an example of the stanford manipulator.

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Jimenez, Belmonte, Garrido, Ruz, and Vazquez. "Software Tool for Acausal Physical Modelling and Simulation." Symmetry 11, no. 10 (September 24, 2019): 1199. http://dx.doi.org/10.3390/sym11101199.

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Modelling and simulation are key tools for analysis and design of systems and processes from almost any scientific or engineering discipline. Models of complex systems are typically built on acausal Differential-Algebraic Equations (DAE) and discrete events using Object-Oriented Modelling (OOM) languages, and some of their key concepts can be explained as symmetries. To obtain a computer executable version from the original model, several algorithms, based on bipartite symmetric graphs, must be applied for automatic equation generation, removing alias equations, computational causality assignment, equation sorting, discrete-event processing or index reduction. In this paper, an open source tool according to OOM paradigm and developed in MATLAB is introduced. It implements such algorithms adding an educational perspective about how they work, since the step by step results obtained after processing the model equations can be shown. The tool also allows to create models using its own OOM language and to simulate the final executable equation set. It was used by students in a modelling and simulation course of the Automatic Control and Industrial Electronics Engineering degree, showing a significant improvement in their understanding and learning of the abovementioned topics after their assessment.

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Amin, Md Ruhul, and Marc R. Roussel. "Graph-theoretic analysis of a model for the coupling between photosynthesis and photorespiration." Canadian Journal of Chemistry 92, no. 2 (February 2014): 85–93. http://dx.doi.org/10.1139/cjc-2013-0315.

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We develop and analyze a mathematical model based on a previously enunciated hypothesis regarding the origin of rapid, irregular oscillations observed in photosynthetic variables when a leaf is transferred to a low-CO2 atmosphere. This model takes the form of a set of differential equations with two delays. We review graph-theoretical methods of analysis based on the bipartite graph representation of mass-action models, including models with delays. We illustrate the use of these methods by showing that our model is capable of delay-induced oscillations. We present some numerical examples confirming this possibility, including the possibility of complex transient oscillations. We then use the structure of the identified oscillophore, the part of the reaction network responsible for the oscillations, along with our knowledge of the plausible range of values for one of the delays, to rule out this hypothetical mechanism.

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Vol’pert, A. I. "Differential Equations on Graphs." Mathematical Modelling of Natural Phenomena 10, no. 5 (2015): 6–15. http://dx.doi.org/10.1051/mmnp/201510502.

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Bothe, Dieter. "Multivalued differential equations on graphs." Nonlinear Analysis: Theory, Methods & Applications 18, no. 3 (February 1992): 245–52. http://dx.doi.org/10.1016/0362-546x(92)90062-j.

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Malinowski, Marek T. "Bipartite Fuzzy Stochastic Differential Equations with Global Lipschitz Condition." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/3830529.

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We introduce and analyze a new type of fuzzy stochastic differential equations. We consider equations with drift and diffusion terms occurring at both sides of equations. Therefore we call them the bipartite fuzzy stochastic differential equations. Under the Lipschitz and boundedness conditions imposed on drifts and diffusions coefficients we prove existence of a unique solution. Then, insensitivity of the solution under small changes of data of equation is examined. Finally, we mention that all results can be repeated for solutions to bipartite set-valued stochastic differential equations.

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Fukuizumi, Reika, Jeremy Marzuola, Dmitry Pelinovsky, and Guido Schneider. "Nonlinear Partial Differential Equations on Graphs." Oberwolfach Reports 14, no. 2 (April 27, 2018): 1805–68. http://dx.doi.org/10.4171/owr/2017/29.

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Pokornyi, Yu V., and A. V. Borovskikh. "Differential Equations on Networks (Geometric Graphs)." Journal of Mathematical Sciences 119, no. 6 (March 2004): 691–718. http://dx.doi.org/10.1023/b:joth.0000012752.77290.fa.

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Pröll, Sebastian, Jan Lunze, and Fabian Jarmolowitz. "From Structural Analysis to Observer–Based Residual Generation for Fault Detection." International Journal of Applied Mathematics and Computer Science 28, no. 2 (June 1, 2018): 233–45. http://dx.doi.org/10.2478/amcs-2018-0017.

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Abstract This paper combines methods for the structural analysis of bipartite graphs with observer-based residual generation. The analysis of bipartite structure graphs leads to over-determined subsets of equations within a system model, which make it possible to compute residuals for fault detection. In observer-based diagnosis, by contrast, an observability analysis finds observable subsystems, for which residuals can be generated by state observers. This paper reveals a fundamental relationship between these two graph-theoretic approaches to diagnosability analysis and shows that for linear systems the structurally over-determined set of model equations equals the output connected part of the system. Moreover, a condition is proved which allows us to verify structural observability of a system by means of the corresponding bipartite graph. An important consequence of this result is a comprehensive approach to fault detection systems, which starts with finding the over-determined part of a given system by means of a bipartite structure graph and continues with designing an observerbased residual generator for the fault-detectable subsystem found in the first step.

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Avdonin, Sergei, and Victor Mikhaylov. "Controllability of partial differential equations on graphs." Applicationes Mathematicae 35, no. 4 (2008): 379–93. http://dx.doi.org/10.4064/am35-4-1.

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Dissertations / Theses on the topic "Differential equations. Bipartite graphs"

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Dimitrov, Youri. "Polynomially-divided solutions of bipartite self-differential functional equations." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1155149204.

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Books on the topic "Differential equations. Bipartite graphs"

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Litvinov, G. L. (Grigoriĭ Lazarevich), 1944- editor of compilation and Sergeev, S. N., 1981- editor of compilation, eds. Tropical and idempotent mathematics and applications: International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia. Providence, Rhode Island: American Mathematical Society, 2014.

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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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Motives, quantum field theory, and pseudodifferential operators: Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, June 2-13, 2008, Boston University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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4

An Introduction To Grids Graphs And Networks. Oxford University Press Inc, 2014.

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Grigor’yan, Alexander, and Yuhua Sun, eds. Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110700763.

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Pozrikidis, C. Introduction to Grids, Graphs, and Networks. Oxford University Press, Incorporated, 2014.

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Dynamical Systems, Graphs, and Algorithms. Springer, 2006.

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8

Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs : April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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Pascal, Auscher, Coulhon T, and Grigoryan A, eds. Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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(Editor), Pascal Auscher, T. Coulhon (Editor), and A. Grigoryan (Editor), eds. Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces: Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on ... Borel Centre of (Contemporary Mathematics). American Mathematical Society, 2004.

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Book chapters on the topic "Differential equations. Bipartite graphs"

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Lagnese, John E., and Günter Leugering. "Partial Differential Equations on Graphs." In Domain Decomposition Methods in Optimal Control of Partial Differential Equations, 71–106. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7885-2_3.

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Mugnolo, Delio. "A Frucht Theorem for Quantum Graphs." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 481–90. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_28.

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Waurick, Marcus, and Michael Kaliske. "On the Well-posedness of Evolutionary Equations on Infinite Graphs." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations, 653–66. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_39.

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Lagnese, John E., and Günter Leugering. "Optimal Control of One-Dimensional Partial Differential Equations on Graphs." In Domain Decomposition Methods in Optimal Control of Partial Differential Equations, 131–57. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7885-2_5.

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Kogut, Peter I., and Günter R. Leugering. "Asymptotic Analysis of Optimal Control Problems on Periodic Singular Graphs." In Optimal Control Problems for Partial Differential Equations on Reticulated Domains, 409–40. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8149-4_11.

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Karp, Richard M. "Random graphs, random walks, differential equations and the probabilistic analysis of algorithms." In STACS 98, 1–2. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0028543.

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Cho, Ilwoo, and Palle E. T. Jorgensen. "A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes." In Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, 603–51. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55556-0_7.

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Leugering, Günter. "Partial Differential Equations on Metric Graphs: A Survey of Results on Optimization, Control, and Stabilizability Problems with Special Focus on Shape and Topological Sensitivity Problems." In Mathematical Modelling, Optimization, Analytic and Numerical Solutions, 77–115. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-0928-5_4.

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Zuk, Andrzej. "From Partial Differential Equations to Groups." In Analysis and Geometry on Graphs and Manifolds, 368–81. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108615259.015.

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Fischer, T., and G. Leugering. "On Instantaneous Control of Singularly Perturbed Hyperbolic Equations on Graphs." In Partial Differential Equations On Multistructures. CRC Press, 2001. http://dx.doi.org/10.1201/9780203902196.ch5.

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Conference papers on the topic "Differential equations. Bipartite graphs"

1

Malinowski, Marek T. "On Bipartite Fuzzy Stochastic Differential Equations." In 8th International Conference on Fuzzy Computation Theory and Applications. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0006079501090114.

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Reid, G. J., and A. Boulton. "Reduction of systems of differential equations to standard form and their integration using directed graphs." In the 1991 international symposium. New York, New York, USA: ACM Press, 1991. http://dx.doi.org/10.1145/120694.120741.

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3

Alicchio, Corey J., Justin S. Vitiello, and Pradeep Radhakrishnan. "Demonstrating the Generation of Bond Graphs From 3D Assemblies." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-24043.

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Abstract The bond graph method provides a generic and simple way to compute differential equations and dynamic responses for complex mechatronic systems. This paper will illustrate the process of automatically generating bond graphs from 3D CAD assemblies of gear-trains. Using appropriate CAD application programming interfaces (APIs), information on parts and mates within an existing assembly is extracted. The extracted information is stored as an identity graph, which also stores all geometry and mass related information of every part. Grammar rules are then used to transform the identity graph to a system graph, which is then converted to bond graph using an existing bond graph generation program. The paper will discuss the process, challenges and planned future work.

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Margetts, Rebecca, and Roger F. Ngwompo. "Comparison of Modeling Techniques for a Landing Gear." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39722.

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A wide range of modeling techniques is available to the engineer. The objective of this paper is to compare some typical modeling techniques for the simulation of a multi-domain mechatronic system. Usual dynamic modeling methods, such as block diagrams and iconic diagrams, can cause problems for the engineer. Differential algebraic equations (DAEs) and algebraic loops can significantly increase simulation times and cause numeric errors. Bond graphs are less common in industry, and are presented here as a method which allows the engineer to easily identify causal loops and elements in differential causality. These can indicate DAEs in the underlying equations. An aircraft landing gear is given as an example of a multi-domain system, and is modeled as a block diagram, an iconic diagram and as a bond graph. The time to construct the model, time to solve and problems faced by the analyst are presented. Bond graphs offer distinct advantages in terms of the ease of implementing algebraic equations and visibility of causality. The time taken to model a system can be significantly reduced and the results appear free from computational errors. Bond graphs are therefore recommended for this type of multi-domain systems analysis.

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Ghaith, Fadi A., and Ahmad Ayub. "Elastodynamic Modeling and Simulation of an Axially Accelerating Beam." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46644.

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This paper aims to develop an accurate nonlinear mathematical model which may describe the coupled in-plane motion of an axially accelerating beam. The Extended Hamilton’s Principle was utilized to derive the partial differential equations governing the motion of a simply supported beam. The set of the ordinary differential equations were obtained by means of the assumed mode method. The derived elastodynamic model took into account the geometric non-linearity, the time-dependent axial velocity and the coupling between the transverse and longitudinal vibrations. The developed equations were solved numerically using the Runge-Kutta method and the obtained results were presented in terms of the vibrational response graphs and the system natural frequencies. The system dynamic characteristics were explored with a major focus on the influence of the velocity, acceleration and the excitation force frequency. The obtained results showed that the natural frequency decreased significantly at high axial velocities. Also it was found that the system may exhibit unstable behavior at high accelerations.

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Nandkeolyar, R., P. Sibanda, and Md S. Ansari. "Unsteady Hydromagnetic Radiative Flow of a Dusty Fluid Past a Porous Plate With Ramped Wall Temperature." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-66699.

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The combined effects of applied magnetic field, thermal radiation and suction on the flow and free convective heat transfer of a viscous, incompressible, electrically conducting dusty fluid past a flat plate with ramped temperature are studied. The governing partial differential equations for momentum and energy transfers, for both the fluid and particle phases, are solved using Laplace transform technique. The inverse Laplace transform is obtained numerically using Matlab. A comparison of Numerical solution and analytical solution for energy transfer is made which shows an excellent agreement. The effects of pertinent flow parameters are analyzed with the help of graphs and tables.

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Olson, Matthew L., Stephen P. Gent, Taylor N. Suess, and Michael P. Twedt. "Creating an Application to Predict Operational Characteristics and Efficiency of Continuous Cross-Flow Corn Drying." In ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ht2013-17327.

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The purpose of this study is to create a computer simulation which numerically predicts the drying conditions within a continuous cross-flow grain drying system. The model is based on a system of four partial differential equations using energy and mass balances for the air, grain, and moisture within the column. This simulation includes: (1) a graphical user interface for varying the operating conditions, (2) a numerical scheme for solving the system of equations based on a backwards finite difference scheme, and (3) graphical and tabular output data. The output includes graphs of moisture content, air temperature, and grain temperature inside the column, as well as the predicted energy consumption of the system. Using this program, the grain drying model is analyzed in order to gain insight towards the optimal operating conditions for the grain dryer. The study also makes adjustments to the model in order to improve accuracy and ease of use. In particular, the Page equation for single-kernel drying is implemented. Model assumptions are also analyzed for validity, and the solutions are verified using experimental data collected in a previous study. The overall goal of this research is to improve grain dryer design and optimize operating conditions in order to reduce energy costs, improve grain quality, and increase the understanding of deep bed grain drying models.

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