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Journal articles on the topic 'Dynamical'

To see the other types of publications on this topic, follow the link: Dynamical.

Author: Grafiati

Published: 4 June 2021

Last updated: 25 April 2022

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1

Koelink, Erik, and Yvette Van Norden. "The dynamicalU(n)quantum group." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–30. http://dx.doi.org/10.1155/ijmms/2006/65279.

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We study the dynamical analogue of the matrix algebraM(n), constructed from a dynamicalR-matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these corepresentations. These elements are studied in more detail, especially the action of the comultiplication and Laplace expansions. Using the Laplace expansions we can prove that the dynamical quantum determinant is almost central, and adjoining an inverse the antipode can be defined. This results in the dynamicalGL(n)quantum group associated to the dynamicalR-matrix. We study a∗-structure leading to the dynamicalU(n)quantum group, and we obtain results for the canonical pairing arising from theR-matrix.

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2

Caballero, Rubén, Alexandre N. Carvalho, Pedro Marín-Rubio, and José Valero. "Robustness of dynamically gradient multivalued dynamical systems." Discrete & Continuous Dynamical Systems - B 24, no. 3 (2019): 1049–77. http://dx.doi.org/10.3934/dcdsb.2019006.

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3

Dietrich, Eric, and Arthur B. Markman. "Dynamical description versus dynamical modeling." Trends in Cognitive Sciences 5, no. 8 (August 2001): 332. http://dx.doi.org/10.1016/s1364-6613(00)01705-8.

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4

Aonishi, Toru, and Masato Okada. "Dynamically Coupled Oscillators: Cooperative Behavior via Dynamical Interaction." Journal of the Physical Society of Japan 72, no. 6 (June 15, 2003): 1334–37. http://dx.doi.org/10.1143/jpsj.72.1334.

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5

Karolinsky, E., A. Stolin, and V. Tarasov. "From Dynamical to Non-Dynamical Twists." Letters in Mathematical Physics 71, no. 3 (March 2005): 173–78. http://dx.doi.org/10.1007/s11005-005-0158-8.

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6

Wang, Guangwa, and Yongluo Cao. "Dynamical Spectrum in Random Dynamical Systems." Journal of Dynamics and Differential Equations 26, no. 1 (November 27, 2013): 1–20. http://dx.doi.org/10.1007/s10884-013-9340-3.

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7

Szpiro, George G. "Measuring dynamical noise in dynamical systems." Physica D: Nonlinear Phenomena 65, no. 3 (May 1993): 289–99. http://dx.doi.org/10.1016/0167-2789(93)90164-v.

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8

Bildik, Necdet, and Mustafa İnç. "On some Extensions of Dynamical Homeomorphism and Dynamical Isomorphism in Dynamical System." Mathematical and Computational Applications 4, no. 2 (August 1, 1999): 189–94. http://dx.doi.org/10.3390/mca4020189.

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9

BALADI, VIVIANE. "Periodic orbits and dynamical spectra (Survey)." Ergodic Theory and Dynamical Systems 18, no. 2 (April 1998): 255–92. http://dx.doi.org/10.1017/s0143385798113925.

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Basic results in the rigorous theory of weighted dynamical zeta functions or dynamically defined generalized Fredholm determinants are presented. Analytic properties of the zeta functions or determinants are related to statistical properties of the dynamics via spectral properties of dynamical transfer operators, acting on Banach spaces of observables.

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10

Matsumoto, Diogo Kendy. "Dynamical braces and dynamical Yang–Baxter maps." Journal of Pure and Applied Algebra 217, no. 2 (February 2013): 195–206. http://dx.doi.org/10.1016/j.jpaa.2012.06.012.

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11

Li, Desheng. "On Dynamical Stability in General Dynamical Systems." Journal of Mathematical Analysis and Applications 263, no. 2 (November 2001): 455–78. http://dx.doi.org/10.1006/jmaa.2001.7620.

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12

Baez, Maria Laura, Marcel Goihl, Jonas Haferkamp, Juani Bermejo-Vega, Marek Gluza, and Jens Eisert. "Dynamical structure factors of dynamical quantum simulators." Proceedings of the National Academy of Sciences 117, no. 42 (October 2, 2020): 26123–34. http://dx.doi.org/10.1073/pnas.2006103117.

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The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors and, hence, offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are bounded-error quantum polynomial time (BQP)-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate-scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.

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13

Singh, Pooja, and Dania Masood. "Dynamical properties of relative semi-dynamical systems." Journal of Dynamical Systems and Geometric Theories 13, no. 2 (July 3, 2015): 115–24. http://dx.doi.org/10.1080/1726037x.2015.1076226.

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14

Szydłowski, Marek, and Orest Hrycyna. "Dynamical dark energy models – dynamical system approach." General Relativity and Gravitation 38, no. 1 (January 2006): 121–35. http://dx.doi.org/10.1007/s10714-005-0211-z.

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15

Sapsis, Themistoklis P., and Pierre F. J. Lermusiaux. "Dynamically orthogonal field equations for continuous stochastic dynamical systems." Physica D: Nonlinear Phenomena 238, no. 23-24 (December 2009): 2347–60. http://dx.doi.org/10.1016/j.physd.2009.09.017.

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16

Debastiani, V. R., E. Oset, J. M. Dias, and H. W. Liang. "Dynamical Hadrons." Acta Physica Polonica B Proceedings Supplement 11, no. 3 (2018): 475. http://dx.doi.org/10.5506/aphyspolbsupp.11.475.

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17

Chillingworth, D. R. J., D. K. Arrowsmith, and C. M. Place. "Dynamical Systems." Mathematical Gazette 79, no. 484 (March 1995): 233. http://dx.doi.org/10.2307/3620112.

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18

Ovchinnikov, A. A., and V. V. Atrazhev. "Dynamical process." Physica A: Statistical Mechanics and its Applications 247, no. 1-4 (December 1997): 331–37. http://dx.doi.org/10.1016/s0378-4371(97)00379-8.

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19

OLLE, H., P. YUVAL, and E. JEFFREY. "Dynamical Percolation." Annales de l'Institut Henri Poincare (B) Probability and Statistics 33, no. 4 (1997): 497–528. http://dx.doi.org/10.1016/s0246-0203(97)80103-3.

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20

Hornstein, John, and V. I. Arnold. "Dynamical Systems." American Mathematical Monthly 96, no. 9 (November 1989): 861. http://dx.doi.org/10.2307/2324864.

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21

Levine, R. D. "Dynamical symmetries." Journal of Physical Chemistry 89, no. 11 (May 1985): 2122–29. http://dx.doi.org/10.1021/j100257a001.

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22

Jacob, G. "Dynamical systems." Mathematics and Computers in Simulation 42, no. 4-6 (November 1996): 639. http://dx.doi.org/10.1016/s0378-4754(97)84413-8.

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23

Dai, Xi. "Dynamical anomaly." Nature Physics 16, no. 4 (March 6, 2020): 374. http://dx.doi.org/10.1038/s41567-020-0844-6.

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24

Zaslavsky, G. M. "Dynamical traps." Physica D: Nonlinear Phenomena 168-169 (August 2002): 292–304. http://dx.doi.org/10.1016/s0167-2789(02)00516-x.

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25

Wright, Alison. "Dynamical breaking." Nature Physics 10, no. 5 (April 30, 2014): 332. http://dx.doi.org/10.1038/nphys2969.

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26

Németh, J., G. Papp, C. Ngô, and M. Barranco. "Dynamical Multifragmentation." Physica Scripta T32 (January 1, 1990): 160–64. http://dx.doi.org/10.1088/0031-8949/1990/t32/026.

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27

Balucani, Umberto, M. Howard Lee, and Valerio Tognetti. "Dynamical correlations." Physics Reports 373, no. 6 (January 2003): 409–92. http://dx.doi.org/10.1016/s0370-1573(02)00430-1.

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28

Meiss, James. "Dynamical systems." Scholarpedia 2, no. 2 (2007): 1629. http://dx.doi.org/10.4249/scholarpedia.1629.

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29

Bunimovich, Leonid. "Dynamical billiards." Scholarpedia 2, no. 8 (2007): 1813. http://dx.doi.org/10.4249/scholarpedia.1813.

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30

Švarný, Petr. "Dynamical branching." AUC PHILOSOPHICA ET HISTORICA 2015, no. 1 (August 8, 2016): 93–101. http://dx.doi.org/10.14712/24647055.2016.11.

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31

Cottrell, A. "Dynamical recovery." Journal of Materials Science 39, no. 12 (June 2004): 3865–70. http://dx.doi.org/10.1023/b:jmsc.0000031467.75584.88.

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32

Choi, Kiwoon, and Jihn E. Kim. "Dynamical axion." Physical Review D 32, no. 7 (October 1, 1985): 1828–34. http://dx.doi.org/10.1103/physrevd.32.1828.

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33

Aldroubi, A., C. Cabrelli, U. Molter, and S. Tang. "Dynamical sampling." Applied and Computational Harmonic Analysis 42, no. 3 (May 2017): 378–401. http://dx.doi.org/10.1016/j.acha.2015.08.014.

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34

MACKEY, MICHAEL C., and JOHN G. MILTON. "Dynamical Diseases." Annals of the New York Academy of Sciences 504, no. 1 Perspectives (July 1987): 16–32. http://dx.doi.org/10.1111/j.1749-6632.1987.tb48723.x.

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35

Svensmark, H. "Dynamical squeezing." Physical Review A 45, no. 3 (February 1, 1992): 1924–31. http://dx.doi.org/10.1103/physreva.45.1924.

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36

Gomes, M., V. G. Kupriyanov, and A. J. da Silva. "Dynamical noncommutativity." Journal of Physics A: Mathematical and Theoretical 43, no. 28 (June 14, 2010): 285301. http://dx.doi.org/10.1088/1751-8113/43/28/285301.

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37

Reyssat, Mathilde, Denis Richard, Christophe Clanet, and David Quéré. "Dynamical superhydrophobicity." Faraday Discussions 146 (2010): 19. http://dx.doi.org/10.1039/c000410n.

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38

Deutch, J. M. "Dynamical catalysis." Journal of Chemical Physics 108, no. 3 (January 15, 1998): 937–42. http://dx.doi.org/10.1063/1.475457.

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39

BROWN, RAY, and LEON O. CHUA. "DYNAMICAL INTEGRATION." International Journal of Bifurcation and Chaos 03, no. 01 (February 1993): 217–22. http://dx.doi.org/10.1142/s0218127493000179.

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In this letter we show how to use a new form of integration, called dynamical integration, that utilizes the dynamics of a system defined by an ODE to construct a map that is in effect a one-step integrator. This method contrasts sharply with classical numerical methods that utilize polynomial or rational function approximations to construct integrators. The advantages of this integrator is that it uses only one step while preserving important dynamical properties of the solution of the ODE: First, if the ODE is conservative, then the one-step integrator is measure preserving. This is significant for a system having a highly nonlinear component. Second, the one-step integrator is actually a one-parameter family of one-step maps and is derived from a continuous transformation group as is the set of solutions of the ODE. If each element of the continuous transformation group of the ODE is topologically conjugate to its inverse, then so is each member of the one-parameter family of one-step integrators. If the solutions of the ODE are elliptic, then for sufficiently small values of the parameter, the one-step integrator is also elliptic. In the limit as the parameter of the one-step family of maps goes to zero, the one-step integrator satisfies the ODE exactly. Further, it can be experimentally verified that if the ODE is chaotic, then so is the one-step integrator. In effect, the one-step integrator retains the dynamical characteristics of the solutions of the ODE, even with relatively large step sizes, while in the limit as the parameter goes to zero, it solves the ODE exactly. We illustrate the dynamical, in contrast to numerical, accuracy of this integrator with two distinctly different examples: First we use it to integrate the unforced Van der Pol equation for large ∊, ∊≥10 which corresponds to an almost continuous square-wave solution. Second, we use it to obtain the Poincaré map for two different versions of the periodically forced Duffing equation for parameter values where the solutions are chaotic. The dynamical accuracy of the integrator is illustrated by the reproduction of well-known strange attractors. The production of these attractors is eleven times longer when using a conventional fourth-order predictor-corrector method. The theory presented here extends to higher dimensions and will be discussed in detail in a forthcoming paper. However, we caution that the theory we present here is not intended as a line of research in numerical methods for ODEs.

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40

Sitarz, Andrzej. "Dynamical noncommutativity." Journal of High Energy Physics 2002, no. 09 (September 15, 2002): 034. http://dx.doi.org/10.1088/1126-6708/2002/09/034.

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41

Gaveau, B., and L. S. Schulman. "Dynamical metastability." Journal of Physics A: Mathematical and General 20, no. 10 (July 11, 1987): 2865–73. http://dx.doi.org/10.1088/0305-4470/20/10/031.

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42

Rota, Gian-Carlo. "Dynamical systems." Advances in Mathematics 58, no. 3 (December 1985): 322. http://dx.doi.org/10.1016/0001-8708(85)90129-x.

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43

Garban, Christophe. "Dynamical Liouville." Journal of Functional Analysis 278, no. 6 (April 2020): 108351. http://dx.doi.org/10.1016/j.jfa.2019.108351.

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44

Peng, Shige. "Dynamical evaluations." Comptes Rendus Mathematique 339, no. 8 (October 2004): 585–89. http://dx.doi.org/10.1016/j.crma.2004.09.015.

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45

Noakes, Lyle, and Alistair Mees. "Dynamical signatures." Physica D: Nonlinear Phenomena 58, no. 1-4 (September 1992): 243–50. http://dx.doi.org/10.1016/0167-2789(92)90112-z.

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46

Pavlov, V. P., and V. M. Sergeev. "Dynamical principle." Theoretical and Mathematical Physics 153, no. 1 (October 2007): 1364–72. http://dx.doi.org/10.1007/s11232-007-0120-2.

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47

Ferrero, Renata, and Roberto Percacci. "Dynamical diffeomorphisms." Classical and Quantum Gravity 38, no. 11 (May 7, 2021): 115011. http://dx.doi.org/10.1088/1361-6382/abf627.

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48

Hagy, Matthew C., and Rigoberto Hernandez. "Dynamical simulation of dipolar Janus colloids: Dynamical properties." Journal of Chemical Physics 138, no. 18 (May 14, 2013): 184903. http://dx.doi.org/10.1063/1.4803864.

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49

Bekenstein, Jacob D., and Eyal Maoz. "Dynamical friction from fluctuations in stellar dynamical systems." Astrophysical Journal 390 (May 1992): 79. http://dx.doi.org/10.1086/171260.

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50

Li, Zhiming, Minghan Wang, and Guo Wei. "Induced hyperspace dynamical systems of symbolic dynamical systems." International Journal of General Systems 47, no. 8 (October 3, 2018): 809–20. http://dx.doi.org/10.1080/03081079.2018.1524467.

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