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Journal articles on the topic 'Algebraic dynamics'

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

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

VIALLET, C. M. "ALGEBRAIC DYNAMICS AND ALGEBRAIC ENTROPY." International Journal of Geometric Methods in Modern Physics 05, no. 08 (December 2008): 1373–91. http://dx.doi.org/10.1142/s0219887808003375.

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We give the definition of algebraic entropy, which is a global index of complexity for dynamical systems with a rational evolution. We explain its geometrical meaning, and different methods, heuristic or exact to calculate this entropy. This quantity is a very good integrability detector. It also has remarkable properties, which make it an interesting object of study by itself. It is in particular conjectured to be the logarithm of algebraic integer, with a limited range of values, still to be explored.

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2

Lindahl, Karl-Olof. "Applied algebraic dynamics." P-Adic Numbers, Ultrametric Analysis, and Applications 2, no. 4 (November 25, 2010): 360–62. http://dx.doi.org/10.1134/s2070046610040084.

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3

Zhang, Hua, WeiTao Lu, and ShunJin Wang. "Algebraic dynamics solution and algebraic dynamics algorithm of Burgers equations." Science in China Series G: Physics, Mechanics and Astronomy 51, no. 11 (August 21, 2008): 1647–52. http://dx.doi.org/10.1007/s11433-008-0156-9.

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4

Zhang, Shou-Wu. "Distributions in algebraic dynamics." Surveys in Differential Geometry 10, no. 1 (2005): 381–430. http://dx.doi.org/10.4310/sdg.2005.v10.n1.a9.

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5

Wang, ShunJin, and Hua Zhang. "Symplectic algebraic dynamics algorithm." Science in China Series G: Physics, Mechanics and Astronomy 50, no. 2 (April 2007): 133–43. http://dx.doi.org/10.1007/s11433-007-0013-2.

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6

Wang, Shunjin, and Hua Zhang. "Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations." Science in China Series G: Physics, Mechanics and Astronomy 49, no. 6 (December 2006): 716–28. http://dx.doi.org/10.1007/s11433-006-2017-8.

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7

Zhang, Hua, WeiTao Lu, and ShunJin Wang. "Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation." Science in China Series G: Physics, Mechanics and Astronomy 51, no. 10 (August 11, 2008): 1470–78. http://dx.doi.org/10.1007/s11433-008-0148-9.

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8

MATSUNO, YOSHIMASA. "DYNAMICS OF INTERACTING ALGEBRAIC SOLITONS." International Journal of Modern Physics B 09, no. 17 (July 30, 1995): 1985–2081. http://dx.doi.org/10.1142/s0217979295000811.

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A survey is made which highlights recent topics on the dynamics of algebraic solitons, which are exact solutions to a certain class of nonlinear integrodifferential evolution equations. The model equations that we consider here are the Benjamin-Ono (BO) and its higher-order equations together with the BO-Burgers equation, a model equation for deep-water waves, the sine-Hilbert (sH) equation and a damped sH equation. While these equations have their origin either in physics or in mathematics, each equation exhibits a novel type of algebraic soliton solution and hence its characteristic is worth studying in its own right. After deriving these equations, we are concerned with each equation separately. We first present explicit N-soliton solutions and then summarize related mathematical properties of the equation. Subsequently, a detailed description is given to the interaction process of two algebraic solitons using the pole expansion of the solution. Particular attention is paid to investigating the effects of small perturbations on the overtaking collision of two BO solitons by employing a direct multisoliton perturbation theory. It is shown that the dynamics of interacting algebraic solitons reveal new aspects which have never been observed in the interaction process of usual solitons expressed in terms of exponential functions.

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9

Leschber, Yorck, and J. P. Draayer. "Algebraic realization of rotational dynamics." Physics Letters B 190, no. 1-2 (May 1987): 1–6. http://dx.doi.org/10.1016/0370-2693(87)90829-x.

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10

Alonso, L. Martinez, and E. Olmedilla Moreno. "Algebraic geometry and soliton dynamics." Chaos, Solitons & Fractals 5, no. 12 (December 1995): 2213–27. http://dx.doi.org/10.1016/0960-0779(94)e0096-8.

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11

Mencinger, Matej. "On Algebraic Approach in Quadratic Systems." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/230939.

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When considering friction or resistance, many physical processes are mathematically simulated by quadratic systems of ODEs or discrete quadratic dynamical systems. Probably the most important problem when such systems are applied in engineering is the stability of critical points and (non)chaotic dynamics. In this paper we consider homogeneous quadratic systems via the so-called Markus approach. We use the one-to-one correspondence between homogeneous quadratic dynamical systems and algebra which was originally introduced by Markus in (1960). We resume some connections between the dynamics of the quadratic systems and (algebraic) properties of the corresponding algebras. We consider some general connections and the influence of power-associativity in the corresponding quadratic system.

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12

Srivastava, Sunita, C. N. Kumar, and K. Tankeshwar. "Dynamics of gelling liquids: algebraic relaxation." Journal of Physics: Condensed Matter 21, no. 33 (July 24, 2009): 335106. http://dx.doi.org/10.1088/0953-8984/21/33/335106.

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13

Robinson, James D., and M. John D. Hayes. "THE DYNAMICS OF A SINGLE ALGEBRAIC SCREW PAIR." Transactions of the Canadian Society for Mechanical Engineering 35, no. 4 (December 2011): 491–503. http://dx.doi.org/10.1139/tcsme-2011-0029.

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The algebraic screw pair, or A-pair, represents a new class of kinematic constraint that exploits the self-motions inherent to a specific configuration of Griffis-Duffy platform. Using the A-pair as a joint in a hybrid parallel-serial kinematic chain results in a sinusoidal coupling of rotation and translation between adjacent links. The resulting linkage is termed an A-chain. This paper reveals the dynamic equations of motion of a single A-pair and examines the impact of the inertial properties of the legs of the A-pair on the dynamics. A numerical example illustrates the impact of the leg effects from different perspectives and shows that while the gravity effects of the legs are significant, it may be possible to neglect the leg kinetic energy from the dynamics model.

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14

Wang, ShunJin, and Hua Zhang. "Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems." Science in China Series G: Physics, Mechanics and Astronomy 51, no. 6 (May 17, 2008): 577–90. http://dx.doi.org/10.1007/s11433-008-0055-0.

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15

Chatzidakis, Zoé, and Ehud Hrushovski. "Difference fields and descent in algebraic dynamics. I." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (October 2008): 653–86. http://dx.doi.org/10.1017/s1474748008000273.

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AbstractWe draw a connection between the model-theoretic notions of modularity (or one-basedness), orthogonality and internality, as applied to difference fields, and questions of descent in in algebraic dynamics. In particular we prove in any dimension a strong dynamical version of Northcott's theorem for function fields, answering a question of Szpiro and Tucker and generalizing a theorem of Baker's for the projective line.The paper comes in three parts. This first part contains an exposition some of the main results of the model theory of difference fields, and their immediate connection to questions of descent in algebraic dynamics. We present the model-theoretic notion of internality in a context that does not require a universal domain with quantifier-elimination. We also note a version of canonical heights that applies well beyond polarized algebraic dynamics. Part II sharpens the structure theory to arbitrary base fields and constructible maps where in part I we emphasize finite base change and correspondences. Part III will include precise structure theorems related to the Galois theory considered here, and will enable a sharpening of the descent results for non-modular dynamics.

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16

ADAMCZEWSKI, BORIS, and YANN BUGEAUD. "Dynamics forβ-shifts and Diophantine approximation." Ergodic Theory and Dynamical Systems 27, no. 6 (December 2007): 1695–711. http://dx.doi.org/10.1017/s0143385707000223.

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AbstractWe investigate theβ-expansion of an algebraic number in an algebraic baseβ. Using tools from Diophantine approximation, we prove several results that may suggest a strong difference between the asymptotic behaviour of eventually periodic expansions and that of non-eventually periodic expansions.

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17

MENCINGER, MATEJ, and MILAN KUTNJAK. "THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE." International Journal of Bifurcation and Chaos 19, no. 01 (January 2009): 117–33. http://dx.doi.org/10.1142/s0218127409022786.

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The dynamics of discrete homogeneous quadratic planar maps is considered via the algebraic approach. There is a one-to-one correspondence between these systems and 2D commutative algebras (c.f. [Markus, 1960]). In particular, we consider the systems corresponding to algebras which contain some nilpotents of rank two (i.e. NQ-systems). Markus algebraic classification is used to obtain the class representatives. The case-by-case dynamical analysis is presented. It is proven that there is no chaos in NQ-systems. Yet, some cases are really interesting from the dynamical and bifurcational points of view.

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18

Gogoussis, A., and M. Donath. "A Method for the Real Time Solution of the Forward Dynamics Problem for Robots Incorporating Friction." Journal of Dynamic Systems, Measurement, and Control 112, no. 4 (December 1, 1990): 630–39. http://dx.doi.org/10.1115/1.2896188.

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A modular and computationally efficient method for solving the forward dynamics problem of robot mechanisms incorporating Coulomb friction is developed. This hybrid approach incorporates both analog and digital components that facilitate real time solutions. Coulomb friction effects associated with both transmissions and bearings are considered. Moreover, the methods accounts for joint flexibility as well as actuator gyroscopic effects. In our approach, the inverse dynamics formulation is used for solving the forward dynamics problem. The positive definiteness property of the inertia matrix of the dynamic equations of motion is exploited by intentionally introducing algebraic loops so that simultaneous algebraic equations are solved without iterations. By resolving these algebraic loops using linear electronics, one avoids the computational burden and time delays associated with purely digital solutions, thus facilitating real time operation. A proof of stability is also presented. The formulation developed here is useful in cases requiring either or both the inverse and forward dynamics solutions typically associated with design and control.

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19

LIN, JAN-LI. "On the arithmetic dynamics of monomial maps." Ergodic Theory and Dynamical Systems 39, no. 12 (March 13, 2018): 3388–406. http://dx.doi.org/10.1017/etds.2018.5.

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We prove several results for the arithmetic dynamics of monomial maps, including Silverman’s conjectures on height growth, dynamical Mordell–Lang conjecture, and dynamical Manin–Mumford conjecture. These results were originally known for monomial maps on algebraic tori. We extend them to arbitrary toric varieties.

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20

Majidi-Zolbanin, M., N. Miasnikov, and L. Szpiro. "Entropy and flatness in local algebraic dynamics." Publicacions Matemàtiques 57 (July 1, 2013): 509–44. http://dx.doi.org/10.5565/publmat_57213_12.

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21

Xie, Junyi. "Algebraic dynamics of the lifts of Frobenius." Algebra & Number Theory 12, no. 7 (October 27, 2018): 1715–48. http://dx.doi.org/10.2140/ant.2018.12.1715.

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22

Toutounji, Mohamad. "Algebraic approach to electronic spectroscopy and dynamics." Journal of Chemical Physics 128, no. 16 (April 28, 2008): 164103. http://dx.doi.org/10.1063/1.2903748.

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23

Bagarello, F., and C. Trapani. "Algebraic dynamics inO*-algebras: A perturbative approach." Journal of Mathematical Physics 43, no. 6 (June 2002): 3280–92. http://dx.doi.org/10.1063/1.1467609.

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24

Pineiro, Jorge. "Heights, algebraic dynamics and Berkovich analytic spaces." São Paulo Journal of Mathematical Sciences 3, no. 1 (June 30, 2009): 77. http://dx.doi.org/10.11606/issn.2316-9028.v3i1p77-94.

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25

Ghioca, Dragos, and Junyi Xie. "Algebraic dynamics of skew-linear self-maps." Proceedings of the American Mathematical Society 146, no. 10 (June 29, 2018): 4369–87. http://dx.doi.org/10.1090/proc/14104.

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26

Panakkal, Susan Mathew, Parameswaran R, and M. J. Vedan. "A geometric algebraic approach to fluid dynamics." Physics of Fluids 32, no. 8 (August 1, 2020): 087111. http://dx.doi.org/10.1063/5.0017344.

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27

Valls, Claudia. "Invariant algebraic surfaces for a virus dynamics." Zeitschrift für angewandte Mathematik und Physik 66, no. 4 (October 14, 2014): 1315–28. http://dx.doi.org/10.1007/s00033-014-0464-z.

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28

LI, ZHIQIANG, and DAIZHAN CHENG. "ALGEBRAIC APPROACH TO DYNAMICS OF MULTIVALUED NETWORKS." International Journal of Bifurcation and Chaos 20, no. 03 (March 2010): 561–82. http://dx.doi.org/10.1142/s0218127410025892.

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Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums; (b) the numbers of cycles of different lengths; (c) transient period, the minimum time for all points to enter the set of attractors, respectively. A method to reconstruct the logical network from its network transition matrix is also presented. This approach can also be used to convert the dynamics of a multivalued control network into a discrete-time bilinear system. Then, the structure and the controllability of multivalued logical control networks are revealed.

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29

Beardmore, R. E., and Y. H. Song. "Differential-Algebraic Equations: A Tutorial Review." International Journal of Bifurcation and Chaos 08, no. 07 (July 1998): 1399–411. http://dx.doi.org/10.1142/s0218127498001091.

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This article (Funded by EPSRC and the National Grid Company.) explores some introductory principles of differential-algebraic equations (DAEs) and makes a connection with the theory of dynamical systems. Some results which are new in the field of DAEs are also surveyed. Most treatments on DAE emphasize the differences that exist when compared with the ODE case. Here we seek to underline the similarities so that readers with a very basic knowledge of nonlinear dynamics can understand some of their consequences in this more general context.

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30

Cheng, Zai Bin, Wei Jiang, Ge Xue Ren, Jian Liang Zhou, Shi Quan Jiang, Cai Jin Yang, and Bao Sheng He. "A Multibody Dynamical Model for Full Hole Drillstring Dynamics." Applied Mechanics and Materials 378 (August 2013): 91–96. http://dx.doi.org/10.4028/www.scientific.net/amm.378.91.

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The research on drillstring dynamics is necessary for improving drilling efficiency and safety. In this investigation, a multibody dynamical model for 3D full hole drillstring system is presented based on the Absolute Nodal Coordinate Formulation (ANCF). The drillstring is modeled with the ANCF beam element. The absolute nodal coordinate formulation of the beam element as well as the boundary conditions at the top-drive and drill-bit, and the contact/friction model between drillstring and wellbore are also investigated. The dynamic governing equation for full hole drillstring system is given and solved by the backward differentiation formulation (BDF) for differential algebraic equations (DAEs). The developed multibody dynamic solver is capable of analyzing full coupled vibration for the full hole drillstring system. It can play a certain role in drillstring dynamics researches and engineering applications.

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31

Ayasun, Saffet. "Effects of algebraic singularities on the voltage dynamics of differential-algebraic power system model." European Transactions on Electrical Power 18, no. 6 (September 2008): 547–61. http://dx.doi.org/10.1002/etep.209.

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32

Batra, Anjula, and Patrick Morton. "Algebraic Dynamics of Polynomial Maps on the Algebraic Closure of a Finite Field, II." Rocky Mountain Journal of Mathematics 24, no. 3 (September 1994): 905–32. http://dx.doi.org/10.1216/rmjm/1181072380.

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33

Batra, Anjula, and Patrick Morton. "Algebraic Dynamics of Polynomial Maps on the Algebraic Closure of a Finite Field, I." Rocky Mountain Journal of Mathematics 24, no. 2 (June 1994): 453–81. http://dx.doi.org/10.1216/rmjm/1181072411.

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34

Chatzidakis, Zoé, and Ehud Hrushovski. "Difference fields and descent in algebraic dynamics. II." Journal of the Institute of Mathematics of Jussieu 7, no. 4 (October 2008): 687–704. http://dx.doi.org/10.1017/s1474748008000170.

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AbstractThis second part of the paper strengthens the descent theory described in the first part to rational maps and arbitrary base fields. We obtain in particular a decomposition of any difference field extension into a tower of finite, field-internal and one-based difference field extensions. This is needed in order to obtain the ‘dynamical Northcott’ Theorem 1.11 of Part I in sharp form.

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35

Fakhruddin, Najmuddin. "The algebraic dynamics of generic endomorphisms of ℙn." Algebra & Number Theory 8, no. 3 (May 31, 2014): 587–608. http://dx.doi.org/10.2140/ant.2014.8.587.

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36

Madhavi Sastry, G., and V. Sabareesh. "The Lie-algebraic approach to hemeprotein-ligand dynamics." Chemical Physics Letters 369, no. 5-6 (February 2003): 691–97. http://dx.doi.org/10.1016/s0009-2614(03)00041-1.

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37

Nagul, N. V. "The logic-algebraic equations method in system dynamics." St. Petersburg Mathematical Journal 24, no. 4 (May 24, 2013): 645–62. http://dx.doi.org/10.1090/s1061-0022-2013-01258-1.

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38

Franz, Silvio, and Giorgio Parisi. "Quasi-equilibrium in glassy dynamics: an algebraic view." Journal of Statistical Mechanics: Theory and Experiment 2013, no. 02 (February 1, 2013): P02003. http://dx.doi.org/10.1088/1742-5468/2013/02/p02003.

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39

Tsakiris, M. C., and D. C. Tarraf. "Algebraic decompositions of DP problems with linear dynamics." Systems & Control Letters 85 (November 2015): 46–53. http://dx.doi.org/10.1016/j.sysconle.2015.09.001.

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40

Emmrich, Etienne, and Volker Mehrmann. "Operator Differential-Algebraic Equations Arising in Fluid Dynamics." Computational Methods in Applied Mathematics 13, no. 4 (October 1, 2013): 443–70. http://dx.doi.org/10.1515/cmam-2013-0018.

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Abstract. Existence and uniqueness of generalized solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations covers, in particular, the Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid but also their spatial semi-discretization. The equations are governed by a block operator matrix with entries that fulfill suitable inf-sup conditions. The problem data are required to satisfy appropriate consistency conditions. The results in infinite dimensions are compared in detail with those known for the DAEs that arise after semi-discretization in space. Explicit solution formulas are derived in both cases.

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41

Adler, Stephen L., and Yong-Shi Wu. "Algebraic and geometric aspects of generalized quantum dynamics." Physical Review D 49, no. 12 (June 15, 1994): 6705–8. http://dx.doi.org/10.1103/physrevd.49.6705.

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42

Linder, Daniel F., and Grzegorz A. Rempala. "Algebraic statistical model for biochemical network dynamics inference." Journal of Coupled Systems and Multiscale Dynamics 1, no. 4 (December 1, 2013): 468–75. http://dx.doi.org/10.1166/jcsmd.2013.1032.

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43

Anashin, Vladimir S. "Noncommutative algebraic dynamics: Ergodic theory for profinite groups." Proceedings of the Steklov Institute of Mathematics 265, no. 1 (July 2009): 30–58. http://dx.doi.org/10.1134/s0081543809020035.

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44

Pawełczyk, Jacek, and Harold Steinacker. "Algebraic brane dynamics on SU(2): excitation spectra." Journal of High Energy Physics 2003, no. 12 (December 5, 2003): 010. http://dx.doi.org/10.1088/1126-6708/2003/12/010.

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45

De Filippo, S., G. Landi, G. Marmo, and G. Vilasi. "An algebraic description of the electron—monopole dynamics." Physics Letters B 220, no. 4 (April 1989): 576–80. http://dx.doi.org/10.1016/0370-2693(89)90789-2.

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46

Bell, Jason, Richard Miles, and Thomas Ward. "Towards a Pólya–Carlson dichotomy for algebraic dynamics." Indagationes Mathematicae 25, no. 4 (June 2014): 652–68. http://dx.doi.org/10.1016/j.indag.2014.04.005.

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47

Benner, Michael, and Alfred Rieckers. "Spectral Properties Of Weakly Inhomogeneous Bcs-Models In Different Representations." Zeitschrift für Naturforschung A 60, no. 5 (May 1, 2005): 343–65. http://dx.doi.org/10.1515/zna-2005-0506.

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For a class of Bardeen-Cooper-Schrieffer (BCS)-models, with complex, weakly momentum dependent interaction coefficients, the representation dependent effective Hamiltonians and their spectra are reconsidered in order to obtain a consistent physical picture by means of operator algebraic methods. The starting point is the limiting dynamics, the existence of which had been proved in a previous work, in terms of a C*-dynamical system acting in a classically extended, electronic Canonical Anticommutation Relations (CAR)-algebra. The C*-algebraic KMS-theory, including the low temperature limit, specifies the order parameters. These appear as classical observables, which commute with all other observables, constituting elements of the center of the algebra. The algebraic spectral theory, in the sense of Arveson, is first applied to the dynamics in general pure energy state representations. The spectra of the finite temperature representations are analyzed, identifying the gap as the lowest of those energy values, which are stable under local perturbations. Further insights are obtained by decomposing the thermal dynamical systems into the pure energy state Heisenberg dynamics, after having first extended them to more comprehensive W*-dynamical systems. The decomposing orthogonal measure is transferred to the infinite product space of quasi-particle occupation numbers and its support is characterized in terms of 0-1-laws leading to an asymptotic ratio of quasi-particles and holes, which depends on the temperature. This ratio is connected with an algebraic invariant of the representation dependent observable algebra. Energy renormalization aspects and pair occupation probabilities are discussed. The latter reveal, beside other things, the difference between macroscopic term occupation and coherent macroscopic term occupation for a condensate.

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48

Wang, D. "Algebraic analysis of stability and bifurcation for nonlinear flight dynamics." Aeronautical Journal 115, no. 1168 (June 2011): 345–49. http://dx.doi.org/10.1017/s0001924000005868.

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Abstract This note presents an application of algebraic methods to derive exact conditions for certain nonlinear flight dynamical systems to exhibit stability and bifurcation. The roll-coupling flight model is taken as an example to show the feasibility of algebraic analysis. Some of the previous stability and bifurcation results obtained using numerical analysis for this model are confirmed.

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49

NIU, HONG, and QINGLING ZHANG. "GENERALIZED PREDICTIVE CONTROL FOR DIFFERENCE-ALGEBRAIC BIOLOGICAL ECONOMIC SYSTEMS." International Journal of Biomathematics 06, no. 06 (November 2013): 1350037. http://dx.doi.org/10.1142/s179352451350037x.

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In this paper, a nonlinear difference-algebraic system is used to model some populations with stage structure when the harvest behavior and the economic interest are considered. The stability analysis is studied at the equilibrium points. After the nonlinear difference-algebraic system is changed into a linear system with the unmodeled dynamics, a generalized predictive controller with feedforward compensator is designed to stabilize the system. Adaptive-network-based fuzzy inference system (ANFIS) is used to make the unmodeled dynamic compensated. An example illustrates the effectiveness of the proposed control method.

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50

Zahariev, E. V. "Earthquake dynamic response of large flexible multibody systems." Mechanical Sciences 4, no. 1 (February 20, 2013): 131–37. http://dx.doi.org/10.5194/ms-4-131-2013.

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Abstract. In the paper dynamics of large flexible structures imposed on earthquakes and high amplitude vibrations is regarded. Precise dynamic equations of flexible systems are the basis for reliable motion simulation and analysis of loading of the design scheme elements. Generalized Newton–Euler dynamic equations for rigid and flexible bodies are applied. The basement compulsory motion realized because of earthquake or wave propagation is presented in the dynamic equations as reonomic constraints. The dynamic equations, algebraic equations and reonomic constraints compile a system of differential algebraic equations which are transformed to a system of ordinary differential equations with respect to the generalized coordinates and the reactions due to the reonomic constraints. Examples of large flexible structures and wind power generator dynamic analysis are presented.

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