Journal articles: 'Nonlinear Chemical Dynamics'

1

Sagués, Francesc, and Irving R. Epstein. "Nonlinear chemical dynamics." Dalton Transactions, no. 7 (March 10, 2003): 1201–17. http://dx.doi.org/10.1039/b210932h.

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2

Field, Richard J., and F. W. Schneider. "Oscillating chemical reactions and nonlinear dynamics." Journal of Chemical Education 66, no. 3 (March 1989): 195. http://dx.doi.org/10.1021/ed066p195.

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3

Wang, Jichang, Hongyan Sun, Stephen K. Scott, and Kenneth Showalter. "Uncertain dynamics in nonlinear chemical reactions." Physical Chemistry Chemical Physics 5, no. 24 (2003): 5444. http://dx.doi.org/10.1039/b310923b.

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4

Hubler, Alfred, and Andrew Friedl. "Nonlinear response of chemical reaction dynamics." Complexity 19, no. 1 (September 2013): 6–8. http://dx.doi.org/10.1002/cplx.21473.

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5

Field, Richard J. "Chaos in the Belousov–Zhabotinsky reaction." Modern Physics Letters B 29, no. 34 (December 20, 2015): 1530015. http://dx.doi.org/10.1142/s021798491530015x.

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The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov–Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle.

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6

Karimov, A. R. "Nonlinear Dynamics of Flows with Chemical Reactions." Journal of Russian Laser Research 26, no. 4 (July 2005): 283–87. http://dx.doi.org/10.1007/s10946-005-0022-4.

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7

Epstein, Irving R., and Kenneth Showalter. "Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos." Journal of Physical Chemistry 100, no. 31 (January 1996): 13132–47. http://dx.doi.org/10.1021/jp953547m.

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8

Perelomova, Anna. "Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions." Canadian Journal of Physics 88, no. 1 (January 2010): 29–34. http://dx.doi.org/10.1139/p09-099.

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The weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium and nonequilibrium regimes of the chemical reactions.

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9

Kadakia, Yash A., Atharva Suryavanshi, Aisha Alnajdi, Fahim Abdullah, and Panagiotis D. Christofides. "Encrypted Model Predictive Control of a Nonlinear Chemical Process Network." Processes 11, no. 8 (August 20, 2023): 2501. http://dx.doi.org/10.3390/pr11082501.

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This work focuses on developing and applying Encrypted Lyapunov-based Model Predictive Control (LMPC) in a nonlinear chemical process network for Ethylbenzene production. The network, governed by a nonlinear dynamic model, comprises two continuously stirred tank reactors that are connected in series and is simulated using Aspen Plus Dynamics. For enhancing system cybersecurity, the Paillier cryptosystem is employed for encryption–decryption operations in the communication channels between the sensor–controller and controller–actuator, establishing a secure network infrastructure. Cryptosystems generally require integer inputs, necessitating a quantization parameter d, for quantization of real-valued signals. We utilize the quantization parameter to quantize process measurements and control inputs before encryption. Through closed-loop simulations under the encrypted LMPC scheme, where the LMPC uses a first-principles nonlinear dynamical model, we examine the effect of the quantization parameter on the performance of the controller and the overall encryption to control the input calculation time. We illustrate that the impact of quantization can outweigh those of plant/model mismatch, showcasing this phenomenon through the implementation of a first-principles-based LMPC on an Aspen Plus Dynamics process model. Based on the findings, we propose a strategy to mitigate the quantization effect on controller performance while maintaining a manageable computational burden on the control input calculation time.

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10

Wu, Shu Jing, Da Zhong Wang, and Shigenori Okubo. "Control for Nonlinear Chemical System." Key Engineering Materials 467-469 (February 2011): 1450–55. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.1450.

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In this paper, we propose a new design of the feedback control of state vector for the plants with polynomial dynamics. A genetic algorithm is employed to find suitable gain, and algebraic geometric concept is used to simplify the design. Finally, an example is given to illustrate the effectiveness of the proposed method.

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11

Annaswamy, A. M., C. Thanomsat, N. Mehta, and Ai-Poh Loh. "Applications of Adaptive Controllers to Systems With Nonlinear Parametrization." Journal of Dynamic Systems, Measurement, and Control 120, no. 4 (December 1, 1998): 477–87. http://dx.doi.org/10.1115/1.2801489.

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Nonlinear parametrizations occur in dynamic models of several complex engineering problems. The theory of adaptive estimation and control has been applicable, by and large, to problems where parameters appear linearly. We have recently developed an adaptive controller that is capable of estimating parameters that appear nonlinearly in dynamic systems in a stable manner. In this paper, we present this algorithm and its applicability to two problems, temperature regulation in chemical reactors and precise positioning using magnetic bearings both of which contain nonlinear parametrizations. It is shown in both problems that the proposed controller leads to a significantly better performance than those based on linear parametrizations or linearized dynamics.

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12

Engel, H., and M. Braune. "Dynamics of nonlinear waves in chemical active media." Physica Scripta T49B (January 1, 1993): 685–90. http://dx.doi.org/10.1088/0031-8949/1993/t49b/052.

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13

Jonnalagadda, S. B. "Nonlinear dynamics in closed biological and chemical systems." Pure and Applied Chemistry 70, no. 3 (March 30, 1998): 645–50. http://dx.doi.org/10.1351/pac199870030645.

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14

Sonnemann, G. R., and M. Grygalashvyly. "On the two-day oscillations and the day-to-day variability in global 3-D-modeling of the chemical system of the upper mesosphere/mesopause region." Nonlinear Processes in Geophysics 12, no. 5 (July 12, 2005): 691–705. http://dx.doi.org/10.5194/npg-12-691-2005.

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Abstract. The integration of the photochemical system of the upper mesosphere/mesopause region brought evidence that the system is able to respond in a nonlinear manner under certain conditions. Under the action of the diurnally-periodic insolation, the system creates subharmonic oscillations or chaos if disregarding strong diffusion, and under special conditions it possesses multiple solutions. The models used in the past were simplified and idealized in view of the number of dimensions and the consideration of the full dynamics. On the basis of our global 3-D-model of the dynamics and chemistry of the middle atmosphere (COMMA-IAP), we also found a nonlinear response in the photochemistry under realistic conditions. The model under consideration is not yet self-consistent, but the chemical model uses the dynamical fields calculated by the dynamic model. From our calculations we got period-2 oscillations of the photochemical system within confined latitudinal regions around the solstices but not during the equinoxes. The consequence of the period-2 oscillation of the chemical active minor constituents is that a marked two-day variation of the chemical heating rates is an important thermal pumping mechanism. We discuss these findings particularly in terms of the influence of realistic dynamics on the creation of nonlinear effects.

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15

Liu, Ruijie, Zheng Wang, Ran Dong, Huapeng Li, Jingmin Hou, Zhaofei Dong, and Tongtong Xie. "Robust Optimization of Chemical Networks Based on Dynamic Nonlinear Load Capacity Model." Journal of Physics: Conference Series 2549, no. 1 (July 1, 2023): 012023. http://dx.doi.org/10.1088/1742-6596/2549/1/012023.

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Abstract In the research on the robustness of chemical network, predecessors described the robustness of chemical network by establishing a cascade failure model, and then optimized the robustness. However, in the previous research, it was mainly static, without considering the network dynamics formed by the complex internal structure and strong correlation between variables of chemical network. At the same time, the previous research mainly focuses on static and does not consider the network dynamics formed by the complex internal structure of the chemical network and the strong correlation between variables. Therefore, this paper considers the dynamic characteristics of the actual chemical process system network, establishes a dynamic cascade failure model based on a nonlinear model of load capacity, and proposes a target node protection strategy to protect specific target nodes for robust optimization after considering the influence of specific nodes on neighboring nodes, which reduces the failure probability after the network suffers a failure and provides a It provides a theoretical basis for improving the cascade failure resistance of chemical networks.

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16

Chang, Kil Sang, and Rutherford Aris. "Nonlinear dynamics and strange attractors." Korean Journal of Chemical Engineering 4, no. 2 (September 1987): 95–104. http://dx.doi.org/10.1007/bf02697424.

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17

Olabodé, Dagbégnon Luc, Batablinlè Lamboni, and Jean Bio Chabi Orou. "Active Control of Chaotic Oscillations in Nonlinear Chemical Dynamics." Journal of Applied Mathematics and Physics 07, no. 03 (2019): 547–58. http://dx.doi.org/10.4236/jamp.2019.73040.

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18

Kurtanjek, Želimir. "Modeling of chemical reactor dynamics by nonlinear principal components." Chemometrics and Intelligent Laboratory Systems 46, no. 2 (March 1999): 149–59. http://dx.doi.org/10.1016/s0169-7439(98)00182-8.

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19

Zhabotinsky, A. M., and A. B. Rovinsky. "Mechanism and nonlinear dynamics of an oscillating chemical reaction." Journal of Statistical Physics 48, no. 5-6 (September 1987): 959–75. http://dx.doi.org/10.1007/bf01009526.

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20

RESNIKOVA, VERA, and ARKADY ROVINSKY. "Nonlinear Dynamics of a Far-from-Equilibrium Chemical System." Annals of the New York Academy of Sciences 661, no. 1 Frontiers of (December 1992): 367. http://dx.doi.org/10.1111/j.1749-6632.1992.tb26064.x.

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21

Sontag, Eduardo D., and Abhyudai Singh. "Exact Moment Dynamics for Feedforward Nonlinear Chemical Reaction Networks." IEEE Life Sciences Letters 1, no. 2 (August 2015): 26–29. http://dx.doi.org/10.1109/lls.2015.2483820.

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22

BARATTI, Roberto, Stefania TRONCI, Alexander SCHAUM, and Jesus ALVAREZ. "Dynamics of nonlinear chemical process with multiplicative stochastic noise." IFAC-PapersOnLine 49, no. 7 (2016): 869–74. http://dx.doi.org/10.1016/j.ifacol.2016.07.299.

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23

Oppenheim, Irwin. "Chemical Dynamics in Condensed Phases." Journal of Statistical Physics 126, no. 6 (February 14, 2007): 1287–89. http://dx.doi.org/10.1007/s10955-007-9295-z.

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24

Nicolis, G., and F. Baras. "Nonequilibrium dynamics in chemical systems." Physica D: Nonlinear Phenomena 17, no. 3 (December 1985): 345–48. http://dx.doi.org/10.1016/0167-2789(85)90218-0.

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25

Megam Ngouonkadi, E. B., Hilaire B. Fotsin, and P. H. Louodop Fotso. "The Combined Effect of Dynamic Chemical and Electrical Synapses in Time-Delay-Induced Phase-Transition to Synchrony in Coupled Bursting Neurons." International Journal of Bifurcation and Chaos 24, no. 05 (May 2014): 1450069. http://dx.doi.org/10.1142/s0218127414500692.

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In this paper, we study the combined effect of dynamic chemical and electrical synapses in time-delay-induced phase-transition to synchrony in coupled bursting neurons. Time-delay in coupled nonlinear oscillators or in a network of coupled nonlinear oscillators has been found to be responsible for striking dynamical behaviors such as phase-flip-transitions. These phenomena lead to synchrony or out of synchrony in different oscillators of the system. Here, we show that synaptic parameters, more precisely the neurotransmitters binding time constant influences the phase-flip-transitions of the system. We discuss how the system goes to the phase-flip-transitions when both electrical and dynamic chemical synapses are taken into account. The fourth-order Hindmarsh–Rose neuronal oscillator is considered here for the study of these transitions. A discussion on the importance of these results in brain researches is given, particularly to understand the collective dynamics of bursting neurons.

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26

Warren, Keith, and Raymond C. Hawkins. "Multiscale Nonlinearity in a Time Series of Weekly Alcohol Intake." Psychological Reports 90, no. 3 (June 2002): 957–67. http://dx.doi.org/10.2466/pr0.2002.90.3.957.

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Several authors have discussed the possibility that nonlinear dynamics might clarify substance abuse and chemical dependence. Nonlinear dynamical structure implies the possibility of oscillatory dynamics and high sensitivity to external perturbation. In this single-subject case study we analyzed the alcohol intake of a substance-abusing participant over a period of about five years using nonlinear time series analysis. The intake is measured in ounces per week and ounces per four weeks—approximately one month—yielding time series at two different time scales. We present statistical evidence that the participant's alcohol intake is nonlinear on both weekly and monthly time scales. We then discuss the implications of this multiscale nonlinearity for our understanding of substance abuse.

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27

Zhang, Shu, Joseph Bentsman, Xinsheng Lou, Carl Neuschaefer, Yongseok Lee, and Hamza El-Kebir. "Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed." Energies 13, no. 7 (April 7, 2020): 1759. http://dx.doi.org/10.3390/en13071759.

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Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

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28

Hunt, K. L. C., P. M. Hunt, and J. Ross. "Nonlinear Dynamics and Thermodynamics of Chemical Reactions Far From Equilibrium." Annual Review of Physical Chemistry 41, no. 1 (October 1990): 409–39. http://dx.doi.org/10.1146/annurev.pc.41.100190.002205.

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29

Kozlovskaya, E. D. "Seminar on Nonlinear Dynamics of Chemical Reactions, Processes, and Reactors." Theoretical Foundations of Chemical Engineering 40, no. 4 (July 2006): 443–44. http://dx.doi.org/10.1134/s004057950604018x.

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30

Das, D., and D. S. Ray. "Multiple time scale based reduction scheme for nonlinear chemical dynamics." European Physical Journal Special Topics 222, no. 3-4 (July 2013): 785–98. http://dx.doi.org/10.1140/epjst/e2013-01882-3.

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31

Tretyakov, A., A. Provata, and G. Nicolis. "Nonlinear Chemical Dynamics in Low-Dimensional Lattices and Fractal Sets." Journal of Physical Chemistry 99, no. 9 (March 1995): 2770–76. http://dx.doi.org/10.1021/j100009a036.

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32

Provata, A., J. W. Turner, and G. Nicolis. "Nonlinear chemical dynamics in low dimensions: An exactly soluble model." Journal of Statistical Physics 70, no. 5-6 (March 1993): 1195–213. http://dx.doi.org/10.1007/bf01049428.

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33

Galushkin, M. G., E. B. Gordon, M. S. Drozdov, and K. A. Sviridov. "Chemical Intensification of Nonlinear Multi-Wave Interactions." Laser Chemistry 12, no. 3-4 (January 1, 1992): 199–209. http://dx.doi.org/10.1155/lc.12.199.

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Nonlinear interaction of laser emission with a chemically reactive medium, in which a branched chain reaction may readily occur, has been analyzed aiming at essential intensification the contrast of photochemically induced phase gratings. For the model system CS2/O2, the degenerated four-wave mixing is theoretically studied under the assumption of CS2 photodissociation followed by subsequent secondary reactions induced by reactive photodissociation products. For varied CS2 concentrations and incident flux intensities, the dynamics of nonlinear reflection has been analyzed and same laser applications of such systems are suggested.

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34

Gevelber, M. A., M. Bufano, and M. Toledo-Quin˜ones. "Dynamic Modeling Analysis for Control of Chemical Vapor Deposition." Journal of Dynamic Systems, Measurement, and Control 120, no. 2 (June 1, 1998): 164–69. http://dx.doi.org/10.1115/1.2802405.

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A nonlinear dynamic model of the chemical vapor deposition (CVD) process has been developed to aid design of a closed-loop control system. A lumped control volume analysis is used to capture important mass and fluid transients and spatial affects, while a simplified single variable equation is used to represent the complex reaction chemistry. Steady-state experimental results and model predictions are compared and the control implications of the process dynamics are discussed.

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35

Zhao, Jian Wei, Xin Chun Lu, and Yong Yong He. "The Model of Transfer Robot in Chemical Mechanical Polishing." Advanced Materials Research 647 (January 2013): 867–74. http://dx.doi.org/10.4028/www.scientific.net/amr.647.867.

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Transfer robot of chemical mechanical polishing (TRCMP) has some joints. For an important kind of special transfer robot, it is used as automatic material processing equipment in the semiconductor manufacture. The TRCMP has nonlinear, strongly coupled, multi-joints and under actuated, and these characteristics brought some difficulties to model and control. A dynamic model of the TRCMP was based on Lagrange equation and Newton dynamics theory. Then linearization of the dynamics model was done and its state-space equations were established. This structure of the model established is very simple, and it can control the TRCMP effectively and easy. Simulation results proved the system stability, and experiment results analyzed verified that the model of TRCMP is valid and rational.

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36

Suo, Liangcheng, Jiamin Ren, Zemeng Zhao, and Chi Zhai. "Study on the Nonlinear Dynamics of the Continuous Stirred Tank Reactors." Processes 8, no. 11 (November 10, 2020): 1436. http://dx.doi.org/10.3390/pr8111436.

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Chemical processes often exhibit nonlinear dynamics and tend to generate complex state trajectories, which present challenging operational problems due to complexities such as output multiplicity, oscillation, and even chaos. For this reason, a complete knowledge of the static and dynamic nature of these behaviors is required to understand, to operate, to control, and to optimize continuous stirred tank reactors (CSTRs). Through nonlinear analysis, the possibility of output multiplicity, self-sustained oscillation, and torus dynamics are studied in this paper. Specifically, output multiplicity is investigated in a case-by-case basis, and related operation and control strategies are discussed. Bifurcation analysis to identify different dynamic behaviors of a CSTR is also implemented, where operational parameters are identified to obtain self-oscillatory dynamics and possible unsteady-state operation strategy through designing the CSTR as self-sustained periodic. Finally, a discussion on codimension-1 bifurcations of limits cycles is also provided for the exploration of periodic forcing on self-oscillators. Through this synergistic study on the CSTRs, possible output multiplicity, oscillatory, and chaotic dynamics facilitates the implementation of novel operation/control strategies for the process industry.

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37

Zhou, Linlin, Huange Fu, Ting Lv, Chengbo Wang, Hui Gao, Daqian Li, Leimin Deng, and Wei Xiong. "Nonlinear Optical Characterization of 2D Materials." Nanomaterials 10, no. 11 (November 16, 2020): 2263. http://dx.doi.org/10.3390/nano10112263.

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Characterizing the physical and chemical properties of two-dimensional (2D) materials is of great significance for performance analysis and functional device applications. As a powerful characterization method, nonlinear optics (NLO) spectroscopy has been widely used in the characterization of 2D materials. Here, we summarize the research progress of NLO in 2D materials characterization. First, we introduce the principles of NLO and common detection methods. Second, we introduce the recent research progress on the NLO characterization of several important properties of 2D materials, including the number of layers, crystal orientation, crystal phase, defects, chemical specificity, strain, chemical dynamics, and ultrafast dynamics of excitons and phonons, aiming to provide a comprehensive review on laser-based characterization for exploring 2D material properties. Finally, the future development trends, challenges of advanced equipment construction, and issues of signal modulation are discussed. In particular, we also discuss the machine learning and stimulated Raman scattering (SRS) technologies which are expected to provide promising opportunities for 2D material characterization.

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38

Baudin, Emmanuel, Michael E. Hayden, Geneviève Tastevin, and Pierre-Jean Nacher. "Nonlinear NMR dynamics in hyperpolarized liquid 3He." Comptes Rendus Chimie 11, no. 4-5 (April 2008): 560–67. http://dx.doi.org/10.1016/j.crci.2007.07.005.

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39

Lustfeld, H., and Z. Neufeld. "Chemical dynamics versus transport dynamics in a simple model." Journal of Physics A: Mathematical and General 32, no. 20 (January 1, 1999): 3717–31. http://dx.doi.org/10.1088/0305-4470/32/20/305.

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40

Olabodé, D. L., C. H. Miwadinou, A. V. Monwanou, and J. B. Chabi Orou. "Horseshoes chaos and its passive control in dissipative nonlinear chemical dynamics." Physica Scripta 93, no. 8 (July 11, 2018): 085203. http://dx.doi.org/10.1088/1402-4896/aacef0.

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41

Bozhevol’nov, V. E., and E. D. Kozlovskaya. "Seminar on the Nonlinear Dynamics of Chemical Reactions, Processes, and Reactors." Theoretical Foundations of Chemical Engineering 44, no. 2 (April 2010): 222. http://dx.doi.org/10.1134/s0040579510020156.

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42

Li, Yongfeng, Hong Qian, and Yingfei Yi. "Nonlinear Oscillations and Multiscale Dynamics in a Closed Chemical Reaction System." Journal of Dynamics and Differential Equations 22, no. 3 (February 2, 2010): 491–507. http://dx.doi.org/10.1007/s10884-010-9156-3.

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43

Karimov, A. R., A. M. Korshunov, and V. V. Beklemishev. "Influence of chemical reactions on the nonlinear dynamics of dissipative flows." Physica Scripta 90, no. 8 (June 24, 2015): 085203. http://dx.doi.org/10.1088/0031-8949/90/8/085203.

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44

Epstein, Irving R., John A. Pojman, and Gregoire Nicolis. "An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos." Physics Today 52, no. 11 (November 1999): 68. http://dx.doi.org/10.1063/1.882734.

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45

Xin, Houwen, and Zhonghuai Hou. "On the study of nonlinear dynamics of complex chemical reaction systems." Science in China Series B 49, no. 1 (January 2006): 1–11. http://dx.doi.org/10.1007/s11426-005-0077-7.

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46

Marquardt, Wolfgang, and Martin Mönnigmann. "Constructive nonlinear dynamics in process systems engineering." Computers & Chemical Engineering 29, no. 6 (May 2005): 1265–75. http://dx.doi.org/10.1016/j.compchemeng.2005.02.009.

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47

Li, Shih-Yu, Shun-Hung Tsai, Chin-Sheng Chen, and Lap-Mou Tam. "Adaptive Control of Advanced G-L Fuzzy Systems with Several Uncertain Terms in Membership-Matrices." Processes 10, no. 5 (May 23, 2022): 1043. http://dx.doi.org/10.3390/pr10051043.

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In this paper, a set of novel adaptive control strategies based on an advanced G-L (proposed by Ge-Li-Tam, called GLT) fuzzy system is proposed. Three main design points can be summarized as follows: (1) the unknown parameters in a nonlinear dynamic system are regarded as extra nonlinear terms and are further packaged into so-called nonlinear terms groups for each equation through the modeling process, which reduces the complexity of the GLT fuzzy system; (2) the error dynamics are further rearranged into two parts, adjustable membership function and uncertain membership function, to aid the design of the controllers; (3) a set of adaptive controllers change with the estimated parameters and the update laws of parameters are provided following the current form of error dynamics. Two identical nonlinear dynamic systems based on a Quantum-CNN system (Q-CNN system) with two added terms are employed for simulations to demonstrate the feasibility as well as the effectiveness of the proposed fuzzy adaptive control scheme, where the tracking error can be eliminated efficiently.

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48

Huang, Sui, Fangting Li, Joseph X. Zhou, and Hong Qian. "Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters." Journal of The Royal Society Interface 14, no. 130 (May 2017): 20170097. http://dx.doi.org/10.1098/rsif.2017.0097.

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The notion of an attractor has been widely employed in thinking about the nonlinear dynamics of organisms and biological phenomena as systems and as processes. The notion of a landscape with valleys and mountains encoding multiple attractors, however, has a rigorous foundation only for closed, thermodynamically non-driven, chemical systems, such as a protein. Recent advances in the theory of nonlinear stochastic dynamical systems and its applications to mesoscopic reaction networks, one reaction at a time, have provided a new basis for a landscape of open, driven biochemical reaction systems under sustained chemostat. The theory is equally applicable not only to intracellular dynamics of biochemical regulatory networks within an individual cell but also to tissue dynamics of heterogeneous interacting cell populations. The landscape for an individual cell, applicable to a population of isogenic non-interacting cells under the same environmental conditions, is defined on the counting space of intracellular chemical compositions x = ( x 1 , x 2 , … , x N ) in a cell, where x ℓ is the concentration of the ℓth biochemical species. Equivalently, for heterogeneous cell population dynamics x ℓ is the number density of cells of the ℓth cell type. One of the insights derived from the landscape perspective is that the life history of an individual organism, which occurs on the hillsides of a landscape, is nearly deterministic and ‘programmed’, while population-wise an asynchronous non-equilibrium steady state resides mostly in the lowlands of the landscape. We argue that a dynamic ‘blue-sky’ bifurcation, as a representation of Waddington's landscape, is a more robust mechanism for a cell fate decision and subsequent differentiation than the widely pictured pitch-fork bifurcation. We revisit, in terms of the chemostatic driving forces upon active, living matter, the notions of near-equilibrium thermodynamic branches versus far-from-equilibrium states. The emergent landscape perspective permits a quantitative discussion of a wide range of biological phenomena as nonlinear, stochastic dynamics.

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49

Sands, J. D., D. J. Needham, and J. Uddin. "A fundamental model exhibiting nonlinear oscillatory dynamics in solid oxide fuel cells." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2164 (April 8, 2014): 20130551. http://dx.doi.org/10.1098/rspa.2013.0551.

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Abstract:

In this paper, we address the phenomenon of temporal, self-sustained oscillations which have been observed under quite general conditions in solid oxide fuel cells. Our objective is to uncover the fundamental mechanisms giving rise to the observed oscillations. To this end, we develop a model based on the fundamental chemical kinetics and transfer processes which take place within the fuel cell. This leads to a three-dimensional dynamical system, which, under typical operating conditions, is rationally reducible to a planar dynamical system. The structural dynamics of the planar dynamical system are studied in detail. Self-sustained oscillations are shown to arise through Hopf bifurcations in this planar dynamical system, and the key parameter ranges for the occurrence of such oscillations are identified.

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50

Buchete, Nicolae-Viorel. "Santosh K. Upadhyay. Chemical Kinetics and Reaction Dynamics." Journal of Statistical Physics 129, no. 2 (September 21, 2007): 407–8. http://dx.doi.org/10.1007/s10955-007-9418-6.

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Journal articles on the topic 'Nonlinear Chemical Dynamics'

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