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Автор: Grafiati
Опубліковано: 7 вересня 2023

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Статті в журналах з теми "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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Анотація:
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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Дисертації з теми "Nonlinear Chemical Dynamics"

1

Tsamopoulos, John Abraham. "Nonlinear dynamics of simple and compound drops." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/119604.

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Анотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1985.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.
Bibliography: leaves 176-186.
by John Abraham Tsamopoulos.
Ph.D.
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2

McKinley, Gareth Huw. "Nonlinear dynamics of viscoelastic flows in complex geometries." Thesis, Massachusetts Institute of Technology, 1991. http://hdl.handle.net/1721.1/13921.

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3

Perrman, Delmar. "Nonlinear effects in chemical dynamics and chemical kinetics: Chaos in physical chemistry." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/9500.

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This work shows that nonlinear dynamic systems are quite different from linear dynamic systems. The usual phase plots of linear and nonlinear dynamical systems are also distinctly different, even before damping or forcing terms are added. It is also shown that the usual phase plot allows for the visualization of unobservable information that is present in the times series. The higher-order phase plots give yet additional information that is not present in the existing methods of plotting the data. Higher-order phase plots were originated and applied for the first time to a dynamical system (Morse oscillator) for the purpose of earlier detection of nonlinear effects. The dynamics of a weakly forced and weakly damped Morse oscillator is examined. The novel tool of higher-order phase plots is used to visualize the importance of the higher harmonics in the phase which are essential for the dynamics to be complicated and dissociative. Expansions of the higher-order phase plots in regions about x$\sp{(n-1)}$ = 0, x$\sp{(n)}$ = 0 are considered and it is shown that there is a topological change that occurs sequentially for each higher-order phase plot. After the topological change, which occurs at a critical value of initial total energy E(0) for a particular value of forcing F, the higher-order phase space structure has a circular loop. As F or E(0) is further increased the phase space trajectory loops an increasing number of times in the higher-order phase plot. It is shown that for F = $1.0\times10\sp{-3}$ the topological change occurs around E(0) = 0.96 for the fifth-order phase plot and around E(0) = 0.94 for the eleventh-order phase plot. This is also illustrated with a series of higher-order phase plots (2$\sp{nd}$-10$\sp{th}$) for F = $1\times10\sp{-3}$ and E(0) = 0.97. These plots indicate that although the 5$\sp{th}$ order phase plot forms loops the 4$\sp{th}$ forms only half-loops. Thus the higher-order phase plots are increasingly sensitive probes of the phase space dynamics as the order increases. Qualitatively this is because, as the order increases, part of each higher-order phase space structure is increasingly close to the point (x$\sp{(n)}$,x$\sp{(n-1)}$) = (0,0). For larger values of F the topological change occurs at a smaller value of E(0) for each higher-order phase plot, as the radius of the loop centered on x$\sp{(n-1)}$ = 0, x$\sp{(n)}$ = 0 is larger. While the phase space trajectory loops the energy is approximately constant with small oscillations. The circular loop in the higher-order phase plot is the higher-order space structure that is expected for the weakly forced and weakly damped free particle. The significance of the circular loop is that the lower the order of the higher-order phase plot in which the phase space trajectory loops, the closer the Morse oscillator is to dissociation. From this viewpoint, the Morse oscillator dissociates when the value of F or E(0) becomes sufficiently large that the topological change occurs in the usual phase plot. That is, the Morse oscillator dissociates when the phase space structure becomes open for the usual phase plot. (Abstract shortened by UMI.)
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4

McIlwaine, Rachel Elizabeth. "Nonlinear dynamics of acid- and base-regulated chemical systems." Thesis, University of Leeds, 2007. http://etheses.whiterose.ac.uk/797/.

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Interest in the interdisciplinary field of nonlinear dynamics has increased significantly over the past three decades. Nonlinear dynamics is the study of the temporal and spatio-temporal evolution of dynamical systems whose behaviour depends on the values of the key variables in a nonlinear manner. Nonlinear chemical reactions, chemical oscillations and their spatial behaviour play an important part in the field of nonlinear dynamics. This thesis is concerned primarily with those chemical systems which feature the proton, or its counterpart the hydroxide ion, as a main kinetic driving species. A review of the area is presented to provide a background for the developments discussed in this thesis. Experimental and numerical investigation of the methylene glycol-sulfite reaction leads to the development of a complete kinetic model for this system. This new mechanism provides the basis of a reduced model for the design of novel pH oscillators. This reduced model, discussed in chapter 4, is used to design the first organic substrate based, non-redox, pH oscillating reaction, the methylene glycolsulfite-gluconolactone system. In an open reactor this reaction displays large amplitude oscillations in pH which are well modelled with a proposed mechanism. In chapter 5 experimental results of an acid autocatalytic reaction performed in nano-meter size water droplets are presented. The effects of confinement on the kinetics is established and shown to be affected by changes in droplet size and dispersion of droplets. The effect of the microheterogeneties of the microenvironment on reaction-diffusion fronts in this system is also investigated. The results show the propagation of acid fronts with interesting structural instabilities.
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5

Ali, Fathei M. "On the nonlinear chemical dynamics of the imperfectly mixed CSTR." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ33891.pdf.

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6

Sands, Jonathan David. "Current oscillations arising from nonlinear chemical dynamics in solid oxide fuel cells." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5973/.

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Fuel cells are becoming increasingly important in the conversion of our society to clean, and renewable energy sources. However, there are some technical, as well as commercial barriers, which remain to be overcome before the fuel cell industry may be counted a success. One such problem is that of nonlinear current fluctuations, which have been observed under quite general conditions, in solid oxide fuel cells. This thesis attempts to elucidate the mechanisms driving this undesirable be- haviour, by developing a rational mathematical model based on fundamental chemical kinetics, and mass transfer effects, which take place within the porous anode of the fuel cell. A system of nonlinear, coupled ordinary differential equations is derived to describe the reaction and transfer processes associated with this fundamental model. This system is then rationally reduced to a planar dynamical system and the cases of weakly and fully humidified fuel streams are considered. Self-sustained, temporal oscillations are shown to arise through Hopf bifurcations in each case, and key parameter regimes leading to oscillatory behaviour are identified. Experiments have been conducted on commercial fuel cells, with results presented in Chapter 5.
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7

Alonso, Eva Vicente. "Nonlinear dynamics of a nematic liquid crystal in the presence of a shear flow." Thesis, University of Southampton, 2000. https://eprints.soton.ac.uk/50628/.

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In this thesis we describe the complex array of behaviours of a homogeneous thermotropic nematic liquid crystal in the context of a Landau-de Gennes theory. There exist two parameters that control the behaviour of the system: the temperature and the shear rate, and by employing continuation and bifurcation theory we describe the different time dependent states for the two and three dimensional cases. For the two dimensional case we compute the steady state solution branches finding that the flow favours an in-plane nematic state at higher temperatures, while at lower temperatures it favours a nematic state with preferred direction of alignment perpendicular to the shear plane, the so-called log-rolling state. We have found excellent agreement between the numerical calculations and analytical results in the limit of very low and very large values of the shear rate. The existence of a Takens-Bogdanov bifurcation in the underlying bifurcation diagram organises the steady and the time dependent solutions in the state diagram. The periodic orbits can be either of the wagging type, at intermediate values of the shear rate or of the tumbling type at lower shear rates. We complete the analysis of the two dimensional case, by considering a general planar flow and studying the influences of strain and vorticity in the system. We provide a very detailed account of the behaviour of the liquid crystal in the three dimensional case, when the direction of alignment of the molecules that constitute the liquid crystal is allowed out of the shear plane. We establish that the only out-of-plane steady solution of the system is an anomalous continuum of equilibria, and therefore the Landau-de Gennes model that we are employing is structurally unstable. The time dependent solutions of the liquid crystal fall into one of the following categories: in plane periodic orbits, which are the tumbling and wagging solutions and out-of-plane periodic orbits, the so-called kayaking state. The use of bifurcation theory in the context of nematodynamics allows us to give a complete summary of the nonlinear behaviour of a nematic liquid crystal in a shear flow, for the two and three dimensional cases.
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8

Huynh, Nguyen. "Digital control and monitoring methods for nonlinear processes." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-100906-083012/.

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Анотація:
Dissertation (Ph.D.)--Worcester Polytechnic Institute.
Keywords: Parametric optimization; nonlinear dynamics; functional equations; chemical reaction system dynamics; time scale multiplicity; robust control; nonlinear observers; invariant manifold; process monitoring; Lyapunov stability. Includes bibliographical references (leaves 92-98).
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9

Dziekan, Piotr. "Dynamics of far-from-equilibrium chemical systems : microscopic and mesoscopic approaches." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066402/document.

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La plupart des systèmes non linéaires loin de l'équilibre sont sensibles aux fluctuations internes. Dans ce travail, les effets stochastiques dans des modèles génériques de réaction-diffusion sont étudiés à deux échelles différentes. Dans l'approche mésoscopique, l'évolution du système est gouvernée par une équation maîtresse résolue par des simulations de Monte Carlo cinétique. A l'échelle microscopique, des simulations de dynamique des particules sont réalisées. Ces approches stochastiques sont comparées à des équations macroscopiques, déterministes de réaction-diffusion. Dans l'introduction, les différentes échelles, les concepts concernant les systèmes non linéaires et les méthodes numériques utilisées sont présentés. La première partie du chapitre consacré aux résultats est dédiée à l'étude de la perturbation de la distribution des vitesses des particules induite par la réaction pour un système bistable et la propagation d'un front d'onde. Une équation maîtresse incluant cette perturbation est écrite et comparée à des simulations de la dynamique microscopique. La seconde partie concerne la formation de structures dans les systèmes réaction-diffusion dans le contexte de la biologie du développement. Une méthode pour simuler des structures de Turing à l'échelle microscopique est développée à partir de l'algorithme DSMC (direct simulation Monte Carlo). Ensuite, des expériences consistant à perturber la formation de la colonne vertébrale sont expliquées dans le cadre du mécanisme de Turing. Enfin, un modèle de réaction-diffusion associé à un mécanisme différent, connu sous le nom de "Clock and wavefront", est proposé pour rendre compte de la segmentation
Many nonlinear systems under non-equilibrium conditions are highly sensitive to internal fluctuations. In this dissertation, stochastic effects in some generic reaction-diffusion models are studied using two approaches of different precision. In the mesoscopic approach, evolution of the system is governed by the master equation, which can be solved numerically or used to set up kinetic Monte Carlo simulations. On the microscopic level, particle computer simulations are used. These two stochastic approaches are compared with deterministic, macroscopic reaction-diffusion equations.In the Introduction, key information about the different approaches is presented, together with basics of nonlinear systems and a presentation of numerical algorithms used.The first part of the Results chapter is devoted to studies on reaction-induced perturbation of particle velocity distributions in models of bistability and wave front propagation. A master equation including this perturbation is presented and compared with microscopic simulations.The second part of the Results deals with pattern formation in reaction-diffusion systems in the context of developmental biology. A method for simulating Turing patternsat the microscopic level using the direct simulation Monte Carlo algorithm is developed. Then, experiments consisting of perturbing segmentation of vertebrate embryo’s bodyaxis are explained using the Turing mechanism. Finally, a different possible mechanism of body axis segmentation, the “clock and wavefront” model, is formulated as a reaction-diffusion model
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10

Zheng, Yexin. "MOLECULAR DYNAMICS SIMULATION STUDY OF NONLINEAR MECHANICAL BEHAVIOR FOR POLYMER GLASSES AND POLYMER RHEOLOGY." University of Akron / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=akron1595776504507743.

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Книги з теми "Nonlinear Chemical Dynamics"

1

Ing, Hlavácek Vladimír, ed. Dynamics of nonlinear systems. New York: Gordon and Breach, 1986.

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2

Baldea, Michael. Dynamics and nonlinear control of integrated process systems. Cambridge: Cambridge University Press, 2012.

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3

1962-, Pojman John A., ed. An introduction to nonlinear chemical dynamics: Oscillations, waves, patterns, and chaos. New York: Oxford University Press, 1998.

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4

1957-, Continillo G., Crescitelli S. 1943-, Giona M, and DINIP 2000 Conference (2000 : Rome, Italy), eds. Nonlinear dynamics and control in process engineering: Recent advances. Milano: Springer, 2002.

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5

Ogli, Aliyev Soltan Ali, ed. Fluid mechanics and heat transfer: Advances in nonlinear dynamics modeling. Oakville, ON: Apple Academic Press, 2016.

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6

Garzó, Vicente. Kinetic Theory of Gases in Shear Flows: Nonlinear Transport. Dordrecht: Springer Netherlands, 2003.

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7

H, Busse F., and Müller S. C. 1949-, eds. Evolution of spontaneous structures in dissipative continuous systems. Berlin: Springer, 1998.

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8

V, Tuchin V., and Society of Photo-optical Instrumentation Engineers., eds. Complex dynamics, fluctuations, chaos, and fractals in biomedical photonics: 25 January 2004, San Jose, California, USA. Bellingham, Wash., USA: SPIE, 2004.

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9

International, Workshop on Dynamism and Regulation in Nonlinear Chemical Systems (1995 Tsukuba Japan). Dynamism and regulation in nonlinear chemical systems: ... International Workshop on Dynamism and Regulation in Nonlinear Chemical Systems, Tsukuba, Japan, 22-25 March 1995. Amsterdam: North-Holland, 1995.

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10

Epstein, Irving R., and John A. Pojman. An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.001.0001.

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Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.
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Частини книг з теми "Nonlinear Chemical Dynamics"

1

Chattaraj, P. K. "Nonlinear Chemical Dynamics." In Symmetries and Singularity Structures, 172–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-76046-4_17.

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2

Müller, S. C., and B. Hess. "Nonlinear Dynamics in Chemical Systems." In Springer Series in Synergetics, 307–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-74554-6_77.

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3

Plath, P. J., M. Baune, M. Buhlert, C. Gerlach, A. Kouzmitchev, P. Thangavel, E. van Raaij, H. Mathes, S. Diaz Alfonso, and Th Rabbow. "Nonlinear Dynamics in Chemical Engineering and Electro-Chemical Manufactory Technologies." In Nonlinear Dynamics of Production Systems, 527–57. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527602585.ch30.

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4

Mariani, Alberto, Stefano Fiori, Giulio Malucelli, Silvia Pincin, Laura Ricco, and Saverio Russo. "Recent Chemical Advances in Frontal Polymerization." In Nonlinear Dynamics in Polymeric Systems, 121–34. Washington, DC: American Chemical Society, 2003. http://dx.doi.org/10.1021/bk-2004-0869.ch010.

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5

Pojman, John A. "Nonlinear Chemical Dynamics In Synthetic Polymer Systems." In Chemomechanical Instabilities in Responsive Materials, 221–40. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2993-5_9.

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6

Sowmiya, C., and B. Rushi Kumar. "Effects of Radiation and Chemical Reaction on MHD Mixed Convection Flow over a Permeable Vertical Plate." In Nonlinear Dynamics and Applications, 351–65. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99792-2_30.

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7

Mönnigmann, M., J. Hahn, and W. Marquardt. "Towards Constructive Nonlinear Dynamics - Case Studies in Chemical Process Design." In Nonlinear Dynamics of Production Systems, 503–26. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527602585.ch29.

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8

McCormick, W. D. "Complex Dynamics in Experiments on a Chemical Reaction." In Nonlinear Evolution and Chaotic Phenomena, 329. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-1017-4_27.

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9

Sebastian, Anupama, S. V. Amrutha, Shreyas Punacha, and T. K. Shajahan. "Dynamics of Chemical Excitation Waves Subjected to Subthreshold Electric Field in a Mathematical Model of the Belousov-Zhabotinsky Reaction." In Nonlinear Dynamics and Applications, 1241–49. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99792-2_105.

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Feng, Peihua, Rong Wang, and Ying Wu. "Critical Behaviors of Regular Pattern Selection in Neuronal Networks with Chemical Synapses." In New Trends in Nonlinear Dynamics, 163–71. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-34724-6_17.

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Тези доповідей конференцій з теми "Nonlinear Chemical Dynamics"

1

Oraevsky, Anatoly N. "Nonlinear dynamics of gas flow lasers." In Ninth International Symposium on Gas Flow and Chemical Lasers, edited by Costas Fotakis, Costas Kalpouzos, and Theodore G. Papazoglou. SPIE, 1993. http://dx.doi.org/10.1117/12.144654.

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2

Arneodo, A., F. Argoul, and P. Richetti. "Symbolic dynamics in the Belousov-Zhabotinskii reaction: from Rössler’s intuition to experimental evidence for Shil’nikov homoclinic chaos." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/nldos.1990.is2.

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Анотація:
The Belousov-Zhabotinskii reaction has revealed most of the well-known scenarios to chaos including period-doubling, intermittency, quasiperiodicity, frequency locking, fractal torus …. However, although the data have been shown to display unambiguous features of deterministic chaos, the understanding of the nature and the origin of the observed behavior has been incomplete. In 1976, Rössler suggested an intuitive interpretation to explain chemical chaos. His feeling was that nonperiodic wandering trajectories might arise in chemical systems from a pleated slow manifold (Fig. 1a), if the flow on the lower surface of the pleat had the property of returning trajectories to a small neighborhood of an unstable focus lying on the upper surface. In this communication, we intend to revisit the terminology introduced by Rössler of “spiral-type”, “screw-type” and “funnel-type” strange attractors in terms of chaotic orbits that occur in nearly homoclinic conditions. According to a theorem by Shil’nikov, there exist uncountably many nonperiodic trajectories in systems which display a homoclinic orbit biasymptotic to a saddle-focus O, providing the following condition is fulfilled: ρ/λ < 1, where the eigenvalue of O are (−λ, ρ ± iω). This subset of chaotic trajectories is actually in one to one correspondance with a shift automorphism with an infinite number of symbols. Since homoclinic orbits are structurally unstable objects which lie on codimension-one hypersurfaces in the constraint space, one can reasonably hope to cross these hypersurfaces when following a one-parameter path. The bifurcation structure encountered near homoclinicity involves infinite sequences of saddle-node and period-doubling bifurcations. The aim of this paper is to provide numerical and experimental evidences for Shil’nikov homoclinic chaos in nonequilibrium chemical systems.
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3

Haken, H. "Pattern Formation, Pattern Recognition, and Associative Memory." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.wc2.

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Spatial and temporal patterns can be spontaneously formed in a variety of systems treated in physics, chemistry, biology and other disciplines. Such patterns may be coherent oscillations in the laser and their interactions with each other, spatio-temporal patterns in fluids, chemical reactions and a great variety of morphogenetic processes in biology.
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4

Trushin, S. A., Werner Fuss, K. K. Pushpa, and W. E. Schmid. "Ultrafast chemical dynamics by intense-laser field dissociative ionization." In XVII International Conference on Coherent and Nonlinear Optics (ICONO 2001), edited by Andrey Y. Chikishev, Valentin A. Orlovich, Anatoly N. Rubinov, and Alexei M. Zheltikov. SPIE, 2002. http://dx.doi.org/10.1117/12.468909.

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5

Provata, A., and J. W. Turner. "Nonlinear Dynamics in Low-Dimensional Lattices: A Chemical Reaction Model." In 101st WE-Heraeus-Seminar. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814503648_0005.

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6

Kogemyakin, Alexey O., Vadim R. Meshkov, Alexander V. Omelchenko, and Vladimir N. Uskov. "Gas-dynamical constraints under solution of nonlinear problems of supersonic gas dynamics." In Twelfth International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. SPIE, 1998. http://dx.doi.org/10.1117/12.334479.

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7

Mudunuru, M. K., M. Shabouei, and K. B. Nakshatrala. "On Local and Global Species Conservation Errors for Nonlinear Ecological Models and Chemical Reacting Flows." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52760.

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Advection-controlled and diffusion-controlled oscillatory chemical reactions appear in various areas of life sciences, hydrogeological systems, and contaminant transport. In this conference paper, we analyze whether the existing numerical formulations and commercial packages provide physically meaningful values for concentration of the chemical species for two popular oscillatory chemical kinetic schemes. The first one corresponds to the chlorine dioxide-iodine-malonic acid reaction while the second one is a simplified version of Belousov-Zhabotinsky reaction of a non-linear chemical oscillator. The governing equations for species balance are presented based on the theory of interacting continua. This results in a set of coupled non-linear partial differential equations. Obtaining analytical solutions is not practically viable. Moreover, it is well-known in literature that if the local dynamics becomes complex, the range of possible dynamic behavior in the presence of diffusion and advection becomes practically unlimited. We resort to numerical solutions, which are obtained using two popular stabilized formulations: Streamline Upwind/Petrov Galerkin and Galerkin/Least Squares. In order to make the computational analysis tractable, an estimate on the range of system-dependent parameters is obtained based on model reduction performed on the strong-form of the governing equations. Finally, we quantify the errors in satisfying the local and global species balance for various realistic benchmark problems. Through these representative numerical examples, we shall demonstrate the need and importance of developing locally conservative non-negative numerical formulations for chaotic and oscillatory chemically reacting systems.
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8

Rosenwaks, S. "Applications of Nonlinear Optics Methods in Molecular Dynamics Studies." In The European Conference on Lasers and Electro-Optics. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/cleo_europe.1996.cwc1.

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The possibility of directing the course of chemical reactions by photoexcitation of specific modes of nuclear motion, so called mode-selective chemistry, continues to intrigue physicists, chemists and biologists. In this presentation we will address the application of stimulated Raman excitation, coherent anti-Stokes Raman scattering, overtone infrared excitation, laser induced fluorescence and multiphoton ionization techniques to preparation and detection of particular rovibrational states of the parent and product species in photodissociation and reactions of small molecules. Bond- and mode- selective processes in these species arc particularly appealing for both theoretical and experimental studies. This is because they are small enough to allow ab initio calculations of potential surfaces and photodynamics and yet retain the complexity of different vibrational degrees of freedom. However, quantitative comparison with theory requires experiments that prepare reactant molecules in specific initial states to avoid the averaging over different quantum states. Also, it is necessary to determine accurately the populations in the various final quantum states of the photofragments.
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9

Kotomtseva, Liudmila A., and Sergey G. Rusov. "Models for description of nonlinear dynamics and switching regimes in a laser with a saturable absorber." In XIII International Symposium on Gas Flow and Chemical Lasers and High-Power Laser Conference. SPIE, 2001. http://dx.doi.org/10.1117/12.414096.

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10

Radhakrishnan, Anand N. P., Marc Pradas, Serafim Kalliadasis, and Asterios Gavriilidis. "Nonlinear Dynamics of Gas-Liquid Separation in a Capillary Microseparator." In ASME 2018 16th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icnmm2018-7613.

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Micro-engineered devices (MED) are seeing a significant growth in performing separation processes1. Such devices have been implemented in a range of applications from chemical catalytic reactors to product purification systems like microdistillation. One of the biggest advantages of these devices is the dominance of capillarity and interfacial tension forces. A field where MEDs have been used is in gas-liquid separations. These are encountered, for example, after a chemical reactor, where a gaseous component being produced needs immediate removal from the reactor, because it can affect subsequent reactions. The gaseous phase can be effectively removed using an MED with an array of microcapillaries. Phase-separation can then be brought about in a controlled manner along these capillary structures. For a device made from a hydrophilic material (e.g. Si or glass), the wetted phase (e.g. water) flows through the capillaries, while the non-wetted dispersed phase (e.g. gas) is prevented from entering the capillaries, due to capillary pressure. Separation of liquid-liquid flows can also be achieved via this approach. However, the underlying mechanism of phase separation is far from being fully understood. The pressure at which the gas phase enters the capillaries (gas-to-liquid breakthrough) can be estimated from the Young-Laplace equation, governed by the surface tension (γ) of the wetted phase, capillary width (d) and height (h), and the interface equilibrium contact angle (θeq). Similarly, the liquid-to-gas breakthrough pressure (i.e. the point at which complete liquid separation ceases and liquid exits through the gas outlet) can be estimated from the pressure drop across the capillaries via the Hagen-Poiseuille (HP) equation. Several groups reported deviations from these estimates and therefore, included various parameters to account for the deviations. These parameters usually account for (i) flow of wetted phase through ‘n’ capillaries in parallel, (ii) modification of geometric correction factor of Mortensen et al., 2005 2 and (iii) liquid slug length (LS) and number of capillaries (n) during separation. LS has either been measured upstream of the capillary zone or estimated from a scaling law proposed by Garstecki et al., 2006 3. However, this approach does not address the balance between the superficial inlet velocity and net outflow of liquid through each capillary (qc). Another shortcoming of these models has been the estimation of the apparent contact angle (θapp), which plays a critical role in predicting liquid-to-gas breakthrough. θapp is either assumed to be equal to θeq or measured with various techniques, e.g. through capillary rise or a static droplet on a flat substrate, which is significantly different from actual dynamic contact angles during separation. In other cases, the Cox-Voinov model has been used to calculate θapp from θeq and capillary number. Hence, the empirical models available in the literature do not predict realistic breakthrough pressures with sufficient accuracy. Therefore, a more detailed in situ investigation of the critical liquid slug properties during separation is necessary. Here we report advancements in the fundamental understanding of two-phase separation in a gas-liquid separation (GLS) device through a theoretical model developed based on critical events occurring at the gas-liquid interfaces during separation.
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Звіти організацій з теми "Nonlinear Chemical Dynamics"

1

Stewart, Stephen E., and P. A. Cox. Nonlinear Dynamic Response Analysis of 115 mm Chemical Rocket Packing Impacts. Fort Belvoir, VA: Defense Technical Information Center, June 1985. http://dx.doi.org/10.21236/ada190702.

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2

[Mechano-chemical self-organization and nonlinear dynamics in sedimentary basins]. Office of Scientific and Technical Information (OSTI), January 1993. http://dx.doi.org/10.2172/7018941.

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3

(Mechano-chemical self-organization and nonlinear dynamics in sedimentary basins). Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/5605366.

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4

[Mechano-chemical self-organization and nonlinear dynamics in sedimentary basins]. Technical progress report. Office of Scientific and Technical Information (OSTI), March 1993. http://dx.doi.org/10.2172/10128315.

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5

[Mechano-chemical self-organization and nonlinear dynamics in sedimentary basins]. Technical progress report. Office of Scientific and Technical Information (OSTI), April 1992. http://dx.doi.org/10.2172/10133809.

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