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An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol?1)·T?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH3 group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition. 相似文献
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Abstract Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood. 相似文献
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Nonlinear Dynamics - In the present article, a combination of numerical and experimental studies is undertaken to comprehend the influence of noise on the responses of continuous-time dynamical... 相似文献
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This work concerns the nature of chaotic dynamical processes. Sheldon Newhouse wrote on dynamical processes (depending on a parameter )x
x+1=T(x
n
; ), wherex is in the plane, such as might arise when studying Poincaré return maps for autonomous differential equations in IR3. He proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane, and that such parameter values would be dense in some interval. The fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes. We prove, for an apparently typical situation, that Newhouse's construction yields only a set of parameter values of measure zero.This research was supported in part by grants from the Air Force Office of Scientific Research AFOSR 81-0217, the Consiglio Nazionale delle Ricerche-Comitato per le Matematiche, and the National Science Foundation DMS 84-19110On leave from: Dipartimento di Matematica G. Castel nuovo Universita di Roma La Sapienza P. le Aldo Moro 5, I-00185 Rome, Italy 相似文献
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We investigate numerically complex dynamical systems where a fixed point is surrounded by a disk or ball of quasi-periodic orbits, where there is a change of variables (or conjugacy) that converts the system into a linear map. We compute this “linearization” (or conjugacy) from knowledge of a single quasi-periodic trajectory. In our computations of rotation rates of the almost periodic orbits and Fourier coefficients of the conjugacy, we only use knowledge of a trajectory, and we do not assume knowledge of the explicit form of a dynamical system. This problem is called the Babylonian problem: determining the characteristics of a quasi-periodic set from a trajectory. Our computation of rotation rates and Fourier coefficients depends on the very high speed of our computational method “the weighted Birkhoff average”. 相似文献
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The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics. 相似文献
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This paper deals with the problem “Can a noisy orbit be tracked by a real orbit?” In particular, we will study the one-parameter family of tent maps and the one-parameter family of quadratic maps. We writeg μ for eitherf μ orF μ withf μ (x)=μx forx≦1/2 andf μ (x)=μ(1?x) forx≧1/2, andF μ (x)=μx(1?x). For a given μ we will say:g μ permits increased parameter shadowing if for each δ x >0 there exists someδ μ >0 and some δ f >0 such that every δ f -pseudog μ -orbit starting in some invariant interval can be δ x -shadowed by a realg α -orbit with α=μ+δ μ . We show thatg μ typically permits increased parameter shadowing. 相似文献