On the global existence and finite time blow-up of shadow systems

Shadow systems are often used to approximate reaction-diffusion systems when one of the diffusion rates is large. In this paper, we study the global existence and blow-up phenomena for shadow systems. Our results show that even for these fundamental aspects, there are serious discrepancies between the dynamics of the reaction-diffusion systems and that of their corresponding shadow systems.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.     

Bayesian estimation of finite time ruin probabilities

In this paper, we consider Bayesian inference and estimation of finite time ruin probabilities for the Sparre Andersen risk model. The dense family of Coxian distributions is considered for the approximation of both the inter‐claim time and claim size distributions. We illustrate that the Coxian model can be well fitted to real, long‐tailed claims data and that this compares well with the generalized Pareto model. The main advantage of using the Coxian model for inter‐claim times and claim sizes is that it is possible to compute finite time ruin probabilities making use of recent results from queueing theory. In practice, finite time ruin probabilities are much more useful than infinite time ruin probabilities as insurance companies are usually interested in predictions for short periods of future time and not just in the limit. We show how to obtain predictive distributions of these finite time ruin probabilities, which are more informative than simple point estimations and take account of model and parameter uncertainty. We illustrate the procedure with simulated data and the well‐known Danish fire loss data set. Copyright © 2009 John Wiley & Sons, Ltd.     

强迫布鲁塞尔子二维重构延迟时间的分框确定

本文利用常微方程系统二维重构变换的雅可比行列式，对强迫Brusselator吸引子进行了分框计算，确定出二维重构的延迟时间．     

Fast response in TN liquid-crystal cells: effect of functionalised carbon nanotubes

The optical response time of a nematic liquid crystal (NLC) decreases due to incorporation of carbon nanotubes (CNTs) in the liquid-crystal host. Such reduction is believed to be due to an increase in the elastic constant of the nanotube-doped LC system. In this paper, we present the effect on optical response due to doping an NLC with octadecylamine functionalised single-walled carbon nanotubes (ODA-SWCNT) in a twisted alignment mode. The electro-optic switching amplitude of ODA-SWCNT nanocomposites of NLC decreases compared to pure NLC. A fast response time is observed with an increase in the concentration of ODA-SWCNT in NLC host. Additionally, optical response of pure NLC in a twisted nematic (TN) cell fabricated using mixtures of polyimide (PI) and ODA-SWCNT as an alignment layer is investigated. The optical response time decreased by ~75% in a TN cell fabricated with a mixture of PI and ODA-SWCNT compared to that of a TN cell prepared using a pure PI alignment layer. The presence of ODA-SWCNT in the alignment layer enhances the surface anchoring of the NLC molecules leading to an increase in the elastic constant and a decrease in the optical response time of NLC.     

Vibronic dynamics in the low-lying coupled electronic states of methyl cyanide radical cation

Static and dynamic aspects of the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) interactions between the ground and first excited electronic states of the methyl cyanide radical cation are theoretically investigated here. The latter involves construction of a theoretical model by ab initio computation of electronic potential energy surfaces and their coupling surfaces and simulation of the nuclear dynamics employing time-independent and time-dependent quantum mechanical methods. The present system represents yet another example belonging to the (E + A)  e JT–PJT family, with common JT and PJT active degenerate (e) vibrational modes. The theoretical results are found to be in very good accord with the recent experimental data revealing that the JT interactions are particularly weak in the ground electronic manifold of methyl cyanide radical cation, On the other hand, the PJT interactions of this ground electronic manifold with the first excited electronic state of the radical cation are stronger which cause an increase of the spectral line density. The effect of deuteration on the JT–PJT dynamics of the methyl cyanide radical cation is also discussed.     

A Time‐Resolved Spectroscopic Study of the Bichromophoric Phototrigger 3′,5′‐Dimethoxybenzoin Diethyl Phosphate: Interaction Between the Two Chromophores Determines the Reaction Pathway

3′,5′‐Dimethoxybenzoin (DMB) is a bichromophoric system that has widespread application as a highly efficient photoremovable protecting group (PRPG) for the release of diverse functional groups. The photodeprotection of DMB phototriggers is remarkably clean, and is accompanied by the formation of a biologically benign cyclization product, 3′,5′‐dimethoxybenzofuran (DMBF). The underlying mechanism of the DMB deprotection and cyclization has, however, until now remained unclear. Femtosecond transient absorption (fs‐TA) spectroscopy and nanosecond time‐resolved resonance Raman (ns‐TR³) spectroscopy were employed to detect the transient species directly, and examine the dynamic transformations involved in the primary photoreactions for DMB diethyl phosphate (DMBDP) in acetonitrile (CH₃CN). To assess the electronic character and the role played by the individual sub‐chromophore, that is, the benzoyl, and the di‐meta‐methoxybenzylic moieties, for the DMBDP deprotection, comparative fs‐TA measurements were also carried out for the reference compounds diethyl phosphate acetophenone (DPAP), and 3′,5′‐dimethoxybenzylic diethyl phosphate (DMBnDP) in the same solvent. Comparison of the fs‐TA spectra reveals that the photoexcited DMBDP exhibits distinctly different spectral character and dynamic evolution from those of the reference compounds. This fact, combined with the related steady‐state spectral and density functional theoretical results, strongly suggests the presence in DMBDP of a significant interaction between the two sub‐chromophores, and that this interaction plays a governing role in determining the nature of the photoexcitation and the reaction channel of the subsequent photophysical and photochemical transformations. The ns‐TR³ results and their correlation with the fs‐TA spectra and dynamics provide evidence for a novel concerted deprotection–cyclization mechanism for DMBDP in CH₃CN. By monitoring the direct generation of the transient DMBF product, the cyclization time constant was determined unequivocally to be ≈1 ns. This indicates that there is little relevance for the long‐lived intermediates (>10 ns) in giving the DMBF product, and excludes the stepwise mechanism proposed in the literature as the major pathway for the DMB cyclization reaction. This work provides important new insights into the origin of the 3′,5′‐dimethoxy substitution effect for the DMB photodeprotection. It also helps to clarify the many different views presented in previous mechanistic studies of the DMB PRPGs. In addition to this, our fs‐TA results on the reference compound DMBnDP in CH₃CN provide the first direct observation (to the best of our knowledge) showing the predominance of a prompt (≈2 ps) heterolytic bond cleavage after photoexcitation of meta‐methoxybenzylic compounds. This provides insight into the long‐term controversies about the photoinitiated dissociation mode of related substituted benzylic compounds.     

The minimum heat consumption for heat-driven binary separation processes with linear phenomenological heat transfer law

The optimal performance of heat-driven binary separation processes with linear phenomenological heat transfer law(q∝△(T-1)) is analyzed by taking the processes as heat engines which work between high-and low-temperature reservoirs and produce enthalpy and energy flows out of the system,and the temperatures of the heat reservoirs are assumed to be time-and space-variables.A numerical method is employed to solve convex optimization problem and Lagrangian function is employed to solve the average optimal contr...     

Photodissociation Dynamics of Benzaldehyde (C6H5CHO) at 266, 248, and 193 nm

The photodissociation of gaseous benzaldehyde (C₆H₅CHO) at 193, 248, and 266 nm using multimass ion imaging and step‐scan time‐resolved Fourier‐transform infrared emission techniques is investigated. We also characterize the potential energies with the CCSD(T)/6‐311+G(3df,2p) method and predict the branching ratios for various channels of dissociation. Upon photolysis at 248 and 266 nm, two major channels for formation of HCO and CO, with relative branching of 0.37:0.63 and 0.20:0.80, respectively, are observed. The C₆H₅+HCO channel has two components with large and small recoil velocities; the rapid component with average translational energy of approximately 25 kJ mol^?1 dominates. The C₆H₆+CO channel has a similar distribution of translational energy for these two components. IR emission from internally excited C₆H₅CHO, ν₃ (v=1) of HCO, and levels v≤2, J≤43 of CO are observed; the latter has an average rotational energy of approximately 13 kJ mol^?1 and vibrational energy of approximately 6 kJ mol^?1. Upon photolysis at 193 nm, similar distributions of energy are observed, except that the C₆H₅+HCO channel becomes the only major channel with a branching ratio of 0.82±0.10 and an increased proportion of the slow component; IR emission from levels ν₁ (v=1) and ν₃ (v=1 and 2) of HCO and v≤2, J≤43 of CO are observed; the latter has an average energy similar to that observed in photolysis at 248 nm. The observed product yields at different dissociation energies are compared to statistical‐theory predicted results based on the computed singlet and triplet potential‐energy surfaces.     

A global potential energy surface and time‐dependent quantum wave packet calculation of Au + H2 reaction

A global potential energy surface (PES) corresponding to the ground state of AuH₂ system has been constructed based on 22 853 ab initio energies calculated by the multireference configuration interaction method with a Davidson correction. The neural network method is used to fit the PES, and the root mean square error is only 1.87 meV. The topographical features of the novel global PES are compared with previous PES which is constructed by Zanchet et al. (Zanchet PES). The global minimum energy reaction paths on the two PESs both have a well and a barrier. Relative to the Au + H₂ reactants, the energy of well is 0.316 eV on the new PES, which is 0.421 eV deeper than Zanchet PES. The calculation of Au(²S) + H₂(X¹Σ_g⁺) → AuH(X¹Σ⁺) + H(²S) dynamical reaction is carried out on new PES, by the time‐dependent quantum wave packet method (TDWP) with second order split operator. The reaction probabilities, integral cross‐sections (ICSs) and differential cross‐sections are obtained from the dynamics calculation. The threshold in the reaction is about 1.46 eV, which is 0.07 eV smaller than Zanchet PES due to the different endothermic energies on the two PESs. At low collision energy (<2.3 eV), the total ICS is larger than the result obtained on Zanchet PES, which can be attributed to the difference of the wells and endothermic energies.