Testing Transition State Theory on Kac-Zwanzig Model

A variant of the Kac-Zwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a double-well external potential and coupled to N free particles through linear springs. While the Kac-Zwanzig model is deterministic, under appropriate choice of the model parameters the evolution of the distinguished particle can be approximated by a two-state Markov chain whose transition rate constants can be computed exactly in suitable limit. Here, these transition rate constants are compared with the predictions of TST and VTST. It is shown that the application of TST with a naive (albeit natural) choice of dividing surface leads to the wrong prediction of the transition rate constants. This is due to crossings of the dividing surface that do not correspond to actual transition events. However, optimizing over the dividing surface within VTST allows one to eliminate completely these spurious crossings, and therefore derive the correct transition rate constants for the model. The reasons why VTST is successful in this model are discussed, which allows one to speculate on the reliability of VTST in more complicated systems.     

Mapping quantum many-body system to decoupled harmonic oscillators: General discussions and examples

We present a class of quantum systems that can be mapped to decoupled harmonic oscillators through appropriate similarity transformations. We will take advantage of these similarity transformations to discover hidden ladder operators, such that the eigenstates of the system can be constructed like those of harmonic oscillator. We also provide five systems belonging to this family as examples.     

Supersymmetry and duality in relativistic oscillator systems

A simple mapping is defined which takes the relativistic oscillator on a (1+1)-dimensional spacetime into a dual system consisting of a nonrelativistic oscillator confined to a circular space. The radius of the circle in the dual system measures the size of relativistic effects in the original system. It is shown that both of the dual oscillator systems have supersymmetric partners, and the exact wavefunctions and energy levels of all four of the intertwined systems are found.     

On the importance of using scandium to normalize geochemical data preceding multivariate analyses applied to archaeometric pottery studies

This work enhances the importance on determining regional geochemical background by normalizing chemical data of archaeological ceramics, using one element as grain-size and mineralogical proxy, prior to any further statistical approach. It is well established that more relevant information can be derived from the concentration of any element when it is compared with some reference element. The main question is which element should be chosen to normalize concentration. A discussion on this issue is presented here.A case study is presented, which includes the geochemical tracing of Roman kilns productions, differentiating between and within two sedimentary basins pottery assembly, belonging to several Roman ceramic production centres identified in the Tagus and Sado basins of Portugal. Due to the homogeneity of the used raw materials (estuarine sediments), the distinction and establishment of signatures for each production center become difficult.A multivariate statistical approach after normalization of the chemical contents to a conservative element (Sc) is presented, well differentiating the three production centers and allowing the establishment of provenance for amphorae.     

A new method for exact integration of some perturbed stiff linear systems of oscillatory type

This article presents a new family of real functions with values within the ring of M(m,R) matrices, Φ-functions for perturbed linear systems and a numerical method adapted for integration of this type of problem. This method permits the system solution to be expressed as a series of Φ-functions. The coefficients of this series are obtained through recurrences in which the perturbation intervenes.The Φ-functions series method has the advantage of being exactly integrated in the perturbed problem. For this purpose an appropriate B matrix is selected and used to construct the operator described in this article, thus annihilating the disturbance terms, transforming the system into a homogenous second-order system, which is exactly integrated with the two first Φ-functions.The article ends with a detailed study of four perturbed systems which illustrate how the method is used in stiff problems or in highly oscillatory problems, contrasting its behaviour by studying its accuracy in comparison with other well-known codes.     

Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings

The integrate-and-fire cardiac pacemaker model of the pulse coupled oscillators was introduced by C. Peskin. Due to the function of the pacemaker, two famous synchronization conjectures for identical and not identical oscillators were formulated. There are still many issues related to the nature and types of couplings. The couplings may be impulsive, continuous, delayed or advanced, and oscillators may be locally or globally connected. Consequently, it is reasonable to consider various ways of synchronization, if one wants the biological and mathematical analyses to interact productively. We investigate the integrate-and-fire model in both cases-one with identical, and another with not quite identical oscillators. A combination of continuous and pulse couplings that sustain the firing in unison is carefully constructed. Moreover, we obtain conditions on the parameters of continuous couplings that make possible a rigorous mathematical investigation of the problem. The technique developed for differential equations with discontinuities at non-fixed moments and a special continuous map lies on the basis of the analysis. This is the first analytically derived synchronization result for a model with continuous couplings. Illustrative examples are provided.     

Indirect determination of ascorbic acid by solid-phase spectrophotometry

Solid-phase spectrophotometry (SPS) technique, in the visible region, was used for the spectrophotometric determination of ascorbic acid based on the reducing effect on iron(III) ion, followed by formation of the iron(II)-ferrozine chelate. The chelate is easily sorbed on a dextran-type anion-exchange gel and the absorbance of the resin at 567 and 800 nm, packed in a 1 mm cell, is measured directly. The apparent molar absorptivity using 100 ml of sample was 2.1×10⁷ l mol⁻¹ cm⁻¹ and it allowed the determination of ascorbic acid in the range 5–90 ng ml⁻¹; the detection limit was 0.91 ng ml⁻¹ and the RSD 0.91% for a concentration of 50 ng ml⁻¹ of ascorbic acid (n=10). The proposed method permits a highly sensitive and selective determination of ascorbic acid without any preconcentration and it has been satisfactorily applied for its determination in fruit juices, pharmaceuticals, urine and conservative liquids.     

可逆型化学振荡器

该文给出了可逆型化学振荡器的定义、意义和可能存在的类型。这些类型包括：（1）自发乳化，通电破乳；（2）乳液中自发产生的甘油三酯水解振荡反应及通电逆向酯化反应；（3）用表面活性剂有机溶液代替盐桥，形成新型的电化学振荡，通电逆向电解。文章对这3种类型可逆型化学振荡器的来源、组成、实验方法、理论分析方法和应用前景进行了深入的讨论和分析。它们还可以进一步组合，形成更多的类型。其主要的研究方法为用正交实验确定最佳配方，由相关分析确定影响因素。这些可逆型化学振荡器的关键组分都是表面活性剂，是表面活性剂在非线性化学动力学研究中的又一应用。对可逆型化学振荡器的研究必将大大促进远离平衡态的复杂反应动力学研究及新型交流蓄电池的开发设计。