罗丹明B在无机分析中的应用

本文从分光光度法、荧光光度法、散射三个方面系统的综述了近年来罗丹明B在无机分析中的应用情况及研究进展,引用文献49篇。     

Analytical thermodynamics. Part I. Thermostatics—General theory

A new axiomatic treatment of equilibrium thermodynamics—thermostatics—is presented. The equilibrium states of a thermal system are assumed to be represented by a differentiable manifold of dimensionn + 1 (n finite). The empirical temperature is defined by the notion of thermal equilibrium. Empirical entropy is shown to exist for all systems with the property that the total work delivered along closed adiabats is zero. Absolute entropy and temperature follow from the additivity of heat and energy for two separate systems in thermal equilibrium considered as a whole. The absolute temperature is defined up to a multiplicative constant. The exterior differentiable calculus of Cartan is introduced and in a subsequent paper its use for the derivation of standard results in thermostatics will be explained.     

A model of modulated diffusion. I. Analytical results

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.     

Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation

We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated rigorously; tube renewal is taken into account in an approximation motivated by random walk theory. We find microstructure effects to be present for remarkably large times and long chains, affecting essentially all present-day computer experiments. The various asymptotic power laws commonly considered as typical for reptation hold only for extremely long chains. Furthermore, for an arbitrary segment even in a very long chain, we find a rich variety of fairly broad crossovers, which for practicably accessible chain lengths overlap and smear out the asymptotic power laws. Our analysis suggests observables specifically adapted to distinguish reptation from motions dominated by disorder of the environment.     

Infinite Compressibility States in the Hierarchical Reference Theory of Fluids. I. Analytical Considerations

In its customary formulation for one-component fluids, the Hierarchical Reference Theory yields a quasilinear partial differential equation (PDE) for an auxiliary quantity f that can be solved even arbitrarily close to the critical point, reproduces non-trivial scaling laws at the critical singularity, and directly locates the binodal without the need for a Maxwell construction. In the present contribution we present a systematic exploration of the possible types of behavior of the PDE\ for thermodynamic states of diverging isothermal compressibility _T as the renormalization group theoretical momentum cutoff approaches zero. By purely analytical means we identify three classes of asymptotic solutions compatible with infinite _T, characterized by uniform or slowly varying bounds on the curvature of f, by monotonicity of the build-up of diverging _T, and by stiffness of the PDE in part of its domain, respectively. These scenarios are analzyed and discussed with respect to their numerical properties. A seeming contradiction between two of these alternatives and an asymptotic solution derived earlier [Parola et al., Phys. Rev. E 48:3321 (1993)] is easily resolved.     

New strings for old Veneziano amplitudes: I. Analytical treatment

The bosonic string theory evolved as an attempt to find a physical/quantum mechanical model capable of reproducing Euler’s beta function (Veneziano amplitude) and its multidimensional analogue. The multidimensional analogue of beta function was studied mathematically for some time from different angles by mathematicians such as Selberg, Weil and Deligne, among many others. The results of their studies apparently were not taken into account in physics literature on string theory. In a recent publication [IJMPA 19 (2004) 1655] an attempt was made to restore the missing links. The results of this publication are incomplete, however, since no attempts were made at reproduction of known spectra of both open an closed bosonic strings or at restoration of the underlying model(s) reproducing such spectra. Nevertheless, as discussed in this publication the existing mathematical interpretation of the multidimensional analogue of Euler’s beta function as one of the periods associated with the corresponding differential form “living” on the Fermat-type (hyper)surfaces, happens to be crucial for restoration of the quantum/statistical mechanical model reproducing such generalized beta function. Unlike the traditional formulations, this model is supersymmetric. Details leading to restoration of this model will be presented in the forthcoming Parts 2–4 of our work. They are devoted, respectively, to the group-theoretic, symplectic and combinatorial treatments of this model. In this paper the discussion is restricted mainly to the study of analytical properties of the multiparticle Veneziano and Veneziano-like (tachyon-free) amplitudes. In the last case, we demonstrate that the Veneziano-like amplitudes alone (with parameters adjusted accordingly) are capable of reproducing known spectra of both open and closed bosonic strings. The choice of parameters is subject to some constraints dictated by the mathematical interpretation of these amplitudes as periods of Fermat-type (hyper)surfaces considered as complex manifolds of Hodge-type.     

Sedimentation equilibria of ferrofluids: I. Analytical centrifugation in ultrathin glass capillaries

Analytical centrifugation is used for the first time to measure sedimentation equilibrium concentration profiles of a ferrofluid, a concentrated colloidal dispersion of strongly absorbing magnetic nanoparticles. To keep the optical absorbance from becoming too strong, the optical path length is restricted to 50 μm by placing the dispersion in a flat glass capillary. The concentration profile is kept from becoming too steep, despite the relatively high buoyant mass of the nanoparticles, by making novel use of a low-velocity analytical centrifuge that was not designed to measure equilibrium profiles. The experimental approach is validated by comparison with profiles obtained using an analytical ultracentrifuge. At concentrations of a few hundred grams per liter, the osmotic pressures calculated from the equilibrium profiles are lower than expected for hard spheres or non-interacting particles, due to magnetic dipolar interactions. By following the presented experimental approach, it will now also be possible to characterize the interparticle interactions of other strongly absorbing colloidal particles not studied before by analytical centrifugation.     

Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part I. Analytical results

We consider two single-species reaction-diffusion models on one-dimensional lattices of lengthL: the coagulation-decoagulation model and the annihilation model. For the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions. This system of differential equations grows quadratically withL in the latter case. The equations are solved analytically and exact expressions for the concentration are derived. We investigate the finite-size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions. We show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.     

Second-Harmonic Generation from a Thin Cylindrical Layer. I. An Analytical Solution

Optics and Spectroscopy - The problem of second-harmonic generation by a plane elliptically polarized electromagnetic wave from a thin optically nonlinear layer on the surface of a cylindrical...     

Analytical mechanics methods for solving Whittaker equations

The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange--Noether method, Hamilton--Poisson method and potential integral method.     

Analytical methods for AMC and EBG characterizations

AMC and EBG behaviors are respectively characterized by reflection phase method and dispersion diagram. A fast and simple analytical model based on transmission line theory is proposed for each analysis. The validity of these analytical methods is verified by a comparison between circuit representations, measurements and numerical results.     

Analytical methods for quality control of combinatorial libraries

This literature review covers the applications of analytical techniques to solid phase organic chemistry and combinatorial chemistry published between June 96 and September 1997. Highlighted are mass spectrometry, NMR, IR and chromatographic analyses of solid phase synthesis reactions and combinatorial libraries.     

Analytical methods of solution of the relaxational equations

The master equations system for rotational, vibrational and chemical kinetics in nonuniform gas flows with the sources is studied. Two approximate analytical methods of its solution for the arbitrary rate constants are developed for the case of the smooth distributions. The first method is based on the introduction of slow variables to the discrete equations. The second one uses WKB solution for diffusion approximation in Fokker-Planck form. The particular cases of harmonic and weakly anharmonic oscillators relaxation are examined.     

Grassmann phase space methods for fermions. I. Mode theory

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum–atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics.     

Analytical and numerical methods in the theory of random wave processes

Summary This paper deals with the evaluation of a two-parameter, two-index, imaginary integral function . The motivation for this analysis arose from the application of stochastic process theory to random ocean wave properties. Physically represents the normalized cross spectrum between any two components of a random state vector whose components are defined by wave amplitude, vector particle velocity, vector particle acceleration and linearized vector hydrodynamic force on a submerged object. The function , however, is developed in a general fashion so as to be applicable to any two-dimensional random wave process. Numerical and analytical methods are employed to develop techniques for the evaluation of and sample graphs are presented.

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Riassunto Si valuta la funzione integrale immaginaria a 2 parametri e 2 indici necessaria per l’applicazione della teoria dei processi stocastici alle proprietà delle onde oceaniche casuali. Fisicamente rappresenta lo spettro normalizzato incrociato preso fra due componenti qualsiasi di un vettore di stato casuale definito dall’ampiezza dell’onda, dal vettore velocità delle particelle, dal vettore accelerazione delle particelle e dal vettore linearizzato forza idrodinamica agente su un oggetto sommerso. La funzione è peraltro sviluppata in modo del tutto generale in modo da risultare applicabile a qualsiasi processo casuale ondoso in 2 dimensioni. Sono presentati metodi sia numerici che analitici, e grafici di esempio.

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Резюме Эта работа посвящена вычислению двух-параметрической, двух-индексной, мнимой целой функции . Указанный анализ связан с применением теории стохастических процессов к изучению свойств случайных океанических волн. Физически представляет нормированный перекрестный спектр между двумя произвольными компонентами случайного вектора состояния, компоненты которого определяются амплитудой волны, вектором скорости частицы, вектором ускорения частицы и линеаризованной векторной гидродинамической силой, действующей на погруженный объект. Однако, функция вычисляется обычным образом для применения к произвольному двумерному случайному волновому процессу. Используются численные и аналитические методы для вычисления и предлагаются графики в качестве примера.

     

Study of stochastic differential equations by constructive methods. I

In this work we give an algorithm to express as a convergent series the stationary averages for a class of gradient perturbations of a nonsymmetric (nongradient) Ornstein—Uhlenbeck process. The method relies on a cluster expansion in time of the Girsanov-Cameron-Martin formula for the density of the perturbed measure with respect to the Ornstein-Uhlenbeck measure. In the second paper of this series, the approach is extended to more general perturbations.