Frequency Domain Fluorescence Lifetime Study of Crude Petroleum Oils

Frequency domain (FD) fluorescence lifetime data was collected for a series of 20 crude petroleum oils using a 405 nm excitation source and over a spectral range of ~426 to ~650 nm. Average fluorescence lifetimes were calculated using three different models: discrete multi-exponential, Gaussian distribution, and Lorentzian distribution. Fitting the data to extract accurate average lifetimes using the various models proved easier and less time consuming for the FD data than with Time Correlated Single Photon Counting (TCSPC) methods however the analysis of confidence intervals to the computed average lifetimes proved cumbersome for both methods. The uncertainty in the average lifetime was generally larger for the discrete lifetime multi-exponential model when compared to the distribution-based models. For the lifetime distributions, the data from the light crude oils with long lifetimes generally fit to a single decay term. Heavier oils with shorter lifetimes required multiple decay terms. The actual value for the average lifetime is more dependant on the specific fitting model employed than the data acquisition method used. Correlations between average fluorescence lifetimes and physical and chemical parameters of the crude oils were made with a view to developing a quantitative model for predicting the gross chemical composition of crude oils. It was found that there was no significant benefit gained by using FD over TCSPC other than more rapid data analysis in the FD case. For the FD data the Gaussian distribution model for fluorescence lifetime gave the best correlations with chemical composition allowing a qualitative correlation to some bulk oil parameters.

l-Dityrosine: A time-resolved fluorescence investigation

We have investigated the time-resolved fluorescence properties ofll-dityrosine in aqueous solution. Typically, three exponential components were needed to fit the fluorescence pattern adequately, with pure decay terms for the low-intensity, high-energy state (_em = nm) but with a pronounced subnanosecond rise phase for the predominant red-edge fluorescence (_em > 380). Dual fluorescence behavior is indicative of an intramolecular precursorsuccessor pair, i.e., a consecutive intramolecular excited-state reaction. We suggest that this reaction is a torsional motion of the (deprotonated) monoanion along the biphenolic bond. Analysis of the fluorescence anisotropy decay of dityrosine yielded two rotational correlation times, the longer of which is associated with a negative preexponential term. The increase with time in the horizontally polarized component of the intensity decay is interpreted as the result of an electronic rearrangement in the excited state when the successor form of dityrosine is generated. Lifetime distributions of experimental data were probed by an unbiased exponential series method which uses a Tikhonov-type regularization function. The procedure revealed three well-separated groups of lifetimes, the short-lived ensemble forming a formally negative distribution. A photophysical model is introduced which interprets the biexponential decay of dityrosine in terms of overlapping emission signals from the precursor and the successor molecule.     

Distance distributions recovered from steady-state fluorescence measurements on thirteen donor-acceptor pairs with different Förster distances

The end-to-end distance distribution of a flexible molecule was recovered from steady-state fluorescence energy transfer measurements using the method suggested by Cantor and Pechukas (Proc. Natl. Acad. Sci. USA 68, 2099–2101, 1971). In this method, the Förster distance (R ₀) is varied by attaching different donor-acceptor (D-A) pairs to the flexible linker of interest. Distance distributions are then recovered from energy transfer efficiency measurements on the set of D-A pairs with differentR ₀ values. Thirteen D-A pair compounds were synthesized withR ₀ values ranging from 6 to 32 Å. Each compound contained a tryptamine donor linked by an alkyl chain (10 carbons) to 1 of 13 acceptors. Using these compounds, we have experimentally confirmed the Cantor and Pechukas method for recovering distance distributions. The measured transfer efficiencies, as a function ofR ₀, were fit to the transfer efficiencies predicted for both Gaussian and skewed Gaussian distance distributions. The data support the existence of a skewed Gaussian distribution, and we believe that this is the first experimental observation of an asymmetric distribution for a flexible molecule using fluorescence resonance energy transfer measurements. Finally, the experimentally recovered distance distribution was found to be in good agreement with the distribution predicted from the rotational isomeric state model of Flory (Statistical Mechanics of Chain Molecules, John Wiley & Sons, New York, 1969, Chaps. 1, 3, and 5) but not with the predicted distribution for a freely rotating or freely jointed chain.     

The exact expression of the Voigt profile function

We solve in exact and closed-form a classical problem of mathematical physics of great interest in spectroscopy: the convolution of a Gaussian and a Lorentzian distribution that define the Voigt profile function, V(x). The solution is based in three steps: a power series development following the integral expression for V(x), the ordinary differential equation (ODE) satisfied by that expansion, and the corresponding solution of the ODE. This work converts in obsolete all graphical, numerical and semi-analytical approximations published previously. All results are clearly expressed in terms of the complementary error function Φ_c(a)=1-erf(a), where is, basically, the relation between Lorentzian and Gaussian widths.     

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes \( \mu \) on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for \(\hbox {Sine}_2 , \hbox {Airy}_2 , \hbox {Bessel}_2 \), and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.     

Continuous lifetime distributions of β-cyclodextrin-anilinonaphthalene sulfonic acid inclusion complexes

Fluorescence lifetimes are reported for a series of anilinonaphthalene sulfonate (ANS) probe molecules complexed with -cyclodextrin (-CD). The fluorescence decay kinetics are recovered by multifrequency phase and modulation measurements in concert with a global analysis scheme. In all cases studied, a continuous Lorentzian distribution of lifetimes is observed, resulting from the dynamical nature of the ANS--CD complex and free ANS. Trends are discussed and comparisons made between bound and free fluorophore and between different isomeric ANS structures.     

Far-field solution of the Helmholtz equation for double heterostructure diode lasers

On the basis of the Helmholtz equation the far-field distribution is derived for double heterostructure lasers. The results show that the far-field distribution in the direction normal to the junction plane approaches a Lorentzian function, but parallel to the junction it may be approximated by a Gaussian function. The far-field intensity patterns have analogous elliptic form. It is also shown, for the first time, that the separability condition is not strictly valid for the far-field of a laser diode. Only in the vicinity of the optical axis the field can be expressed as a product of two separate functions, each of which depends only on one of the two transverse coordinates parallel and perpendicular to the diode junction.     

Effects of light on cesium 6S-8S two-photon transition

This work presents a simple approach for determining the contribution of Lorentzian or Gaussian statistics by data fitting the spectrum to a Voigt profile. The fitting result shows that the Lorentzian width remains almost constant (∼1.51 MHz) and the Gaussian width increases (∼1.0-2.0 MHz) while changing the laser intensity or atomic density. The frequency shift associated with the cesium 6S-8S two-photon transition as a function of laser power is approximately ), agrees closely with the theoretical value. These results can be used to improve the optical secondary frequency standard in the near infrared region.     

Influence of the Axial-Vector Coupling Constant and the Energy Distribution Function on <Emphasis Type="Italic">β</Emphasis>-Decay Rates Within the Gross Theory of Beta Decay

We evaluate the β-decay rates within the gross theory of beta decay (GTBD) and compare the results for different values of the axial-vector coupling constant, g_A =?0.76, g_A =?0.88, g_A =?1, g_A =?1.13, and g_A =?1.26, and also different energy distribution functions like Gaussian, exponential, Lorentzian, and modified Lorentzian ones. We use new sets of parameters as well as updated experimental mass defects and also an improved approximation for the Fermi function. We compare our calculated results for a set of 94 nuclei of interest in pre-supernova phase, with experimental data in terrestrial conditions and also with other theoretical models like the QRPA, the shell model (SM), and different versions of the GTBD. We show that best results are obtained with g_A =?1 using Gaussian and Lorentzian distributions, being the rates for the 74 and 80% of our sample, respectively, of the same order of magnitude that of experimental data. Finally, we show that the present results within the GTBD are better than those within the QRPA model and also older versions of the GTBD for the isotopes of cobalt and iron families, and comparable with SM for some elements.     

2-Naphthol-phosphatidylethanolamine: A fluorescent phospholipid analogue for excited-state proton transfer studies in membranes

The fluorescence properties of the phospholipid derivative,N-[1-(2-naphthol)]-phosphatidylethanolamine (NAPH-PE), have been studied by steady-state and time-resolved fluorescence techniques. The new probe is a naphthol adduct of phosphatidylethanolamine. The emission spectrum of the fluorescent phospholipid depends on the pH and on the proton acceptor concentration as expected for a typical two-state excited-state proton transfer reaction. In ethanol solutions at an apparent pH of 6.7 and in the presence of acetate anion (0.14M), a biexponential decay is obtained from global analysis of the data. The lifetimes, ₁=3.9 ns and ₂=6.2 ns. are constant across the spectral region 350–460 nm. The decay-associated spectra and the species-associated spectra reproduce well the profiles reported for a two-state excited-state proton transfer reaction. The fluorescent phospholipid has been incorporated into dimyristoyllecithin and dipalmitoyllecithin vesicles. Although lower proton transfer is found, the reaction appears to be dependent on the gel-to-liquid-crystalline phase transition of the lipid membrane. In addition, the steady-state anisotropy of NAPH-PE measured as a function of temperature trace the phase transition of the two vesicle systems. Thus, it is shown that the physical state of the bilayer affects a reaction which takes place at the membrane surface. In the presence of acetate ions (0.3M), global analysis, performed in terms of fluorescence decay parameters, recovers preexponential coefficients that are consistent with an excited-state proton transfer reaction. The short lifetime drops from 3.9 to 0.44 ns without significant changes of the longer-lifetime component.     

Probing the Conformational Stability of Two Different Copper Proteins: A Dynamic Fluorescence Study on Azurin and Ascorbate Oxidase

Tryptophan fluorescence is extremely useful to monitor structural conformational transitions in proteins. Denaturant-induced unfolding of azurin and ascorbate oxidase has been studied by dynamic fluorescence measurements in the frequency domain and the results have been interpreted in terms of continuous distribution of lifetimes. The data add new information on the unfolding mechanism that was previously analyzed by steady-state emission spectroscopy. In particular, the existence of multiple, parallel unfolding pathways may be envisaged and correlated, in both cases, to the two protein structures. The effect of metal depletion has been also characterized by fluorescence lifetime measurements. In the case of azurin, a monomeric protein, the data demonstrate that copper removal yields a totally different unfolding pathways with respect to the holo protein, indicating that metal ion plays a fundamental structural role in the wild type, native protein. In the case of ascorbate oxidase a dimer of 140 kDa, only minor effects have been detected by copper removal. However, the analysis of the fluorescence decay in presence of different amounts of guanidinium hydrochloride gives new important insights on the unfolding intermediates. In particular the data support the hypothesis of a partial exposure of an outer layer of dimer at intermediate denaturant concentration. This ability of dynamic fluorescence to pinpoint the presence of structural micro-heterogeneity in the unfolding pathways of proteins demonstrates the greater power of this technique compared to the most commonly used steady-state measurements.     

Morse theory on timelike and causal curves

It is shown that the set of timelike curves in a globally hyperbolic space-time manifold can be given the structure of a Hubert manifold under a suitable definition of timelike. The causal curves are the topological closure of this manifold. The Lorentzian energy (corresponding to Milnor's energy, except that the Lorentzian inner product is used) is shown to be a Morse function for the space of causal curves. A fixed end point index theorem is obtained in which a lower bound for the index of the Hessian of the Lorentzian energy is given in terms of the sum of the orders of the conjugate points between the end points.     

The Crossover Regime for the Weakly Asymmetric Simple Exclusion Process

We consider the asymmetric simple exclusion process in one dimension with weak asymmetry (WASEP) and 0–1 step initial condition. Our interest are the fluctuations of the time-integrated particle current at some prescribed spatial location. One expects a crossover from Gaussian to Tracy-Widom distributed fluctuations. The appropriate crossover scale is an asymmetry of order \(\sqrt{\varepsilon}\), times of order ε ^?2, and a spatial location of order ε ^?3/2. For this parameter window we obtain the limiting distribution function of the integrated current in terms of an integral over the difference of two Fredholm determinants. For large times, on the scale ε ^?2, this distribution function converges to the one of Tracy-Widom.     

常用激光峰值功率公式误差分析

为分析脉冲激光中常用峰值功率公式的误差,对高斯脉冲、双曲正割脉冲、洛仑兹脉冲、非对称双曲正割脉冲的常用峰值功率公式的误差进行了解析计算。结果表明：高斯脉冲、双曲正割脉冲、洛仑兹脉冲、非对称双曲正割脉冲中,常规峰值功率公式的结果与实际峰值功率的误差分别为6.3%,13.6%,22.1%,20.9%。在具体实验基础上采用数值方法分析了非常规脉冲的情形,给出了精确计算峰值功率的方法。     

The output of amplified spontaneous emission lasers

The output of amplified spontaneous emission (ASE) lasers such as X-ray lasers operated without mirrors is calculated exactly for Gaussian and Lorentzian small signal gain profiles by a simple Taylor series expansion. The accuracy of the ‘Linford’ formula commonly used as an approximation for the output of ASE lasers is evaluated by comparison to our exact solutions. The Linford formula is accurate to better than 10% for intensities produced by a Gaussian gain profile, but requires multiplication by a correction factor of at gain length product greater than 5 for Lorentzian gain profiles.     

Noncommutative Wormholes in f(R) Gravity with Lorentzian Distribution

In this paper, we derive some new exact solutions of static wormholes in f(R) gravity supported by the matter possesses Lorentzian density distribution of a particle-like gravitational source. We derive the wormhole’s solutions in two possible schemes for a given Lorentzian distribution: assuming an astrophysically viable F(R) function such as a power-law form and discuss several solutions corresponding to different values of the exponent (here $F =\frac{df}{dR}$ ). In the second scheme, we consider particular form of two shape functions and have reconstructed f(R) in both cases. We have discussed all the solutions with graphical point of view.     

Optimizing accuracy and precision in spectral data

Parameters derived by computer fitting of Gaussian or Lorentzian curves to spectral data suffer from inaccuracies derived by the data gathering strategy, by instrumental errors and by the inherent statistical fluctuation of the measurements. When measurements of extreme quality are required, minimum uncertainty for peak centroid and linewidth for a given data collection time is obtained by proper choice of the number of ‘channels’ in the peak. The optimum conditions that are derived analytically are supported by results of fitting spectra with Gaussian curves. Fittings were done with the simplex procedure yielding precise values of the centroid and linewidth. Data used were x‐ray fluorescence signals and computer‐simulated spectral peaks. Results of the theoretical calculations and of computer fittings to both empirical data and simulated spectra indicate that the optimum number of channels in a peak, for the best quality of measurements of the peak centroid and its linewidth, is independent of the peak integral and has full width at half‐maximum in the neighborhood of 2.5 channels. Copyright © 2005 John Wiley & Sons, Ltd.     

Novel model for the optical function of GaN

In this work we propose an analytical expression for the complex dielectric function which includes both discrete and continuum exciton effects. We have introduced Lorentzian broadening into Elliott’s formula. The introduction of broadening leads to equations for the dielectric function containing only elementary functions. We have applied the proposed model to the dielectric function of wurtzite GaN in the spectral region 1–10 eV. Excellent agreement with the experimental data has been obtained. We show that the Lorentzian-broadened dielectric function decays more slowly than the experimental data for hexagonal GaN at the low-energy side. This indicates that the broadening of the absorption edge in GaN is not purely Lorentzian. The agreement with the experimental data can be improved using adjustable broadening modification. Received: 29 January 2001 / Accepted: 30 May 2001 / Published online: 25 July 2001     

Approximation of Mössbauer spectra of metallic glasses

Mössbauer spectra of iron-rich metallic glasses are approximated by means of six broadened lines which have line position relations similar to those of -Fe. It was shown via the results of the DISPA lineshape analysis that each spectral peak is broadened owing to a sum of Lorentzian lines weighted by a Gaussian distribution in the peak position. This paper presents the Mössbauer parameters of amorphous metallic Fe₈₃B₁₇ and Fe₄₀Ni₄₀B₂₀ alloys derived from the fitted spectra.We would like to thank Dr. P. Duhaj for the preparation of amorphous samples.