Positive exponential sum method of inverting Laplace transform applied to photon correlation spectroscopy

A computer program for the positive exponential sum method of inverting Laplace transform of photon autocorrelation curves has been written and applied to both simulated and experimental data. The method recovers the decay time spectra from autocorrelation curves by replacing the decay time distribution by a set of delta peaks whose envelope roughly follows this distribution. Spacing of this set becomes slightly denser with decreasing noise and is about two peaks per decade under usual conditions (noise level about 10^–3). Occasional irregularities in peak spacing and an appearance of weak artifact peaks in regions where the decay time spectrum is of zero density may make the physical interpretation of results difficult.     

Testing of the constrained regularization method of inverting Laplace transform on simulated very wide quasielastic light scattering autocorrelation functions

Provencher's constrained regularization method of inverting the Laplace transform was tested on 7 decades wide simulated quasielastic light scattering (QELS) data. The standard method with integration and logarithmic grid was shown to undersmooth seriously theG(Γ) distribution in the region of largeΓ (small relaxation timeτ). The regularization can be considerably improved by switching the integration off. Then, smooth distributions of relaxation timeτ of the generalized exponential type are reproduced essentially correctly with a tendency to replace asymmetric peaks by more symmetric ones with shoulders (in the Gaussian distribution ofτ) or side peaks (in the Gaussian distribution of 1/τ) on the slow decrease sides. In distributions with singularities such as edges of histogram bins or delta functions, the coarse shape of the distribution is recovered essentially correctly, but smoothing of singularities causes a distortion of wide regions of the relaxation spectrum usually in the form of sinusoidal waves. The bias introduced by taking the square root of theg ₂ function was shown to worsen sometimes the CONTIN results considerably. Thus, the use of Provencher's CONTIN program with logarithmic grid and integration switched off is recommended for the analysis of very wide QELS autocorrelation curves.     

On QCD sum rules of the Laplace transform type and light quark masses

We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in QCD. Two specific examples corresponding to the ?-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwyler's formula for the current algebra quark masses is also given.     

Kinoform optics applied to X‐ray photon correlation spectroscopy

Moderate‐demagnification higher‐order silicon kinoform focusing lenses have been fabricated to facilitate small‐angle X‐ray photon correlation spectroscopy (XPCS) experiments. The geometric properties of such lenses, their focusing performance and their applicability for XPCS measurements are described. It is concluded that one‐dimensional vertical X‐ray focusing via silicon kinoform lenses significantly increases the usable coherent flux from third‐generation storage‐ring light sources for small‐angle XPCS experiments.     

On the Laplace transform of the Weinberg type sum rules and on the properties of pseudoscalar mesons

We reanalyse the Weinberg type sum rules in the light of the Laplace transform sum rule and including the leading non-perturbative effects. We then estimate the light quark invariant masses \(\hat m_s /\hat m_d ,\hat m_u \hat m_d \) ; the pion decay amplitudef _π and theA ₁ coupling and mass. Using other type of sum rules, we derive bounds on the pseudoscalar decay amplitudesf _p (P≡π, K, D, F) as well as on the gluon component of theU(1) _A meson mass. Our main results are summarized in Sect. 4.     

Sum peak method applied to the study of decay of Ir-192

The electron capture probabilities to 690.70 and 580.37 keV levels and theK-conversion coefficients of 205.9 and 316.5 keV transitions in the decay of Ir-192 have been determined from the measurement of gamma-ray intensities in conjunction with an analysis of theKX-ray-γ-ray sum peaks observed with a co-axial HPGe detector. TheK-capture probability to 690.70 keV level was determined by an approach which is independent ofK-shell fluorescence yield and absolute detection efficiency forKX-rays. TheK-shell fluorescence yields of the daughter products, namely, Os and Pt of Ir-192 have also been determined by the same technique and were found to be 0.964±0.077 and 0.969±0.068 respectively.     

Off-angle correlation spectroscopy applied to spin-1/2 and quadrupolar nuclei

A two-dimensional correlation experiment is described, in which homonuclear dipolar couplings are used to realize through-space magnetization exchange on spin-1/2 (³¹P) and on quadrupolar nuclei (²³Na and ¹¹B). In the detection period, Magic Angle Spinning is applied to enhance resolution, and the dipole couplings are re-introduced in the mixing period by spinning off the Magic Angle. The dependency of the exchange rates on the mixing time and the spinning angle is investigated. The influence of strong spin-locking during mixing is discussed, and shown in the spin-1/2 case to remove the dependence on chemical shift offset effects. For quadrupolar spins, the experiment yields information on the relative tensor orientations of the coupled quadrupoles. Applications to crystalline sodium aluminum diphosphate, sodium sulphite, and potassium borate glasses are shown.     

A weighting window applied to the digital image correlation method

In the digital image correlation method, two steps are used to calculate the displacements of tested images. The first step is to locate the integer-pixel displacement, and the next one is to compute the sub-pixel displacement based on the first step. The benefit from the computation method for the integer-pixel displacement is that its results directly affect the displacement accuracy of each point in tested images. In this paper, a new method is developed to calculate the displacement fields between two images taken before and after deformation of an object. A new correlation function with a weighting factor related to the position of each point in the image is taken into account. The analysis and experimental results confirm the validity of the new method. In addition, the calculation results from our method have more accuracy than that of the traditional one.     

Application of the derivative transform method in reflectance spectroscopy

The possibility of using the derivative transform method in reflectance spectroscopy is analyzed. It is shown that the first derivative of the external-reflectance spectrum obtained under near normal-incidence conditions allows straightforward determination of the position of the absorption-band maximum for low-intensity bands.     

Theoretical investigation on resonance characteristics of a vapor bubble based on Laplace transform method

In the present paper, resonance characteristics of the vapor bubble oscillating in an acoustic field are investigated analytically. The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius during the transient process in the initial oscillation stage is explicitly obtained and physically analyzed at the resonance situation based on the Laplace transform method. And the typical oscillation behaviors obtained from the analytical solution are thoroughly exhibited and analyzed in the time and frequency domains. In addition, the corresponding oscillation behaviors at the non-resonance situation are also investigated for the purpose of comparisons. Through our investigation, several essential conclusions can be drawn as follows: (1) The analytical solution of the non-dimensional perturbation of the instantaneous bubble radius can be divided into four terms according to the physical meaning. Among them, it is the term related to the acoustic field that causes the progressively violent bubble oscillation. (2) The vapor bubble with a smaller equilibrium radius could respond faster and more significantly to the acoustic field during the oscillation. (3) The bubble oscillation characteristics always exhibit significant differences at the resonance and non-resonance situations in both the time and frequency domains, even if the difference between the natural frequency of the oscillating vapor bubble and the angular frequency of the acoustic field is greatly small.     

New method for solving fractional partial integro-differential equations by combination of Laplace transform and resolvent kernel method

In this article, we obtained the approximate solution for a new class of Time-Fractional Partial Integro-Differential Equation (TFPIDE) of the Caputo-Volterra type in which the integral is not limited to the convolution type. This new class of TFPIDE is distinct from the common problem with the convolution integral kernel. The general expression of the analytical solution for this special type of TFPIDE was derived using a combination of Laplace transform and the resolvent kernel method. In the process, Laplace transform will transform the equation into a second kind Volterra integral equation in terms of the transformed function. Two main problems in deriving the approximate analytical solutions were identified as Case I and Case II problems. To obtain the approximate solutions for Case I and Case II problems, numerical methods were designed based on approximation of the resolvent kernel with truncated Neumann series as well as approximation of the Laplace transform based on truncated Taylor series. Several numerical examples are presented to indicate the plausibility, mechanism and performance of the proposed methods.     

Lowest order constrained variational method applied to liquid $^\mathsf{3}$He

The energy of normal liquid ³He is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of the cluster expansion series, the three-body cluster energy is calculated, with the LOCV correlation functions, and by imposing the normalization constraint on the two-body distribution function which includes three-body cluster correlations (LOCVE). It is shown that the normalization constraint plays an important role in keeping the higher cluster terms small. The resulting LOCVE calculation for the ground state energy of liquid ³He is compared with the available experimental data and the prediction from different theoretical techniques.Received: 26 May 2003, Published online: 30 January 2004PACS: 61.20.Gy Theory and models of liquid structure - 61.20.Ne Structure of simple liquids - 67.55.-s Normal phase of liquid ³He     

基于小波变换的新型数字散斑相关方法

通过将小波分析的方法应用到传统的空域相关计算中,提出了基于小波变换的数字散斑相关方法。详细介绍了该方法的原理,并对传统空域相关方法与小波相关方法进行了实验计算比较。实验结果表明,与传统的空域相关方法相比,基于小波变换的数字散斑相关方法大大提高了相关计算的精度,精度由0 05像素提高到了0 01像素以下。最后利用该方法测量了编织结构复合材料板在三点弯曲载荷作用下的位移场。     

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.     

The hyperspherical harmonics method applied to 12C

We apply the hyperspherical harmonics method to the low-lying T = 0 states in ¹²C, using the 3-α model. With the results from ref. ¹) we are able to investigate all states up to the 4⁺ level at 14.1 MeV, except for the broken symmetry 1⁺ state at 12.7 MeV. Antisymmetrization effects are included by adopting the local potential approximation²). Energy levels and electron scattering form factors are calculated.     

利用特殊函数和类比法有序化排列正负指数幂算符

研究算符函数的有序化排列是一项重要的数理任务.本文利用特殊函数和正规乘积排序与反正规乘积排序间的互换法则法导出了幂算符(aa+)±n和(a+a)±n的正规与反正规乘积排序.进一步,利用类比法得到了算符(XP)±n和(PX)±n的坐标-动量排序与动量-坐标排序式.最后,对新得到的这些算符结果的应用进行一些讨论.     

Laplace transform approach for the dynamics of N qubits coupled to a resonator

An approach to use the method of Laplace transform for the perturbative solution of the Schrödinger equation at any order of the perturbation for a system of N qubits coupled to a cavity with n photons is suggested. We investigate the dynamics of a system of N superconducting qubits coupled to a common resonator with time-dependent coupling. To account for the contribution of the dynamical Lamb effect to the probability of excitation of the qubit, we consider counter-rotating terms in the qubit-photon interaction Hamiltonian. As an example, we illustrate the method for the case of two qubits coupled to a common cavity. The perturbative solutions for the probability of excitation of the qubit show excellent agreement with the numerical calculations.     

Laser spectroscopy applied to the study of hyperfine interactions

The impact of laser-spectroscopy techniques on the study of hyperfine interactions is illustrated by chosen examples. A brief survey of the theory of hyperfine interactions is given as well as an overview of the available experimental techniques. Results from alkali atoms, alkaline-earth elements and Group III atoms are given with special emphasis on the studies of electronic properties in sequences of Rydberg states and the investigation of nuclear properties for long chains of isotopes of the same element. Recent developments on the theoretical side, particularly what regards the many-body perturbation approach, are also discussed.