Evolution equations for the probabilistic generalization of the Voigt profile function

The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral representation, the Voigt profile can be interpreted as the probability density function of the sum of two independent random variables with Gaussian density (due to the Doppler effect) and Lorentzian density (due to the pressure effect). Since these densities belong to the class of symmetric Lévy stable distributions, a probabilistic generalization is proposed as the convolution of two arbitrary symmetric Lévy densities. We study the case when the widths of the distributions considered depend on a scale factor τ that is representative of spatial inhomogeneity or temporal non-stationarity. The evolution equations for this probabilistic generalization of the Voigt function are here introduced and interpreted as generalized diffusion equations containing two Riesz space-fractional derivatives, thus classified as space-fractional diffusion equations of double order.     

On the scalar-wave propagation in a random elastic layer

Summary We have analysed the response of a random elastic layer to scalar waves incident from a homogeneous medium. Working up to second order in the stochastic fluctuations, we have proposed a rational approximation for the computation of the reflection and amplification coefficients. After successfully checking the method by a numerical simulation, we have considered a problem of interest in earthquake engineering.     

Energy propagation for dispersive waves in dissipative media

University of Bologna, Italy. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 7, pp. 650–664, July, 1993.     

High-performance liquid chromatographic determination of iothalamic acid in human plasma and urine.

A simple, rapid and sensitive method for the determination of iothalamic acid (IA) in both plasma and urine is reported. After extraction with ethyl acetate, IA was determined by strong anion-exchange high-performance liquid chromatography with ultraviolet detection at 254 nm. The lower limit of detection was 0.5 micrograms/ml. The average recovery was 73 and 57% from plasma and urine, respectively. Linearity was found over the investigated concentration range (up to 500 micrograms/ml for plasma and up to 10.0 mg/ml for urine). The reproducibility of the technique was good (coefficient of variation less than 6%) as was the precision and accuracy (coefficient of variation less than 2.5%). No interference from endogenous substances or any of the common drugs tested was found.     

Pressure pulses in fluid filled distensible tubes

Summary By comparing experimental records with model solutions we are led to propose a dispersion relation governing the propagation of pressure pulses in fluid filled distensible tubes. This relation contains a single undetermined parameter having the dimension of time. We show how this parameter may be interpreted and obtain an estimate of its value. Some comments concerning the speed of propagation of pressure waves in the haemodynamics contest are made.

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Sommario Si considera la propagazione di onde di pressione in tubi distensibili riempiti di fluido. Dal confronto delle registrazioni sperimentali con le soluzioni teoriche si propone una semplice relazione di dispersione che contiene un singolo parametro indeterminato avente le dimensioni di un tempo. Si mostra come interpretare tale parametro e come stimare il suo valore. Si conclude con alcune considerazioni sulla velocità di propagazione delle onde di pressione nell'ambito emodinamico.

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This work has been realized within a bilateral project supported by the Italian Research Council (CNR) and the Natural Scinces and Engineering Research Council of Canada (NSERC).     

The fundamental solutions for the fractional diffusion-wave equation

The time fractional diffusion-wave equation is obtained from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative of order 2β with 0 < β ≤ 1/2 or 1/2 < β ≤ 1, respectively. Using the method of the Laplace transform, it is shown that the fundamental solutions of the basic Cauchy and Signalling problems can be expressed in terms of an auxiliary function M(z;β), where z = |x|/t^β is the similarity variable. Such function is proved to be an entire function of Wright type.     

On the viscoelastic characterization of the Jeffreys–Lomnitz law of creep

In 1958, Jeffreys (Geophys J?R Astron Soc 1:92–95) proposed a power law of creep, generalizing the logarithmic law earlier introduced by Lomnitz, to broaden the geophysical applications to fluid-like materials including igneous rocks. This generalized law, however, can be applied also to solid-like viscoelastic materials. We revisit the Jeffreys–Lomnitz law of creep by allowing its power law exponent α, usually limited to the range 0?≤?α?≤?1 to all negative values. This is consistent with the linear theory of viscoelasticity because the creep function still remains a Bernstein function, that is positive with a completely monotone derivative, with a related spectrum of retardation times. The complete range α?≤?1 yields a continuous transition from a Hooke elastic solid with no creep $\left(\alpha \,\to\, -\infty\right)$ to a Maxwell fluid with linear creep $\left(\alpha \,=\,1\right)$ passing through the Lomnitz viscoelastic body with logarithmic creep $\left(\alpha\, =0\right)$ , which separates solid-like from fluid-like behaviors. Furthermore, we numerically compute the relaxation modulus and provide the analytical expression of the spectrum of retardation times corresponding to the Jeffreys–Lomnitz creep law extended to all α?≤?1.     

On the evolution of fractional diffusive waves

Ricerche di Matematica - In physics, phenomena of diffusion and wave propagation have great relevance; these physical processes are governed in the simplest cases by partial differential equations...     

Fractional models of anomalous relaxation based on the Kilbas and Saigo function

We revisit the Kilbas and Saigo functions of the Mittag-Leffler type of a real variable \(t\) , with two independent real order-parameters. These functions, subjected to the requirement to be completely monotone for \(t>0\) , can provide suitable models for the responses and for the corresponding spectral distributions in anomalous (non–Debye) relaxation processes, found e.g. in dielectrics. Our analysis includes as particular cases the classical models referred to as Cole–Cole (the one-parameter Mittag-Leffler function) and to as Kohlrausch (the stretched exponential function). After some remarks on the Kilbas and Saigo functions, we discuss a class of fractional differential equations of order \(\alpha \in (0,1]\) with a characteristic coefficient varying in time according to a power law of exponent \(\beta \) , whose solutions will be presented in terms of these functions. We show 2D plots of the solutions and, for a few of them, the corresponding spectral distributions, keeping fixed one of the two order-parameters. The numerical results confirm the complete monotonicity of the solutions via the non-negativity of the spectral distributions, provided that the parameters satisfy the additional condition \(0<\alpha +\beta \le 1\) , assumed by us.     

The use of liquid scintillation spectrometry as a very sensitive radioanalytical tool for the determination of alpha,beta and monochromatic electron emitting impurities in radiopharmaceutical compounds

Summary Many labeled compounds are used as radiopharmaceuticals (RP), for emission imaging and metabolic radiotherapy and contain as labeling agents γ, β^-, β⁺, monochromatic e^- and α emitting radionuclides (RN). These labeled compounds very often contain unexpected radionuclidic impurities. Some long-lived isotopic and non-isotopic impurities lead to undesirable radiation doses to the patient and his relatives, as well as to medical/paramedical personnel, other than the general population, due to rad-waste of contaminated specimen and excretion of biological fluids. Use was made of liquid scintillation counting/spectrometry (LSCS) for the detection of tiny amounts of charged particle emitting impurities in RPs labeled with ⁶⁴Cu, ⁶⁷Ga, ⁹⁰Y, ⁹⁰Sr/⁹⁰Y, ¹²³I, ¹⁵³Sm, ¹⁷⁷Lu and ²⁰¹Tl.