Mathematical Analysis of a Cauchy Problem for the Time-Fractional Diffusion-Wave Equation with $$ \alpha \in \left( 0,2\right) $$

This paper deals with a theoretical mathematical analysis of a Cauchy problem for the time-fractional diffusion-wave equation in the upper half-plane, \(x\in \mathbb {R}\), \(t\in \mathbb {R}^+\), where the Caputo fractional derivative of order \(\alpha \in \left( 0,2\right) \) is considered. An explicit solution to this Cauchy problem is obtained via separation of variables. A first proof of the validity of the obtained results is provided for a certain kind of initial conditions. Throughout this work a new expression of the solution to this problem and its utility for carrying out rigurous proofs are presented. Finally, several new properties of the solution are obtained.     

Extreme fluctuation events in a simple high-density traffic model

We revisit a simple car-following model adapting it for simulating high-density traffic dynamics. Simulations in continuum space and discrete time are presented for the case of a single traffic lane, using periodic boundary conditions. The model parameters are fitted to empirical data for the mean car speed versus car density for densities higher than . The time evolution of the car ensemble is studied upon application of different types of random perturbations yielding strong speed fluctuations in all cases, the latter characterized by probability distribution functions displaying fat tails. We attempt to study the phenomenon of stop-and-go along the lane in the absence of perturbations by assuming a stopping cutoff speed, and find the resulting behavior of the ensemble both in space and time.     

Measurement of the exclusive 3He(e,e'p) reaction below the quasielastic peak

New, high-precision measurements of the 3He(e,e(')p) reaction using the A1 Collaboration spectrometers at the Mainz microtron MAMI are presented. These were performed in antiparallel kinematics at energy transfers below the quasielastic peak, and at a central momentum transfer of 685 MeV/c. Cross sections and distorted momentum distributions were extracted and compared to theoretical predictions and existing data. The longitudinal and transverse behavior of the cross section was also studied. Sizable differences in the cross-section behavior from theoretical predictions based on the plane wave impulse approximation were observed in both the two- and three-body breakup channels. Full Faddeev-type calculations account for some of the observed excess cross-section, but significant differences remain.     

A liquid chromatography tandem mass spectrometry method for simultaneous analysis of 46 atmospheric particulate-phase persistent organic pollutants and comparison with gas chromatography/mass spectrometry

A novel multi-analyte method for the simultaneous determination of 46 compounds of environmental concern, most of them belonging to the category of persistent organic pollutants, was developed using high-performance liquid chromatography and the results were compared to those obtained by gas chromatography. This study was performed in perspective of a cumulative exposure assessment of substances of health concern in environments where high levels, relatively to airborne particulate matter, can be found. The target compounds included polychlorinated biphenyls, brominated flame–retardants and derivatives of polycyclic aromatic hydrocarbons.

The multi-analyte method was evaluated in air particulate matter in terms of reproducibility, linearity, recovery, limits of detection and quantification and matrix effect. The recovery was above 70% for all the analytes, whereas limits of quantification ranged between 23 and 390 pg?m^?3 in liquid chromatography and less than ten times in gas chromatography–mass spectrometry.

Matrix effect was generally negligible for both the techniques, except the case of the detection of oxygenated derivatives of polycyclic aromatic hydrocarbons by gas chromatography.

In order to demonstrate the efficacy and to assess the method performances (accuracy and precision), both the techniques were applied to standard reference materials, and the results were compared, discussing their advantages and disadvantages.

The method was finally applied to a real sample of indoor airborne particulate matter with aerodynamic diameter ≤4 μm (PM₄).

We demonstrated that liquid chromatography was the only technique able to analyse the 46 compounds, including thermally degradable ones, with a single chromatographic run without derivatisation steps. On the other hand, gas chromatography still presents higher sensitivity for the detection of some of the investigated compounds. This study can be considered only explorative and further improvements can be expected with new-generation LC-MS instruments (10–100 times more sensitive).     

A simple model to explain the complex kinetic behavior of epoxy/anhydride systems

A survey of the literature dealing with the kinetics of epoxy/anhydride polymerizations initiated by tertiary amines, shows inconsistencies in results reported by several authors. Both first-order and autocatalytic expressions have been used to fit experimental results. In the former case, significantly different values of apparent activation energies were found in isothermal and nonisothermal experiments. A simple kinetic model is proposed to explain these inconsistencies, based on the following steps: (a) a reversible reaction transforming an inactive initiator species into an active one, (b) a propagation step, and (c) a chain transfer step regenerating the active initiator (step not relevant to the kinetic analysis). The simple model explains both the first-order and autocatalytic behaviors reported in the literature. It also leads to the experimental values of the apparent activation energies obtained under different conditions. It is also shown that isoconversional methods should not be applied to obtain fundamental kinetic parameters in systems where the reaction rate depends on the concentration of an active species that varies independently of the conversion of functional groups. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2799–2805, 1999     

Phase separation induced by a chain polymerization: Polysulfone-modified epoxy/anhydride systems

The reaction-induced phase separation in a blend of a commercial polysulfone (PSu) with diepoxide-cyclic anhydride monomers, was studied. The diepoxide was based on diglycidylether of bisphenol A (DGEBA) and the hardener was methyl tetrahydrophthalic anhydride (MTHPA), used in stoichiometric proportion. Benzyldimethylamine (BDMA) was used as initiator. PSu had no influence on the polymerization kinetics, the gel conversion, and the overall heat of reaction per epoxy equivalent. A kinetic model including initiation, propagation, and termination steps was used to estimate the distribution of linear and branched species in the first stages of the chain-wise copolymerization. This distribution, together with the PSu distribution, were taken into account in a thermodynamic model of the blend. The interaction parameter was fitted from experimental determinations of conversions at the start of phase separation, obtained under different conditions. The thermodynamic model was used to explain the complex morphologies developed in materials containing different PSu concentrations as well as their dynamic mechanical response. The shift in glass transition temperatures was explained by the fractionation of different species during the phase separation process. Phase inversion produced a significant decrease of the elastic modulus in the glassy state and a thermoplastic-like behavior of the material in the rubbery region. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1349–1359, 1998     

Thermodynamic analysis of the phase separation in polyetherimide-modified epoxies

The miscibility of polyetherimides (PEIs) with epoxy monomers based on diglycidylether of bisphenol-A (DGEBA), and with reactive mixtures based on stoichiometric amounts of DGEBA and an aromatic diamine (DA) {either 4,4′-diaminodiphenylsulfone (DDS) or 4,4′-methylenebis[3-chloro 2,6-diethylaniline] (MCDEA)}; was experimentally studied. Cloud-point curves (temperature vs. composition) are reported for PEI-DGEBA and PEI-DGEBA-DA initial mixtures. Cloud-point conversions are reported for the reactive mixtures, for various PEI amounts and polycondensation temperatures. A thermodynamic model based on the Flory-Huggins-Staverman approach, taking polydispersity of both components into account, was used to analyze the experimental information. A single relationship between the interaction parameter and temperature, χ(T), could fit experimental results of mixtures of two commercial PEIs with DGEBA. The addition of DDS led to a decrease in miscibility whereas MCDEA improved the initial miscibility. In both cases, the interaction parameter decreased with conversion, meaning that PEI was more compatible with oligomeric species than with the mixture of starting monomers. The phase separation process in initially miscible rubber- or thermoplastic-modified thermosetting polymers is the result of two factors: increase in the average molar size of the thermosetting oligomer (main driving force favoring demixing), and variation of the interaction parameter with conversion, which may act to increase or decrease the cloud-point conversion determined by the first factor. © 1996 John Wiley & Sons, Inc.     

Analysis of tetrahydrocannabinol derivative from cannabis‐infused chocolate by QuEChERS‐thin layer chromatography‐desorption electrospray ionization mass spectrometry

Recently in Canada and some states of the United States, marijuana (cannabis) has become fully legalized and regulated, for both medical and recreational purposes. This fact is going to make cannabis products such as edibles even more popular than ever before. Therefore, it is assumed that there will be a high demand for analytical methods, which are accurate and sensitive enough to be used in different forensic and pharmaceutical cannabis–related applications. Cannabis derivatives have an extreme range and number of constituents with possible interactions with one another. Thus, this characteristic leads to their vast and highly complex chemistry, which requires robust analytical tools to be able to precisely and accurately quantify and qualify them. We developed and validated an analytical method using desorption electrospray ionization (DESI)–mass spectrometry (MS) to accurately detect, characterize, and quantify cannabinoids and also offer an easy, cost‐effective, and reliable technique, which can be performed in a short time for infused edibles in complex matrices such as chocolate. We evaluated a quantitative analysis of tetrahydrocannabinol (THC) in cannabis‐infused chocolate with thin‐layer chromatography (TLC)–DESI‐MS and QuEChERS extraction method. Both techniques of TLC and QuEChERS are cost‐effective and can be run in short time.