An experimental study of the expansion process of the vapour cloud in open atomizers

Using an oscilloscope the absorbance above a filament atomizer has been measured as a function of the position of the optical axis with respect to the sample position. For the elements investigated (Cd, Pb and Ag) an asymmetrical distribution of the atoms has been found. The vertical velocity of the sample cloud border was constant for each element and twice the horizontal velocity. The experiments have shown that the extension in an open atomizer at atmospheric pressure cannot be described by a pure diffusion process.     

Plasma confinement by a magnetic shell configuration

The confinement properties of a new magnetic shell configuration have been investigated experimentally. The diffusion coefficient D has been determined.     

No pre-critical enhancement observed in 13C(π+, γ)13N(g.s.) at q ≅ 2mπ

The cross section and angular distribution for the reaction ¹³C(π⁺, γ)¹³N(g.s.) have been measured from 37 to 85° in the laboratory, at a pion energy of 115.5 MeV. The observed cross section ranges from 320 to 660 $\text{nb}\text{sr}$. These results do not show the large magnitude and wide-angle peaking expected if pre-critical effects due to nascent pion condensation were present. In addition, the observed cross section is less than one-half of the predictions of available theoretical calculations which do not include the pre-critical effect. Data on the reaction ¹H(π^?, γ)n at T_π = 116.6 MeV were also obtained for calibration purposes. These data agree with expectations based on knowledge of the inverse reaction and previous measurements.     

Precise half-life measurements for 38Ca and 39Ca

The half-lives of ³⁸Ca and ³⁹Ca have been measured at ISOLDE of CERN. The REXTRAP facility was used to prepare ultra-clean samples of radioactive nuclei for precision decay spectroscopy. ³⁸Ca is one of the T _z = - 1 , 0⁺ $ \rightarrow$ 0⁺ $ \beta$ -emitting nuclides used to determine the vector coupling constant of the weak interaction and the V_ud quark-mixing matrix element. The result obtained, T _1/2 = 443.8(19) ms, is four times more precise than the average of previous measurements. For ³⁹Ca , a half-life of T _1/2 = 860.7(10) ms is obtained, a result in agreement with the average value from the literature.     

Spectroscopic studies of trimetoxypropylsilane and bis(trimethoxysilyl)ethane sol-gel coatings on aluminum and copper

Trimethoxypropylsilane (TMPS) and bis(trimethoxysilyl)ethane (BTMSE) were used as surface modifiers of metal vie the sol-gel process and dip coating. In addition to the single coating of Al, Cu and Sn, double treatments of Al were also conducted by combining coatings with these sol-gels in different sequences. Reflection and absorption infrared spectroscopy (RAIR) was employed to characterize and to trace the proceeding of the sol-gel process of the films. It was found that the silanol condensation occurs in the coating films on Al and the covalent linkage exists between the TMPS film and copper surface. From the assigned vibration modes, two conformers were identified in pure TMPS, TMPS sol-gel and coated film. A series of dip coating experiments with different concentrations of TMPS sol-gel was conducted, and the results from the collected RAIR spectra of the coated samples suggested that the coated Cu consistently has a better RAIR spectrum than that of the coated Al. The TMPS sol-gel appeared to have a better affinity to Cu than to Al. The temperature effect and the aging effect in the coating films were studied. X-ray photoelectronic spectroscopy (XPS) was employed to characterize the coated film, and the XPS data confirm the formation of the siloxane film from the silane coupling agents (SCA). Electrochemical impedance spectra (EIS) have been collected for bare Al and Cu, BTMSE sol-gel coated Al, and TMPS sol-gel coated Cu in 0.15M NaCl solution. The corresponding electronic circuit parameters have been determined to match the experimental EIS data.     

Synthesis and spectroscopic observation of dendrimer-encapsulated gold nanoclusters

We report on the observation of the excitation/emission spectrum of a dendrimer-encapsulated gold nanocluster; the synthesis of Au-PAMAM was based on reduction of HAuCl4 x 3 H2O co-dissolved in methanol together with fourth-generation OH-terminated PAMAM.     

Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators

We give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on Hilbert spaces, which is subject to a Lipschitz continuous perturbation depending on the state. These sets are not necessarily weakly closed as in [3], [4], while the invariance criteria are still written by using only the data of the system. So, no need to the explicit knowledge of neither the solution of this differential inclusion, nor the semi-group generated by the maximal monotone operator. These invariant/viability results are next applied to derive explicit criteria for a-Lyapunov pairs of lower semi-continuous (not necessarily weakly-lsc) functions associated to these differential inclusions. The lack of differentiability of the candidate Lyapunov functions and the consideration of general invariant sets (possibly not convex or smooth) are carried out by using techniques from nonsmooth analysis.     

Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients

It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada–Watanabe theorem (Yamada and Watanabe, 1971, [31,32]) and the Feller test for explosions (Feller, 1951, 1954), there exists a unique stationary distribution with respect to the Markov semigroup of transition probabilities. We consider systems on a restricted domain $D$ of the phase space $\mathbb{R}$ and study the rate of convergence to the stationary distribution. Using a geometrical approach that uses the so called free energy function on the density function space, we prove that the density functions, which are solutions of the Fokker–Planck equation, converge to the stationary density function exponentially under the Kullback–Leibler divergence, thus also in the total variation norm. The results show that there is a relation between the Bakry–Émery curvature dimension condition and the dissipativity condition of the transformed system under the Fisher–Lamperti transformation. Several applications are discussed, including the Cox–Ingersoll–Ross model and the Ait-Sahalia model in finance and the Wright–Fisher model in population genetics.     

On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L² and H^τ norms is considered and illustrated by numerical example.