Determination of Bi in complex oxide samples by atomic absorption spectrometry by using ordinary acetylene – air flame atomization

In the present work the air/acetylene flame atomic absorption spectrometry was used for bismuth determination in complex oxides. Interference studies were carried out, and interference with vanadium and molybdenum was detected. The method of standard additions and traditional calibration curve method were used. Calibration and standard addition curves were fitted with linear and polynomial functions. It was shown that using polynomial function gives better results for the standard additions method for determination of bismuth by acetylene/air flame atomic absorption spectrometry. The calibration curve method was shown to be correct at low ( 10mg/L) concentration of an interferent

Energy localization in carbon nanotubes

In this paper, the energy localization phenomena in low-frequency nonlinear oscillations of single-walled carbon nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied in the framework of the Sanders-Koiter shell theory. Simply supported and free boundary conditions are considered. The effect of the aspect ratio on the analytical and numerical values of the localization threshold is investigated in nonlinear field

Nonlinear vibrations and energy distribution of carbon nanotubes

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. Free boundary conditions are considered. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on the Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations. The total energy distribution of the shell is studied by considering combinations of different vibration modes. The effect of the conjugate modes participation is analysed

Eigenfrequencies and vibration modes of carbon nanotubes

In 1991 Iijima discovered Carbon Nanotubes, he synthesised molecular carbon structures in the form of fullerenes and then reported the preparation of a new type of finite carbon structure consisting of needle-like tubes, the carbon nanotubes, described as helical microtubules of graphitic carbon. Examples of applications of Carbon Nanotubes (CNTs) can be found in ultrahigh frequency nanomechanical resonators, in a large number of nanoelectromechanical devices such as sensors, oscillators, charge detectors and field emission devices. The reduction of the size and the increment of the stiffness of a resonator magnify its resonant frequencies and reduce its energy consumption, improving its sensitivity. The modal analysis of carbon nanotubes is important because it allows to obtain the resonant frequencies and mode shapes, which influence the mechanical and electronic properties of the nanotube resonators. A large number of experiments and atomistic simulations were conducted both on single-walled (SWNTs) and multi-walled carbon nanotubes (MWNTs). The present work is concerned with the analysis of low-frequency linear vibrations of SWNTs: two approaches are presented: a fully analytical method based on a simplified theory and a semi-analytical method based on the theory of thin walled shells. The semi-analytical approach (shortly called “numerical approach”) is based on the Sanders-Koiter shell theory and the Rayleigh-Ritz numerical procedure. The nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields, which are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. The Rayleigh-Ritz method is then applied to obtain numerically approximate natural frequencies and mode shapes. The second approach is based on a reduced version of the Sanders-Koiter shell theory, obtained by assuming small ring and tangential shear deformations. These assumptions allow to condense both the longitudinal and the circumferential displacement fields. A fourth-order partial differential equation for the radial displacement field is derived. Eigenfunctions are formally obtained analytically, then the numerical solution of the dispersion equation gives the natural frequencies and the corresponding normal modes. The methods are fully validated by comparing the natural frequencies of the SWNTs with data available in literature, namely: experiments, molecular dynamics simulations and finite element analyses. A comparison between the results of the numerical and analytical approach is carried out in order to check the accuracy of the last one. It is worthwhile to stress that the analytical model allows to obtain results with very low computational effort. On the other hand the numerical approach is able to handle the most realistic boundary conditions of SWNTs (free-free, clamped-free) with extreme accuracy. Both methods are suitable for a forthcoming extension to multi-walled nanotubes and nonlinear vibrations

Off-Critical SLE(2) and SLE(4): a Field Theory Approach

Using their relationship with the free boson and the free symplectic fermion, we study the off-critical perturbation of SLE(4) and SLE(2) obtained by adding a mass term to the action. We compute the off-critical statistics of the source in the Loewner equation describing the two dimensional interfaces. In these two cases we show that ratios of massive by massless partition functions, expressible as ratios of regularised determinants of massive and massless Laplacians, are (local) martingales for the massless interfaces. The off-critical drifts in the stochastic source of the Loewner equation are proportional to the logarithmic derivative of these ratios. We also show that massive correlation functions are (local) martingales for the massive interfaces. In the case of massive SLE(4), we use this property to prove a factorisation of the free boson measure.Comment: 30 pages, 1 figures, Published versio

LERW as an example of off-critical SLEs

Two dimensional loop erased random walk (LERW) is a random curve, whose continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter kappa=2. In this article we study ``off-critical loop erased random walks'', loop erasures of random walks penalized by their number of steps. On one hand we are able to identify counterparts for some LERW observables in terms of symplectic fermions (c=-2), thus making further steps towards a field theoretic description of LERWs. On the other hand, we show that it is possible to understand the Loewner driving function of the continuum limit of off-critical LERWs, thus providing an example of application of SLE-like techniques to models near their critical point. Such a description is bound to be quite complicated because outside the critical point one has a finite correlation length and therefore no conformal invariance. However, the example here shows the question need not be intractable. We will present the results with emphasis on general features that can be expected to be true in other off-critical models.Comment: 45 pages, 2 figure

Anatomy of the terminal branches of the superior rectal artery during selective doppler controlled dearterialization of the hemorrhoidal nodes (HAL-RAR)

Background: To date, there is no single standard for conducting HAL-RAR operations. The constant discussion raises the question of the number of terminal branches of the superior rectal artery, which must be ligated in the submucosal layer of the rectum in order to provide the adequate dearterialization of hemorrhoids. Aim: To study the anatomy of the branches of the superior rectal artery and to develop recommendations for the optimal ligation of the terminal branches of the superior rectal artery. Methods: 150 protocols of the previous operations have been studied. In order to further objectify our results, the results of radiation diagnostics (CT and MRI) were revised for 100 patients without pathological changes of the rectum and anal canal to study the variant anatomy of the superior rectal artery and its terminal branches in the rectal wall. Results: In 148 patients, 6 terminal branches were identified, in 2 (1.333%) patients, 5 branches were found. 100 cases without pathological changes were also analyzed (60 MRI and 40 CT scans). In all the cases, 6 terminal branches of the superior rectal artery were determined, located at 1, 3, 5, 7, 9 and 11 o'clock positions of the conventional dial. At the same time, a large number of identified anatomical options for the branching of the VPA and the method for reaching the rectal wall should be noted, which we used as a basis to propose a classification. Conclusion: In the vast majority of cases, there are 6 terminal branches of the superior rectal artery, located in the lower ampulla of the rectum at approximately 1, 3, 5, 7, 9 and 11 hours of the conventional dial. A number of variants of the vascular anatomy of the proximal branches are possible, but 6 distal branches are involved in the direct blood supply of the hemorrhoids. When performing selective Doppler-controlled dearterialization of hemorrhoids, it is expedient to ligate 6 arterial vessels

Top quark mass measurement using the template method at CDF

We present a measurement of the top quark mass in the lepton+jets and dilepton channels of $t\bar{t}$ decays using the template method. The data sample corresponds to an integrated luminosity of 5.6 fb$^{-1}$ of $p\bar{p}$ collisions at Tevatron with $\sqrt{s}=1.96$ TeV, collected with the CDF II detector. The measurement is performed by constructing templates of three kinematic variables in the lepton+jets and two kinematic variables in the dilepton channel. The variables are two reconstructed top quark masses from different jets-to-quarks combinations and the invariant mass of two jets from the $W$ decay in the lepton+jets channel, and a reconstructed top quark mass and $m_{T2}$, a variable related to the transverse mass in events with two missing particles, in the dilepton channel. The simultaneous fit of the templates from signal and background events in the lepton+jets and dilepton channels to the data yields a measured top quark mass of $M_{top} = 172.1 \pm 1.1(stat) \pm 0.9(syst).$Comment: submitted to Phys. Rev.

Evidence for the exclusive decay Bc+- to J/psi pi+- and measurement of the mass of the Bc meson

We report first evidence for a fully reconstructed decay mode of the B_c^{\pm} meson in the channel B_c^{\pm} \to J/psi \pi^{\pm}, with J/psi \to mu^+mu^-. The analysis is based on an integrated luminosity of 360 pb$^{-1} in p\bar{p} collisions at 1.96 TeV center of mass energy collected by the Collider Detector at Fermilab. We observe 14.6 \pm 4.6 signal events with a background of 7.1 \pm 0.9 events, and a fit to the J/psi pi^{\pm} mass spectrum yields a B_c^{\pm} mass of 6285.7 \pm 5.3(stat) \pm 1.2(syst) MeV/c^2. The probability of a peak of this magnitude occurring by random fluctuation in the search region is estimated as 0.012%.Comment: 7 pages, 3 figures. Version 3, accepted by PR