Fractional Schrödinger Operator With Delta Potential Localized On Circle

We consider a system governed by the fractional Schödinger operator with a delta potential supported by a circle in R 2. We find out the function counting the number of bound states, in particular, we give the necessary and sufficient conditions for the absence of bound state in our system. Furthermore, we reproduce the form of eigenfunctions and analyze the asymptotic behavior of eigenvalues for the strong coupling constant case. © 2012 American Institute of Physics.533Albeverio, S., Gesztesy, F., Høegh-Krohn, R., Holden, H., (2004) Solvable Models in Quantum Mechanics, , 2nd ed. (with Appendix by P. Exner), (American Mathematical Society, Providence, RI)Bandrowski, B., Karczewska, A., Rozmej, P., Numerical solutions to integral equations equivalent to differential equations with fractional time derivative (2010) Int. J. Appl. Math Comput. Sci., 20 (2), pp. 261-269. , 10.2478/v10006-010-0019-1Bandrowski, B., Rozmej, P., On fractional Schrödinger equation (2010) Comput. Methods Sci. Technol., 16 (2), pp. 191-194. , http://www.man.poznan.pl/cmst/2010/_V_16_2/14_Rozmej_G.pdfBraaksma, B.L.J., Asymptotic expansions and analytic continuations for a class of Barnes-integrals (1962) Compos. Math., 15, pp. 239-341. , http://archive.numdam.org/ARCHIVE/CM/CM_1962-1964__15_/CM_1962-1964__15__239_0/CM_1962-1964__15__239_0.pdfCapelas de Oliveira, E., Silva Costa, F., Vaz, J., The fractional Schödinger operator equation for delta potentials (2010) J. Math. Phys., 51, p. 123517. , 10.1063/1.3525976Capelas de Oliveira, E., Vaz, J., Tunneling in fractional quantum mechanics (2011) J. Phys. A: Math. Theor., 44, p. 185303. , 10.1088/1751-8113/44/18/185303Exner, P., Ichinose, T., Geometrically induced spectrum in curved leaky wires (2001) J. Phys. A, 34, pp. 1439-1450. , 10.1088/0305-4470/34/7/315Exner, P., Kondej, S., Curvature-induced bound states for a δ interaction supported by a curve in (2002) Ann. Henri Poincaré, 3, pp. 967-981. , 10.1007/s00023-002-8644-3Exner, P., Kondej, S., Bound states due to a strong delta interaction supported by a curved surface (2003) J. Phys. A, 36, pp. 443-457. , 10.1088/0305-4470/36/2/311Exner, P., Tater, M., Spectra of soft ring graphs (2004) Waves Random Complex MediaMedia, 14, pp. S47-60. , 10.1088/0959-7174/14/1/010Guo, X., Xu, M., Some physical applications of fractional Schrr̈odinger equation (2006) J. Math. Phys., 47, p. 082104. , 10.1063/1.2235026Gradshteyn, I.S., Ryzhik, I.M., (2007) Table of Integrals, Series, and Products, , 7th ed., (Academic, New York)Jeng, M., Xu, S.-L.-Y., Hawkins, E., Schwarz, J.M., On the nonlocality of the fractional Schrödinger equation (2010) J. Math. Phys., 51, p. 062102. , 10.1063/1.3430552Dong, J., Xu, M., Some solutions to the space fractional Schrödinger equation using momentum representation method (2007) J. Math. Phys., 48, p. 072105. , 10.1063/1.2749172Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., (2006) Theory and Applications of Fractional Differential Equations, , (Elsevier, Amsterdam)Laskin, N., Fractional quantum mechanics and Lévy path integrals (2000) Phys. Lett. A, 268, pp. 298-305. , 10.1016/S0375-9601(00)00201-2Laskin, N., Fractional quantum mechanics (2000) Phys. Rev. E, 62, pp. 3135-3145. , 10.1103/PhysRevE.62.3135Laskin, N., Fractal and quantum mechanics (2000) Chaos, 10, pp. 780-790. , 10.1063/1.1050284Mathai, A.M., Saxena, R.K., Haubold, H.J., (2009) The H-Function, , (Springer, New York)Naber, M., Time fractional Schrödinger equation (2004) J. Math. Phys., 45, pp. 3339-3352. , 10.1063/1.1769611Oberhetting, F., (1974) Tables of Mellin Transforms, , (Springer, New York)Reed, M., Simon, B., (1975) Methods of Modern Mathematical Physics. II. Fourier Analysis, , (Academic, New York)Posilicano, A., A Krein-like formula for singular perturbations of self-adjoint operators and applications (2001) J. Funct. Anal., 183, pp. 109-147. , 10.1006/jfan.2000.3730Stollmann, P., Voigt, J., Perturbation of Dirichlet forms by measures (1996) Potential Anal., 5, pp. 109-138. , 10.1007/BF0039677

POLYMER MELT FLOW IN SUDDEN EXPANSIONS: THE EFFECTS OF VISCOUS HEATING

Sudden expansion is a typical geometry found at the entrance of a mould cavity and is generally known in industry as ‘gate’. Flow simulation of this class of problems poses some difficulties owing to coupling of momentum and energy laws, existence of re-circulation and steep pressure variations. This work focuses on the physical analysis of the laminar and incompressible polymer melt flow inside channels with sudden expansions aimed at mapping the viscous heating effect. The mathematical model comprises the mass, momentum and energy conservation laws. The pressure-velocity coupling is treated on solving a Poisson equation for pressure. The Cross constitutive model is adopted to describe the non-Newtonian behavior of the flow. The governing equations are discretized using the finite difference method based on central, second order accurate formulae for both convective and diffusive terms. Artificial smoothing terms are added to control the odd-even decoupling problem. The main results demonstrate that the flow parameters, such as pressure drop along the channel and Nusselt number at the walls, are affected by viscous heating. It has been found that, in such problems, any reliable solution must account for the non-isothermal effects

The Mass Spectrum of Neutrinos

In a previous paper we showed that Weyl equation possess superluminal solutions and moreover we showed that those solutions that are eigenstates of the parity operator seem to describe a coupled pair of a monopole anti-monopole system. This result suggests to look for a solution of Maxwell equation \partialF^{\infty}=-gJ with a current J as source and such that the Lorentz force on the current is null. We first identify a solution where J={\gamma}^{5}J_{m}is a spacelike field (even if F is not a superluminal solution of the homogeneous Maxwell equation). More surprisingly we find that there exists a solution F of the free Maxwell \partialF=0 that is equivalent to the non homogeneous equation for F^{\infty}. Once this result is proved it suggests by itself to look for more general subluminal and superluminal solutions F of the free Maxwell equation equivalent to a non homogeneous Maxwell equation for a field F_{0} with a current term as source which may be subluminal or superluminal. We exhibit one such subluminal solution, for which the Dirac-Hestenes spinor field {\psi} associated the electromagnetic field F_{0} satisfies a Dirac equation for a bradyonic neutrino under the ansatz that the current is ce^{{\lambda}{\gamma}^{5}}g{\psi}{\gamma}^{0}{\psi}, with g the quantum of magnetic charge and {\lambda} a constant to be determined in such a way that the auto-force be null. Together with Dirac's quantization condition this gives a quantized mass spectrum (Eq.49) for the neutrinos, with the masses of the different flavor neutrinos being of the same order of magnitude (Eq.50) which is in accord with recent experimental findings. As a last surprise we show that the mass spectrum found in the previous case continues to hold if the current is taken spacelike, i.e., ce^{{\lambda}{\gamma}^{5}}g{\psi}_{>}{\gamma}^{3}{\psi}_{>} with {\psi}_{>}, in this case, satisfying a tachyonic Dirac-Hestenes equation.Comment: This version corrects some misprints, has a new remark and a new referenc

Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $i c t$, with the unit imaginary producing the correct spacetime distance $x^2 - c^2 t^2$, and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary $i = \sqrt{-1}$, with the Clifford bivector $\iota = e_1 e_2$ for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis $e_1$ and $e_2$. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.Comment: 29 pages, 2 figure

Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles

The EPRB experiment with massive partcles can be formulated if one defines spin in a relativistic way. Two versions are discussed: The one using the spin operator defined via the relativistic center-of-mass operator, and the one using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction for the EPRB experiment: The degree of violation of the Bell inequality DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The phenomenon can be physically understood as a combined effect of the Lorentz contraction and the Moller shift of the relativistic center of mass. The effect is therefore stronger than standard relativistic phenomena such as the Lorentz contraction or time dilatation. The fact that the Bell inequality is in general less violated than in the nonrelativistic case will have to be taken into account in tests for eavesdropping if massive particles will be used for a key transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important in the formula for eigenvector in Sec. IV); link to the unpublished 1984 paper containing the results (without typos!) of Sec. IV is adde

Electrochemical behavior of parent and photodegradation products of some selected pesticides

Electrochemical behavior of pesticides is extensively studied, but little attention has been given to the study of their degradation products (by-products) by electrochemical methods. However, the degradation products of pesticides can be even more toxic then the parent products and such studies should be encouraged. Therefore, the objective of this work was to evaluate the electroactivity of by-products of imazaquin, methylparathion, bentazon and atrazine, generated by UV irradiation and measured using cyclic and differential pulse voltammetry and UV-visible absorption spectrophotometry. Results have shown that several by-products exhibit electroactivity, allowing, in some cases, the simultaneous determination of both parent and degradation products.EMBRAPACoordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)CNPqFAPES

Fluoromycobacteriophages for rapid, specific, and sensitive antibiotic susceptibility testing of Mycobacterium tuberculosis

Rapid antibiotic susceptibility testing of Mycobacterium tuberculosis is of paramount importance as multiple- and extensively- drug resistant strains of M. tuberculosis emerge and spread. We describe here a virus-based assay in which fluoromycobacteriophages are used to deliver a GFP or ZsYellow fluorescent marker gene to M. tuberculosis, which can then be monitored by fluorescent detection approaches including fluorescent microscopy and flow cytometry. Pre-clinical evaluations show that addition of either Rifampicin or Streptomycin at the time of phage addition obliterates fluorescence in susceptible cells but not in isogenic resistant bacteria enabling drug sensitivity determination in less than 24 hours. Detection requires no substrate addition, fewer than 100 cells can be identified, and resistant bacteria can be detected within mixed populations. Fluorescence withstands fixation by paraformaldehyde providing enhanced biosafety for testing MDR-TB and XDR-TB infections. © 2009 Piuri et al

AN APPROACH FOR THE OPTIMUM HYDRODYNAMIC DESIGN OF HYDROKINETIC TURBINE BLADES

This work aims to develop a simple and efficient mathematical model applied to optimization of horizontal-axis hydrokinetic turbine blades considering the cavitation effect. The approach uses the pressure minimum coefficient as a criterion for the cavitation limit on the flow around the hydrokinetic blades. The methodology corrects the chord and twist angle at each blade section by a modification on the local thrust coefficient in order to takes into account the cavitation on the rotor shape. The optimization is based on the Blade Element Theory (BET), which is a well known method applied to design and performance analysis of wind and hydrokinetic turbines, which usually present good agreement with experimental data. The results are compared with data obtained from hydrokinetic turbines designed by the classical Glauert's optimization. The present method yields good behavior, and can be used as an alternative tool in efficient hydrokinetic turbine designs

A Pilot Study on the Metabolic Impact of Mediterranean Diet in Type 2 Diabetes: Is Gut Microbiota the Key?

The Mediterranean diet (MD) has been recommended for type 2 diabetes (T2D) treatment. The impact of diet in shaping the gut microbiota is well known, particularly for MD. However, the link between MD and diabetes outcome improvement is not completely clear. This study aims to evaluate the role of microbiota modulation by a nonpharmacological intervention in patients with T2D. In this 12-week single-arm pilot study, nine participants received individual nutritional counseling sessions promoting MD. Gut microbiota, biochemical parameters, body composition, and blood pressure were assessed at baseline, 4 weeks, and 12 weeks after the intervention. Adherence to MD [assessed by Mediterranean Diet Adherence Screener (MEDAS) score] increased after the intervention. Bacterial richness increased after 4 weeks of intervention and was negatively correlated with fasting glucose levels and Homeostatic Model Assessment for Insulin Resistance (HOMA-IR). Prevotella to Bacteroides ratio also increased after 4 weeks. In contrast, glycated haemoglobin (HbA1c) and HOMA-IR were only decreased at the end of study. Alkaline phosphatase activity was assessed in fecal samples and was negatively correlated with HbA1c and positively correlated with bacterial diversity. The results of this study reinforce that MD adherence results in a better glycemic control in subjects with T2D. Changes in gut bacterial richness caused by MD adherence may be relevant in mediating the metabolic impact of this dietary intervention.info:eu-repo/semantics/publishedVersio