979 resultados para approximate calculation of sums


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The Gibbs-Bogoliubov formalism in conjunction with the pseudopotential theory is applied to the calculation of the vapour pressure of eight liquid metals from Groups I to IV of the periodic table and of alloys (Na-K). The calculated vapour pressure of the elements and their temperature dependencies, the partial pressures, activities and boiling points of the alloys are all found to be in reasonable agreement with measured data.

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The microscopic electron theory based on the pseudopotential formalism has been applied to the calculation of the heats of mixing and of activities in liquid Al·Sn alloys. The calculated values for both quantities were found to be in reasonable agreement with ,the experimental data.

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Relation between X-ray scattering intensities, mean square thermal fluctuations and thermodynamic properties. High temperature X-ray diffraction study of liquid Fe-Ni and Fe-Si alloys using reflection and transmission geometries. Calculation of the structure factor as a function of wave vector. Extrapolation to zero wave vector. Calculation of the concentration-concentration correlation function defined by A. B. Bhatia and D. E. Thorton. Computation of thermodynamic quantities of mixing A G, LlH and LlS for the binary alloys. Comparison with direct thermodynamic measurements reported in the literature.

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On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

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The effectiveness of series capacitors used with long distance transmission lines in improving system stability is analyzed. Compensation efficiency is defined as the effectiveness of series capacitors. The influence of various factors on compensation efficiency such as capacitor location, line length, and degree of series compensation is investigated. Proper use of shunt reactors with series capacitors, in addition to limiting power frequency over- voltages, increases the maximum power transfer. Analytical expressions are included to aid in the calculation of compensation efficiency for a few typical cases. Curves are also presented indicating the critical value of shunt Mvar required for various degrees of series compensation and line lengths.

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A method for calculating the bends in the glide slope due to uneven terrain is presented. A computer program written for the purpose enables the calculation of the difference in depth of modulation (DDM) at any point, taking into account the effect of uneven terrain. Results are presented for a hypothetical case of a hill in front of the runway. The program enables us to predict the glide slope bends due to irregular terrain, so that proper selection of glide slope antenna location can be made.

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Breakout noise from HVAC ducts is important at low frequencies, and the coupling between the acoustic waves and the structural waves plays a critical role in the prediction of the transverse transmission loss. This paper describes the analytical calculation of breakout noise by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The first step in the breakout noise prediction is to calculate the inside duct pressure field and the normal duct wall vibration by using the solution of the governing differential equations in terms of Green's function. The resultant equations are rearranged in terms of impedance and mobility, which results in a compact matrix formulation. The Green's function selected for the current problem is the cavity Green's function with modification of wave number in the longitudinal direction in order to incorporate the terminal impedance. The second step is to calculate the radiated sound power from the compliant duct walls by means of an ``equivalent unfolded plate'' model. The transverse transmission loss from the duct walls is calculated using the ratio of the incident power due to surface source inside the duct to the acoustic power radiated from the compliant duct walls. Analytical results are validated with the FE-BE numerical models.

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Organo-clay was prepared by incorporating different amounts (in terms of CEC, ranging from 134-840 mg of quaternary ammonium cation (QACs) such as hexadecytrimethylammonium bromide (C19H42N]Br) into the montmorillonite clay. Prepared organo-clays are characterized by CHN analyser and XRD to measure the amount of elemental content and interlayer spacing of surfactant modified clay. The batch experiments of sorption of permanganate from aqueous media by organo-clays was studied at different acidic strengths (pH 1-7). The experimental results show that the rate and amount of adsorption of permanganate was higher at lower pH compared to raw montmorillonite. Laboratory fixed bed experiments were conducted to evaluate the breakthrough time and nature of breakthrough curves. The shape of the breakthrough curves shows that the initial cationic surfactant loadings at 1.0 CEC of the clay is enough to enter the permanganate ions in to the interlamellar region of the surfactant modified smectile clays. These fixed bed studies were also applied to quantify the effect of bed-depth and breakthrough time during the uptake of permanganate. Calculation of thermodynamic parameters shows that the sorption of permanganate is spontaneous and follows the first order kinetics.

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Othman et al. (Intermetallics 2012;22:1-6) recently published a manuscript on ``Effects of current density on the formation and microstructure of Sn-9Zn, Sn-8Zn-3Bi and Sn-3Ag-0.5Cu solder joints''. We found problems in calculation of diffusion parameters. Even the comment on the formation of Cu5Zn8 instead of Cu6Sn5 is not correct. In this comment, we have explained the correct procedure to calculate the diffusion coefficients. Further, we have also explained the reason for the formation of Cu5Zn8 instead of Cu6Sn5 in the Cu/Sn-9Zn system. (C) 2012 Elsevier Ltd. All rights reserved.

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We extend our analysis of transverse single spin asymmetry in electroproduction of J/psi to include the effect of the scale evolution of the transverse momentum dependent (TMD) parton distribution functions and gluon Sivers function. We estimate single spin asymmetry for JLab, HERMES, COMPASS, and eRHIC energies using the color evaporation model of charmonium production, using an analytically obtained approximate solution of TMD evolution equations discussed in the literature. We find that there is a reduction in the asymmetry compared with our predictions for the earlier case considered by us, wherein the Q(2) dependence came only from DGLAP evolution of the unpolarized gluon densities and a different parametrization of the TMD Sivers function was used.

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A new family of supramolecular organogelators, based on chiral amino acid derivatives of 2,4,6-trichloro-pyrimidine-5-carbaldehyde, has been synthesized. L-alanine was incorporated as a spacer between the pyrimidine core and long hydrocarbon tails to compare the effect of chirality and hydrogen bonding to that of the achiral analogue. The role of aromatic moiety on the chiral spacer was also investigated by introducing L-phenyl alanine moieties. The presence of intermolecular hydrogen-bonding leading to the chiral self-assembly was probed by concentration-dependent FTIR and UV/Vis spectroscopies, in addition to circular dichroism (CD) studies. Temperature and concentration-dependent CD spectroscopy ascribed to the formation of -sheet-type H-bonded networks. The morphology and the arrangements of the molecules in the freeze-dried gels were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), and X-ray diffraction (XRD) techniques. Calculation of the length of each molecular system by energy minimization in its extended conformation and comparison with the small-angle XRD pattern reveals that this class of gelator molecules adopts a lamellar organization. Polarized optical microscopy (POM) and differential scanning calorimetry (DSC) indicate that the solid state phase behavior of these molecules is totally dependent on the choice of their amino acid spacers. Structure-induced aggregation properties based on the H-bonding motifs and the packing of the molecule in three dimensions leading to gelation was elucidated by rheological studies. However, viscoelasticity was shown to depend only marginally on the H-bonding interactions; rather it depends on the packing of the gelators to a greater extent.

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N-Decanoyl-L-alanine (DA) was mixed with either colorless 4,4-bipyridine (BP) or various derivatives such as chromogenic oligo(p-phenylenevinylene) (OPV) functionalized with isomeric pyridine termini in specific molar ratios. This mixtures form salt-type gels in a water/ethanol (2:1, v/v) mixture. The gelation properties of these two-component mixtures could be modulated by variation of the position of the N atom of the end pyridyl groups in OPVs. The presence of acid-base interactions in the self-assembly of these two-component systems leading to gelation was probed in detail by using stoichiometry-dependent UV/Vis and FTIR spectroscopy. Furthermore, temperature-dependent UV/Vis and fluorescence spectroscopy clearly demonstrated a J-type aggregation mode of these gelator molecules during the sol-to-gel transition process. Morphological features and the arrangement of the molecules in the gels were examined by using scanning electron microscopy (SEM), atomic force microscopy (AFM), and X-ray diffraction (XRD) techniques. Calculation of the length of each molecular system by energy minimization in its extended conformation and comparison with the XRD patterns revealed that this class of gelator molecules adopts lamellar organizations. Rheological properties of these two-component systems provided clear evidence that the flow behavior could be modulated by varying the acid/amine ratio. Polarized optical microscopy (POM), differential scanning calorimetry (DSC), and XRD results revealed that the solid-phase behavior of such two-component mixtures (acid/base=2:1) varied significantly upon changing the proton-acceptor part from BP to OPV. Interestingly, the XRD pattern of these acid/base mixtures after annealing at their associated isotropic temperature was significantly different from that of their xerogels.

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We extend our analysis of transverse single spin asymmetry in electroproduction of J/ψ to include the effect of the scale evolution of the transverse momentum dependent (TMD) parton distribution functions and gluon Sivers function. We estimate single spin asymmetry for JLab, HERMES, COMPASS, and eRHIC energies using the color evaporation model of charmonium production, using an analytically obtained approximate solution of TMD evolution equations discussed in the literature. We find that there is a reduction in the asymmetry compared with our predictions for the earlier case considered by us, wherein the Q2 dependence came only from DGLAP evolution of the unpolarized gluon densities and a different parametrization of the TMD Sivers function was used.

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Solid diffusion couple experiments are conducted to analyse the growth mechanism of the phases and the diffusion mechanism of the components in the Ti-Si system. The calculation of the parabolic growth constants and the integrated diffusion coefficients substantiates that the analysis is intrinsically prone to erroneous conclusions if it is based on just the parabolic growth constants determined for a multiphase interdiffusion zone. The location of the marker plane is detected based on the uniform grain morphology in the TiSi2 phase, which indicates that this phase grows mainly because of Si diffusion. The growth mechanism of the phases and morphological evolution in the interdiffusion zone are explained with the help of imaginary diffusion couples. The activation enthalpies for the integrated diffusion coefficient of TiSi2 and the Si tracer diffusion are calculated as 190 +/- 9 and 197 +/- 8 kJ/mol, respectively. The crystal structure, details on the nearest neighbours of the components, and their relative mobilities indicate that the vacancies are mainly present on the Si sublattice.

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This paper presents the design technique that has been adopted for packaging of Polyvinylidene fluoride (PVDF) nasal sensor for biomedical applications. The PVDF film with the dimension of length 10mm, width 5mm and thickness 28 mu m was firmly adhered on one end of plastic base (8mmx5mmx30 mu m) in such a way that it forms a cantilever configuration leaving the other end free for deflection. Now with the leads attached on the surface of the PVDF film, the cantilever configuration becomes the PVDF nasal sensor. For mounting a PVDF nasal sensor, a special headphone was designed, that can fit most of the human head sizes. Two flexible strings are soldered on either side of the headphone. Two identical PVDF nasal sensors were then connected to either side of flexible string of the headphone in such a way that they are placed below the right and left nostrils respectively without disturbing the normal breathing. When a subject wares headphone along with PVDF nasal sensors, two voltage signals due to the piezoelectric property of the PVDF film were generated corresponding to his/her nasal airflow from right and left nostril. The entire design was made compact, so that PVDF nasal sensors along with headphone can be made portable. No special equipment or machines are needed for mounting the PVDF nasal sensors. The time required for packaging of PVDF nasal sensors was less and the approximate cost of the entire assembly (PVDF nasal sensors + headphone) was very nominal.