An efficient approximation for arbitrary port suppression of multiport scattering parameters

The multiport scattering (S‐) parameter matrix is increasingly utilized to compose models of large bit‐width interconnect systems with broadband characteristics (frequency range of zero to tens of gigahertz) to perform increasingly accurate signal‐integrity and power‐integrity simulations. The search for an optimal solution space often requires generation of S‐parameter models of interconnect systems for various signal/ground pin mappings, a process that can be computationally costly if the structure is electromagnetically solved for each distinct pin mapping. To expedite this model‐generation process, we propose a method in which an N‐port structure is electromagnetically solved only once to yield an N × N S‐matrix; then, a linear system is formulated and solved to yield an (N − M) × (N − M) post‐suppressed S‐matrix (where M is the number of suppressed ports). This approach results in significant computational savings through elimination of electromagnetic field‐solver runs for each distinct pin mapping. Included in this paper is a discussion about the limitations of this technique and several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Double broadband matching and the problem of reciprocal reactance 2n-port cascade decomposition

Let N, N₁, N₂ and N₃ be prescribed reciprocal reactance 2n-ports. Then, under certain mild restrictions, this paper supplies answers to the following two related problems:. P₁. Find the necessary and sufficient conditions for the physical extractability of N₁ from the front-end of N. P₂. Given that N₂ and N₃ are individually physically extractable from the back and front-ends of N. respectively, find a set of sharp sufficient conditions for their simulations physical extractability from N. The criteria are formulated in terms of the associated scattering matrices and are reasonably simple to apply. Moreover, they also have a clear-cut network significance involving transmission zeros. to illustrate their use, a recent result for the design of non-degenerate double broadband-matching equalizers⁶ is generalized to a 2n-port setting in Theorem 2, corollary 2. Lastly, to round out the development, impedance versions of both Theorem 1 and Theorem 2, corollary 2, are presented in Section 2. This restatement is accomplished with the aid of a new Darlington 2n-port embedding for passive reciprocal n-ports that is phrased entirely in the language of impedance matrices.     

Effect of Concentration of SH U 555A Labeled Human Melanoma Cells on MR Spin Echo and Gradient Echo Signal Decay at 0.2, 1.5, and 3T

In the current study the effect of increasing concentrations of superparamagnetic iron oxide labeled cells on the MRI signal decay at magnetic field strengths of 0.2, 1.5, and 3 T was evaluated. The spin echo and gradient echo cellular transverse relaxivity was systematically studied for various concentrations (N = 1, 5, 10, 20, 40, and 80 cells/μl_gel) of homogeneously suspended SH U 555A labeled SK-Mel28 human melanoma cells. For all field strengths investigated a linear relationship between cellular transverse relaxation enhancement and cell concentration was found. In the spin echo case, the cellular relaxivities [i.e., d(ΔR ₂)/dN] were determined to 0.12 s⁻¹ (cell/μl)⁻¹ at 0.2 T, 0.16 s⁻¹ (cell/μl)⁻¹ at 1.5 T, and 0.17 s⁻¹ (cell/μl) at 3 T. In the gradient echo case, the calculated cellular relaxivities (i.e., d(ΔR ₂ ^* )/dN) were 0.51 s⁻¹ (cell/μl)⁻¹ at 0.2 T, 0.69 s⁻¹ (cell/μl)⁻¹ at 1.5 T, and 0.71 s⁻¹ (cell/μl)⁻¹ at 3 T. The proposed preparation technique has proven to be a simple and reliable approach to quantify effects of magnetically labeled cells in vitro. On the basis of this quantification well suited tissue specific models can be derived.     

Oriented growth of Bi3.25La0.75Ti3O12 thin films on RuO2/SiO2/Si substrates by using the polymeric precursor method: Structural, microstructural and electrical properties

c-axis oriented Bi_3.25La_0.75Ti₃O₁₂ (BLT) thin films were grown on a RuO₂ top electrode deposited on a (100) SiO₂/Si substrate by the polymeric precursor method. X-ray diffraction and atomic force microscope investigations indicate that the films exhibit a dense, well crystallized microstructure having random orientations with a rather smooth surface morphology. The electrical properties of preferred oriented Bi_3.25La_0.75Ti₃O₁₂ (BLT) thin films deposited on RuO₂ bottom electrode leaded to a large remnant polarization (P _r ) of 17.2 μC/cm² and (V _c ) of 1.8 V, fatigue free characteristics up to 10¹⁰ switching cycles and a current density of 2.2 μA/cm² at 5 V. We found that the polarization loss is insignificant with nine write/read voltages at a waiting time of 10,000 s. Independently of the applied electric field the retained switchable polarization approached a nearly steady-state value after a retention time of 10 s.     

Discussion on population kinetics and number densities of excited species of low‐pressure discharge nitrogen plasma

A numerical model is constructed to calculate the number densities of some excited species of nitrogen in low‐pressure discharge nitrogen plasma, together with simultaneous solution of the self‐consistent electron energy distribution function and N₂‐vibration distribution function. We consider species N₂(X), N₂(A), N₂(B), N₂(C), N₂(a), N₂(a′), N2+, N4+, N(⁴S) ande⁻. In addition to electron collisional reactions, diffusion losses and molecular relations are included. It is found that the ratio of number densities of N₂(B) and N₂(C) states can be a good measure of the electron kinetic temperature. The N₂(C) state is found to be almost in a corona equilibrium, whereas the N₂(B) state becomes mainly populated by N₂(X,v≥6) + N₂(A) reaction and depopulated by collisional relaxation by the ground‐state N₂(X) molecule. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

SnO2 nanocrystallines decorated g-C3N4 composites with enhanced visible-light photocatalytic activity

Abstract

A series of SnO₂ nanocrystallines decorated g-C₃N₄ architectures were synthesized using a facile solvothermal method. The structural, morphological, and optical properties of the as-prepared nanocomposites were characterized in detail, indicating that SnO₂ nanocrystallines with diameter ～ 4?nm were well-dispersed on the surface of g-C₃N_4. The photocatalytic activity of the composites was investigated by degrading rhodamine B (RhB) under visible light irradiation. The CNS2 heterostructure exhibits enhanced photocatalytic activity than bare SnO₂ and g-C₃N₄. Kinetic study revealed a promising degradation rate constant of 0.0593?min^?1 for the CNS2, which is 118 and 7 times higher than that of pure SnO₂ and g-C₃N₄, respectively. What’s more, the CNS2 still retained the photocatalytic activity after three cycle measurements. The enhanced photocatalytic performances of the nanocomposite may be due to its large surface area (116.2 m²/g), appropriate ratio of SnO₂/g-C₃N₄ and the compact structure of the junction between the SnO₂ nanocrystallines and the g-C₃N₄, which inhibits the recombination of photogenerated electrons and holes.     

Optical bistability in lead magnesium niobate ceramics: An integrated photonic flow-rate/pressure gauge based upon thermal focussing and convection

We have discovered an unusual form of optical bistability in hot-pressed ceramic PMN (PbMg_0.3Nb_0.5Ti_0.1O₃) in which the thermal focussing of laser light at very low power densities (<1 kW/cm²) oscillates between two metastable states. At low laser powers P the phenomenon is highly aperiodic but extremely reproducible; the oscillation events occur at times t_N empirically given by the equation t_N = A/(P-P_N ), where the threshold power P_N for the N-th switching event is found to be NP_o , with P _o = 45 mW [i.e., 3.6 W/cm²]. At higher laser power the switching events become periodic, ca. 8 Hz, and resemble the phenomenon reported by Vasnetsov in thin films of thermotropic liquids. One of the two metastable spatial light patterns is doughnut-shaped; the other resembles a Bessel function, with large intensity in the center. Therefore by setting a Si-diode detector in the center of the pattern, we can monitor the oscillation. The oscillation event times (or frequency) are strongly dependent upon convection from the sides of the PMN thermal lens. Therefore the device acts as an optical (“photonic”) sensor that is extremely acute to pressure and flow rate of the surrounding atmosphere. We have measured pressure changes of 10^?2 Torr and flow rate changes of 0.1 cu. ft/hr. (0.3 m/s) in air.     

Electrostatic fluctuation measurements in the periphery of reversed field pinch plasma

In this paper, the authors study the magnetic and electric properties of ferromagnetic substance/semimetal (Fe/Bi) system multilayered thin films prepared by ion beam sputtering. The multilayered thin film was prepared with 99.6% Fe and 99.99% Bi. The experimental results are summarized as follows. From XRD in the small‐degree region (2θ = 2 to 4^°), Fe/Bi system thin films for N = 3,4, and 5 Fe layers have formed multilayer structures. Coercive force H_c increased with increasing number of Fe layers. The maximum value was 4.522 kA/m at N = 6 Fe layers. The coercive force then decreased and its value was constant at more than 15 layers. Electrical resistivity, ρ, of Fe/Bi system multilayered thin films changed from conductivity to semiconductivity at temperatures in the range for T = 380 to 400 K. Magneto‐resistance (MR) ratio decreased with increasing applied field H when the current was parallel to an applied magnetic field (I‖H). MR ratio reached a maximum of 0.154% at N = 4 Fe layers at room temperature. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(1): 1–8, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20068     

Quality assurance of PASADENA hyperpolarization for 13C biomolecules

Object  Define MR quality assurance procedures for maximal PASADENA hyperpolarization of a biological ¹³C molecular imaging reagent. Materials and methods  An automated PASADENA polarizer and a parahydrogen generator were installed. ¹³C enriched hydroxyethyl acrylate, 1-¹³C, 2,3,3-d₃ (HEA), was converted to hyperpolarized hydroxyethyl propionate, 1-¹³C, 2,3,3-d₃ (HEP) and fumaric acid, 1-¹³C, 2,3-d₂ (FUM) to hyperpolarized succinic acid, 1-¹³C, 2,3-d₂ (SUC), by reaction with parahydrogen and norbornadiene rhodium catalyst. Incremental optimization of successive steps in PASADENA was implemented. MR spectra and in vivo images of hyperpolarized ¹³C imaging agents were acquired at 1.5 and 4.7 T. Results  Application of quality assurance (QA) criteria resulted in incremental optimization of the individual steps in PASADENA implementation. Optimal hyperpolarization of HEP of P = 20% was achieved by calibration of the NMR unit of the polarizer (B ₀ field strength ± 0.002 mT). Mean hyperpolarization of SUC, P = [15.3 ± 1.9]% (N = 16) in D ₂O, and P = [12.8 ± 3.1]% (N = 12) in H ₂O, was achieved every 5–8 min (range 13–20%). An in vivo ¹³C succinate image of a rat was produced. Conclusion  PASADENA spin hyperpolarization of SUC to 15.3% in average was demonstrated (37,400 fold signal enhancement at 4.7 T). The biological fate of ¹³C succinate, a normally occurring cellular intermediate, might be monitored with enhanced sensitivity.     

An induction motor model with deep-bar effect and leakage inductance saturation

Contents A two-phase dynamic induction motor model is derived which includes the effects of rotor bar eddy currents and leakage inductance saturation. The model is based on approximate analysis of the air-gap and slot electromagnetic fields which leads directly to lumped circuit equations. New expressions are given for the variation of the zig-zag and slot leakage inductance with saturation. — The model is applied to the calculation of both steady state and dynamic characteristics for a large induction motor.

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Ein Modell des Asynchronmotors mit Hochstabläufer-Effekt und Sättigung der Streuinduktivität

Übersicht Es wird ein zweisträngiges Modell eines Asynchronmotors abgeleitet, das Wirbelströme in den Läuferstäben und die Sättigung der Streuinduktivität berücksichtigt. Grundlage des Modells ist eine angenäherte Analyse der Felder im Luftspalt und in den Nuten, die direkt auf Gleichungen mit konzentrierten Elementen führt. Es werden neue Ausdrücke für die Abhängigkeit der doppeltverketteten und der Nutstreuung von der Sättigung angegeben. Das Modell wird für die Berechnung stationärer und dynamischer Vorgänge bei einem großen Asynchronmotor angewendet.

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List of Symbols A magnetic vector potential - B flux density - G describing function - g air-gap length - H magnetic field intensity - I _Om rotor saturation current - I _r rotor current matrix - l _r ^j current in thejth rotor slot - l _rm amplitude of the fundamental ofI _bir ^j distribution - I _rr rotor harmonic conceptual current matrix - I _s stator current matrix - I _ss stator harmonic conceptual current matrix - i _mne m, nth modal eddy current in thejth rotor slot - i _nb nth harmonic conceptual current at the interface betweenjth rotor slot and slot neck regions - i _n ^rj nth harmonic conceptual current at the opening of thejth rotor slot - i _n ^sj nth harmonic conceptual current at the opening of thejth stator slot - i _Ob rotor zero order conceptual current matrix - i _Oi ^j conceptual current at thejth rotor slot due to daturation of the tooth tips - K _nw nth harmonic winding distribution factor effective length of the motor - L _nc self inductance of the eddy current modei _One ^j - L _r rotor inductance matrix - L _s stator inductance matrix - P _p pole pitch - M _ne mutual inductance betweeni _One ^j andI _r ^j and rotor modal eddy currents - M _ri mutual inductance matrix between rotor winding and rotor conceptual winding due to saturation of the tooth tips - M _rr mutual inductance matrix between rotor winding and rotor conceptual winding - M _rss mutual inductance matrix between rotor winding and stator conceptual winding - M _si mutual inductance matrix between stator winding and rotor conceptual winding due to saturation of the rotor tooth tips - M _sr mutual inductance matrix between stator and rotor windings - M _srr mutual inductance matrix between stator winding and rotor conceptual winding - M _ss mutual inductance matrix between stator winding and stator conceptual winding - N ₁,N ₂ number of stator and rotor slots - R _ne resistance of eddy current modei _One ^j - R _r rotor resistance matrix - R _s stator resistance matrix - s ₁,d ₁ dimensions of a stator slot - s ₂,d ₂ rotor slot opening and rotor slot neck height - s _b ,d _b dimensions of a rotor bar - s _p slot pitch - N _c number of turns per slot - U _s applied voltage matrix - q number of slots per pole phase group - rotor flux linkage matrix - y_s stator flux linkage matrix - , inductance coefficients - O angular position - conductivity of rotor bars - eigenvalues - resistivity of rotor bars     

FERROELECTRIC,PIEZOELECTRIC AND DIELECTRIC PROPERTIES OF Nb MODIFIED Bi4Ti3O12-SrBi4Ti4O15 INTERGROWTH

ABSTRACT

Doping and constructing intergrowth are found to be an effectual approach to modify the electrical properties of bismuth layer-structured ferroelectrics. In this work, ferroelectric, piezoelectric and dielectric properties of Nb-doped Bi₄Ti₃O₁₂-SrBi₄Ti₄O₁₅ (BTN-SBTN-x) intergrowth ceramics were investigated. The ferroelectric property of Bi₄Ti₃O₁₂-SrBi₄Ti₄O₁₅ was improved by niobium doping. The remanent polarization (2P _r ) increases at first, then decreases with the increase of niobium content, while the coercive field changes little with Nb-doping. As niobium content is 0.06, the 2P _r maximizes at a value of 34.9 μC/cm², which is increased by about 75% in comparison with that of Bi₄Ti₃O₁₂-SrBi₄Ti₄O₁₅ (2P _r = 20.0 μC/cm²). The Curie temperature of the samples varies hardly upon Nb-doping, which indicates that the good thermal stability of Bi₄Ti₃O₁₂-SrBi₄Ti₄O₁₅ is not deteriorated after Nb addition. Piezoelectric coefficient d₃₃ was increased from 9.3 pC·N^?1 to 18.6 pC·N^?1 due to the enlargement of 2P _r .     

Refractive index properties of SiN thin films and fabrication of SiN optical waveguide

SiN thin films having excellent surface morphology for the optical device application were synthesized using a plasma enhanced chemical vapor deposition (PECVD) method at low temperature (350^°C) using silane (SiH₄) and nitrogen (N₂). The effects of the SiH₄/N₂ flow ratio, rf power and annealing on the SiN films were investigated. The optical and structural properties of SiN films were characterized using an ellipsometry, a fourier-transform infrared spectroscopy (FT-IR), and an atomic force microscope (AFM). The refractive index increased from 1.6 to 2.3 as the SiH₄/N₂ ratio was increased from 0.17 to 1.67. The rms surface roughness decreased from 14.1 to 3.6Å after post-deposition annealing process performed at 800^°C for 1hr in an air ambient. We could fabricate straight waveguides based on a three layer structure and have no problems with step coverage.     

Piezoelectric and ferroelectric properties of new Pb9Ce2Ti12O36 and lead-free Ba2NdTi2Nb3O15 ceramics

In this paper, measurements of the nonlinear ferroelectric, piezoelectric and dielectric properties of Pb₉Ce₂Ti₁₂O₃₆ (Pb₉CTO) and Ba₂NdTi₂Nb₃O₁₅ (BNTN) ferroelectric ceramics are presented. Hysteresis P(E) loops were measured as a function of applied electric field, frequency and temperature. The coercive field (E _c) and remnant polarization (P _r) displayed temperature and frequency dependence. Lead-free BNTN ceramics exhibited a coercive field E _c?>?2.4 kV mm^?1 and a piezoelectric coefficient d ₃₃?=?2 pC N^?1. The hysteresis loop was pinched above 110°C and a linear response was observed at 155°C, typical of a paraelectric material. Pb₉CTO was shown to be ferroelectric with coercive field E _c?=?1.2 kV mm^?1 and a d ₃₃?=?65 pC N^?1. The frequency dependences of the impedance of the Pb₉CTO discs were analyzed.     

A neural network for signal decomposition problems

This paper presents the design of a neural network for signal decomposition problems with application examples. For this class of problems the proposed network has the same dynamics as the Hopfield net, but it is shown to realize the O(M²) connection paths among the M neurons with a number of wires and conductances increasing only linearly with increasing M, i.e. reducing this number by one dimension with respect to the quadratically increasing number of wires and conductances required in the Hopfield net. Other advantages of the proposed neural network are discussed in relation to classical examples of decomposition problems. In particular, a new architecture for an N-bit A/D converter is presented employing 4N conductances instead of the N(N + 1) Hopfield A/D conductances.     

Titania-PMMA nanohybrids of enhanced nanocrystallinity

Nanohybrid thin films consisting of titania nanoparticles embedded in a suitable polymer matrix represent a new class of functional materials for optoelectronic applications. For instance, our previous studies show that titania-poly(methylmethacrylate) or TiO₂-PMMA nanohybrids derived from in situ sol-gel technique are promising as nonlinear optical materials since they can demonstrate a very fast recovery time of ∼1.5 picosecond and a large third-order nonlinear susceptibility, χ⁽³⁾ up to 1.93 × 10⁻⁹ esu, as observed by pump-probe and Z-scan techniques. However, it was realized that the conventional in situ sol-gel technique employed led to a largely amorphous TiO₂ phase in the PMMA matrix. In order to overcome this limitation, we have performed two modification approaches making use of high pressure water vapor, i.e.: pre-and post-hydrothermal treatments applied on the sol-gel precursors. The degree of TiO₂ crystallinity in the resulting nanohybrids was studied by XRD, FTIR, and TEM. Both approaches can enhance the nanocrystallinity TiO₂ phase considerably and at the same time preserve the integrity of polymer matrix. It was found, however, that while the nanohybrid thin films derived from the pre-hydrothermal treatment show a high absorption in the visible length, those derived from the post-hydrothermal treatment are highly transparent. Nonlinear optical measurement using the Z-scan technique on the latter sample shows a significant enhancement in χ⁽³⁾ as high as 5.27 × 10⁻⁹ esu.     

Adaptive estimation of hidden nearly completely decomposable Markov chains with applications in blind equalization

This paper proposes maximum likelihood (ML) estimation schemes for nearly completely decomposable Markov chains (NCDMCs) in white Gaussian Noise. Aggregation techniques based on stochastic complementation are applied to significantly reduce the dimension of the resulting hidden Markov model (HMM) and hence substantially reduce the computational requirements of the estimation algorithms. Stochastic complementation results in exact aggregation in that no approximations are involved in the steady state probability distribution of the Markov chain. We then present an off-line estimation algorithm for the parameters and states of the HMM based on the estimation of the aggregated HMM. This off-line algorithm is an ML estimation scheme and is based on the expectation maximization (EM) algorithm. It has a significantly reduced computational complexity compared with the standard (full-order) EM-based HMM estimation scheme. Finally we present an application of our techniques. We show that hidden NCDMCs can be used to formulate the blind equalization problem for noisy FIR channels with Markov inputs, e.g. phase-shiftkeyed (PSK) signals. We then propose recursive EM and gradient estimation techniques for the aggregated HMM resulting in on-line estimates of the channel coefficients and signal estimate. For an N_a-state Markov chain our aggregate-based estimation scheme has a computational complexity O(N^?2_a), whereas standard algorithms have a complexity O(N_a^{?L + 1}) at each time instant, where L is the length of the FIR channel.     

Magnetic properties of iron-based materials (nitrogen interstitially modified 1:12 compounds and Fe3B-Nd) for low rare-earth bonded magnets

Hard magnetic properties of nitrogen interstitially modified NdM_xFe_12-xN_y compounds and Fe₃B-based ultra-fine crystalline Nd? Fe? Co? T? B alloys of low Nd content of 3 to 5 at. % are studied. The nitrogen-modified compounds have been prepared via the rapid solidification route and the mechanical alloying route both followed by gas nitrogenation using N₂. The Fe₃B-based materials have been prepared by means of rapid solidification and crystallization treatment. The latter materials appear promising as the base material for high-remanence, easy-to-magnetize bonded magnets with small temperature coefficients of remanence. Typical magnetic properties of compaction isotropic bonded magnets produced from this material are B_r = 0.80 T, H_cJ = 350 kA/m, and (BH)_max = 60.5 kJ/m³.     

Large increases in1H metaboliteT 2's after cerebral hypoxia-ischemia correlate with ATP depletion

In vivo proton (¹H) magnetic resonance spectroscopy (MRS) can measure cerebral metabolite concentrations and nuclear relaxation times. Function of the sodium (Na⁺)/potassium (K⁺) pump in cell membranes depends on adequate adenosine triphosphate (ATP) levels: intracellular Na⁺ is normally extruded in exchange for extracellular K⁺. Low ATP will cause pump dysfunction and loss of K⁺ accompanied by influx of Na⁺and water. Raised intracellular water may increase molecular mobility and this might be detectable as increased apparent transverse relaxation times (T ₂'s).¹H-MRS of the brains of newborn piglets during acute hypoxia-ischemia revealed enigmatic increases in the peak area of creatine + phosphocreatine (Cr) relative to those of choline-containing compounds (Cho) andN-acetylaspartate (NAA). Interleaved¹H and phosphorus (³¹P) MRS showed that theT ₂'s of both Cr and lactate (Lac) increased during acute hypoxia-ischemia and these changes correlated with reductions in nucleotide triphosphate (NTP; largely ATP). Within 50 h of metabolic recovery from the primary insult, as delayed energy failure developed, theT ₂'s of Cho, Cr, NAA, and Lac increased greatly. TheseT ₂ changes also correlated with NTP depletion. These observations demonstrate important relationships betweenT ₂'s and function of the ATP-dependent Na⁺/K⁺ pump.     

Power losses in a conducting ring enclosing a conductor with a transient current

Contents In the paper Joule power losses are calculated in a conducting ring enclosing a conductor with a transient current having an alternating component.—Theoretical calculation and numerical computation are worked out basing on a link Bubnov-Galerkin method in its numerical version using the finite elements for the conductor with the Time-Stepping algorithm for the time discretization.—On the basis of numerical computation, graphs of the relative power losses are plotted as a time function.

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Leistungsverluste in einem leitenden Ring, der einen Leiter mit einem instationären Strom umschließt

Übersicht In diesem Beitrag werden die Joulschen Leistungsverluste in einem leitenden Ring berechnet, der einen Leiter umschließt, in dem ein instationärer Strom mit Wechselanteil fließt. Die theoretischen Betrachtungen und numerischen Berechnungen hat man in Anlehnung an die Bubnov-Galerkin-Methode (in ihrer numerischen Variante, die von einen Leiter unter Verwendung der Methode der finiten Elemente realisiert wird) in Verbindung mit einem Schritt-Algorithmus mit der diskretisierten Zeit ausgeführt. Auf der Grundlage numerischer Berechnungen sind Diagramme für die relative Leistung in Abhängigkeit von der Zeit dargestellt.

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List of symbols Symbol Unit Physical parameter - B Wb/m² magnetic induction vector - H A/m magnetic field intensity vector - H, H A/m -component of the magnetic field vector - E V/m electrical field vector - E _r ,E _z V/m components of the electric field - f s^–1 frequency - I A current intensity (r.m.s. value) - L H inductance - P W power losses - P ₀ W power losses for d.c. - R resistance - t sec time - ^–1 m_–1 electric conductivity of the conductor - Hm^–1 magnetic permeability - _ijk m² finite element area - basis function - rad s^–1 pulsation - N _i ,N _j ,N _k function of finite element shape - 3.141593... - region - ² Laplace's operator - r, ,z cylindrical coordinates - ^h region approximating the region - ^e finite element region - M number of discretization points of the region - V number of finite elements - (N–1) number of steps - i, j, k indices of vertices of triangular finite element     

Rapid 3-D mapping of hyperpolarized 3He spin-lattice relaxation times using variable flip angle gradient echo imaging with application to alveolar oxygen partial pressure measurement in rat lungs

Objective  

The purpose of this work was to develop a rapid 3-D, variable flip angle (VFA) method for measurement of hyperpolarized ³He T ₁ which accounts for the effects of radiofrequency (RF) pulses without the need for additional flip angle information.