Stability of the FDTD scheme containing macromodels

Stability analysis of the finite difference time domain scheme containing macromodels is presented. It is shown that for a stable macromodel, the stability of the combined scheme depends on the field interpolation at the macromodel boundary. The maximal allowable time step is shown to be much larger than for subgridding.     

Thermal conductivity of doped PbTe-based solid solutions with off-center impurities

The coefficients of thermopower and electrical and thermal conductivity in the PbTe_0.8Se_0.1 S _0.1 solid solution with electron concentration (4.6–54) × 10¹⁸ cm^?3 are studied in the range of 85–300 K (and in some cases up to 700 K). The temperature dependences of electrical and thermal conductivity indicate that the low-temperature electron and phonon scattering initiated by the off-center impurity of sulfur exists. The temperature dependences of the electronic and lattice components of thermal conductivity are calculated in the approximation of a parabolic spectrum and electron scattering by acoustic phonons and neutral substitutional impurities. The lattice thermal conductivity is found to have a feature in the form of a shallow minimum in the range of 85–250 K. A similar feature, while not so clearly pronounced, is found to exist also in Pb_1?x Sn_xTe_1?x Se_x alloys (x≥0.15) with an off-center tin impurity. An analysis of the possible origins of this effect suggests that, at low temperatures, the Lorentz numbers L of the materials under study are smaller than the L₀ numbers employed which correspond to the above scattering mechanisms. The cause of the decrease in L is related to electron scattering at two-level systems, a mechanism whose effect grows with increasing electron energy. An analysis of experimental data obtained at high temperatures, as well as on undoped samples with the lowest possible carrier concentrations, yields the values of L for samples with different electron densities. The minimum value L/L₀ = 0.75 is obtained for a lightly doped sample at ～130 K.     

Quadrature Mismatch Shaping for Digital-to-Analog Converters

Quadrature sigma-delta analog-to-digital converters require a feedback path for both the I and the Q parts of the complex feedback signal. If two separate multibit feedback digital-to-analog converters (DACs) are used, mismatch among the unit DAC elements leads to additional mismatch noise in the output spectrum as well as an I/Q imbalance. This paper proposes new quadrature bandpass (QBP) mismatch shaping techniques. In our approach, the I and Q DACs are merged into one complex DAC, which leads to near-perfect I/Q balance. To select the unit DAC elements of the complex multibit DAC, the well-known butterfly shuffler and tree structure are generalized towards a complex structure, and necessary constraints for their correct functioning are derived. Next, a very efficient first-order QBP shaper implementation is proposed. Finally, the newly presented complex structures are simulated to prove their effectiveness and are compared with each other with respect to performance     

Nondiffusive weak localization in two-dimensional systems with spin-orbit splitting of the spectrum

The effect of spin splitting caused by structural asymmetry (Rashba’s contribution) and bulk asymmetry (Dresselhaus’s contribution) on the magnetoconductance of two-dimensional structures with high mobility of charge carriers is studied. The theory of weak localization with regard to both of the contributions is developed. The theory is valid in the entire region of classically low magnetic fields for arbitrary relations between the frequencies of spin precession and elastic collisions. The suppression of the correction for antilocalization is demonstrated in the case of equal contributions of structural anisotropy and bulk anisotropy to the spin splitting. The effect of the contribution, cubic in the wave vector, to the spin splitting on the quantum magnetoresistance is studied.     

Nash equilibria of packet forwarding strategies in wireless ad hoc networks

In self-organizing ad hoc networks, all the networking functions rely on the contribution of the participants. As a basic example, nodes have to forward packets for each other in order to enable multihop communication. In recent years, incentive mechanisms have been proposed to give nodes incentive to cooperate, especially in packet forwarding. However, the need for these mechanisms was not formally justified. In this paper, we address the problem of whether cooperation can exist without incentive mechanisms. We propose a model,based on game theory and graph theory to investigate equilibrium conditions of packet forwarding strategies. We prove theorems about the equilibrium conditions for both cooperative and noncooperative strategies. We perform simulations to estimate the probability that the conditions for a cooperative equilibrium hold in randomly generated network scenarios.. As the problem is involved, we deliberately restrict ourselves to a static configuration. We conclude that in static ad hoc networks where the relationships between the nodes are likely to be stab le-cooperation needs to be encouraged.     

Higher Stability Limits for the Symplectic FDTD Method by Making Use of Chebyshev Polynomials

A new scheme is introduced for obtaining higher stability performance for the symplectic finite-difference time-domain (FDTD) method. Both the stability limit and the numerical dispersion of the symplectic FDTD are determined by a function zeta. It is shown that when the zeta function is a Chebyshev polynomial the stability limit is linearly proportional to the number of the exponential operators. Thus, the stability limit can be increased as much as possible at the cost of increased number of operators. For example, the stability limit of the four-exponential operator scheme is 0.989 and of the eight-exponential operator scheme it is 1.979 for fourth-order space discretization in three dimensions, which is almost three times the stability limit of previously published symplectic FDTD schemes with a similar number of operators. This study also shows that the numerical dispersion errors for this new scheme are less than those of the previously reported symplectic FDTD schemes     

Hopping and optical absorption of electrons in nano-porous crystal 12CaO·7Al2O3

Recently it has been discovered that a nano-porous main group oxide 12CaO·7Al₂O₃ (C12A7) can be converted from a wide-gap insulator to a good transparent conductor. Using ab initio modelling we explain good conductivity of this material by very small barriers for hopping of localised electrons between neighbouring positive cages. We show that optical absorption of C12A7 in infrared region and at energies higher than 2.7 eV is due to inter-cage and intra-cage electron transitions, respectively. The proposed mechanisms can be useful in further search for conducting transparent media.     

Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).     

Numerical Study of Finite Element Method Based Solutions for Propagation of Wetting Fronts in Unsaturated Soil

The accurate prediction of the propagation of a wetting front in an unsaturated soil subjected to surficial infiltration is of practical importance to many geotechnical and geoenvironmental problems. The finite element method is the most common solution technique as the hydraulic soil properties are highly nonlinear. Two important issues are often found to create difficulties in such analyses. First, numerical oscillations are usually observed in the calculated pore pressures at the wetting front. Second, when a reasonable mesh size and time step are used, the elevation of the wetting front may be seriously overpredicted. This paper is focused on the second issue. The under-relaxation (UR) technique used in the iterative process within each time step is found to have a serious impact on rate of convergence with refinement in mesh size and time step. Two different techniques are typically used; the first evaluates the hydraulic conductivity using an average of heads calculated from the preceding time node and the most recent iteration of the current time node (UR1), and the second evaluates the hydraulic conductivity using the average of heads calculated from the two most recent iterations of the current time nodes (UR2). The study shows that UR1, which is adopted in programs such as SEEP/W, ensures that the solution converges rapidly to a stable solution within a time step, but may converge to the wrong wetting front at a given elapsed time unless a sufficiently refined mesh is used. UR2 converges much more slowly within a time step, but the error in the wetting front is smaller than that generated by UR1.     

Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) technique is an unconditionally stable time-domain numerical scheme, allowing the /spl Delta/t time step to be increased beyond the Courant-Friedrichs-Lewy limit. Execution time of a simulation is inversely proportional to /spl Delta/t, and as such, increasing /spl Delta/t results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for electromagnetic compatibility problems. Once the basics of the ADI-FDTD technique are presented and the differences of the relative accuracy of ADI-FDTD and standard FDTD are discussed, the problems that benefit greatly from ADI-FDTD are described. A discussion is given on the true time savings of applying the ADI-FDTD technique. The feasibility of using higher order spatial and temporal techniques with ADI-FDTD is presented. The incorporation of frequency dependent material properties (material dispersion) into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one-dimensional and three-dimensional problem space. The scheme is shown to be both accurate and unconditionally stable.