The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent "accurately" harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of...

A field-theoretic description of the critical behavior of weakly disordered systems with a p-component order parameter is given. For systems of an arbitrary dimension in the range from three to four, a renormalization group analysis of the effective replica Hamiltonian of the model with an interaction potential without replica symmetry is given in the two-loop approximation. For the case of the...

Using H∞ control, the design problem is formulated in terms of user defined weighting polynomials on the process closed-loop Sensitivity functions to achieve desired closed-loop performance and robust stability in the presence of process modelling error. In this paper stability conditions , in terms of the process sensitivity functions, are derived for processes containing a pure time delay for...

w x Ž . In 1948, Paul Erdos E1 proved the irrationality of h 1 . Recently, ̋ 2 w x Peter Borwein used Pade approximation techniques B1 and some coḿ w x Ž . plex analysis methods B2 to prove the irrationality of both h 1 and q Ž . Ln 2 . Here we present a proof in the spirit of Apery’s magnificent proof ́ q Ž . w x of the irrationality of z 3 A , which was later delightfully accounted by w x Alf v...

A gyrokinetic toroidal particle code for a 3-dimensional nonlinear turbulence simulation (GT3D) has been developed to study the ion temperature gradient driven – trapped electron mode (ITG-TEM) turbulence in tokamak plasmas. From linear zonal flow damping tests and nonlinear ITG simulations, it is shown that a new method based on a canonical Maxwellian distribution is essential to simulate corr...

Abstract: A space-time multiscale model for wave propagation in heterogeneous media is developed. The model builds on the authors’ previous work on the higher-order mathematical homogenization theory with multiple spatial and temporal scales, and is aimed at addressing the issues of stability and mathematical consistency. Starting from the weak forms of homogenized macroscopic equations of moti...

Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (M...

We have extended the utility of NMR as a technique to probe porous media structure over length scales of ;100–2000 mm by using the spin 1/2 noble gas Xe imbibed into the system’s pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coef...

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-depe...