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Analytical Equations (analytical + equation)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Space-Charge Limited Current from Plasma-Facing Material Surface

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 1-3 2004
S. Takamura
Abstract We have derived an exact theoretical expression for the space-charge limited current from the solid surfaces adjacent to plasmas that is applicable for an arbitrary sheath voltage. Our expression shows that the spacecharge limited current tends to saturate with the sheath voltage. This new formula is evaluated by 1-D Particle in Cell (PIC) simulation and experiment, and is in a good agreement with the simulation and experimental results. We have also obtained an analytical equation fitted to the new formula based on conventional Child-Langmuir formula by taking into account a more sophisticated dependence of the electrode potential and the plasma density through the effect of Debye shielding and a sheath expansion due to increased voltage across the sheath. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A Distributed Object-Oriented Finite-Element Analysis Program Architecture

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2001
Hung-Ming Chen
This article presents a distributed object-oriented design for a nonlinear finite-element analysis using the message-passing paradigm and a single-program, multiple-data scheme. The architecture is an extension of an existing sequential object-oriented architecture. The design recognizes the costly communication startup time penalty by attempting to minimize the frequency of communications. This is facilitated by distributing not only the elements in the model but also their associated nodes and mapping between the degrees of freedom and the analytical equations of equilibrium. The proposed object design was implemented and tested on a nonlinear static pushover analysis of three moment-resisting frames. [source]

Power-delay optimization of D-latch/MUX source coupled logic gates

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 1 2005
M. Alioto
In this paper a design strategy for MUX, XOR and D-latch source coupled logic (SCL) gates is proposed. To this end, an analytical model of the delay and the noise margin as a function of the transistors' aspect ratio and bias current is first introduced. Successively, analytical equations of the transistors' aspect ratio to meet a given noise margin specification are derived as a function of the bias current, and are then used along with the delay model to express the delay as an explicit function of the bias current and noise margin. The simplified delay expression explicitly relates speed performance to power dissipation and the noise margin, thereby providing the designer with the required understanding of the trade-offs involved in the design. Therefore, the criteria proposed allow the designer to consciously manage the power-delay trade-off. The delay dependence on the logic swing is also investigated with results showing that this delay is not necessarily reduced by reducing the logic swing, in contrast with the usual assumption. Since the results obtained are valid for all SCL gates and are independent of the CMOS process used, the guidelines provided afford a deeper understanding of SCL gates from a design point of view. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Concentration polarization in a narrow reverse osmosis membrane channel

AICHE JOURNAL, Issue 1 2010
Lianfa Song
Abstract Concentration polarization in a narrow reverse osmosis channel is bounded by the channel height and under the influence of variable transverse velocity. An attempt was made in this article to quantify concentration polarization in such a narrow membrane channel. The transverse velocity in the membrane channel was first determined and its impact on concentration polarization was investigated. Based on the concept of retained salt, analytical equations were developed for the wall salt concentration at an arbitrary point in the narrow membrane channel. Finally, development of concentration polarization in typical reverse osmosis channels under various conditions was numerically simulated and discussed. Interesting results on the details of concentration polarization in the narrow reverse osmosis channel that had never been reported before were revealed with this mechanistic model. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source]

A Mathematical Model for Photopolymerization From a Stationary Laser Light Source

MACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2005
Michael F. Perry
Abstract Summary: A mathematical model of photopolymerization is presented for a stationary laser. Termination by radical combination and radical trapping is considered. Using simplifying assumptions, we derive analytical equations for the concentration of photoinitiator and monomer in the system. With these equations, we show that the light intensity and the initial amount of photoinitiator highly influence the polymerization process and determine the shape of the polymer that is formed. We also provide an analytic expression to determine the amount of polymer formed during dark reactions. Percent conversion of monomer as a function of time at z,=,0 and r,=,0 (Data from Table 1). [source]

A new analytical method to extract the small-signal equivalent circuit of high frequency FET transistors

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2008
J. L. Olvera Cervantes
Abstract A new set of simply analytical equations is proposed as an alternative method to calculate the intrinsic transistor elements of an extended model for microwave FET's. This method is based on Y-parameters as well as on a new process to determine the differential resistances Rfs and Rfd, including the frequency effect, in such way that measurements at very low frequencies are not required and long iterative methods are avoided. The method was applied to FET's transistors and the validity of the model is certified by direct comparison with measured data from 1 to 45 GHz. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 453,457, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23130 [source]