scholarly journals Three-dimensional lattice logic circuits, Part III: Solving 3D volume congestion problem

2005 ◽  
Vol 18 (1) ◽  
pp. 29-43 ◽  
Author(s):  
Anas Al-Rabadi
Keyword(s):  
Three Dimensional ◽  
Logic Circuits ◽  
Two Dimensional ◽  
Regular Lattice ◽  
3D Design ◽  
Dimensional Lattice ◽  
Multiple Valued Logic ◽  
Multi Stage ◽  
3D Volume ◽  
Logic Functions

This part is a continuation of the first and second parts of my paper. In a previous work, symmetry indices have been related to regular logic circuits for the realization of logic functions. In this paper, a more general treatment that produces 3D regular lattice circuits using operations on symmetry indices is presented. A new decomposition called the Iterative Symmetry Indices Decomposition (ISID) is implemented for the 3D design of lattice circuits. The synthesis of regular two-dimensional circuits using ISID has been introduced previously, and the synthesis of area-specific circuits using ISID has been demonstrated. The new multiple-valued ISID algorithm can have several applications such as: (1) multi-stage decompositions of multiple valued logic functions for various lattice circuit layout optimizations, and (2) the new method is useful for the synthesis of ternary functions using three-dimensional regular lattice circuits whenever volume-specific layout constraints have to be satisfied.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

Design of Two-Dimensional Ultrasonic Phased Array Transducers

2005 ◽  
Vol 127 (3) ◽  
pp. 336-344 ◽  
Author(s):  
Shyamal C. Mondal ◽  
Paul D. Wilcox ◽  
Bruce W. Drinkwater
Keyword(s):  
Phased Array ◽  
Three Dimensional ◽  
Array Element ◽  
Two Dimensional ◽  
Circular Array ◽  
Single Location ◽  
Ultrasonic Phased Array ◽  
3D Point Spread Function ◽  
3D Volume ◽  
Simulation And Evaluation

Two-dimensional (2D) phased arrays have the potential to significantly change the way in which engineering components in safety critical industries are inspected. In addition to enabling a three-dimensional (3D) volume of a component to be inspected from a single location, they could also be used in a C-scan configuration. The latter would enable any point in a component to be interrogated over a range of solid angles, allowing more accurate defect characterization and sizing. This paper describes the simulation and evaluation of grid, cross and circular 2D phased array element configurations. The aim of the cross and circle configurations is to increase the effective aperture for a given number of elements. Due to the multitude of possible array element configurations a model, based on Huygens’ principle, has been developed to allow analysis and comparison of candidate array designs. In addition to the element configuration, key issues such as element size, spacing, and frequency are discussed and quantitatively compared using the volume of the 3D point spread function (PSF) as a measurand. The results of this modeling indicate that, for a given number of elements, a circular array performs best and that the element spacing should be less than half a wavelength to avoid grating lobes. A prototype circular array has been built and initial results are presented. These show that a flat bottomed hole, half a wavelength in diameter, can be imaged. Furthermore, it is shown that the volume of the 3D reflection obtained experimentally from the end of the hole compares well with the volume of the 3D PSF predicted for the array at that point.

scholarly journals Three-dimensional lattice logic circuits, Part II: Formal methods

2005 ◽  
Vol 18 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Anas Al-Rabadi
Keyword(s):  
Formal Methods ◽  
Fault Localization ◽  
Three Dimensional ◽  
Logic Circuits ◽  
Design Methods ◽  
Algebraic Methods ◽  
Automatic Design ◽  
Important Class ◽  
Dimensional Lattice ◽  
Future Technologies

This paper introduces formal algebraic methods for the design of three-dimensional (3D) lattice circuits that were discussed in the first part of my article. New regular 3D logic circuits are introduced, where the application of ternary decompositions into regular three-dimensional lattice circuits is shown. Lattice circuits represent an important class of regular logic circuits that allow for local interconnections, predictable timing fast fault localization, and self-repair. The introduced design methods can be used for the automatic design of logic circuits in 3D for applications and future technologies that require such topologies.

scholarly journals Three-dimensional lattice logic circuits, Part I: Fundamentals

2005 ◽  
Vol 18 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Anas Al-Rabadi
Keyword(s):  
Circuit Design ◽  
Fault Localization ◽  
Three Dimensional ◽  
Logic Circuits ◽  
Logic Circuit ◽  
Device Performance ◽  
Important Class ◽  
Future Directions ◽  
Dimensional Lattice ◽  
Current Technology

Fundamentals of regular three-dimensional (3D) lattice circuits are introduced. Lattice circuits represent an important class of regular circuits that allow for local interconnections, predictable timing, fault localization, and self-repair. In addition, three-dimensional lattice circuits can be potentially well suited for future 3D technologies, such as nanotechnologies, where the intrinsic physical delay of the irregular and lengthy interconnections limits the device performance. Although the current technology does not offer a menu for the immediate physical implementation of the proposed three-dimensional circuits, this paper deals with three-dimensional logic circuit design from a fundamental and foundational level for a rather new possible future directions in designing digital logic circuits.

A COMPARISON BETWEEN THE TWO-DIMENSIONAL AND THREE-DIMENSIONAL LATTICES

2004 ◽  
Vol 18 (25) ◽  
pp. 1301-1309 ◽  
Author(s):  
ANDREI DOLOCAN ◽  
VOICU OCTAVIAN DOLOCAN ◽  
VOICU DOLOCAN
Keyword(s):  
Lattice Constant ◽  
Cohesive Energy ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Dimensional Lattice ◽  
Analytical Formulae ◽  
Three Dimensional Space

By using a new Hamiltonian of interaction we have calculated the interaction energy for two-dimensional and three-dimensional lattices. We present also, approximate analytical formulae and the analytical formulae for the constant of the elastic force. The obtained results show that in the three-dimensional space, the two-dimensional lattice has the lattice constant and the cohesive energy which are smaller than that of the three-dimensional lattice. For appropriate values of the coupling constants, the two-dimensional lattice in a two-dimensional space has both the lattice constant and the cohesive energy, larger than that of the two-dimensional lattice in a three-dimensional space; this means that if there is a two-dimensional space in the Universe, this should be thinner than the three-dimensional space, while the interaction forces should be stronger. On the other hand, if the coupling constant in the two-dimensional lattice in the two-dimensional space is close to zero, the cohesive energy should be comparable with the cohesive energy from three-dimensional space but this two-dimensional space does not emit but absorbs radiation.

Design Methods of Volute Casings for Turbocharger Turbine Applications

1996 ◽  
Vol 210 (2) ◽  
pp. 149-156 ◽  
Author(s):  
H Chen
Keyword(s):  
Experimental Data ◽  
Potential Flow ◽  
Design Method ◽  
Three Dimensional ◽  
Design Methods ◽  
Two Dimensional ◽  
Aerodynamic Design ◽  
3D Design ◽  
Flow Equations ◽  
Good Agreement

This paper discusses aerodynamic design methods of volute casings used in turbocharger turbines. A quasi-three-dimensional (Q-3D) design method is proposed in which a group of extended two-dimensional potential flow equations and the streamline equation are numerically solved to obtain the geometry of spiral volutes. A tongue loss model, based on the turbulence wake theory, is also presented, and good agreement with experimental data is shown.

(TP-EDOT)2PF6—Two-dimensional spin array in a three-dimensional lattice

2006 ◽  
Vol 142 (3-4) ◽  
pp. 285-290
Author(s):  
H. Yamochi ◽  
M. Soeda ◽  
J. Hagiwara ◽  
G. Saito
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Lattice
Sign in / Sign up

Export Citation Format

Share Document