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.

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).

scholarly journals Flux tubes in three-dimensional lattice gauge theories

1993 ◽  
Vol 48 (5) ◽  
pp. 2290-2298 ◽  
Author(s):  
Howard D. Trottier ◽  
R. M. Woloshyn
Keyword(s):  
Gauge Theories ◽  
Three Dimensional ◽  
Flux Tubes ◽  
Dimensional Lattice ◽  
Lattice Gauge ◽  
Lattice Gauge Theories

Automation of seismic design of high-rise structure with braced steel frame

2021 ◽  
Author(s):  
Xin Zhao ◽  
Gang Wang ◽  
Jinlun Cai ◽  
Junchen Guo
Keyword(s):  
Seismic Performance ◽  
Seismic Design ◽  
Structural Design ◽  
Structure Design ◽  
Steel Frame ◽  
Design Methods ◽  
Automatic Design ◽  
Component Level ◽  
Design Algorithm ◽  
High Rise

<p>With the continuous development and progress of society, the structure of high-rise buildings has been paid more and more attention by the engineering community. However, the existing high- rise structure design methods often have a lot of redundancy and have a lot of room for optimization. Most of the existing seismic design methods of high-rise structures are based on engineering experience and manual iterative methods, so that the efficiency of design can not meet the needs of the society. if the method of design automation is adopted, the workload of designers can be greatly reduced and the efficiency of structural design can be improved. Based on the digital modeling theory, this paper proposes a MAD automatic design algorithm, in which the designer provides the initial design of the structure, and the algorithm carries out the modeling, analysis, optimization and design of each stage of the structure, and finally obtains the optimal structure. The structural design module of this algorithm starts from the component level, when the component constraint design meets the limit requirements of the specification, it enters and completes the component constraint design and the global constraint design of the structure in turn. In this paper, taking a ten-story braced steel frame high-rise structure as an example, the optimal design is carried out, and its seismic performance is analyzed. the results show that the MAD automatic design algorithm can distribute the materials to each part reasonably, which can significantly improve the seismic performance of the structure and realize the effective seismic design.</p>

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