scholarly journals Concurrent Ternary Galois-based Computation using Nano-apex Multiplexing Nibs of Regular Three-dimensional Networks, Part III: Layout Congestion-free Effectuation

2020 ◽  
Vol 11 (6) ◽  
pp. 21-37
Author(s):  
Anas N. Al-Rabadi
Keyword(s):  
Field Emission ◽  
Autonomous Robots ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Ic Design ◽  
Dimensional Lattice ◽  
Controlled Switching ◽  
Multi Stage ◽  
Special Case ◽  
General Method

Novel layout realizations for congestion-free three-dimensional lattice networks using the corresponding carbon-based field emission controlled switching is introduced in this article. The developed nano-based implementations are performed in three dimensions to perform the required concurrent computations for which two-dimensional implementations are a special case. The introduced realizations for congestion-free concurrent computations utilize the field-emission controlled switching devices that were presented in the first and second parts of the article for the solution of synthesis congestion and by utilizing field-emission from carbon nanotubes and nanotips. Since the concept of symmetry indices has been related to regular logic design, a more general method called Iterative Symmetry Indices Decomposition that produces regular three-dimensional lattice networks via carbon field-emission multiplexing is presented, where one obtains multi-stage decompositions whenever volume-specific layout constraints have to be satisfied. The introduced congestion-free nano-based lattice computations form new and important paths in regular lattice realizations, where applications include low-power IC design for the control of autonomous robots and for signal processing implementations.

scholarly journals Concurrent Ternary Galois-based Computation using Nano-apex Multiplexing Nibs of Regular Three-dimensional Networks, Part I: Basics

2020 ◽  
Vol 11 (5) ◽  
pp. 1-24
Author(s):  
Anas N. Al-Rabadi
Keyword(s):  
Field Emission ◽  
Carbon Fibers ◽  
Three Dimensional ◽  
Minimum Size ◽  
Dimensional Lattice ◽  
Controlled Switching ◽  
Concurrent Processing ◽  
High Regularity ◽  
Minimum Power Consumption

New implementations within concurrent processing using three-dimensional lattice networks via nano carbon-based field emission controlled-switching is introduced in this article. The introduced nano-based three-dimensional networks utilize recent findings in nano-apex field emission to implement the concurrent functionality of lattice networks. The concurrent implementation of ternary Galois functions using nano threedimensional lattice networks is performed by using carbon field-emission switching devices via nano-apex carbon fibers and nanotubes. The presented work in this part of the article presents important basic background and fundamentals with regards to lattice computing and carbon field-emission that will be utilized within the follow-up works in the second and third parts of the article. The introduced nano-based three-dimensional lattice implementations form new and important directions within three-dimensional design in nanotechnologies that require optimal specifications of high regularity, predictable timing, high testability, fault localization, self-repair, minimum size, and minimum power consumption.

scholarly journals General Method for Extending Discrete Global Grid Systems to Three Dimensions

2020 ◽  
Vol 9 (4) ◽  
pp. 233 ◽  
Author(s):  
Benjamin Ulmer ◽  
John Hall ◽  
Faramarz Samavati
Keyword(s):  
Three Dimensional ◽  
Use Cases ◽  
Three Dimensions ◽  
Grid Systems ◽  
3D Data ◽  
Third Dimension ◽  
2D And 3D ◽  
Polyhedral Projection ◽  
Global Grid ◽  
General Method

Geospatial sensors are generating increasing amounts of three-dimensional (3D) data. While Discrete Global Grid Systems (DGGS) are a useful tool for integrating geospatial data, they provide no native support for 3D data. Several different 3D global grids have been proposed; however, these approaches are not consistent with state-of-the-art DGGSs. In this paper, we propose a general method that can extend any DGGS to the third dimension to operate as a 3D DGGS. This extension is done carefully to ensure any valid DGGS can be supported, including all refinement factors and non-congruent refinement. We define encoding, decoding, and indexing operations in a way that splits responsibility between the surface DGGS and the 3D component, which allows for easy transference of data between the 2D and 3D versions of a DGGS. As a part of this, we use radial mapping functions that serve a similar purpose as polyhedral projection in a conventional DGGS. We validate our method by creating three different 3D DGGSs tailored for three specific use cases. These use cases demonstrate our ability to quickly generate 3D global grids while achieving desired properties such as support for large ranges of altitudes, volume preservation between cells, and custom cell aspect ratio.

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

Crystallography of quasi-crystals

1986 ◽  
Vol 42 (4) ◽  
pp. 261-271 ◽  
Author(s):  
T. Janssen
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Crystal Phase ◽  
Two Dimensional ◽  
Space Group ◽  
Quasi Crystals ◽  
Special Case

The symmetry of quasi-crystals, a class of materials that has recently aroused interest, is discussed. It is shown that a quasi-crystal is a special case of an incommensurate crystal phase and that it can be described by a space group in more than three dimensions. A number of relevant three-dimensional quasi-crystals is discussed, in particular dihedral and icosahedral structures. The symmetry considerations are also applied to the two-dimensional Penrose patterns.

scholarly journals Estimating oxygen distribution from vasculature in three-dimensional tumour tissue

2016 ◽  
Vol 13 (116) ◽  
pp. 20160070 ◽  
Author(s):  
David Robert Grimes ◽  
Pavitra Kannan ◽  
Daniel R. Warren ◽  
Bostjan Markelc ◽  
Russell Bates ◽  
...  
Keyword(s):  
Kernel Method ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Oxygen Distribution ◽  
Two Dimensional ◽  
Dose Painting ◽  
Positron Emission ◽  
Boost Dose ◽  
Tumour Oxygenation ◽  
General Method

Regions of tissue which are well oxygenated respond better to radiotherapy than hypoxic regions by up to a factor of three. If these volumes could be accurately estimated, then it might be possible to selectively boost dose to radio-resistant regions, a concept known as dose-painting. While imaging modalities such as 18 F-fluoromisonidazole positron emission tomography (PET) allow identification of hypoxic regions, they are intrinsically limited by the physics of such systems to the millimetre domain, whereas tumour oxygenation is known to vary over a micrometre scale. Mathematical modelling of microscopic tumour oxygen distribution therefore has the potential to complement and enhance macroscopic information derived from PET. In this work, we develop a general method of estimating oxygen distribution in three dimensions from a source vessel map. The method is applied analytically to line sources and quasi-linear idealized line source maps, and also applied to full three-dimensional vessel distributions through a kernel method and compared with oxygen distribution in tumour sections. The model outlined is flexible and stable, and can readily be applied to estimating likely microscopic oxygen distribution from any source geometry. We also investigate the problem of reconstructing three-dimensional oxygen maps from histological and confocal two-dimensional sections, concluding that two-dimensional histological sections are generally inadequate representations of the three-dimensional oxygen distribution.

THREE-BODY FORCE MODELS OF NONHYPERCENTRAL HARMONIC AND ANHARMONIC POTENTIALS IN THREE-DIMENSIONAL POTENTIALS

2008 ◽  
Vol 23 (40) ◽  
pp. 3411-3417 ◽  
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI
Keyword(s):  
Exact Solution ◽  
Body Force ◽  
Three Dimensional ◽  
Hyperspherical Harmonic ◽  
Three Dimensions ◽  
Systematic Analysis ◽  
Relative Coordinates ◽  
Internal Particle ◽  
Three Body ◽  
Special Case

We present a theoretical approach to the internal motion of a system based on three-body forces among particles in a special case, using three-body potentials. The three-body force models are more easily introduced and treated within the hyperspherical harmonic formalism. The internal particle motion is usually described by means of the Jacobian relative coordinates ρ, λ and R. The problems related to three-body nonhypercentral potentials in three dimensions are investigated. While the difficulties that arise in the study of nonhypercentral potentials are explicitly shown, we discuss some results obtained using nonhypercentral harmonic and anharmonic and some inverse power terms; however the potential can be easily generalized in order to allow a systematic analysis, which presents an exact solution to the wave function. The method is also applied to some other types of potentials.

scholarly journals Incidences with Curves in $\mathbb{R}^d$

10.37236/5840 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Micha Sharir ◽  
Adam Sheffer ◽  
Noam Solomon
Keyword(s):  
Recent Result ◽  
Degrees Of Freedom ◽  
Algebraic Curves ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Bounded Degree ◽  
Four Dimensions ◽  
Mild Conditions ◽  
Point Line ◽  
Special Case

We prove that the number of incidences between $m$ points and $n$ bounded-degree curves with $k$ degrees of freedom in ${\mathbb R}^d$ is\[ O\left(m^{\frac{k}{dk-d+1}+\varepsilon}n^{\frac{dk-d}{dk-d+1}}+ \sum_{j=2}^{d-1} m^{\frac{k}{jk-j+1}+\varepsilon}n^{\frac{d(j-1)(k-1)}{(d-1)(jk-j+1)}} q_j^{\frac{(d-j)(k-1)}{(d-1)(jk-j+1)}}+m+n\right),\]for any $\varepsilon>0$, where the constant of proportionality depends on $k, \varepsilon$ and $d$, provided that no $j$-dimensional surface of degree $\le c_j(k,d,\varepsilon)$, a constant parameter depending on $k$, $d$, $j$, and $\varepsilon$, contains more than $q_j$ input curves, and that the $q_j$'s satisfy certain mild conditions. This bound generalizes the well-known planar incidence bound of Pach and Sharir to $\mathbb{R}^d$. It generalizes a recent result of Sharir and Solomon concerning point-line incidences in four dimensions (where d=4 and k=2), and partly generalizes a recent result of Guth (as well as the earlier bound of Guth and Katz) in three dimensions (Guth's three-dimensional bound has a better dependency on $q_2$). It also improves a recent d-dimensional general incidence bound by Fox, Pach, Sheffer, Suk, and Zahl, in the special case of incidences with algebraic curves. Our results are also related to recent works by Dvir and Gopi and by Hablicsek and Scherr concerning rich lines in high-dimensional spaces. Our bound is not known to be tight in most cases.

On the measurement of turbulent magnetic diffusivities: the three-dimensional case

2013 ◽  
Vol 735 ◽  
pp. 457-472
Author(s):  
F. Cattaneo ◽  
S. M. Tobias
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Passive Scalar ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Turbulent Diffusivity ◽  
Dynamo Action ◽  
Thermally Driven ◽  
Special Case

AbstractIt has been shown that it is possible to measure the turbulent diffusivity of a magnetic field by a method involving oscillatory sources. So far the method has only been tried in the special case of two-dimensional fields and flows. Here we extend the method to three dimensions and consider the case where the flow is thermally driven convection in a large-aspect-ratio domain. We demonstrate that if the diffusing field is horizontal the method is successful even if the underlying flow can sustain dynamo action. We show that the resulting turbulent diffusivity is comparable with, although not exactly the same as, that of a passive scalar. We were not able to measure unambiguously the diffusivity if the diffusing field is vertical, but argue that such a measurement is possible if enough resources are utilized on the problem.

scholarly journals ON GOOD TRIANGULATIONS IN THREE DIMENSIONS

1992 ◽  
Vol 02 (01) ◽  
pp. 75-95 ◽  
Author(s):  
TAMAL KRISHNA DEY ◽  
CHANDERJIT L. BAJAJ ◽  
KOKICHI SUGIHARA
Keyword(s):  
Convex Hull ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Convex Polyhedra ◽  
Finite Precision ◽  
Robust Implementation ◽  
Guaranteed Quality ◽  
Point Set ◽  
Finite Precision Arithmetic ◽  
Special Case

In this paper, we give an algorithm that triangulates the convex hull of a three dimensional point set with guaranteed quality tetrahedra. Good triangulations of convex polyhedra are a special case of this problem. We also give a bound on the number of additional points used to achieve these guarantees and report on the techniques we use to produce a robust implementation of this algorithm under finite precision arithmetic.

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.

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