scholarly journals Resistivity modeling for arbitrarily shaped two dimensional structures. Part I. Theoretical formulation

1976 ◽  
Author(s):  
A. Dey ◽  
H.F. Morrison
Keyword(s):  
Two Dimensional ◽  
Theoretical Formulation ◽  
Resistivity Modeling

scholarly journals Random Assignment Problems on 2d Manifolds

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
D. Benedetto ◽  
E. Caglioti ◽  
S. Caracciolo ◽  
M. D’Achille ◽  
G. Sicuro ◽  
...  
Keyword(s):  
Assignment Problem ◽  
Unit Area ◽  
Constant Term ◽  
Beltrami Operator ◽  
Explicit Calculation ◽  
Dimensional Manifold ◽  
Two Dimensional ◽  
Random Assignment ◽  
Assignment Problems ◽  
Theoretical Formulation

AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$ Ω of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$ E Ω ( N ) ∼ 1 / 2 π ln N with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$ ln N ln ln N . In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$ Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$ Ω . We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

2017 ◽  
Vol 31 (06) ◽  
pp. 1730001 ◽  
Author(s):  
Jorge V. José
Keyword(s):  
Phase Structure ◽  
Vortex Pair ◽  
Spin Correlation ◽  
Coulomb Gas ◽  
Theoretical Physics ◽  
Xy Model ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Abelian Gauge ◽  
Gauge Symmetries

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii–Kosterlitz–Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin–spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical [Formula: see text] temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.

A Method to Predict Rudder Stall Inception from Two-dimensional Airfoil Data

2014 ◽  
Vol 58 (01) ◽  
pp. 1-19
Author(s):  
Michael J. Hughes ◽  
Young T. Shen
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Stall Inception ◽  
Low Aspect Ratio ◽  
Aspect Ratios ◽  
Flow Similarity ◽  
Naca 0015 ◽  
Naca 0012

The behavior of the force on a rudder changes significantly after the inception of stall, requiring different mathematical formulae to compute rudder forces prior-and poststall. Determining the inception angle at which stall occurs is important for predicting the rudder force on a maneuvering ship. A method to compute the inception angle of stall on a rudder is presented in this article. The theoretical formulation is based on a flow similarity approach, which relates three-dimensional rudder stall inception with two-dimensional airfoil data. Rudders are low-aspect ratio wings, and the three-dimensional lift is based on the low-aspect ratio wing theory. The two-dimensional airfoil stall data are obtained from National Advisory Committee for Aeronautics (NACA) reports. The derived theory is first validated with wind tunnel data from foils with a NACA 0015 profile of aspect ratios 1, 2, and 3. The theory is also validated with data from foils with a NACA 0012 profile and an aspect ratio of 2, 3, and 6.

GAUGE THEORY BASED ON NONLINEAR LIE SUPERALGEBRAS AND STRUCTURE OF 2D DILATON SUPERGRAVITY

1994 ◽  
Vol 09 (07) ◽  
pp. 1137-1151 ◽  
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Gauge Theory ◽  
Lie Superalgebras ◽  
Gravitation Theory ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Poincaré Algebra ◽  
Symmetry Structure

We construct a gauge theory based on general nonlinear Lie superalgebras. The generic form of "dilaton" supergravity is derived from nonlinear super-Poincaré algebra, which exhibits a gauge-theoretical formulation in two-dimensional gravitation theory, and clarifies the symmetry structure of two-dimensional dilaton supergravity.

Synthetic aperture diffraction tomography for three-dimensional imaging

2009 ◽  
Vol 465 (2109) ◽  
pp. 2877-2895 ◽  
Author(s):  
Francesco Simonetti ◽  
Lianjie Huang
Keyword(s):  
World War Ii ◽  
High Resolution ◽  
Three Dimensional ◽  
Synthetic Aperture ◽  
Sensor Technology ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Three Dimensional Objects ◽  
Aperture Diffraction

Tomography of complex three-dimensional objects with ultrasound or microwave has been a long-standing goal since the introduction of these technologies after World War II. While current state-of-the-art systems can provide high-resolution images of cylindrical objects characterized by a two-dimensional structure, the three-dimensional case remains an open challenge owing to current limitations of sensor technology and computer power. Here, this problem is addressed by means of a synthetic aperture technique that, while using hardware technology developed for two-dimensional problems, accounts for the complexity of three-dimensional scattering and leads to high-resolution three-dimensional reconstructions. In this paper, we present the theoretical formulation of this new approach and illustrate it by means of a numerical example.

2-D resistivity modeling: An approach to arrays parallel to the strike direction

Geophysics ◽  
1991 ◽  
Vol 56 (7) ◽  
pp. 941-950 ◽  
Author(s):  
P. Queralt ◽  
J. Pous ◽  
A. Marcuello
Keyword(s):  
Mixed Boundary ◽  
Electrical Potential ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Exponential Functions ◽  
Direction Parallel ◽  
Strike Direction ◽  
Resistivity Modeling ◽  
Shape Of Potential

An algorithm for two‐dimensional electrical resistivity modeling using the finite‐element method with mixed boundary conditions can calculate the electrical potential along any arbitrary direction. In the particular case of the direction parallel to the strike of the structure, a numerical singularity occurs. We resolved it by calculating the potential near the singularity and improving the involved interpolation of the transformed potential. Investigating the shape of potential in the Fourier transformed space, we conclude that this interpolation may combine logarithmic and exponential functions.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

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