MAPPING NEARLY VERTICAL DISCONTINUITIES BY EARTH RESISTIVITIES

Geophysics ◽  
1954 ◽  
Vol 19 (4) ◽  
pp. 739-760 ◽  
Author(s):  
Ö. Logn
Keyword(s):  
Potential Distribution ◽  
Apparent Resistivity ◽  
Vertical Plane ◽  
Sufficient Accuracy ◽  
Maxwell Theory ◽  
Current Electrode ◽  
Small Thickness ◽  
Integral Formulas ◽  
Approximation Formulas ◽  
The One

Following a procedure similar to the method used by Stefanesco et al. (1930) in resistivity computations for a horizontally bedded earth, integral formulas are evaluated for the potential distribution around one current electrode placed in the neighbourhood of (a) one vertical plane of discontinuity and (b) two vertical planes of discontinuity. The integral formulas are shown to be identical to the series evaluated by Hedström (1932) using a Maxwell theory of images. The apparent resistivity in the one‐current‐electrode configuration is defined, and integral formulas are given for planes of discontinuity. Because the evaluation of apparent resistivity curves across a gangue of small thickness is troublesome by these formulas, approximation formulas for a thin vertical sheet are evaluated, these are found to be of sufficient accuracy in most cases met in the field. It is suggested that nearly vertical faults, rock boundaries, and breccias in many cases give geoelectrical anomalies which can be assumed to be caused by vertical planes of discontinuity. As an example, resistivity data are presented which were taken across a breccia in Meheia, near Kongsberg, Norway.

scholarly journals Monodromy defects in free field theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenzo Bianchi ◽  
Adam Chalabi ◽  
Vladimír Procházka ◽  
Brandon Robinson ◽  
Jacopo Sisti
Keyword(s):  
Entanglement Entropy ◽  
Free Field ◽  
Operator Product ◽  
Dirac Fermions ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Defect Operator ◽  
Crucial Information ◽  
The One ◽  
Group Flow

Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free $$ \mathcal{N} $$ N = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

Instrumental expertise and musical timbre modulate the spatial representation of pitch

2020 ◽  
Vol 73 (8) ◽  
pp. 1162-1172 ◽  
Author(s):  
Carlotta Lega ◽  
Zaira Cattaneo ◽  
Noemi Ancona ◽  
Tomaso Vecchi ◽  
Luca Rinaldi
Keyword(s):  
Mental Representation ◽  
Horizontal Plane ◽  
Spatial Representation ◽  
Vertical Plane ◽  
Unified Framework ◽  
Instrumental Training ◽  
Younger Age ◽  
Bottom Side ◽  
The One ◽  
Pitch Space

Humans show a tendency to represent pitch in a spatial format. A classical finding supporting this spatial representation is the Spatial–Musical Association of Response Codes (SMARC) effect, reflecting faster responses to low tones when pressing a left/bottom-side key and to high tones when pressing a right/top-side key. Despite available evidence suggesting that the horizontal and vertical SMARC effect may be differently modulated by instrumental expertise and musical timbre, no study has so far directly explored this hypothesis in a unified framework. Here, we investigated this possibility by comparing the performance of professional pianists, professional clarinettists and non-musicians in an implicit timbre judgement task, in both horizontal and vertical response settings. Results showed that instrumental expertise significantly modulates the SMARC effect: whereas in the vertical plane a comparable SMARC effect was observed in all groups, in the horizontal plane the SMARC effect was significantly modulated by the specific instrumental expertise, with pianists showing a stronger pitch–space association compared to clarinettists and non-musicians. Moreover, the influence of pitch along the horizontal dimension was stronger in those pianists who started the instrumental training at a younger age. Results also showed an influence of musical timbre in driving the horizontal, but not the vertical, SMARC effect, with only piano notes inducing a pitch–space association. Taken together, these findings suggest that sensorimotor experience due to instrumental training and musical timbre affect the mental representation of pitch on the horizontal space, whereas the one on the vertical space would be mainly independent from musical practice.

Deformation Behavior of Cu-8wt%Ag Alloy during Equal Channel Angular Pressing

2015 ◽  
Vol 1101 ◽  
pp. 93-98
Author(s):  
Yue Shen ◽  
Chuan Ting Ren ◽  
Guo Quan Zhang ◽  
Ming Xie ◽  
Ming Wen ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Equal Channel Angular Pressing ◽  
Deformation Behavior ◽  
Shear Bands ◽  
Vertical Plane ◽  
Vertical Shear ◽  
Ecap Processing ◽  
Angular Pressing ◽  
Micro Level ◽  
The One

The shear deformation behavior of the course-grained Cu-8wt%Ag alloy processed by one pass of equal channel angular pressing (ECAP) was revealed through the metallurgical microscope and the scanning electron microscope. Through the macro-level and micro-level synthesis analysis, it is confirmed that there are two shear deformation during the ECAP processing: the one along the intersection plane (IP) and the other along the vertical plane to the IP. And it is estimated that theoretical ranges of two shear angles are-32°<θ1<0° and 43°<θ2<58° respectively. Finally, it is also proved that the evolution of the shear bands is affected by the parallel and vertical shear to the IP of the ECAP die, and that, besides the shear along the IP, the shear along the vertical plane to the IP also plays an important role during the plastic deformation.

MAGNETIC FIELDS AND VACUUM POLARIZATION AT THE PLANCK ERA

2003 ◽  
Vol 12 (07) ◽  
pp. 1289-1298 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vacuum State ◽  
Background Field ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Maxwell Theory ◽  
Yang Mills ◽  
Electron Positron ◽  
The One

The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫Bc, where [Formula: see text], yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures [Formula: see text], analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B g .

Gravity-induced wrinkle lines in vertical membranes

1981 ◽  
Vol 375 (1762) ◽  
pp. 307-325 ◽  
Keyword(s):  
Heat Flow ◽  
Diffusion Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Prime Objective ◽  
Flow Through ◽  
Flexible Membranes ◽  
The One

A theory is presented for the behaviour under self-weight of inextensible but perfectly flexible membranes supported in a vertical plane. Slack in the membrane manifests itself in the formation of (curved) wrinkle lines whose determination is the prime objective. The equilibrium and strain conditions are derived and solutions are given for several simple cases. It is shown that the wrinkle lines satisfy the one-dimensional diffusion equation and hence there are analogies, for example, with heat flow through a slab.

Pipe Self-Reinforcing Outlets: Nonlinear Analysis Towards Rational Design

1995 ◽  
Author(s):  
Claudio Carino ◽  
Fabio Carli ◽  
Carlo Cinquini ◽  
Mauro Gobbi
Keyword(s):  
Mesh Generation ◽  
Software Package ◽  
Rational Design ◽  
Structural Reliability ◽  
Sufficient Accuracy ◽  
Element Analysis ◽  
Proof Testing ◽  
Material Usage ◽  
And Performance ◽  
The One

Abstract A class of self-reinforcing outlets addressed to a wide variety of plants and pipelines is analyzed in this paper in order to examine computer simulation in comparison with bursting tests commonly adopted in industry. Based on a specific pre-processor for mesh generation, finite element analysis is performed on a workstation by a software package suitably accounting for both geometrical and material nonlinearities. Besides stress distribution visualization, high-resolution post-processor capability allows to predict, with sufficient accuracy, plastic strain trend in critical area. This may provide, on the one hand, a powerful tool in view of anticipating proof testing results and, on the other hand, a useful guideline for design purposes in view of a more rational material usage and joint configuration, paying particular attention to the overall structural reliability and performance.

Study on Autopilot Dynamics with Robust Guidance Law and Terminal Constraint in Mechanical Engineering

2013 ◽  
Vol 644 ◽  
pp. 77-80
Author(s):  
Zhi Ping Li ◽  
Jun Zhou ◽  
Jian Guo Guo
Keyword(s):  
Mechanical Engineering ◽  
Tracking Error ◽  
Vertical Plane ◽  
Lyapunov Stability Theory ◽  
Mathematic Model ◽  
Impact Angle ◽  
Guidance System ◽  
Guidance Law ◽  
The One ◽  
The Impact

A new nonlinear robust guidance law was proposed by considering autopilot dynamics. Firstly, the mathematic model was built according to relationship between target and missile in vertical plane, by introducing the one-order dynamics of autopilot in Mechanical Engineering. Secondly, the nonlinear terminal guidance was obtained by applying the H∞ control theory under the performance index of minimizing the terminal angular constraint tracking error and control energy, and the asymptotic stability of guidance system was strictly proven by Lyapunov stability theory avoiding the estimation of the time-to-go. Finally, an illustrative example was given to show that the guidance law was more robust and both the impact angle and guidance precision were met in the case of no any target information.

A brief comparison of some Kirchhoff integral formulas for migration and inversion

Geophysics ◽  
1991 ◽  
Vol 56 (8) ◽  
pp. 1164-1169 ◽  
Author(s):  
Paul Docherty
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Reflection Coefficients ◽  
Acoustic Wave Equation ◽  
Inversion Formulas ◽  
Kirchhoff Migration ◽  
Integral Formulas ◽  
The One ◽  
And Inversion ◽  
Kirchhoff Integral

Kirchhoff migration has traditionally been viewed as an imaging procedure. Usually, few claims are made regarding the amplitudes in the imaged section. In recent years, a number of inversion formulas, similar in form to those of Kirchhoff migration, have been proposed. A Kirchhoff‐type inversion produces not only an image but also an estimate of velocity variations, or perhaps reflection coefficients. The estimate is obtained from the peak amplitudes in the image. In this paper prestack Kirchhoff migration and inversion formulas for the one‐parameter acoustic wave equation are compared. Following a heuristic approach based on the imaging principle, a migration formula is derived which turns out to be identical to one proposed by Bleistein for inversion. Prestack Kirchhoff migration and inversion are, thus, seen to be the same—both in terms of the image produced and the peak amplitudes of the output.

Distortion in resistivity logging at shallow depth

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1058-1069 ◽  
Author(s):  
Tien‐Chang Lee ◽  
Brian N. Damiata
Keyword(s):  
Point Source ◽  
Line Source ◽  
Apparent Resistivity ◽  
Homogeneous Medium ◽  
Radial Distance ◽  
Ground Surface ◽  
Current Electrode ◽  
Potential Electrode ◽  
Resistivity Logging ◽  
Source Array

Owing to the proximity of an insulating ground surface, normal resistivity logging at shallow depths (less than 30 m) can yield an apparent resistivity that exceeds 200% of the formation resistivity for a homogeneous medium. The distortion is more acute for long‐normal than for short‐normal logging. Three examples from a landfill site in southern California are presented to show such distortion. The patterns of distortion are similar for logging devices consisting of either two point‐source electrodes or one point‐source and one finite length, line‐source electrode. The former electrode array is a generally accepted approximation of the latter. However, the simulated apparent resistivity for the line‐source array is greater than that for the point‐source array at any given depth. A resistivity contrast between the formation and the borehole fluid can shift the magnitude of the background apparent resistivity but does not significantly alter the pattern of distortion. The magnitude of the distortion can be reduced by placing the reference‐ground potential electrode at a radial distance that is about equal to the spacing between the downhole upper potential electrode and the upper current electrode. It can also be removed by including the radial distance in an array‐dependent geometric factor that accounts for the resistivity of the borehole fluid and the proximity of the logging device to the ground surface.

Sign in / Sign up

Export Citation Format

Share Document