scholarly journals Validation of the stream function method used for reconstruction of experimental ionospheric convection patterns

2000 ◽  
Vol 18 (4) ◽  
pp. 454-460
Author(s):  
P.L. Israelevich ◽  
V. O. Papitashvili ◽  
A. I. Ershkovich
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Stream Function ◽  
Electric Fields ◽  
Electric Potential ◽  
Potential Distribution ◽  
Function Method ◽  
Polar Cap ◽  
Ionospheric Convection ◽  
Convection Patterns

Abstract. In this study we test a stream function method suggested by Israelevich and Ershkovich for instantaneous reconstruction of global, high-latitude ionospheric convection patterns from a limited set of experimental observations, namely, from the electric field or ion drift velocity vector measurements taken along two polar satellite orbits only. These two satellite passes subdivide the polar cap into several adjacent areas. Measured electric fields or ion drifts can be considered as boundary conditions (together with the zero electric potential condition at the low-latitude boundary) for those areas, and the entire ionospheric convection pattern can be reconstructed as a solution of the boundary value problem for the stream function without any preliminary information on ionospheric conductivities. In order to validate the stream function method, we utilized the IZMIRAN electrodynamic model (IZMEM) recently calibrated by the DMSP ionospheric electrostatic potential observations. For the sake of simplicity, we took the modeled electric fields along the noon-midnight and dawn-dusk meridians as the boundary conditions. Then, the solution(s) of the boundary value problem (i.e., a reconstructed potential distribution over the entire polar region) is compared with the original IZMEM/DMSP electric potential distribution(s), as well as with the various cross cuts of the polar cap. It is found that reconstructed convection patterns are in good agreement with the original modelled patterns in both the northern and southern polar caps. The analysis is carried out for the winter and summer conditions, as well as for a number of configurations of the interplanetary magnetic field.Key words: Ionosphere (electric fields and currents; plasma convection; modelling and forecasting)

scholarly journals Magnetospheric convection from Cluster EDI measurements compared with the ground-based ionospheric convection model IZMEM

2009 ◽  
Vol 27 (8) ◽  
pp. 3077-3087 ◽  
Author(s):  
M. Förster ◽  
Y. I. Feldstein ◽  
S. E. Haaland ◽  
L. A. Dremukhina ◽  
L. I. Gromova ◽  
...  
Keyword(s):  
High Latitude ◽  
Electric Potential ◽  
Potential Distribution ◽  
Spatial And Temporal Variation ◽  
Convection Pattern ◽  
Polar Cap ◽  
Ionospheric Convection ◽  
Electric Potential Distribution ◽  
Convection Model ◽  
The Imf

Abstract. Cluster/EDI electron drift observations above the Northern and Southern polar cap areas for more than seven and a half years (2001–2008) have been used to derive a statistical model of the high-latitude electric potential distribution for summer conditions. Based on potential pattern for different orientations of the interplanetary magnetic field (IMF) in the GSM y-z-plane, basic convection pattern (BCP) were derived, that represent the main characteristics of the electric potential distribution in dependence on the IMF. The BCPs comprise the IMF-independent potential distribution as well as patterns, which describe the dependence on positive and negative IMFBz and IMFBy variations. The full set of BCPs allows to describe the spatial and temporal variation of the high-latitude electric potential (ionospheric convection) for any solar wind IMF condition near the Earth's magnetopause within reasonable ranges. The comparison of the Cluster/EDI model with the IZMEM ionospheric convection model, which was derived from ground-based magnetometer observations, shows a good agreement of the basic patterns and its variation with the IMF. According to the statistical models, there is a two-cell antisunward convection within the polar cap for northward IMFBz+≤2 nT, while for increasing northward IMFBz+ there appears a region of sunward convection within the high-latitude daytime sector, which assumes the form of two additional cells with sunward convection between them for IMFBz+≈4–5 nT. This results in a four-cell convection pattern of the high-latitude convection. In dependence of the ±IMFBy contribution during sufficiently strong northward IMFBz conditions, a transformation to three-cell convection patterns takes place.

scholarly journals IMF <i>B</i><sub><i>y</i></sub> effects in the plasma flow at the polar cap boundary

2011 ◽  
Vol 29 (7) ◽  
pp. 1305-1315 ◽  
Author(s):  
R. Lukianova ◽  
A. Kozlovsky
Keyword(s):  
Solar Wind ◽  
Electric Fields ◽  
Plasma Flow ◽  
Relative Reduction ◽  
Polar Cap ◽  
Azimuthal Component ◽  
Ionospheric Convection ◽  
Quantitative Characteristics ◽  
Night Side ◽  
The Imf

Abstract. We used the dataset obtained from the EISCAT Svalbard Radar during 2000–2008 to study statistically the ionospheric convection in a vicinity of the polar cap boundary as related to IMF By conditions separately for northward and southward IMF. The effect of IMF By is manifested in the intensity and direction of the azimuthal component of ionospheric flow. The most significant effect is observed on the day and night sides whereas on dawn and dusk the effect is essentially less prominent. However, there is an asymmetry with respect to the noon-midnight meridian. On the day side the intensity of By-related azimuthal flow is maximal exactly at noon, whereas on the night side the maximum is shifted toward the post-midnight hours (~03:00 MLT). On the dusk side the relative reduction of the azimuthal flow is much larger than that on the dawn side. Overall, the magnetospheric response to IMF By seems to be stronger in the 00:00–12:00 MLT sector compared to the 12:00–24:00 MLTs. Quantitative characteristics of the IMF By effect are presented and partly explained by the magnetospheric electric fields generated due to the solar wind and also by the position of open-closed boundary for different IMF orientation.

Seismoelectric numerical modeling on a grid

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. N57-N65 ◽  
Author(s):  
Seth S. Haines ◽  
Steven R. Pride
Keyword(s):  
Electric Fields ◽  
Electric Potential ◽  
Potential Distribution ◽  
Seismic Waves ◽  
Fresnel Zone ◽  
Near Field ◽  
Fluid Pressure ◽  
Heterogeneous Porous Media ◽  
Time Step ◽  
Electric Potential Distribution

Our finite-difference algorithm provides a new method for simulating how seismic waves in arbitrarily heterogeneous porous media generate electric fields through an electrokinetic mechanism called seismoelectric coupling. As the first step in our simulations, we calculate relative pore-fluid/grain-matrix displacement by using existing poroelastic theory. We then calculate the electric current resulting from the grain/fluid displacement by using seismoelectric coupling theory. This electrofiltration current acts as a source term in Poisson’s equation, which then allows us to calculate the electric potential distribution. We can safely neglect induction effects in our simulations because the model area is within the electrostatic near field for the depth of investigation (tens to hundreds of meters) and the frequency ranges ([Formula: see text] to [Formula: see text]) of interest for shallow seismoelectric surveys.We can independently calculate the electric-potential distribution for each time step in the poroelastic simulation without loss of accuracy because electro-osmotic feedback (fluid flow that is perturbed by generated electric fields) is at least [Formula: see text] times smaller than flow that is driven by fluid-pressure gradients and matrix acceleration, and is therefore negligible. Our simulations demonstrate that, distinct from seismic reflections, the seismoelectric interface response from a thin layer (at least as thin as one-twentieth of the seismic wavelength) is considerably stronger than the response from a single interface. We find that the interface response amplitude decreases as the lateral extent of a layer decreases below the width of the first Fresnel zone. We conclude, on the basis of our modeling results and of field results published elsewhere, that downhole and/or crosswell survey geometries and time-lapse applications are particularly well suited to the seismoelectric method.

scholarly journals A new method to reconstruct the ionospheric convection patterns in the polar cap

1999 ◽  
Vol 17 (6) ◽  
pp. 743-748
Author(s):  
P. L. Israelevich ◽  
A. I. Ershkovich
Keyword(s):  
Stream Function ◽  
New Method ◽  
Satellite Orbits ◽  
Polar Ionosphere ◽  
Plasma Convection ◽  
Convection Pattern ◽  
Polar Cap ◽  
Minimum Number ◽  
Convection Patterns ◽  
Modelling And Forecasting

Abstract. A new method to reconstruct the instantaneous convection pattern in the Earth's polar ionosphere is suggested. Plasma convection in the polar cap ionosphere is described as a hydrodynamic incompressible flow. This description is valid in the region where the electric currents are field aligned (and hence, the Lorentz body force vanishes). The problem becomes two-dimensional, and may be described by means of stream function. The flow pattern may be found as a solution of the boundary value problem for stream function. Boundary conditions should be provided by measurements of the electric field or plasma velocity vectors along the satellite orbits. It is shown that the convection pattern may be reconstructed with a reasonable accuracy by means of this method, by using only the minimum number of satellite crossings of the polar cap. The method enables us to obtain a reasonable estimate of the convection pattern without knowledge of the ionospheric conductivity.Key words. Ionosphere (modelling and forecasting; plasma convection; polar ionosphere)

An Electric Node Concept for Solid-Shell Elements for Laminate Composite Piezoelectric Structures

2005 ◽  
Vol 72 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Lin-Quan Yao ◽  
Li Lu
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Electric Fields ◽  
Electric Potential ◽  
Potential Distribution ◽  
Smart Structure ◽  
Finite Element Models ◽  
Solid Shell ◽  
Shell Elements ◽  
Electric Potential Distribution

The eight-node solid-shell finite element models have been developed for the analysis of laminated composite plate/shell structures embedded with piezoelectric actuators and sensors. To resolve the locking problems of the solid-shell elements in laminated materials and improve accuracy, the assumed natural strain method and hybrid stress method are employed. Introduction of the concept of the electric nodes can effectively eliminate the burden of constraining the equality of the electric potential for the nodes lying on the same electrode. Furthermore, the nonlinear electric potential distribution in piezoelectric layer is described by introducing internal electric potential. The developed finite element models, especially electric potential node model, are simpler over other models but can still obtain same accuracy as exact solution described. Several examples are studied and compared with exact solution and other predicted results to illustrate the accuracy of the present model, and efficacy and effect caused by nonlinear electric potential distribution on frequency and electric fields in smart structure modeling.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

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