Some Notes on the Interpretation of Rapid Fluctuations in Earth-Currents Observed in High Latitudes

[PREFACE] This report was prepared as a part of the Interdisciplinary study of the upper atmospheric disturbance in the polar regions that is conducted at the Geophysical Institute under Dr, C. T. Elvey, Director of the Institute. The report is primarily intended for the student of geophysics who is interested in this subject. A part of the mathematical procedure that was previously given by Prof. A. T. Price (reference 9 in end of paper) is included in Sections 4 to 6 with some modifications so as to enable the student to follow, without referring to Prof. Price’s paper, the derivation of the formulae which are used in the present discussion* and to apply the method to similar problems. November 15, 1958 M. S.This paper shows that a periodically varying infinite linear current, or a periodically varying turbulent circular current of small radius (here approximated by a magnetic dipole with a changing dipole moment), in the ionosphere, which will give rise to magnetic variations of observed order of magnitude, is adequate for producing voltage differences in the ground of order 0 .1 to 1 volt per kilometer that are frequently observed in high latitudes during disturbed periods. It appears difficult to interpret the earth-current record in terms of its primary origin, unless the distribution of the perturbing magnetic field and that of electric conductivity of the earth are both adequately known. However, the earth-current record is a good indicator of the upper atmospheric disturbance in the polar regions.Ye

A Note on Harmonic Analysis of Geophysical Data with Special Reference to the Analysis of Geomagnetic Storms

Some geophysical characteristics tend to have a fixed distribution relative to the sun. An example is the distribution of air temperature on an ideal earth that is perfectly symmetrical (e.g., in its pattern of land and water) about its axis of rotation. In such a case the geophysical characteristic at any fixed station on the earth undergoes a daily variation that depends only on local time (and latitude and season). This simple pattern of daily change may be modified by intrinsic changes in the solar influences on the earth. The harmonic components of the daily variation at any station may in this case undergo phase changes, in some respects corresponding to Doppler shifts of frequency in optical or sonic phenomena. Care is then needed if the results of harmonic analysis are to be properly interpreted. Such interpretation is discussed with reference to the parts Dst and DS of the magnetic storm variations. Like caution must be observed in cases where the amplitude of a harmonic variation changes,with fixed phase.Scientific Report No. 1 -- Contract No. AF 19(6o4)-2l63 April 18, I960 -- Geophysics Research Directorate Air Force Cambridge Research Center Air Research and Development Command United States Air Force Bedford, MassachusettsYe

Th�nen and the New Economic Geography

In this paper, I explain Th�nen's pioneering work on industrial agglomeration. In my opinion, Th�nen's thinking on industrial agglomeration was not only amazingly advanced for his time, but in many respects remains novel even today. It is shown that if we unify Th�nen's well-known theory on agricultural land use with this pioneering work on industrial agglomeration by using modern tools, then we essentially come up with a prototype of New Economic Geography model.

A Study of the Morphology of Magnetic Storms Great Magnetic Storms

Average characteristics are determined for 74 great magnetic storms with sudden commencements that occurred in 1902-1945. The storm field is resolved for different epochs of storm time into tv;o parts: (i) Dst, which is independent of local time, that is, of longitude A, relative to the sun, and (ii) DS, which depends on A . They are obtained, for each of the three magnetic elements, declination, horizontal force, and vertical force, at eight geomagnetic latitudes ranging from 80°N to 1°S. DS is harmonically analyzed; the first harmonic component is shown to be the main component of DS. The storm-time course of this component is compared with that of Dst; DS attains its maximum earlier and decays more rapidly. The results of the analysis of great storms are compared with those for weak and moderate storms that were reported previously. Some characteristics of Dst change with intensity. Except in magnitude, main characteristics of DS are independent of intensity.The research reported in the document has been sponsored by the Air Force Cambridge Research Center, Air Research and Development Command, under Contract No. AF 19(604)-2163.LIST OF TABLES -- LIST OF FIGURES -- ABSTRACT -- 1. INTRODUCTION -- 2. OBSERVATORIES -- 3. STORM-TIME VARIATIONS : 3.1 Dst in the geomagnetic-north component, Hgm ; 3.2 Dst in the geomagnetic-east component, Egm ; 3.3 Dst in the vertical force Z -- 4. DISTURBANCE DAILY VARIATIONS -- 5. FIRST HARMONIC COMPONENT OF DS -- 6 . HIGHER HARMONIC COMPONENTS OF DS AND SD -- 7. COMPARISON OF Dst AND DS -- 8 . SEASONAL VARIATIONS IN Dst : 8.1 Seasonal variation in Dst(H); season d and season j ; 8.2 Seasonal variation in Dst(H); season e and season s -- 9. SEASONAL VARIATIONS IN DS -- 10. CONCLUSION -- 11. ACKNOWLEDGEMENTS -- REFERENCESYe

A Study of the Morphology of Magnetic Storms: Moderate Magnetic Storms

Some average characteristics are determined for 136 moderate magnetic storms with sudden commencements that occurred during the interval 1902-1945. The average storm field is resolved for different epochs of storm time st into Dst, independent of local time, that is, of longitude X , relative to the sun, and into DS, that depends on X , Part DS is expressed in terms of harmonic components with respect to X , and like Dst, the amplitudes and phases of these components, are functions of st and of geomagnetic latitude. They are determined, for each of the three magnetic elements, declination, horizontal force, and vertical force, at eight geomagnetic latitudes ranging from 80*N to 1°S. In the first, and main harmonic component of DS, its variations with respect to storm time differs notably from that of Dst: its maximum is attained earlier and its decay is more rapid. The storm -time changes of the smaller harmonic components of DS have been less fully determined. The average characteristics of moderate storms are compared with those of weak storms.The research reported in the document has been sponsored by the Air Force Cambridge Research Center, Air Research and Development Command, under Contract No, AF 19(604)-1732. AF 19(604)-1732 AFCRC-TR-57-295 AD 117-256LIST OF TABLES -- LIST OF FIGURES -- ABSTRACT -- 1. INTRODUCTION -- 2. THE OBSERVATORIES -- 3. THE STORM-TIME VARIATIONS : 3.1 Dst in the Geomagnetic-North Component, Hgm ; 3.2 Dst in the Geomagnetic-East Component, Egm ; 3.3 Dst in the Vertical Force -- 4. THE DISTURBANCE DAILY VARIATIONS -- 5. THE FIRST COMPONENT OF DS -- 6 „ THE HIGHER HARMONIC COMPONENTS OF DS AND SD -- 7. COMPARISON OF Dst AND DS -- 8 „ CONCLUSION : 8.1 The Intensity Index of Magnetic Storms ; 8.2 The Dst Variations ; 8.3 The DS and SD Variations ; 8.4 Future Plans -- 9. ACKNOWLEDGEMENTS -- REFERENCESYe

Error estimates of a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations

Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerkin method and Brezzi-Pitkaranta's stabilization method. It maintains the advantages of both methods; (i) It is robust for convection-dominated problems and the system of linear equations to be solved is symmetric. (ii) Since the P1 finite element is employed for both velocity and pressure, the number of degrees of freedom is much smaller than that of other typical elements for the equations, e.g., P2/P1. Therefore, the scheme is efficient especially for three-dimensional problems. The theoretical convergence orders are recognized numerically by two- and three-dimensional computations

The Dynamics of Knowledge Diversity and Economic Growth

How is long run economic growth related to the endogenous diversity of knowledge? We formulate and study a microeconomic model of knowledge creation, through the interactions among a group of heterogeneous R & D workers, embedded in a growth model to address this question. In contrast with the traditional literature, in our model the composition of the research work force in terms of knowledge heterogeneity matters, in addition to its size, in determining the production of new knowledge. Moreover, the heterogeneity of the work force is endogenous. Income to these workers accrues as patent income, whereas transmission of newly created knowledge to all such workers occurs due to public transmission of patent information. Knowledge in common is required for communication, but differential knowledge is useful to bring originality to the endeavor. Whether or not the system reaches the most productive state depends on the strength of the public knowledge transmission technology. Equilibrium paths are found analytically. Long run economic growth is positively related to both the effectiveness of pairwise R & D worker interaction and to the effectiveness of public knowledge transmission.knowledge creation; knowledge externalities; microfoundations of endogenous growth; knowledge diversity and growth