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The problem of averaging fourth-rank tensors with texture describing weight functions has been solved for orthotropic physical symmetry and for orthorhombic crystal symmetry. The results are presented in tabular form. The procedure for extending the tabular results to tetragonal, hexagonal, and cubic crystal symmetries is indicated. The solution requires the coefficients of the generalized spherical harmonic expansion of the weight function up to fourth order, and entails only those approximations required to obtain such coefficients from experimental data.

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We have observed induced currents associated with the fractional quantum Hall effect (FQHE) in a contactless two-dimensional electron gas subjected to a sweeping magnetic field. Their currentvoltage characteristics exhibit pronounced nonlinearities caused by the breakdown of the FQHE at high currents. Our results support the inter-Landau-level-scattering model of breakdown and provide a new local probe of the FQHE energy gaps at n 1͞3 and 2͞3. They are also consistent with the compositefermion picture but yield an effective mass significantly smaller than previously reported values.[S0031-9007(98)07588-7] PACS numbers: 73.40.Hm, 73.20.Dx Since its discovery, the integer quantum Hall effect (IQHE) has been the subject of considerable research activity. In early measurements [1], the IQHE was found to break down under the application of high currents. A variety of models [2][3][4][5] has been proposed to explain the origin and mechanism for the breakdown, but this remains a matter of great debate. The fractional quantum Hall effect [6] (FQHE) is phenomenologically very similar to the IQHE, despite its quite different physical origin as a many-body effect. This similarity has led to attempts to describe the FQHE in similar terms to the IQHE, the most elegant of these being the composite-fermion (CF) scheme proposed by Jain [7]. In this Letter we use a novel contactless measurement of current breakdown in the FQHE which enables direct comparison of breakdown in the IQHE and FQHE, providing a new local probe of the FQHE energy gap and a test of the CF picture.Current breakdown of the IQHE has been investigated thoroughly in GaAs-(Al,Ga)As heterojunctions and has been used to study the current distribution in transport samples. In the initial measurements of breakdown [1,5,8], critical current densities of between 0.5 and 2 Am 21 were reported, corresponding to critical Hall fields of the order of 10 4 V m 21 , inferred assuming a uniform current distribution. In subsequent measurements [9], on constricted Hall bars (with widths of the order 1 mm rather than 300 400 mm), the critical current densities measured gave critical Hall fields of 4.6 3 10 5 V m 21 . Investigation of current breakdown of the quantum Hall effect has recently been extended to fractional filling factors by Takamasu et al. [10], who report critical fields of the order 5 3 10 3 V m 21 for Landau-level filling factors n 1 and 1 3 , with linear dependence on magnetic field for the integers n 1 to 6, and on effective magnetic field B ‫ء‬ jB 2 B 1͞2 j for the fractions. The variation of critical Hall field with sample width in these measurements suggests that neither the current density nor the Hall field is uniform across the Hall bar.MacDonald et al. [11] derived a self-consistent equation describing the charge, current, and Hall-voltage distributions in a two-dimensional electron gas (2DEG) and demonstrated that the current is strongly weighted towards the edges of the sheet, with typically 80% of the Hall voltage dropped within 10 mm of the edges...