We describe the application of the synoptic transport equation to simulate the temporal evolution of the magnetic flux over the solar surface. This provides a means of predicting each day both the synoptic maps for the Carrington rotation starting the next day and the instantaneous map of the solar flux over the whole solar surface for the next day. The reliability of the predicted synoptic maps is tested by comparing the locations of the zero-flux contour with those of the observed maps produced by the National Solar Observatory, Kitt Peak and with the locations of Hα filaments measured on filtergrams obtained by the Big Bear Solar Observatory. We conclude that the best match at high latitudes is obtained by long-term simulations (over 20 rotations) with flux updates each rotation between latitudes ± 60°. We illustrate the use of the simulations to describe the evolution of the polar fields at the time of the polarity reversals in Cycle 23. The reconstruction of the instantaneous maps is tested by comparison with full-disk magnetograms. The method provides a simple means of estimating the large-scale flux distribution over the whole surface. It does not take account of flux emerging after the central meridian passage each rotation so it is only approximate in the activity belts but provides a reliable map beyond those latitudes.

Models of the polarity reversals of the Sun's polar magnetic fields based on the surface transport of flux are discussed and are tested using observations of the polar fields during Cycle 23 obtained by the National Solar Observatory at Kitt Peak. We have extended earlier measurements of the net radial flux polewards of ±60° and confirm that, despite fluctuations of ∼20%, there is a steady decline in the old polarity polar flux which begins shortly after sunspot minimum (although not at the same time in each hemisphere), crosses the zero level near sunspot maximum, and increases, with reversed polarity during the remainder of the cycle. We have also measured the net transport of the radial field by both meridional flow and diffusion across several latitude zones at various phases of the Cycle. We can confirm that there was a net transport of leader flux across the solar equator during Cycle 23 and have used statistical tests to show that it began during the rising phase of this cycle rather than after sunspot maximum. This may explain the early decrease of the mean polar flux after sunspot minimum. We also found an outward flow of net flux across latitudes ±60° which is consistent with the onset of the decline of the old polarity flux. Thus the polar polarity reversals during Cycle 23 are not inconsistent with the surface flux-transport models but the large empirical values required for the magnetic diffusivity require further investigation.

Differences in magnetic susceptibility between various compartments in heterogeneous samples can introduce unanticipated complications to NMR spectra. On the other hand, an understanding of these effects at the level of the underlying physical principles has led to the development of several experimental techniques that provide data on cellular function that are unique to NMR spectroscopy. To illustrate some key features of susceptibility effects we present, among a more general overview, results obtained with red blood cells and a recently described model system involving diethyl phthalate in water. This substance forms a relatively stable emulsion in water and yet it has a significant solubility of 5 mmol/L at room temperature; thus, the NMR spectrum has twice as many resonances as would be expected for a simple solution. What determines the relative intensities of the two families of peaks and can their frequencies be manipulated experimentally in a predictable way? The theory used to interpret the NMR spectra from the model system and cells was first developed in the context of electrostatics nearly a century ago, and yet some of its underlying assumptions now warrant closer scrutiny. While this insight is used in a practical way in this article, the accompanying article deals with the mathematics and physics behind this new analysis.

To make certain quantitative interpretations of spectra from NMR experiments carried out on heterogeneous samples, such as cells and tissues, we must be able to estimate the magnetic and electric fields experienced by the resonant nuclei of atoms in the sample. Here, we analyze the relationships between these fields and the fields obtained by solving the Maxwell equations that describe the bulk properties of the materials present. This analysis separates the contribution to these fields of the molecule in which the atom in question is bonded, the "host" fields, from the contribution of all the other molecules in the system, the "external" fields. We discuss the circumstances under which the latter can be found by determining the macroscopic fields in the sample and then removing the averaged contribution of the host molecule. We demonstrate that the results produced by the, so-called, "sphere of Lorentz" construction are of general validity in both static and time-varying cases. This analytic construct, however, is not "mystical" and its justification rests not on any sphericity in the system but on the local uniformity and isotropy, i.e., spherical symmetry, of the medium when averaged over random microscopic configurations. This local averaging is precisely that which defines the equations that describe the macroscopic fields. Hence, the external microscopic fields, in a suitably averaged sense, can be estimated from the macroscopic fields. We then discuss the calculation of the external fields and that of the resonant nucleus in NMR experiments.

We have used observations obtained by the National Solar Observatory at Kitt Peak to study the reversals of the polar magnetic fields in Cycle 23. We have compared them with corresponding data obtained by the Mt. Wilson Observatory, when these are available, testing both data sets against the locations of Hα filaments. Because of the unreliability of the data at extreme latitudes and because the apparent time of reversal varies with the degree of smoothing applied to the data, it is difficult to determine precise reversal time in each hemisphere from direct observations. However, we show that it is possible to obtain a better-defined and more precise reversal time using polar maps derived from simulations of the synoptic fields. These indirect values, however, depend critically on the diffusivity used in the simulations. We applied various tests to confirm an empirical value for the diffusivity parameter of about 600 km 2 s −1 and hence determined empirical reversal times of CR 1976 in the northern hemisphere and CR 1981 in the south.

Three examples of the unusual development of high-latitude large-scale features during cycle 23 are described. These features are found in synoptic plots constructed using data obtained at both the NSOKP and the MWO Observatories. Several properties of these features cannot be reproduced in direct simulations using a modified form of the flux-transport equation appropriate for synoptic fields and it is inferred that their evolution is not due solely to the advection and diffusion of decaying active region fields. The analysis shows that one feature may be related to a high-latitude bipolar region which emerged in an earlier rotation. By imposing the locations of Hα filaments on enlargements of the NSOKP daily magnetograms, we can identify the location of the other features and study their structure at high resolution. This suggests that they are related to the emergence of small magnetic knots at high latitudes. By repeating the simulations including overlays of non-random patterns of bipoles emerging at appropriate times during the simulations, it is possible to study the effects of different patterns and to reproduce some of the qualitative properties of these features not present in the direct simulations. These results support Stenflo's contention that `quite minute deviations from a random distribution (in the emergence of small-scale fields) would suffice for these fields to have global effects'.

We investigate the reliability with which magnetograph observations of the large-scale polar fields establish the zero-flux contour by comparing magnetic maps from various sources with one another and with the locations of filament structures seen on the disk in Hα filtergrams. The daily MWO and NSOKP magnetograms smoothed over 120 arc sec provide consistent large-scale zero-flux contours which align with the filaments out to heliocentric angles of about 75°. Synoptic maps match in regions where the locations of the zero-flux contour and of the filaments are maintained for several days. Attention is drawn to regions at the tips of unipolar `plumes' and the polar crown gap where the contours are variable from day to day; these are tentatively identified as regions of active reorganization of large-scale flux.

High-resolution mosaics of the solar polar magnetic fields have been constructed using individual magnetograms obtained with the video magnetograph of the Big Bear Solar Observatory, and the properties of these mosaics are demonstrated in this paper. The mosaics show selected regions of the polar fields on several days during the rising phase of Cycle 23, and are related to the global polar fields (i) by superposing the mosaic for a given day on to a full-disk SOHO-MDI magnetogram obtained on the same day, (ii) by plotting the mosaics in polar projection and using these to identify the approximate regions reported by the mosaics on the NSOKP polar synoptic plots, and (iii) by imposing the locations of the Hα filaments on to the mosaics in order to infer the neutral lines of the large-scale fields. We have studied the fine structure of the large-scale unipolar fields near the poles and, in particular, have constructed histograms of the magnetic field intensities within particular regions of the mosaics and, in this way, have estimated the ratios of the number of magnetic knots of opposite polarities within the unipolar plumes. We have also generated enlargements of the polar regions of the NSOKP daily magnetograms. These and statistical studies have shown that on days for which the BBSO mosaics are not available, the NSOKP enlargements may be used to study the high-resolution polar fields. Time-series of mosaics obtained over four-hour periods on September 6 and November 18 show that considerable evolution in the structure of existing flux knots and the formation of several new knots has taken place during these periods.

The evolution of magnetic flux at the solar surface is widely modeled by the flux transport equation. This describes the distribution of flux from instant to instant over the whole surface but does not describe how the synoptic map for one Carrington rotation evolves into the synoptic map for the next rotation. We derive the correct synoptic evolution equation, show that a simple version yields extremely accurate predictions of synoptic maps and discuss the implications for previous studies of the evolution of surface magnetic structures. We also note that the procedure yields a method of reconstructing an approximate map of the flux over the whole surface at any instant.

We have studied the evolution of several high-latitude flux `plumes', i.e., unipolar regions, trailing from active regions which emerged near sunspot maximum in cycle 23. The observed patterns are compared with simulations using a simple flux transport equation based on the observed flux for an earlier Carrington rotation. In addition to the long recognized poleward migration and diffusion of flux from active regions, it is found that the evolution of the trailing plumes may be influenced by flux which emerges above latitude 35° over areas of all scales. We describe two cases in which the emerging flux appears in the form of bipolar flux patterns which are not obviously related to sunspots. Further, we find instances in which the observed surface flux decreases or spreads at rates which cannot be explained solely in terms of diffusion using the normally accepted rates. Thus in several cases the poleward migration of flux cannot be described in terms of passive transport by advection and diffusion as considered here, and further investigation of the processes that contribute to the evolution of the polar fields is required.

The alignment of human erythrocytes in aqueous suspensions in the magnetic field B(0) (called the z-direction) of an NMR spectrometer was shown by calculating the diffusion tensor for water in the sample. The diffusion was measured using a pulsed-field-gradient spin-echo NMR method. The extent of diffusion anisotropy for water was exemplified by the values of the apparent diffusion coefficients with erythrocytes of normal shape and volume: for a typical experiment the values for the x-, y-, and z-directions were (6.88 +/- 0.17) x 10(-10), (7.07 +/- 0.17) x 10(-10), and (10.20 +/- 0.17) x 10(-10) m(2) s(-1), respectively. Cells in hypo- and hyperosmotic media were also studied and they too showed the anisotropy of the apparent diffusion coefficients but the extents were different. A new method of data analysis was developed using the Standard Add-On Packages in a Mathematica program. The experimental findings support evidence of erythrocyte alignment that was previously obtained with a high-field-gradient q-space method.

The NMR “q-space” experiment conducted on water provides information on the sizes of repeated structures on the micrometer-length scale in heterogeneous samples, including cell suspensions or tissues. Under some circumstances these plots display coherence peaks, and it has been implied theoretically that the position of the peaks will vary with the rate of molecular exchange across the membranes. This has been demonstrated (qualitatively) with human erythrocytes in suspension. Thus, in the quest for a quantitative approach to the interpretation of such data, we address here the “inverse problem,” namely the estimate of the permeability coefficient of membranes from q-space experiments. The present work describes theoretical predictions of q-space plots from molecules diffusing in a simple system of parallel semi-permeable membranes arranged with separations that alternate between two different values; this was designed to (loosely) mimic the intra- and extracellular compartments in a suspension of cells or a tissue. The development of the theory was facilitated by symbolic computation, and the analysis of synthetic data was shown to be achievable by the use of a three-layer back-propagation artificial neural network.

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In the preceding chapters we have summarized the observed properties of coronal loop structures; we now turn to the interpretation of these properties and provide an account of the physics of coronal loops. In this chapter we shall describe the models of individual loops and in the following chapter we shall consider systems of loops in the context of global models of the solar corona and of stellar coronae in general.

We here examine an active region model constructed from an ensemble of simple loops placed in a dipole magnetic structure. The emission pattern in EUV and X-rays produced by the model depends sensitively on the model heating function. Of the six models tested, the most realistic emission patterns arose from heating functions with an inverse dependence on the loop volume. Both resonant heating and nanoflare heating theories predict such a dependence and therefore pass the test.

The development of model atmospheres from the 'classical' static but deductive models to present-day dynamic but inductive models is sketched. The main problems facing theory are defined in terms of the need to produce a post-classical inductive model. Attention is focused on the most promising tool available today, the computers able to realize simulations of astrophysical systems. The direction of progress in the areas of radiative transfer, convective transport, waves and oscillations, and MHD is reviewed. It is concluded that the major outstanding radiative and hydrodynamic problems are likely to be elucidated in the foreseeable future, especially if there is a suitable commitment by the international community. However, the understanding of the behaviour of magnetic fields and their associated activity will require a longer, but no less urgent, programme.

AbstractWe discuss the appearance of solar active regions as seen in EUV line radiation in terms of a system of simple static coronal loop models. The loop models are based on those of Rosner et al. (1978) and may be understood in terms of the scaling laws introduced by these authors. We present here some generalized scaling laws which demonstrate that the global properties of loops in fixed length are insensitive to everything but the overall heating rate or the basal pressure. The model and scaling laws appear to describe hot loops (T< 106K) well. Empirically determined temperatures and densities in cooler loops are not in agreement with coronal loop models.We have computed a simple model of an active region using a dipole magnetic structure. The individual loop structures were calculated on the basis of the two different assumptions of constant basal pressure and of constant heating rate. This paper presents a preliminary discussion of the results and a comparison with observation.