Liquid crystalline elastomers: the relationship between macroscopic behaviour and the level of backbone anisotropy

Nematic monodomain liquid crystalline elastomers have been prepared through in situ cross-linking of an acrylate based side-chain liquid crystalline polymer in a magnetic field. At the nematic–isotropic transition, the sample is found to undergo an anisotropic shape change. There is found to be an increase in dimensions perpendicular — and a decrease parallel — to the director, this is consistent with alignment of the polymer backbone parallel to the direction of mesogen alignment in the nematic state. From a quantitative investigation of this behaviour, we estimate the level of backbone anisotropy for the elastomer. As second measure of the backbone anisotropy, the monodomain sample was physically extended. We have investigated, in particular, the situation where a monodomain sample is deformed with the angle between the director and the extension direction approaching 90°. The behaviour on extension of these acrylate samples is related to alternative theoretical interpretations and the backbone anisotropy determined. Comparison of the chain anisotropy derived from these two approaches and the value obtained from previous small-angle neutron scattering measurements on deuterium labelled mixtures of the same polymer shows that some level of chain anisotropy is retained in the isotropic or more strictly weakly paranematic state of the elastomer. The origin and implications of this behaviour are discussed.

Memory effects in liquid crystal elastomers

Free-standing monodomain liquid crystal elastomer samples are shown to have a complete memory of the orientational configuration at the time of cross-linking. This memory is demonstrated through samples in which the parent polymer system is first aligned in a magnetic field prior to cross-linking. These films show reversible nematic-isotropic phase transitions and x-ray scattering patterns characteristic of nematic phases. The liquid crystal elastomer films exhibit a remarkable memory effect, in that the sample may be held at temperatures well above the nematic-isotropic transition for extended periods ( > 2 weeks), but on cooling into the liquid crystal phase region, both the original director alignment and the degree of preferred orientation are recovered. It is demonstrated that these novel memory effects are equilibrium in nature. The origins of this phenomena in terms of coupling between the mesogenic side-chains and the polymer network are discussed.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Inner plasma structure of the low-latitude reconnection layer

We report a clear transition through a reconnection layer at the low-latitude magnetopause which shows a complete traversal across all reconnected field lines during northwestward interplanetary magnetic field (IMF) conditions. The associated plasma populations confirm details of the electron and ion mixing and the time history and acceleration through the current layer. This case has low magnetic shear with a strong guide field and the reconnection layer contains a single density depletion layer on the magnetosheath side which we suggest results from nearly field-aligned magnetosheath flows. Within the reconnection boundary layer, there are two plasma boundaries, close to the inferred separatrices on the magnetosphere and magnetosheath sides (Ssp and Ssh) and two boundaries associated with the Alfvén waves (or Rotational Discontinuities, RDsp and RDsh). The data are consistent with these being launched from the reconnection site and the plasma distributions are well ordered and suggestive of the time elapsed since reconnection of the field lines observed. In each sub-layer between the boundaries the plasma distribution is different and is centered around the current sheet, responsible for magnetosheath acceleration. We show evidence for a velocity dispersion effect in the electron anisotropy that is consistent with the time elapsed since reconnection. In addition, new evidence is presented for the occurrence of partial reflection of magnetosheath electrons at the magnetopause current layer.

Heliospheric modulation of galactic cosmic rays during grand solar minima: past and future variations

Galactic cosmic ray flux at Earth is modulated by the heliospheric magnetic field. Heliospheric modulation potential, Φ, during grand solar minima is investigated using an open solar flux (OSF) model with OSF source based on sunspot number, R, and OSF loss on heliospheric current sheet inclination. Changing dominance between source and loss means Φ varies in- (anti-) phase with R during strong (weak) cycles, in agreement with Φ estimates from ice core records of 10Be concentration, which are in-phase during most of the last 300 years, but anti-phase during the Maunder Minimum. Model results suggest “flat” OSF cycles, such as solar cycle 20 result from OSF source and loss terms temporarily balancing throughout the cycle. Thus even if solar activity continues to decline steadily, the long-term drop in OSF through SC21 to SC23 may plateau during SC24, though reemerge in SC25 with the inverted phase relation.

DK-1D: a drift-kinetic simulation tool for modelling the shear Alfvén wave and its interaction with collisionless plasma

We present a highly accurate tool for the simulation of shear Alfven waves (SAW) in collisionless plasma. SAW are important in space plasma environments because for small perpendicular scale lengths they can support an electric field parallel to the ambient magnetic field. Electrons can be accelerated by the parallel electric field and these waves have been implicated as the source of vibrant auroral displays. However, the parallel electric field carried by SAW is small in comparison to the perpendicular electric field of the wave, making it difficult to measure directly in the laboratory, or by satellites in the near-Earth plasma environment. In this paper, we present a simulation code that provides a means to study in detail the SAW-particle interaction in both space and laboratory plasma. Using idealised, small-amplitude propagating waves with a single perpendicular wavenumber, the simulation code accurately reproduces the damping rates and parallel electric field amplitudes predicted by linear theory for varying temperatures and perpendicular scale lengths. We present a rigorous kinetic derivation of the parallel electric field strength for small-amplitude SAW and show that commonly-used inertial and kinetic approximations are valid except for where the ratio of thermal to Alfv\'{e}n speed is between 0.7 and 1.0. We also present nonlinear simulations of large-amplitude waves and show that in cases of strong damping, the damping rates and parallel electric field strength deviate from linear predictions when wave energies are greater than only a few percent of the plasma kinetic energy, a situation which is often observed in the magnetosphere. The drift-kinetic code provides reliable, testable predictions of the parallel electric field strength which can be investigated directly in the laboratory, and will help to bridge the gap between studies of SAW in man-made and naturally occuring plasma.

Reconstruction and prediction of variations in the open solar magnetic flux and interplanetary conditions

Historic geomagnetic activity observations have been used to reveal centennial variations in the open solar flux and the near-Earth heliospheric conditions (the interplanetary magnetic field and the solar wind speed). The various methods are in very good agreement for the past 135 years when there were sufficient reliable magnetic observatories in operation to eliminate problems due to site-specific errors and calibration drifts. This review underlines the physical principles that allow these reconstructions to be made, as well as the details of the various algorithms employed and the results obtained. Discussion is included of: the importance of the averaging timescale; the key differences between “range” and “interdiurnal variability” geomagnetic data; the need to distinguish source field sector structure from heliospherically-imposed field structure; the importance of ensuring that regressions used are statistically robust; and uncertainty analysis. The reconstructions are exceedingly useful as they provide calibration between the in-situ spacecraft measurements from the past five decades and the millennial records of heliospheric behaviour deduced from measured abundances of cosmogenic radionuclides found in terrestrial reservoirs. Continuity of open solar flux, using sunspot number to quantify the emergence rate, is the basis of a number of models that have been very successful in reproducing the variation derived from geomagnetic activity. These models allow us to extend the reconstructions back to before the development of the magnetometer and to cover the Maunder minimum. Allied to the radionuclide data, the models are revealing much about how the Sun and heliosphere behaved outside of grand solar maxima and are providing a means of predicting how solar activity is likely to evolve now that the recent grand maximum (that had prevailed throughout the space age) has come to an end.

Superhumps, magnetic fields and the mass ratio in AM Canum Venaticorum

We show that the observed K velocities and periodicities of AM CVn can be reconciled given a mass ratio q~0.22 and a secondary star with a modest magnetic field of surface strength B~1 T. We see that the new mass ratio implies that the secondary is most likely semidegenerate. The effect of the field on the accretion disc structure is examined. The theory of precessing discs and resonant orbits is generalized to encompass higher order resonances than 3:2 and shown to retain consistency with the new mass ratio.

Galactic cosmic ray modulation near the heliospheric current sheet

Galactic cosmic rays (GCRs) are modulated by the heliospheric magnetic field (HMF) both over decadal time scales (due to long-term, global HMF variations), and over time scales of a few hours (associated with solar wind structures such as coronal mass ejections or the heliospheric current sheet, HCS). Due to the close association between the HCS, the streamer belt, and the band of slow solar wind, HCS crossings are often associated with corotating interaction regions where fast solar wind catches up and compresses slow solar wind ahead of it. However, not all HCS crossings are associated with strong compressions. In this study we categorize HCS crossings in two ways: Firstly, using the change in magnetic polarity, as either away-to-toward (AT) or toward-to-away (TA) magnetic field directions relative to the Sun and, secondly, using the strength of the associated solar wind compression, determined from the observed plasma density enhancement. For each category, we use superposed epoch analyses to show differences in both solar wind parameters and GCR flux inferred from neutron monitors. For strong-compression HCS crossings, we observe a peak in neutron counts preceding the HCS crossing, followed by a large drop after the crossing, attributable to the so-called ‘snow-plough’ effect. For weak-compression HCS crossings, where magnetic field polarity effects are more readily observable, we instead observe that the neutron counts have a tendency to peak in the away magnetic field sector. By splitting the data by the dominant polarity at each solar polar region, we find that the increase in GCR flux prior to the HCS crossing is primarily from strong compressions in cycles with negative north polar fields due to GCR drift effects. Finally, we report on unexpected differences in GCR behavior between TA weak compressions during opposing polarity cycles.

Transmission of wireless power by magnetic resonance

The work involves investigation of a type of wireless power system wherein its analysis will yield the construction of a prototype modeled as a singular technological artifact. It is through exploration of the artifact that forms the intellectual basis for not only its prototypical forms, but suggestive of variant forms not yet discovered. Through the process it is greatly clarified the role of the artifact, its most suitable application given the constraints on the delivery problem, and optimization strategies to improve it. In order to improve maturity and contribute to a body of knowledge, this document proposes research utilizing mid-field region, efficient inductive-transfer for the purposes of removing wired connections and electrical contacts. While the description seems enough to state the purpose of this work, it does not convey the compromises of having to redraw the lines of demarcation between near and far-field in the traditional method of broadcasting. Two striking scenarios are addressed in this thesis: Firstly, the mathematical explanation of wireless power is due to J.C. Maxwell's original equations, secondly, the behavior of wireless power in the circuit is due to Joseph Larmor's fundamental works on the dynamics of the field concept. A model of propagation will be presented which matches observations in experiments. A modified model of the dipole will be presented to address the phenomena observed in the theory and experiments. Two distinct sets of experiments will test the concept of single and two coupled-modes. In a more esoteric context of the zero and first-order magnetic field, the suggestion of a third coupled-mode is presented. Through the remaking of wireless power in this context, it is the intention of the author to show the reader that those things lost to history, bound to a path of complete obscurity, are once again innovative and useful ideas.

Simulation of field-induced structural formation and transition in electromagnetorheological suspensions

A computer simulation method has been used to study the three-dimensional structural formation and transition of eleetromagnetorheological (EMR) suspensions under compatible electric and magnetic fields. When the fields are applied simultaneously and perpendicularly to each other, the particles rapidly arrange into single layer structures parallel to both fields. In each layer, there is a two-dimensional hexagonal lattice. The single layers then combine together to form thicker sheetlike structures. With the help of the thermal fluctuations, the thicker structures relax into three-dimensional close-packed structures, which may be face-centered cubic (fcc), hexagonal close-packed (hup) lattices, or, more probably, the mixture of them, depending on the initial configurations and the thermal fluctuations. On the other hand, if the electric field is applied first to induce the body-centered tetragonal (bct) columns in the system, and then the magnetic field is applied in the perpendicular direction, the bet to fee structure transition is observed in a very short time. Following that, the structure keeps on evolving due to the demagnetization effect and finally forms close-packed structures with fee and hcp lattice character. The simulation results are in agreement with the theoretical and experimental results.

Comparative Cluster/Double Star observations of the high and low latitude dayside magnetopause

The launch of the Double Star mission has provided the opportunity to monitor events at distinct locations on the dayside magnetopause, in coordination with the quartet of Cluster spacecraft. We present results of two such coordinated studies. In the first, 6 April 2004, both Cluster and the Double Star TC-1 spacecraft were on outbound transits through the dawn-side magnetosphere. Cluster observed northward moving FTEs with +/- polarity, whereas TC-1 saw -/+ polarity FTEs. The strength, motion and occurrence of the FTE signatures changes somewhat according to changes in IMF clock angle. These observations are consistent with ongoing reconnection on the dayside magnetopause, resulting in a series of flux transfer events (FTEs) seen both at Cluster and TC-1. The observed polarity and motion of each FTE signature advocates the existence of an active reconnection region consistently located between the positions of Cluster and TC-1, lying north and south of the reconnection line, respectively. This scenario is supported by the application of a model, designed to track flux tube motion, to conditions appropriate for the prevailing interplanetary conditions. The results from the model confirm the observational evidence that the low-latitude FTE dynamics is sensitive to changes in convected upstream conditions. In particular, changing the interplanetary magnetic field (IMF) clock angle in the model predicts that TC-1 should miss the resulting FTEs more often than Cluster, as is observed. For the second conjunction, on the 4 Jan 2005, the Cluster and TC-1 spacecraft all exited the dusk-side magnetosphere almost simultaneously, with TC-1 lying almost equatorial and Cluster at northern latitudes at about 4 RE from TC-1. The spacecraft traverse the magnetopause during a strong reversal in the IMF from northward to southward and a number of magnetosheath FTE signatures are subsequently observed. One coordinated FTE, studied in detail by Pu et al, [this issue], carries and inflowing energetic electron population and shows a motion and orientation which is similar at all spacecraft and consistent with the predictions of the model for the flux tube dynamics, given a near sub-solar reconnection line. This event can be interpreted either as the passage of two parallel flux tubes arising from adjacent x-line positions, or as a crossing of a single flux tube at different positions.

A numerical model of the ionospheric signatures of time-varying magneticreconnection: I. ionospheric convection

This paper presents a numerical model for predicting the evolution of the pattern of ionospheric convection in response to general time-dependent magnetic reconnection at the dayside magnetopause and in the cross-tail current sheet of the geomagnetic tail. The model quantifies the concepts of ionospheric flow excitation by Cowley and Lockwood (1992), assuming a uniform spatial distribution of ionospheric conductivity. The model is demonstrated using an example in which travelling reconnection pulses commence near noon and then move across the dayside magnetopause towards both dawn and dusk. Two such pulses, 8 min apart, are used and each causes the reconnection to be active for 1 min at every MLT that they pass over. This example demonstrates how the convection response to a given change in the interplanetary magnetic field (via the reconnection rate) depends on the previous reconnection history. The causes of this effect are explained. The inherent assumptions and the potential applications of the model are discussed.

Relationship between the near-Earth interplanetary field and the coronal source flux: dependence on timescale

The Ulysses spacecraft has shown that the radial component of the heliospheric magnetic field is approximately independent of latitude. This has allowed quantification of the total open solar flux from near-Earth observations of the interplanetary magnetic field. The open flux can also be estimated from photospheric magnetograms by mapping the fields up to the ‘‘coronal source surface’’ where the field is assumed to be radial and which is usually assumed to be at a heliocentric distance r = 2.5R_{S} (a mean solar radius, 1R_{S} = 6.96x10^{8} m). These two classes of open flux estimate will differ by the open flux that threads the heliospheric current sheet(s) inside Earth’s orbit at 2.5R_{S} < r < 1R{1} (where the mean Earth-Sun distance, 1R_{1} = 1 AU = 1.5 x 10^{11} m). We here use near-Earth measurements to estimate this flux and show that at sunspot minimum it causes only a very small (approximately 0.5%) systematic difference between the two types of open flux estimate, with an uncertainty that is of order ±24% in hourly values, ±16% in monthly averages, and between -6% and +2% in annual values. These fractions may be somewhat larger for sunspot maximum because of flux emerging at higher heliographic latitudes.

The evolution of the sun’s open magnetic flux: II. full solar cycle simulations

In this paper the origin and evolution of the Sun’s open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun’s open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.