ANALYTICAL INVESTIGATIONS IN MAGNETIC RECORDING

The Fourier method is used to provide new analytic solutions for idealized mathematical models of double-element shielded magnetoresistive (MR) recording heads. The general two-dimensional model allows analysis of various recording head configurations; a single pole head, a ring head, a dual stripe head and a differential head. The analysis accommodates both longitudinal recording (with no soft magnetic underlayer present) and perpendicular recording (in the presence of a soft underlayer). Typical field, spectral response function and output voltage pulse plots for double-element MR heads are given and compared to published, approximate solutions. The integrals arising in the determination of the Fourier series coefficients, magnetic potential and magnetic field components are expressed either as rapidly convergent infinite series or in terms of special functions to provide a more efficient means of evaluation than numerical integration. It is shown that, in many situations, it is only necessary to take the first Fourier coefficient in the calculation of output voltage pulse shapes in order to achieve sufficiently accurate results. Bi-variate regression techniques are used to provide a convenient method to approximate the first Fourier series coefficient for a broad range of typical head dimensions. The thesis goes on to examine high speed switching behaviour in two classes of recording media by considering two different particle orientation distributions; 2D random media - intended to simulate a modern thin film rigid disk, and 3D oriented media- simulating a single domain particulate tape media. The gyromagnetic switching constant of a medium is calculated directly from the Landau - Lifshitz - Gilbert (L-L-G) equation of motion, which is solved numerically. The switching constants produced are discussed and compared with published experimental values for different media

Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions

We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed hypersurface, with a boundary given by a closed spacelike 2-surface. A main result is that we obtain Hamiltonians associated to Dirichlet and Neumann boundary conditions on the gravitational field coupled to matter sources, in particular a Klein-Gordon field, an electromagnetic field, and a set of Yang-Mills-Higgs fields. The Hamiltonians are given by a covariant form of the Arnowitt-Deser-Misner Hamiltonian modified by a surface integral term that depends on the particular boundary conditions. The general form of this surface integral involves an underlying ``energy-momentum'' vector in the spacetime tangent space at the spatial boundary 2-surface. We give examples of the resulting Dirichlet and Neumann vectors for topologically spherical 2-surfaces in Minkowski spacetime, spherically symmetric spacetimes, and stationary axisymmetric spacetimes. Moreover, we show the relation between these vectors and the ADM energy-momentum vector for a 2-surface taken in a limit to be spatial infinity in asymptotically flat spacetimes. We also discuss the geometrical properties of the Dirichlet and Neumann vectors and obtain several striking results relating these vectors to the mean curvature and normal curvature connection of the 2-surface. Most significantly, the part of the Dirichlet vector normal to the 2-surface depends only the spacetime metric at this surface and thereby defines a geometrical normal vector field on the 2-surface. Properties and examples of this normal vector are discussed.Comment: 46 pages; minor errata corrected in Eqs. (3.15), (3.24), (4.37) and in discussion of examples in sections IV B,

Inflatable Aerocapture Decelerators for Mars Orbiters

A multi-disciplinary research program was recently completed, sponsored by NASA Marshall Space Flight Center, on the subject of aerocapture of spacecraft weighing up to 5 metric tons at Mars. Heavier spacecraft will require deployable drag area beyond the dimensional limits of current and planned launch fairings. This research focuses on the approach of lightweight inflatable decelerators constructed with thin films, using fiber reinforcement and having a temperature limitation of 500 C. Trajectory analysis defines trajectories for a range of low ballistic coefficients for which convective heat flux is compatible with the material set. Fluid-Structure Interaction (FSI) tools are expanded to include the rarified flow regime. Several non-symmetrical configurations are evaluated for their capability to develop lift as part of the necessary trajectory control strategy. Manufacturing technology is developed for 3-D stretch forming of polyimide films and for tailored fiber reinforcement of thin films. Finally, the mass of the decelerator is estimated and compared to the mass of a traditional rigid aeroshell

New variables, the gravitational action, and boosted quasilocal stress-energy-momentum

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covariant action principle for the Ashtekar variables. As such, the theory presented here is an Ashtekar-variable reformulation of the metric theory of quasilocal stress-energy-momentum originally due to Brown and York. This work also investigates how the quasilocal densities behave under generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is shown that under such boosts the densities behave in a manner which is similar to the simple boost law for energy-momentum four-vectors in special relativity. The developed formalism is used to obtain a collection of two-surface or boost invariants. With these invariants, one may ``build" several different mass definitions in general relativity, such as the Hawking expression. Also discussed in detail in this paper is the canonical action principle as applied to bounded spacetime regions with ``sharp corners."Comment: Revtex, 41 Pages, 4 figures added. Final version has been revised and improved quite a bit. To appear in Classical and Quantum Gravit

Complex CatSper-dependent and independent [Ca2⁺]i signalling in human spermatozoa induced by follicular fluid

STUDY QUESTION: Does progesterone in human follicular fluid (hFF) activate CatSper and do other components of hFF modulate this effect and/or contribute separately to hFF-induced Ca2+ signaling?SUMMARY ANSWER: hFF potently stimulates CatSper and increases [Ca2+]i, primarily due to high concentrations of progesterone, however,other components of hFF also contribute to [Ca2+]i signaling, including modulation of CatSper channel activity and inhibition of [Ca2+]i oscillations.WHAT IS KNOWN ALREADY: CatSper, the principal Ca2+ channel in spermatozoa, is progesterone-sensitive and essential for fertility. Both hFF and progesterone, which is present in hFF, influence sperm function and increase their [Ca2+]i.STUDY DESIGN, SIZE, DURATION: This basic medical research study used semen samples from >40 donors and hFF from >50 patients who were undergoing surgical oocyte retrieval for IVF/ICSI.PARTICIPANTS/MATERIALS, SETTING, METHODS: Semen donors and patients were recruited in accordance with local ethics approval (13/ES/0091) from the East of Scotland Research Ethics Service REC1. Activities of CatSper and KSper were assessed by patch clamp electrophysiology. Sperm [Ca2+]i responses were examined in sperm populations and single cells. Computer-assisted sperm analysis (CASA) parameters and penetration into viscous media were used to assess functional effects.MAIN RESULTS AND THE ROLE OF CHANCE: hFF and progesterone significantly potentiated CatSper currents. Under quasiphysiologicalconditions, hFF (up to 50%) failed to alter membrane K+ conductance or current reversal potential. hFF and progesterone (at an equivalent concentration) stimulated similar biphasic [Ca2+]i signals both in sperm populations and single cells. At a high hFF concentration (10%), the sustained (plateau) component of the [Ca2+]i signal was consistently greater than that induced by progesterone alone. In single cell recordings, 1% hFF-induced [Ca2+]i oscillations similarly to progesterone but with 10% hFF generation of [Ca2+]i oscillations was suppressed. After treatment to ‘strip’ lipid-derived mediators, hFF failed to significantly stimulate CatSper currents but induced small [Ca2+]i responsesthat were greater than those induced by the equivalent concentration of progesterone after stripping. Similar [Ca2+]i responses were observed when sperm pretreated with 3 μM progesterone (to desensitize progesterone responses) were stimulated with hFF or stripped hFF. hFF stimulated viscous media penetration and was more effective than the equivalent does of progesterone.LARGE SCALE DATA: N/A.LIMITATIONS, REASONS FOR CAUTION: This was an in vitro study. Caution must be taken when extrapolating these results in vivo.WIDER IMPLICATIONS OF THE FINDINGS: This study directly demonstrates that hFF activates CatSper and establishes that the biologically important effects of hFF reflect, at least in part, action on this channel, primarily via progesterone. However, these experiments also demonstrate that other components of hFF both contribute to the [Ca2+]i signal and modulate the activation of CatSper. Simple in vitro experiments performed out of the context of the complex in vivo environment need to be interpreted with caution

Single-cell analysis of [Ca²⁺]i signalling in sub-fertile men:characteristics and relation to fertilization outcome

STUDY QUESTIONWhat are the characteristics of progesterone-induced (CatSper-mediated) single cell [Ca2+]i signals in spermatozoa from sub-fertile men and how do they relate to fertilizing ability?SUMMARY ANSWERSingle cell analysis of progesterone-induced (CatSper-mediated) [Ca2+]i showed that reduced progesterone-sensitivity is a common feature of sperm from sub-fertile patients and is correlated with fertilization rate.WHAT IS KNOWN ALREADYStimulation with progesterone is a widely used method for assessing [Ca2+]i mobilization by activation of CatSper in human spermatozoa. Although data are limited, sperm population studies have indicated an association of poor [Ca2+]i response to progesterone with reduced fertilization ability.STUDY DESIGN, SIZE, DURATIONThis was a cohort study using semen samples from 21 donors and 101 patients attending the assisted conception unit at Ninewells Hospital Dundee who were undergoing ART treatment. Patients were recruited from January 2016 to June 2017.PARTICIPANTS/MATERIALS, SETTING, METHODSSemen donors and patients were recruited in accordance with local ethics approval (13/ES/0091) from the East of Scotland Research Ethics Service (EoSRES) REC1. [Ca2+]i responses were examined by single cell imaging and motility parameters assessed by computer-assisted sperm analysis (CASA).MAIN RESULTS AND THE ROLE OF CHANCEFor analysis, patient samples were divided into three groups IVF(+ve) (successful fertilization; 62 samples), IVF-FF (failed fertilization; eight samples) and ICSI (21 samples). A further 10 IVF samples showed large, spontaneous [Ca2+]i oscillations and responses to progesterone could not be analysed. All patient samples loaded with the [Ca2+]i-indicator fluo4 responded to progesterone stimulation with a biphasic increase in fluorescence (transient followed by plateau) which resembled that seen in progesterone-stimulated donor samples. The mean normalized response (progesterone-induced increase in fluorescence normalized to resting level) was significantly smaller in IVF-FF and ICSI patient groups than in donors. All samples were further analysed by plotting, for each cell, the relationship between resting fluorescence intensity and the progesterone-induced fluorescence increment. In donor samples these plots overlaid closely and had a gradient of ≈ 2 and plots for most IVF(+ve) samples closely resembled the donor distribution. However, in a subset (≈ 10%) of IVF(+ve) samples, 3/8 IVF-FF samples and one-third of ICSI samples the gradient of the plot was significantly lower, indicating that the response to progesterone of the cells in these samples was abnormally small. Examination of the relationship between gradient (regression coefficient of the plot) in IVF samples and fertilization rate showed a positive correlation. In IVF-FF and ICSI groups, the proportion of cells in which a response to progesterone could be detected was significantly lower than in donors and IVF (+ve) patients. Approximately 20% of cells in donor, IVF(+ve) and ICSI samples generated [Ca2+]i oscillations when challenged with progesterone but in IVF-FF samples only ≈ 10% of cells generated oscillations and there was a significantly greater proportion of samples where no oscillations were observed. Levels of hyperactivated motility were lower in IVF(+ve) and IVF-FF groups compared to controls, IVF-FF also having lower levels than IVF(+ve).LIMITATIONS, REASONS FOR CAUTIONThis is an in vitro study and caution must be taken when extrapolating these results in vivo.WIDER IMPLICATIONS OF THE FINDINGSThis study reveals important details of impaired [Ca2+]i signalling in sperm from sub-fertile men that cannot be detected in population studies

Limitations for change detection in multiple Gabor targets

We investigate the limitations on the ability to detect when a target has changed, using Gabor targets as simple quantifiable stimuli. Using a partial report technique to equalise response variables, we show that the log of the Weber fraction for detecting a spatial frequency change is proportional to the log of the number of targets, with a set-size effect that is greater than that reported for visual search. This is not a simple perceptual limitation, because pre-cueing a single target out of four restores performance to the level found when only one target is present. It is argued that the primary limitation on performance is the division of attention across multiple targets, rather than decay within visual memory. However in a simplified change detection experiment without cueing, where only one target of the set changed, not only was the set size effect still larger, but it was greater at 2000 msec ISI than at 250 msec ISI, indicating a possible memory component. The steepness of the set size effects obtained suggests that even moderate complexity of a stimulus in terms of number of component objects can overload attentional processes, suggesting a possible low-level mechanism for change blindness

Evanescent-wave coupled right angled buried waveguide: Applications in carbon nanotube mode-locking

In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions and deletions) and distributed systems such as MapReduce. In the case of dynamic graph streams, we use this primitive to prove the following results: -- Matching: First, there exists an $\tilde{O}(k^2)$ space algorithm that returns an exact maximum matching on the assumption the cardinality is at most $k$. The best previous algorithm used $\tilde{O}(kn)$ space where $n$ is the number of vertices in the graph and we prove our result is optimal up to logarithmic factors. Our algorithm has $\tilde{O}(1)$ update time. Second, there exists an $\tilde{O}(n^2/\alpha^3)$ space algorithm that returns an $\alpha$-approximation for matchings of arbitrary size. (Assadi et al. (2015) showed that this was optimal and independently and concurrently established the same upper bound.) We generalize both results for weighted matching. Third, there exists an $\tilde{O}(n^{4/5})$ space algorithm that returns a constant approximation in graphs with bounded arboricity. -- Vertex Cover and Hitting Set: There exists an $\tilde{O}(k^d)$ space algorithm that solves the minimum hitting set problem where $d$ is the cardinality of the input sets and $k$ is an upper bound on the size of the minimum hitting set. We prove this is optimal up to logarithmic factors. Our algorithm has $\tilde{O}(1)$ update time. The case $d=2$ corresponds to minimum vertex cover. Finally, we consider a larger family of parameterized problems (including $b$-matching, disjoint paths, vertex coloring among others) for which our subgraph sampling primitive yields fast, small-space dynamic graph stream algorithms. We then show lower bounds for natural problems outside this family