When does the algebraic Riccati equation have a negative semi-definite solution?

Find a reasonable necessary and sufficient frequency domain condition, i.e, a condition in terms of the rational matrix ∂W, or possibly in terms of the two-variable rational matrix W, for the existence of a real symmetric negative semi-definite solution of the algebraic Riccati equation

Magnetic Properties of a Superconductor with no Inversion Symmetry

We study the magnetic properties of a superconductor in a crystal without $z \to -z$ symmetry, in particular how the lack of this symmetry exhibits itself. We show that, though the penetration depth itself shows no such effect, for suitable orientation of magnetic field, there is a magnetic field discontinuity at the interface which shows this absence of symmetry. The magnetic field profile of a vortex in the $x-y$ plane is shown to be identical to that of an ordinary anisotropic superconductor except for a shift in the $-z$ direction by ${\tilde \kappa} \lambda_x$ (see errata). For a vortex along $z$, there is an induced magnetization along the radial direction.Comment: J. Low Temp. Physics, 140, 67 (2005); with Errat

Maturation of auditory temporal integration and inhibition assessed with event-related potentials (ERPs)

Background: We examined development of auditory temporal integration and inhibition by assessing electrophysiological responses to tone pairs separated by interstimulus intervals (ISIs) of 25, 50, 100, 200, 400, and 800 ms in 28 children aged 7 to 9 years, and 15 adults.Results: In adults a distinct neural response was elicited to tones presented at ISIs of 25 ms or longer, whereas in children this was only seen in response to tones presented at ISIs above 100 ms. In adults, late N1 amplitude was larger for the second tone of the tone pair when separated by ISIs as short as 100 ms, consistent with the perceptual integration of successive stimuli within the temporal window of integration. In contrast, children showed enhanced negativity only when tone pairs were separated by ISIs of 200 ms. In children, the amplitude of the P1 component was attenuated at ISIs below 200 ms, consistent with a refractory process.Conclusions: These results indicate that adults integrate sequential auditory information into smaller temporal segments than children. These results suggest that there are marked maturational changes from childhood to adulthood in the perceptual processes underpinning the grouping of incoming auditory sensory information, and that electrophysiological measures provide a sensitive, non-invasive method allowing further examination of these changes

ADvanced IMage Algebra (ADIMA): a novel method for depicting multiple sclerosis lesion heterogeneity, as demonstrated by quantitative MRI.

There are modest correlations between multiple sclerosis (MS) disability and white matter lesion (WML) volumes, as measured by T2-weighted (T2w) magnetic resonance imaging (MRI) scans (T2-WML). This may partly reflect pathological heterogeneity in WMLs, which is not apparent on T2w scans

Solar cycle variation in solar f-mode frequencies and radius

Using data from the Global Oscillation Network Group (GONG) covering the period from 1995 to 1998, we study the change with solar activity in solar f-mode frequencies. The results are compared with similar changes detected from the Michelson Doppler Imager (MDI) data. We find variations in f-mode frequencies which are correlated with solar activity indices. If these changes are due to variation in solar radius then the implications are that the solar radius decreases by about 5 km from minimum to maximum activity.Comment: To appear in Solar Physic

Probing the Neutron Star Interior with Glitches

With the aim of constraining the structural properties of neutron stars and the equation of state of dense matter, we study sudden spin-ups, glitches, occurring in the Vela pulsar and in six other pulsars. We present evidence that glitches represent a self-regulating instability for which the star prepares over a waiting time. The angular momentum requirements of glitches in Vela indicate that at least 1.4% of the star's moment of inertia drives these events. If glitches originate in the liquid of the inner crust, Vela's `radiation radius' $R_\infty$ must exceed ~12 km for a mass of 1.4 solar masses. The isolated neutron star RX J18563-3754 is a promising candidate for a definitive radius measurement, and offers to further our understanding of dense matter and the origin of glitches.Comment: Invited talk at the Pacific Rim Conference on Stellar Astrophysics, Hong Kong, Aug. 1999. 9 pages, 5 figure

Experiments on Multidimensional Solitons

This article presents an overview of experimental efforts in recent years related to multidimensional solitons in Bose-Einstein condensates. We discuss the techniques used to generate and observe multidimensional nonlinear waves in Bose-Einstein condensates with repulsive interactions. We further summarize observations of planar soliton fronts undergoing the snake instability, the formation of vortex rings, and the emergence of hybrid structures.Comment: review paper, to appear as Chapter 5b in "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer-Verlag

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning