Engineering planetary lasers for interstellar communication

Spacefaring skills evolved in the twenty-first century will enable missions of unprecedented complexity. One such elaborate project might be to develop tools for efficient interstellar data transfer. Informational links to other star systems would facilitate eventual human expansion beyond our solar system, as well as intercourse with potential extraterrestrial intelligence. This paper reports the major findings of a 600-page, 3-year, NASA-funded study examining in quantitative detail the requirements, some seemingly feasible methods, and implications of achieving reliable extrasolar communications

Modeling the HD32297 Debris Disk with Far-IR Herschel Data

HD32297 is a young A-star (~30 Myr) 112 pc away with a bright edge-on debris disk that has been resolved in scattered light. We observed the HD32297 debris disk in the far-infrared and sub-millimeter with the Herschel Space Observatory PACS and SPIRE instruments, populating the spectral energy distribution (SED) from 63 to 500{\mu}m. We aimed to determine the composition of dust grains in the HD32297 disk through SED modeling, using geometrical constraints from the resolved imaging to break degeneracies inherent in SED modeling. We found the best fitting SED model has 2 components: an outer ring centered around 110 AU, seen in the scattered light images, and an inner disk near the habitable zone of the star. The outer disk appears to be composed of grains > 2{\mu}m consisting of silicates, carbonaceous material, and water ice with an abundance ratio of 1:2:3 respectively and 90% porosity. These grains appear consistent with cometary grains, implying the underlying planetesimal population is dominated by comet-like bodies. We also discuss the 3.7{\sigma} detection of [C II] emission at 158{\mu}m with the Herschel PACS Spectrometer, making HD32297 one of only a handful of debris disks with circumstellar gas detected.Comment: 11 pages, 4 figures, accepted for publication in The Astrophysical Journa

Mechanisms of burst release from pH-responsive polymeric microparticles.

Microencapsulation of drugs into preformed polymers is commonly achieved through solvent evaporation techniques or spray drying. We compared these encapsulation methods in terms of controlled drug release properties of the prepared microparticles and investigated the underlying mechanisms responsible for the “burst release” effect. Using two different pH-responsive polymers with a dissolution threshold of pH 6 (Eudragit L100 and AQOAT AS-MG), hydrocortisone, a model hydrophobic drug, was incorporated into microparticles below and above its solubility within the polymer matrix. Although, spray drying is an attractive approach due to rapid particle production and relatively low solvent waste, the oil-in-oil microencapsulation method is superior in terms of controlled drug release properties from the microparticles. Slow solvent evaporation during the oil-in-oil emulsification process allows adequate time for drug and polymer redistribution in the microparticles and reduces uncontrolled drug burst release. Electron microscopy showed that this slower manufacturing procedure generated non-porous particles whereas thermal analysis and X-ray diffractometry showed that drug loading above the solubility limit of the drug in the polymer generated excess crystalline drug on the surface of the particles. Raman spectral mapping illustrated that drug was homogeneously distributed as a solid solution in the particles when loaded below saturation in the polymer with consequently minimal burst release

Euler number of Instanton Moduli space and Seiberg-Witten invariants

We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish. The partition function is the sum of Euler number of instanton moduli space when it is possible to apply the vanishing theorem. And we get a relation of Euler number labeled by the instanton number $k$ with Seiberg-Witten invariants, too. All calculation in this paper is done without assuming duality.Comment: LaTeX, 34 page

The ADHM Construction of Instantons on Noncommutative Spaces

We present an account of the ADHM construction of instantons on Euclidean space-time $\mathbb{R}^4$ from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parameterised by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal-Groenewold plane $\mathbb{R}^4_\hbar$ and the Connes-Landi plane $\mathbb{R}^4_\theta$.Comment: Latex, 40 page

Einstein Manifolds As Yang-Mills Instantons

It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equations from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang-Mills gauge theory and so Einstein manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.

Stability of Affine G-varieties and Irreducibility in Reductive Groups

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is identical with version 2 (version 3 is empty

Geometry and physics

We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology