Comet dust as a mixture of aggregates and solid particles: model consistent with ground-based and space-mission results

The most successful model of comet dust presents comet particles as aggregates of submicron grains. It qualitatively explains the spectral and angular change in the comet brightness and polarization and is consistent with the thermal infrared data and composition of the comet dust obtained {\it in situ} for comet 1P/Halley. However, it experiences some difficulties in providing a quantitative fit to the observational data. Here we present a model that considers comet dust as a mixture of aggregates and compact particles. The model is based on the Giotto and Stardust mission findings that both aggregates (made mainly of organics, silicates, and carbon) and solid silicate particles are present in the comet dust. We simulate aggregates as {\bf Ballistic Cluster-Cluster Aggregates (BCCA)} and compact particles as polydisperse spheroids with some distribution of the aspect ratio. The particles follow a power-law size distribution with the power -3 that is close to the one obtained for comet dust {\it in situ}, at studies of the Stardust returned samples, and the results of ground-based observations of comets. The model provides a good fit to the angular polarization curve. It also reproduces the positive spectral gradient of polarization, red color of the dust, and {\bf low albedo. It also has the ratio of compact to fluffy particles close to the one found {\it in situ} for comet 1P/Halley} and the mass ratio of silicate to carbonaceous materials equal to unity that is in accordance with the elemental abundances of Halley's dust found by Giotto mission.Comment: "Earth and Planetary Science" (Japan), in pres

Photometry and polarimetry of the nucleus of comet 2P/Encke

Broadband imaging photometry, and broadband and narrowband linear polarimetry was measured for the nucleus of 2P/Encke over the phase-angle range 4 - 28 deg. An analysis of the point spread function of the comet reveals only weak coma activity, corresponding to a dust production of the order of 0.05 kg/s. The nucleus displays a color independent photometric phase function of almost linear slope. The absolute R filter magnitude at zero phase angle is 15.05 +/- 0.05, and corresponds to an equivalent radius for the nucleus of 2.43 +/- 0.06 km (for an adopted albedo of 0.047). The nucleus color V - R is 0.47 +/- 0.07, suggesting a spectral slope of 11 +/- 8 %/100nm. The phase function of linear polarimetry in the V and R filters shows a widely color independent linear increase with phase angle (0.12 +/- 0.02%/deg). We find discrepancies in the photometric and polarimetric parameters between 2P/Encke and other minor bodies in the solar system, which may indicate significant differences in the surface material properties and light-scattering behavior of the bodies. The linear polarimetric phase function of 2P/Encke presented here is the first ever measured for a cometary nucleus, and its analysis encourages future studies of cometary nuclei in order to characterize the light-scattering behavior of comets on firm empirical grounds and provide suitable input to a comprehensive modeling of the light scattering by cometary surfaces.Comment: Accepted by A&

Tighter Connections between Derandomization and Circuit Lower Bounds

We tighten the connections between circuit lower bounds and derandomization for each of the following three types of derandomization: - general derandomization of promiseBPP (connected to Boolean circuits), - derandomization of Polynomial Identity Testing (PIT) over fixed finite fields (connected to arithmetic circuit lower bounds over the same field), and - derandomization of PIT over the integers (connected to arithmetic circuit lower bounds over the integers). We show how to make these connections uniform equivalences, although at the expense of using somewhat less common versions of complexity classes and for a less studied notion of inclusion. Our main results are as follows: 1. We give the first proof that a non-trivial (nondeterministic subexponential-time) algorithm for PIT over a fixed finite field yields arithmetic circuit lower bounds. 2. We get a similar result for the case of PIT over the integers, strengthening a result of Jansen and Santhanam [JS12] (by removing the need for advice). 3. We derive a Boolean circuit lower bound for NEXP intersect coNEXP from the assumption of sufficiently strong non-deterministic derandomization of promiseBPP (without advice), as well as from the assumed existence of an NP-computable non-empty property of Boolean functions useful for proving superpolynomial circuit lower bounds (in the sense of natural proofs of [RR97]); this strengthens the related results of [IKW02]. 4. Finally, we turn all of these implications into equivalences for appropriately defined promise classes and for a notion of robust inclusion/separation (inspired by [FS11]) that lies between the classical "almost everywhere" and "infinitely often" notions

Agnostic Learning from Tolerant Natural Proofs

We generalize the "learning algorithms from natural properties" framework of [CIKK16] to get agnostic learning algorithms from natural properties with extra features. We show that if a natural property (in the sense of Razborov and Rudich [RR97]) is useful also against functions that are close to the class of "easy" functions, rather than just against "easy" functions, then it can be used to get an agnostic learning algorithm over the uniform distribution with membership queries. * For AC0[q], any prime q (constant-depth circuits of polynomial size, with AND, OR, NOT, and MODq gates of unbounded fanin), which happens to have a natural property with the requisite extra feature by [Raz87, Smo87, RR97], we obtain the first agnostic learning algorithm for AC0[q], for every prime q. Our algorithm runs in randomized quasi-polynomial time, uses membership queries, and outputs a circuit for a given Boolean function f that agrees with f on all but at most polylog(n)*opt fraction of inputs, where opt is the relative distance between f and the closest function h in the class AC0[q]. * For the ideal case, a natural proof of strongly exponential correlation circuit lower bounds against a circuit class C containing AC0[2] (i.e., circuits of size exp(Omega(n)) cannot compute some n-variate function even with exp(-Omega(n)) advantage over random guessing) would yield a polynomial-time query agnostic learning algorithm for C with the approximation error O(opt)

Spectropolarimetry of the Deep Impact target comet 9P/Tempel 1 with HiVIS

High resolution spectropolarimetry of the Deep Impact target, comet 9P/ Tempel 1, was performed during the impact event on July 4th, 2005 with the HiVIS Spectropolarimeter and the AEOS 3.67m telescope on Haleakala, Maui. We observed atypical polarization spectra that changed significantly in the few hours after the impact. The polarization of scattered light as a function of wavelength is very sensitive to the size and composition (complex refractive index) of the scattering particles as well as the scattering geometry. As opposed to most observations of cometary dust, which show an increase in the linear polarization with the wavelength (at least in the visible domain and for phase angles greater than about 30%, a red polarization spectrum) observations of 9P/Tempel 1 at a phase angle of 41 degrees beginning 8 minutes after impact and centered at 6:30UT showed a polarization of 4% at 650 nm falling to 3% at 950 nm. The next observation, centered an hour later showed a polarization of 7% at 650 nm falling to 2% at 950nm. This corresponds to a spectropolarimetric gradient, or slope, of -0.9% per 1000 Angstroms 40 minutes after impact, decreasing to a slope of -2.3% per 1000 Angstroms an hour and a half after impact. This is an atypical blue polarization slope, which became more blue 1 hour after impact. The polarization values of 4% and 7% at 650nm are typical for comets at this scattering angle, whereas the low polarization of 2% and 3% at 950nm is not. We compare observations of comet 9P/Tempel 1 to that of a typical comet, C/2004 Machholz, at a phase angle of 30 degrees which showed a typical red slope, rising from 2% at 650nm to 3% at 950nm in two different observations (+1.0 and +0.9% per 1000 Angstroms).Comment: Icarus Deep Impact special issue, accepted Aug 28 200

Comparison of titanium mesh implants with PLA-hydroxyapatite coatings for maxillofacial cancer reconstruction

Since 2013 physics of TPU and oncologists from the TCRI with participation of the “ConMet” company (Moscow) and the “Sintel” company (Tomsk Special Economic Zone resident) have been working on the theme entitled “Development of the composite implants for reconstructive surgery of a craniofacial areas of the traumatological and oncological patients” supported with the Federal Program ”R&D, part 1.3”. The goal was to develop the maxillo-facial implants on the basis of the transformable titanium mesh with PLA & hydroxyapatite coating. According to the Contract No. 14.578.21.0031, the team of developers had to start supplying these advanced implants to the industrial partners up to 2017. This research was supported with the preliminary market researches by the ISPMS SB RAS and the TP “MF”. The stages of preliminary market researches were: 1) research of the Worldwide CMF market; 2) forecasting the BRIC CMF market up to 2020; 3) the total Russian market (epidemiology) estimation as a sum of official calculations and statistics; 4) looking for the best foreign analogue prices, comparing their and our implant properties; 5) search for the best Russian analogues; 6) the investigation of the world patent databaseEspacenet for the last years, and finding the owners and applicants of patents of CMF osteosynthesis plates on the basis of titanium coated with PLA & hydroxyapatite; 7) comparison of the domestic implants, and making conclusions. Several variants of the meshes have got the equal quality with the best foreign and Russian implants. The closest analogues were titanium, polyethylene, PEEK composite meshes suited to the patient shape by the Synthes company in 2014, and the only hybrid titanium "Grey" implant with layers of gelatin, dextran, collagen, HAP & BMP-2 was found. This implant was produced by Russian institution, and it was mentioned in the report on clinical trials by L.A. Pavlova et al., 2014 [1]. There are no manufacturers of the coated implants in Russia. The average price of the similar foreign implants varies from 12 up to 4

Dust in Comet C/2007 N3 (Lulin)

We report optical imaging, optical and near-infrared polarimetry, and Spitzer mid-infrared spectroscopy of comet C/2007 N3 (Lulin). Polarimetric observations were obtained in R (0.676 micron) at phase angles from 0.44 degrees to 21 degrees with simultaneous observations in H (1.65 micron) at 4.0 degrees, exploring the negative branch in polarization. Comet C/2007 N3 (Lulin) shows typical negative polarization in the optical as well as a similar negative branch near-infrared wavelengths. The 10 micron silicate feature is only weakly in emission and according to our thermal models, is consistent with emission from a mixture of silicate and carbon material. We argue that large, low-porosity (akin to Ballistic Particle Cluster Aggregates) rather absorbing aggregate dust particles best explain both the polarimetric and the mid-infrared spectral energy distribution.Comment: 18 pages, 9 figures, 3 table