MRI brain tumor segmentation and necrosis detection using adaptive Sobolev snakes

NASA Astrophysics Data System (ADS)

Nakhmani, Arie; Kikinis, Ron; Tannenbaum, Allen

2014-03-01

Brain tumor segmentation in brain MRI volumes is used in neurosurgical planning and illness staging. It is important to explore the tumor shape and necrosis regions at di erent points of time to evaluate the disease progression. We propose an algorithm for semi-automatic tumor segmentation and necrosis detection. Our algorithm consists of three parts: conversion of MRI volume to a probability space based on the on-line learned model, tumor probability density estimation, and adaptive segmentation in the probability space. We use manually selected acceptance and rejection classes on a single MRI slice to learn the background and foreground statistical models. Then, we propagate this model to all MRI slices to compute the most probable regions of the tumor. Anisotropic 3D di usion is used to estimate the probability density. Finally, the estimated density is segmented by the Sobolev active contour (snake) algorithm to select smoothed regions of the maximum tumor probability. The segmentation approach is robust to noise and not very sensitive to the manual initialization in the volumes tested. Also, it is appropriate for low contrast imagery. The irregular necrosis regions are detected by using the outliers of the probability distribution inside the segmented region. The necrosis regions of small width are removed due to a high probability of noisy measurements. The MRI volume segmentation results obtained by our algorithm are very similar to expert manual segmentation.

The Statistical Sobolev-Rosseland Mean and the Effects of Frequency Redistribution on Wolf-Rayet Wind Driving

NASA Astrophysics Data System (ADS)

Onifer, A. J.; Gayley, K. G.

2003-06-01

The optically thick character of Wolf-Rayet winds implies that stellar continuum photons are multiply scattered, as a result of both free electron opacity and overlapping wind-broadened spectral lines. This allows the wind to accumulate a substantial excess in momentum flux relative to the driving radiation field, as is observationally required. Nevertheless, sustaining such a high degree of multiple scattering requires not only a large optical depth spatially but also substantial spectral blanketing. The latter is difficult to maintain when redistribution during scattering allows radiative flux to shift preferentially into spectral regions with fewer lines, since then the channels carrying much of the flux are also the least well blanketed. This paper parameterizes the potential severity of this effect in simple terms, using a generalization of the Rosseland mean treated in the Sobolev approximation. We show that our approach provides an informative starting point for characterizing and conceptualizing nongray effects in optically thick supersonic flows.

EXACT S-MATRICES FOR AdS3/CFT2

NASA Astrophysics Data System (ADS)

Ahn, Changrim; Bombardelli, Diego

2013-12-01

We propose exact S-matrices for the AdS3/CFT2 duality between type IIB strings on AdS3×S3×M4 with M4 = S3×S1 or T4 and the corresponding two-dimensional conformal field theories. We fix the two-particle S-matrices on the basis of the symmetries su(1|1) and su(1|1)×su(1|1). A crucial justification comes from the derivation of the all-loop Bethe ansatz matching exactly the recent conjecture proposed by Babichenko et al. [J. High Energy Phys.1003, 058 (2010), arXiv:0912.1723 [hep-th

Approximation of functions in variable-exponent Lebesgue and Sobolev spaces by finite Fourier-Haar series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharapudinov, I I

2014-02-28

The paper deals with the space L{sup p(x)} consisting of classes of real measurable functions f(x) on [0,1] with finite integral ∫{sub 0}{sup 1}|f(x)|{sup p(x)} dx. If 1≤p(x)≤ p-bar <∞, then the space L{sup p(x)} can be made into a Banach space with the norm ∥f∥{sub p(⋅)}=inf(α > 0:∫{sub 0}{sup 1}|f(x)/α|{sup p(x)} dx≤ 1). The inequality ∥f−Q{sub n}(f)∥{sub p(⋅)}≤c(p)Ω(f,1/n){sub p(⋅)}, which is an analogue of the first Jackson theorem, is shown to hold for the finite Fourier-Haar series Q{sub n}(f), provided that the variable exponent p(x) satisfies the condition |p(x)−p(y)|ln (1/|x−y|)≤ c. Here, Ω(f,δ){sub p(⋅)} is the modulus of continuity in L{sup p(x)} defined inmore » terms of Steklov functions. If the function f(x) lies in the Sobolev space W{sub p(⋅)}{sup 1} with variable exponent p(x), it is shown that ∥f−Q{sub n}(f)∥{sub p(⋅)}≤c(p)/n∥f{sup ′}∥{sub p(⋅)}. Methods for estimating the deviation |f(x)−Q{sub n}(f,x)| for f(x)∈W{sub p(⋅)}{sup 1} at a given point x∈[0,1] are also examined. The value of sup{sub f∈W{sub p{sup 1}(1)}}|f(x)−Q{sub n}(f,x)| is calculated in the case when p(x)≡p= const, where W{sub p}{sup 1}(1)=(f∈W{sub p}{sup 1}:∥f{sup ′}∥{sub p(⋅)}≤1). Bibliography: 17 titles.« less

Vector-valued Lizorkin-Triebel spaces and sharp trace theory for functions in Sobolev spaces with mixed \\pmb{L_p}-norm for parabolic problems

NASA Astrophysics Data System (ADS)

Weidemaier, P.

2005-06-01

The trace problem on the hypersurface y_n=0 is investigated for a function u=u(y,t) \\in L_q(0,T;W_{\\underline p}^{\\underline m}(\\mathbb R_+^n)) with \\partial_t u \\in L_q(0,T; L_{\\underline p}(\\mathbb R_+^n)), that is, Sobolev spaces with mixed Lebesgue norm L_{\\underline p,q}(\\mathbb R^n_+\\times(0,T))=L_q(0,T;L_{\\underline p}(\\mathbb R_+^n)) are considered; here \\underline p=(p_1,\\dots,p_n) is a vector and \\mathbb R^n_+=\\mathbb R^{n-1} \\times (0,\\infty). Such function spaces are useful in the context of parabolic equations. They allow, in particular, different exponents of summability in space and time. It is shown that the sharp regularity of the trace in the time variable is characterized by the Lizorkin-Triebel space F_{q,p_n}^{1-1/(p_nm_n)}(0,T;L_{\\widetilde{\\underline p}}(\\mathbb R^{n-1})), \\underline p=(\\widetilde{\\underline p},p_n). A similar result is established for first order spatial derivatives of u. These results allow one to determine the exact spaces for the data in the inhomogeneous Dirichlet and Neumann problems for parabolic equations of the second order if the solution is in the space L_q(0,T; W_p^2(\\Omega)) \\cap W_q^1(0,T;L_p(\\Omega)) with p \\le q.

Entropy production of doubly stochastic quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller-Hermes, Alexander, E-mail: muellerh@posteo.net; Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen; Stilck França, Daniel, E-mail: dsfranca@mytum.de

2016-02-15

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an applicationmore » we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.« less

Hardy and Rellich inequalities for submanifolds in Hadamard spaces

NASA Astrophysics Data System (ADS)

Batista, M.; Mirandola, H.; Vitório, F.

2017-11-01

Some of the most known integral inequalities are the Sobolev, Hardy and Rellich inequalities on regions in Euclidean spaces. In the context of submanifolds, the Sobolev inequality was proved by Michael-Simon [13] and Hoffman-Spruck [12]. Since then, a sort of applications to the submanifold theory has been derived from those inequalities. Years later, Carron [6] obtained a Hardy inequality for submanifolds in Hadamard spaces. In this paper, we prove the general Hardy and Rellich Inequalities for submanifolds in Hadamard spaces. Some applications are given and we also analyse the equality cases.

Coesite Assemblages in Deep Continental Lithosphere: Additional Evidence for a Protolith from Subduction of Oceanic Crust

NASA Astrophysics Data System (ADS)

Sobolev, N.

2005-12-01

Inclusions in diamonds (DIs) represent an important source of information about the composition of continental lithospheric mantle. The isolated coesite inclusions in two diamonds (Harris, 1968) and a full set of eclogitic minerals (coesite (Cs), garnet (Ga), omphacite Cpx)) in two Yakutian diamonds (Sobolev et al., 1976), followed by finds of Cs-eclogite xenoliths (Smyth and Hatton, 1977; Ponomarenko et al., 1977) testify to the importance of coesite as a constituent of eclogitic rocks in deep lithospheric environment. Since these earlier times, coesite has been documented in more than 250 natural diamonds from 25 localities worldwide. Some 40 xenoliths of Cs-eclogites were found both in South African and Yakutian kimberlites. However, >50% of DIs of coesite are related to only four (4) diamond localities, including Guaniamo, Venezuela (Sobolev et al., 1998, 2003), Argyle (Jaques et al., 1989; Sobolev et al., 1989), New South Wales, all Australia (Sobolev et al., 1984; Meyer et al., 1997), and North Yakutian alluvials (Sobolev et al., 1999). All described DIs with coesite are from a wide range of assemblages: websterites to kyanite eclogites; grospydites and calcsilicate assemblages, with a large range in Gt [3.7-28.7 wt.% CaO] and Cpx [ 0.9-8.8 wt.% Na2O] compositions. In spite of these occurrences in diamonds, to the present, no coesite has been detected within the assemblage of minerals making up some 400 diamondiferous-eclogite xenoliths; similarly, no diamonds have been found in any Cs-eclogite xenoliths. This apparent paradox may be caused by coesite alteration in the diamondiferous eclogites, whereas coesite eclogites may have formed only outside of the diamond stability field. Indeed, coesite eclogites (without diamonds) may occupy a shallower position within continental lithosphere compared with the normal E-type diamond source. This indicates a broadly basaltic chemistry of the deep eclogitic environment, additional evidence for a protolith from the

Remark on the scattering operator for the cubic nonlinear Dirac equation in three space dimensions

NASA Astrophysics Data System (ADS)

Sasaki, Hironobu

2015-10-01

This paper is concerned with the scattering operator S for the three-dimensional Dirac equation with a cubic nonlinearity. It follows from known results that S is well-defined on a neighborhood of 0 in the Sobolev space Hκ (R3 ;C4) for any κ > 1. In the present paper, we prove that for any M ∈ N and s ≥ max ⁡ { κ , M }, there exists some neighborhood U of 0 in the weighted Sobolev space H s , M (R3 ;C4) such that S (U) ⊂H s , M (R3 ;C4).

Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients

NASA Astrophysics Data System (ADS)

Dong, Hongjie; Kim, Doyoon

2018-04-01

We prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions, i.e., locally they are merely measurable in one direction and have small mean oscillations in the other directions. Using this result, we establish the unique solvability in Muckenhoupt type weighted Sobolev spaces for the system with partially BMO coefficients on a Reifenberg flat domain. We also present weighted a priori Lq-estimates for the system when the domain is the whole Euclidean space or a half space.

Coesite-Diamond Assemblage in Ultrahigh Pressure Crustal and Mantle rocks: Evidence for Carbon Recycling

NASA Astrophysics Data System (ADS)

Sobolev, N. V.

2010-12-01

Coesite, a high-pressure polymorph of silica, was first discovered as part of a coesite-eclogite assemblage (coesite, garnet, omphacite) in equilibrium with diamond as diamond inclusion (DI) in Siberian diamond placers (Sobolev et al., 1976, Dokl. Akad. Nauk SSSR, 230: 1442). In recent years, coesite has become a key mineral coexisting with diamond both in kimberlite (DIs) and in UHP metamorphic rocks of the Kokchetav massif, Kazakhstan (diamondiferous gneisses and calcsilicate rocks). In the UHPM rocks of Kokchetav massif, coesite was first detected as inclusions in zircon associated with diamonds (Sobolev et al., 1991, Dokl. Akad. Nauk SSSR, 321: 184), as a result of the initial studies that had identified diamonds as inclusions in garnets and zircons (Sobolev, Shatsky, 1990, Nature, 343: 742). Garnet and omphacitic clinopyroxene are the principal primary minerals associated with coesite and diamond in UHP mantle and crustal rocks. Their compositions plot distinctly within the eclogitic compositional field and substantiate the existence of coesite presence as DIs in eclogitic (E-type) diamonds, as well as sometimes in xenoliths of diamondiferous eclogites (Shatsky et al., 2008, Lithos, 105:289). One of the major significant features of these eclogitic minerals in both UHPM and kimberlitic mantle occurrences is the K2O contents of the clinopyroxenes, reaching 1.6 wt.%, with Na2O and MnO in Ca-Mg-Fe garnets reaching 0.3 and 6.0 wt.%, respectively. Stable isotope data for C in diamonds and O in garnet, pyroxene and coesite have resulted in establishing a very wide range for these isotopes most typical for crustal conditions - i.e., atypical of mantle values. This is clearly shown for coesite DIs (Schulze et al., 2003, Nature, 428:68), garnets from diamondiferous eclogite xenoliths from Siberian kimberlites (Spetsius et al., 2008, Eur. J. Min., 20:375), garnets and clinopyroxenes from UHP calcsilicate diamondiferous rocks of the Kokchetav massif (Sobolev et al., in

Non-Axisymmetric Line Driven Disc Winds II - Full Velocity Gradient

NASA Astrophysics Data System (ADS)

Dyda, Sergei; Proga, Daniel

2018-05-01

We study non-axisymetric features of 3D line driven winds in the Sobolev approximation, where the optical depth is calculated using the full velocity gradient. We find that non-axisymmetric density features, so called clumps, form primarily at the base of the wind on super-Sobolev length scales. The density of clumps differs by a factor of ˜3 from the azimuthal average, the magnitude of their velocity dispersion is comparable to the flow velocity and they produce ˜20% variations in the column density. Clumps may be observable because differences in density produce enhancements in emission and absorption profiles or through their velocity dispersion which enhances line broadening.

On the synthesis of resonance lines in dynamical models of structured hot-star winds

NASA Technical Reports Server (NTRS)

Puls, J.; Owocki, S. P.; Fullerton, A. W.

1993-01-01

We examine basic issues involved in synthesizing resonance-line profiles from 1-D, dynamical models of highly structured hot-star winds. Although these models exhibit extensive variations in density as well as velocity, the density scale length is still typically much greater than the Sobolev length. The line transfer is thus treated using a Sobolev approach, as generalized by Rybicki & Hummer (1978) to take proper account of the multiple Sobolev resonances arising from the nonmonotonic velocity field. The resulting reduced-lambda-matrix equation describing nonlocal coupling of the source function is solved by iteration, and line profiles are then derived from formal solution integration using this source function. Two more approximate methods that instead use either a stationary or a structured, local source function yield qualitatively similar line-profiles, but are found to violate photon conservation by 10% or more. The full results suggest that such models may indeed be able to reproduce naturally some of the qualitative properties long noted in observed UV line profiles, such as discrete absorption components in unsaturated lines, or the blue-edge variability in saturated lines. However, these particular models do not yet produce the black absorption troughs commonly observed in saturated lines, and it seems that this and other important discrepancies (e.g., in acceleration time scale of absorption components) may require development of more complete models that include rotation and other 2-D and/or 3-D effects.

Fluctuations at the blue edge of saturated wind lines in IUE spectra of O-type stars

NASA Technical Reports Server (NTRS)

Owocki, Stanley P.; Fullerton, Alex

1993-01-01

We examine basic issues involved in synthesizing resonance-line profiles from 1-D, dynamical models of highly structured hot-star winds. Although these models exhibit extensive variations in density as well as velocity, the density scale length is still typically much greater than the Sobolev length. The line transfer is thus treated using a Sobolev approach, as generalized by Rybicki & Hummer (1978) to take proper account of the multiple Sobolev resonances arising from the nonmonotonic velocity field. The resulting reduced-Lambda-matrix equation describing nonlocal coupling of the source function is solved by iteration, and line profiles and then derived from formal solution integration using this source function. The more appropriate methods that instead use either a stationary or a structured, local source function yield qualitatively similar line-profiles, but are found to violate photon conservation by 10 percent or more. The full results suggest that such models may indeed be able to reproduce naturally some of the qualitative properties long noted in observed UV line profiles, such as discrete absorption components in unsaturated lines, or the blue-edge variability in saturated lines. However, these particular models do not yet produce the black absorption troughs commonly observed in saturated lines, and it seems that this and other important discrepancies (e.g., in acceleration time scale of absorption components) may require development of more complete models that include rotation and other 2-D and/or 3-D effects.

Recycled Crust in the Mantle: Is High-Ni Olivine the Smoking Gun or a Red Herring?

NASA Astrophysics Data System (ADS)

Li, C.; Ripley, E. M.

2008-12-01

It is widely accepted that small amounts of recycled crustal components are present in some mantle-derived mafic and ultramafic magmas. This concept is supported by many isotopic and trace element studies of basalts, picrites and komatiites in the last 30 years. Recently Sobolev et al. [1,2] used olivine compositions such as Ni content and Mn/Fe ratio to demonstrate that the amounts of the recycled crustal component (i.e. pyroxenite) in these mantle-derived melts are much larger than previously appreciated. Their calculations show that the pyroxenite-derived component varies mostly between 40 and 80% for Hawaiian shield basalts and Siberian flood basalts, and mostly between 10 and 40% for mid-ocean ridge basalts and Archean komatiities. However, a critical test using olivine-liquid Mg-Fe equilibrium that was overlooked by Sobolev et al. [1,2] reveals that mixing of the two end-members (pyroxenite-derived and peridotite-derived melts) that were used in their models cannot generate the parental melts for the above natural samples. Such a discrepancy prompts us to reexamine the conventional view of a peridotite-dominant source for the Hawaiian shield basalts. This hypothesis has been criticized recently by many people because the contents of Ni in olivine phenocrysts in the basalts are significantly higher than mantle olivines in associated peridotite xenoliths and because total pressure has little effect on olivine-liquid Ni partition coefficient (DNi). What has not been generally considered is that the depth of olivine crystallization/equilibration has a negative effect on olivine Ni content because DNi is negatively correlated with melt temperature which decreases during adiabatic ascent. To evaluate such an effect quantitatively we have used all available experimental results of Ni partitioning between olivine and liquid to construct a robust empirical equation for DNi based on melt composition and temperature. The results of our calculations indicate that the

A novel methodology for radiative transfer in a planetary atmosphere. I - The functions a exponent m and b exponent m of anisotropic scattering

NASA Technical Reports Server (NTRS)

Fymat, A. L.; Kalaba, R. E.

1977-01-01

The original problem of anisotropic scattering in an atmosphere illuminated by a unidirectional source is replaced by an analogous formulation where the incident light is omnidirectional. A radiative-transfer equation for the omnidirectional case is obtained in which the direction of illumination plays no role and the source-function analog, Sobolev's (1972) source function Phi exponent m, contains only a single integral term. For radiation incident on the top or the bottom of the atmosphere, this equation involves the functions b exponent m and h exponent m, respectively, with m corresponding to the order of the harmonic component of the scattered radiation field; these two functions are shown to be only one through some simple reciprocity relations. The transfer problem is then reformulated for the function a exponent m, in which case the source-function analog (Sobolev's function D exponent m) involves incident direction.

Two-dimensional molecular line transfer for a cometary coma

NASA Astrophysics Data System (ADS)

Szutowicz, S.

2017-09-01

In the proposed axisymmetric model of the cometary coma the gas density profile is described by an angular density function. Three methods for treating two-dimensional radiative transfer are compared: the Large Velocity Gradient (LVG) (the Sobolev method), Accelerated Lambda Iteration (ALI) and accelerated Monte Carlo (MC).

Analysis of spectral operators in one-dimensional domains

NASA Technical Reports Server (NTRS)

Maday, Y.

1985-01-01

Results are proven concerning certain projection operators on the space of all polynomials of degree less than or equal to N with respect to a class of one-dimensional weighted Sobolev spaces. The results are useful in the theory of the approximation of partial differential equations with spectral methods.

Corridengum: Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables (2017 Nonlinearity 30 1204)

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Kuna, Tobias; Lucarini, Valerio

2017-08-01

The first main result of Baladi et al (2017 Nonlinearity 30 1204-20) is modified as follows: For any θ in the Sobolev space H^r_p(M) , with 1 and 0, the map t\\mapsto \\int θ dρt is α-Hölder continuous for all \

On the index of elliptic operators for the group of dilations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Savin, Anton Yu; Sternin, Boris Yu; Leibniz University of Hannover

2011-10-31

We investigate nonlocal operators associated with the operators of compression and expansion. We obtain an ellipticity condition, which implies that the problem has the Fredholm property, compute the index, and study how the index depends on the exponent of the Sobolev space in which the problem is considered. Bibliography: 15 titles.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

Minimum Sobolev norm interpolation of scattered derivative data

NASA Astrophysics Data System (ADS)

Chandrasekaran, S.; Gorman, C. H.; Mhaskar, H. N.

2018-07-01

We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data of the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree ≤n given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable, efficient, and of high-order.

Local Existence of MHD Contact Discontinuities

NASA Astrophysics Data System (ADS)

Morando, Alessandro; Trakhinin, Yuri; Trebeschi, Paola

2018-05-01

We prove the local-in-time existence of solutions with a contact discontinuity of the equations of ideal compressible magnetohydrodynamics (MHD) for two dimensional planar flows provided that the Rayleigh-Taylor sign condition {[partial p/partial N] <0 } on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity. MHD contact discontinuities are characteristic discontinuities with no flow across the discontinuity for which the pressure, the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump. This paper is a natural completion of our previous analysis (Morando et al. in J Differ Equ 258:2531-2571, 2015) where the well-posedness in Sobolev spaces of the linearized problem was proved under the Rayleigh-Taylor sign condition satisfied at each point of the unperturbed discontinuity. The proof of the resolution of the nonlinear problem given in the present paper follows from a suitable tame a priori estimate in Sobolev spaces for the linearized equations and a Nash-Moser iteration.

Smoothing the Marmousi Model

NASA Astrophysics Data System (ADS)

Žáček, K.

Summary- The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it. We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness. We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability. Due to the low frequencies in the wavefield of the original Marmousi data set, we have found the Gaussian beams and Gaussian packets at the verge of applicability even in models sufficiently smoothed for ray tracing.

Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: The constraint equations

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

This paper deals with the construction of initial data for the coupled Einstein-Euler system. We consider the condition where the energy density might vanish or tend to zero at infinity, and where the pressure is a fractional power of the energy density. In order to achieve our goals we use a type of weighted Sobolev space of fractional order. The common Lichnerowicz-York scaling method (Choquet-Bruhat and York, 1980 [9]; Cantor, 1979 [7]) for solving the constraint equations cannot be applied here directly. The basic problem is that the matter sources are scaled conformally and the fluid variables have to be recovered from the conformally transformed matter sources. This problem has been addressed, although in a different context, by Dain and Nagy (2002) [11]. We show that if the matter variables are restricted to a certain region, then the Einstein constraint equations have a unique solution in the weighted Sobolev spaces of fractional order. The regularity depends upon the fractional power of the equation of state.

Dynamic Vision for Control

DTIC Science & Technology

2009-02-05

the best of our knowledge, the first approach to design a proper filter (observer) in the infinite - dimensional space of shapes (closed Jordan...curves). This is based on endowing the space with a Riemaimian (Sobolev) metric , then shooting geodesies from the current best estimate of the state...handing nuisance transformations and endowing the models with a

Decay of the compressible magneto-micropolar fluids

NASA Astrophysics Data System (ADS)

Zhang, Peixin

2018-02-01

This paper considers the large-time behavior of solutions to the Cauchy problem on the compressible magneto-micropolar fluid system under small perturbation in regular Sobolev space. Based on the time-weighted energy estimate, the asymptotic stability of the steady state with the strictly positive constant density, vanishing velocity, micro-rotational velocity, and magnetic field is established.

Garnet from diamondiferous metamorphic rocks of Kokchetav massif, Kazakhstan as a peak pressure recorder

NASA Astrophysics Data System (ADS)

Sobolev, N. V.; Palyanov, Y. N.; Shatsky, V. S.; Sokol, A. G.; Tomilenko, A. A.

2003-12-01

Garnet is a key mineral coexisting with diamond both in kimberlite (as xenocrysts, in diamondiferous garnet peridotites and eclogites, as inclusions in diamond) and in UHP metamorphic rocks of Kokchetav massif (diamondiferous gneisses, garnet-pyroxene rocks, dolomitic marbles and diamond facies eclogites). In UHPM rocks garnets are of particular importance as inclusions in zircons protected from retrograde metamorphism. Diamond formation conditions in eclogitic (E-type) upper mantle environment are estimated based upon Grt-Cpx thermometry and coesite barometry (e.g. Sobolev et al., PNAS, 2000, 97:11875) at P=5.5-6.0 GPa and T=1000-1300° C. These data are supported by diamond synthesis in carbonate-silicate fluid (e.g. Palyanov et al., Nature, 1999, 400: 417). E-type garnet may dissolve up to 0.3 wt.% Na2O (Sobolev, Lavrentyev, Contr. Min. Petr., 1971, 31:1) depending on pressure and Na2O contents in coexisting pyroxene and melts (fluids). Majorite component (pyroxene solid solution) was reported in rare garnets from diamonds (e.g. Moore, Gurney, Nature, 1985, 318:553) and UHP conditions were experimentally confirmed for such garnets (Irifune, Phys. Eart. Pl. Int., 1987, 45:324; Gasparik, Phys. Chem. Min., 2002, 29:170; Luth, Am. Miner., 1997, 82:1198). Garnets from Kokchetav diamondiferous metamorphic rocks demonstrate considerably lower Na2O solubility (up to 0.2 wt.% in rare samples) and absence of majorite component. However, coexisting pyroxenes may contain up to 50 mol.% jadeite. Several UHP experiments performed with Kokchetav eclogites and dolomitic marbles using a split-sphere apparatus resulted in detection of up to 0.3-0.4 wt.% Na2O in newly formed eclogitic garnets at P=5.7 and 7.0 GPa, T=1400 and 1700° C respectively. Majorite component was also determined in newly formed garnets reaching about 5% with Si (pfu)=3.05-3.06. Similar garnets without Na2O were also obtained in UHP experiments with diamondiferous dolomitic marbles (e.g. Palyanov et al

Existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Alves, Claudianor O.; Miyagaki, Olímpio H.

2017-08-01

In this paper, we establish some results concerning the existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation. Variational methods are used to get an existence result, as well as, to study the concentration phenomenon, while the regularity is more delicate because we are leading with functions in an anisotropic Sobolev space.

Fourth International Congress on Industrial and Applied Mathematics. Book of Abstracts

DTIC Science & Technology

1999-01-01

Dipartimento di Matematica , Universita’ di Pavia, Italy) Logarithmic Sobolev inequalities for kinetic semiconductor equations In this paper we analyze the...terms of Whitney forms. FERNANDES, Paolo (Istituto per la Matematica Applicata del Consiglio Nazionale delle Ricerche, Italy) Dealing with realistic... Matematica dell Universita di Pavia, Italy. PERUGIA, Ilaria (Diaprtimento di Matematica , Universita’ di Pavia - Italy) An adaptive field-based method

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

Wavelet bases on the L-shaped domain

NASA Astrophysics Data System (ADS)

Jouini, Abdellatif; Lemarié-Rieusset, Pierre Gilles

2013-07-01

We present in this paper two elementary constructions of multiresolution analyses on the L-shaped domain D. In the first one, we shall describe a direct method to define an orthonormal multiresolution analysis. In the second one, we use the decomposition method for constructing a biorthogonal multiresolution analysis. These analyses are adapted for the study of the Sobolev spaces Hs(D)(s∈N).

Global well-posedness and asymptotic behavior of solutions for the three-dimensional MHD equations with Hall and ion-slip effects

NASA Astrophysics Data System (ADS)

Zhao, Xiaopeng; Zhu, Mingxuan

2018-04-01

In this paper, we consider the small initial data global well-posedness of solutions for the magnetohydrodynamics with Hall and ion-slip effects in R^3. In addition, we also establish the temporal decay estimates for the weak solutions. With these estimates in hand, we study the algebraic time decay for higher-order Sobolev norms of small initial data solutions.

Generalized INF-SUP condition for Chebyshev approximation of the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Canuto, Claudio; Maday, Yvon

1986-01-01

An abstract mixed problem and its approximation are studied; both are well-posed if and only if several inf-sup conditions are satisfied. These results are applied to a spectral Galerkin method for the Stokes problem in a square, when it is formulated in Chebyshev weighted Sobolev spaces. Finally, a collocation method for the Navier-Stokes equations at Chebyshev nodes is analyzed.

Virtual continuity of measurable functions and its applications

NASA Astrophysics Data System (ADS)

Vershik, A. M.; Zatitskii, P. B.; Petrov, F. V.

2014-12-01

A classical theorem of Luzin states that a measurable function of one real variable is `almost' continuous. For measurable functions of several variables the analogous statement (continuity on a product of sets having almost full measure) does not hold in general. The search for a correct analogue of Luzin's theorem leads to a notion of virtually continuous functions of several variables. This apparently new notion implicitly appears in the statements of embedding theorems and trace theorems for Sobolev spaces. In fact it reveals the nature of such theorems as statements about virtual continuity. The authors' results imply that under the conditions of Sobolev theorems there is a well-defined integration of a function with respect to a wide class of singular measures, including measures concentrated on submanifolds. The notion of virtual continuity is also used for the classification of measurable functions of several variables and in some questions on dynamical systems, the theory of polymorphisms, and bistochastic measures. In this paper the necessary definitions and properties of admissible metrics are recalled, several definitions of virtual continuity are given, and some applications are discussed. Bibliography: 24 titles.

Lower Bounds for Possible Singular Solutions for the Navier-Stokes and Euler Equations Revisited

NASA Astrophysics Data System (ADS)

Cortissoz, Jean C.; Montero, Julio A.

2018-03-01

In this paper we give optimal lower bounds for the blow-up rate of the \\dot{H}s( T^3) -norm, 1/2Sobolev norms of possible singular solutions to the Euler equations when s>5/2.

USSR Report, Space

DTIC Science & Technology

1986-02-10

determination of space stations’ coordinates. We are also con- ducting scientific studies of celestial mechanics here." The Maksutov-Sobolev camera ...ionosphere, through which the signals propagated. The trajectories of the spacecraft "Vega-1" and "Vega-2" themselves were determined with high...source. The contents of this publication in no way represent the poli- cies, views or attitudes of the U.S. Government. PROCUREMENT OF

Information Based Numerical Practice.

DTIC Science & Technology

1987-02-01

characterization by comparative computational studies of various benchmark problems. See e.g. [MacNeal, Harder (1985)], [Robinson, Blackham (1981)] any...FOR NONADAPTIVE METHODS 2.1. THE QUADRATURE FORMULA The simplest example studied in detail in the literature is the problem of the optimal quadrature...formulae and the functional analytic prerequisites for the study of optimal formulae, we refer to the large monography (808 p) of [Sobolev (1974)]. Let us

The theory of pseudo-differential operators on the noncommutative n-torus

NASA Astrophysics Data System (ADS)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

B-spline goal-oriented error estimators for geometrically nonlinear rods

DTIC Science & Technology

2011-04-01

respectively, for the output functionals q2–q4 (linear and nonlinear with the trigonometric functions sine and cosine) in all the tests considered...of the errors resulting from the linear, quadratic and nonlinear (with trigonometric functions sine and cosine) outputs and for p = 1, 2. If the... Portugal . References [1] A.T. Adams. Sobolev Spaces. Academic Press, Boston, 1975. [2] M. Ainsworth and J.T. Oden. A posteriori error estimation in

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

NASA Astrophysics Data System (ADS)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

Nonuniform dependence on initial data for compressible gas dynamics: The periodic Cauchy problem

NASA Astrophysics Data System (ADS)

Keyfitz, B. L.; Tığlay, F.

2017-11-01

We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space Hs for s > d / 2 + 1 where d is the space dimension. We prove that the data to solution map for periodic data in two dimensions although continuous is not uniformly continuous.

Phase space gradient of dissipated work and information: A role of relative Fisher information

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamano, Takuya, E-mail: yamano@amy.hi-ho.ne.jp

2013-11-15

We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated work in phase space. We present a universal constraint on it via the logarithmic Sobolev inequality. Furthermore, we point out that a possible expression of the lower bound indicates a deep connection in terms of the relative entropy and the Fisher information of the canonical distributions.

Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunez, Manuel

2009-10-15

The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each species, plus the magnetic and electric fields, which yield as an analog of Ohm's law a certain elliptic equation. Therefore, the equations represent a functional evolution system, not a classical one. Nonetheless, a priori estimates and theorems of existence may be obtained in appropriate Sobolev spaces.

Unique determination of stratified steady water waves from pressure

NASA Astrophysics Data System (ADS)

Chen, Robin Ming; Walsh, Samuel

2018-01-01

Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be recovered from data consisting of the wave speed, upstream and downstream density and velocity profile, and the trace of the pressure on the bed. In particular, we prove that this data uniquely determines the wave, both in the (real) analytic and Sobolev regimes.

Initial-boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system

NASA Astrophysics Data System (ADS)

Fei, Mingwen; Han, Daozhi; Wang, Xiaoming

2017-01-01

In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial-boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

Well-posedness of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Secchi, Paolo; Trakhinin, Yuri

2014-01-01

We consider the free-boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the pre-Maxwell dynamics for the magnetic field. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, because of a given surface current on the fixed boundary that forces oscillations. Under a suitable stability condition satisfied at each point of the initial interface, stating that the magnetic fields on either side of the interface are not collinear, we show the existence and uniqueness of the solution to the nonlinear plasma-vacuum interface problem in suitable anisotropic Sobolev spaces. The proof is based on the results proved in the companion paper (Secchi and Trakhinin 2013 Interfaces Free Boundaries 15 323-57), about the well-posedness of the homogeneous linearized problem and the proof of a basic a priori energy estimate. The proof of the resolution of the nonlinear problem given in the present paper follows from the analysis of the elliptic system for the vacuum magnetic field, a suitable tame estimate in Sobolev spaces for the full linearized equations, and a Nash-Moser iteration.

Blow-up and symmetry of sign-changing solutions to some critical elliptic equations

NASA Astrophysics Data System (ADS)

Ben Ayed, Mohamed; El Mehdi, Khalil; Pacella, Filomena

In this paper we continue the analysis of the blow-up of low energy sign-changing solutions of semi-linear elliptic equations with critical Sobolev exponent, started in [M. Ben Ayed, K. El Mehdi, F. Pacella, Blow-up and nonexistence of sign-changing solutions to the Brezis-Nirenberg problem in dimension three, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. In addition we prove axial symmetry results for the same kind of solutions in a ball.

Periodicity and positivity of a class of fractional differential equations.

PubMed

Ibrahim, Rabha W; Ahmad, M Z; Mohammed, M Jasim

2016-01-01

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

Analysis of Multi-Scale Phenomena in Heterogeneous Materials

DTIC Science & Technology

2011-02-22

requires the use of properties of the Catalan numbers to show that the series coefficients are exponentially bounded in the H1 Sobolev norm. This is joint...the use of a small number of optimal local basis functions. The local bases are supported on sub domains of fixed diameter within the computa- tional...not display a currently valid OMB control number . 1. REPORT DATE 22 FEB 2011 2. REPORT TYPE FINAL REPORT 3. DATES COVERED 03-01-2008 to 03-03

Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas

2018-04-01

We prove that Gibbs measures based on 1D defocusing nonlinear Schrödinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity, and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices.

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

NASA Technical Reports Server (NTRS)

Agapov, A. V.; Kolosov, B. I.

1979-01-01

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Bibliography of Soviet Laser Developments, Number 87, January-February 1987

DTIC Science & Technology

1987-12-29

laser. OPMPA, no. 1, 1987, 58-59. 84. Sukhanov , 1.1.; Troitskiy, Yu.V.; Yakushkin, S.V. 0 Investigation of a He-Ne laser, generating a beam with a...2Ye498). * 519. Shelekhov, N.S.; Sukhanov , V.I.; Solomatin, Yu.V.;Ashcheulov, Yu.V. (GOI). Investigation of the possibility of obtaining specimens of...G 46,49 SOBOLEV V B 57 SUETIN N V 26 TIMASHOV A V 11 SOCHIVKIN G M 87 SUKHANOV I 1 11 TIMASHOVA L N 60 SOKOLOV A V 107 SUKHANOV V 1 61 TIMERKAYEV B A

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields

NASA Astrophysics Data System (ADS)

Benguria, R. D.; Van Den Bosch, H.

2015-05-01

We consider the Pauli operator in ℝ3 for magnetic fields in L3/2 that decay at infinity as |x|-2-β with β > 0. In this case, we are able to prove that the existence of a zero mode for this operator is equivalent to a quantity δ(B), defined below, being equal to zero. Complementing a result from Balinsky et al. [J. Phys. A: Math. Gen. 34, L19-L23 (2001)], this implies that for the class of magnetic fields considered, Sobolev, Hardy, and Cwikel, Lieb, Rosenblum (CLR) inequalities hold whenever the magnetic field has no zero mode.

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

Log-Concavity and Strong Log-Concavity: a review

PubMed Central

Saumard, Adrien; Wellner, Jon A.

2016-01-01

We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on ℝ under convolution follows from a fundamental monotonicity result of Efron (1969). We provide a new proof of Efron's theorem using the recent asymmetric Brascamp-Lieb inequality due to Otto and Menz (2013). Along the way we review connections between log-concavity and other areas of mathematics and statistics, including concentration of measure, log-Sobolev inequalities, convex geometry, MCMC algorithms, Laplace approximations, and machine learning. PMID:27134693

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Extremal values of the sojourn time

NASA Astrophysics Data System (ADS)

Astaburuaga, M. A.; Cortés, V. H.; Duclos, P.

2010-11-01

Consider a self-adjoint operator H on a separable Hilbert space \\ {H} with non-trivial absolutely continuous component. We study the general properties of the real-valued functional, \\tau _{H}(\\psi )=\\int _{{\\ R}}|(e^{-itH}\\psi,\\psi )|^2\\,dt, which in quantum mechanics represents the sojourn time (or life time) of an initial state \\psi \\in \\ {H}. We characterize the critical points of the sojourn time, τX, of the operator multiplication by x in L^2({\\ R}), and prove that it attains a global maximum in the unit sphere of the Sobolev space \\ {W}^{1,2}({\\ R}).

Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field

NASA Astrophysics Data System (ADS)

Wen, Huanyao; Zhu, Limei

2018-02-01

In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in H2 (R3) are obtained by introducing a new linearized system with respect to (nγ -n˜γ , n - n ˜ , P - P ˜ , u , H) for constants n ˜ ≥ 0 and P ˜ > 0, and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of (n - n ˜ ,nγ -n˜γ) in H2 (R3) norm.

Density of convex intersections and applications

PubMed Central

Rautenberg, C. N.; Rösel, S.

2017-01-01

In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems. PMID:28989301

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian.

PubMed

Shen, Liejun

2018-01-01

The present study is concerned with the following fractional p -Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p -Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.

Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

NASA Astrophysics Data System (ADS)

Micheli, Mario; Michor, Peter W.; Mumford, David

2013-06-01

Given a finite-dimensional manifold N, the group \\operatorname{Diff}_{ S}(N) of diffeomorphisms diffeomorphism of N which decrease suitably rapidly to the identity, acts on the manifold B(M,N) of submanifolds of N of diffeomorphism-type M, where M is a compact manifold with \\operatorname{dim} M<\\operatorname{dim} N. Given the right-invariant weak Riemannian metric on \\operatorname{Diff}_{ S}(N) induced by a quite general operator L\\colon \\mathfrak{X}_{ S}(N)\\to \\Gamma(T^*N\\otimes\\operatorname{vol}(N)), we consider the induced weak Riemannian metric on B(M,N) and compute its geodesics and sectional curvature. To do this, we derive a covariant formula for the curvature in finite and infinite dimensions, we show how it makes O'Neill's formula very transparent, and we finally use it to compute the sectional curvature on B(M,N).

Numerical simulations of electromagnetic scattering by Solar system objects

NASA Astrophysics Data System (ADS)

Dlugach, Janna M.

2016-11-01

Having been profoundly stimulated by the seminal work of Viktor V. Sobolev, I have been involved in multi-decadal research in the fields of radiative transfer, electromagnetic scattering by morphologically complex particles and particulate media, and planetary remote sensing. Much of this research has been done in close collaboration with other "descendants" of Academician Sobolev. This tutorial paper gives a representative overview of the results of extensive numerical simulations (in the vast majority carried out in collaboration with Michael Mishchenko) used to analyze remote-sensing observations of Solar system objects and based on highly accurate methods of the radiative transfer theory and direct computer solvers of the Maxwell equations. Using the atmosphere of Jupiter as a proving ground and performing T-matrix and radiative-transfer calculations helps demonstrate the strong effect of aerosol-particle shapes on the accuracy of remote-sensing retrievals. I then discuss the application of the T-matrix method, a numerically exact solution of the vector radiative transfer equation, and the theory of coherent backscattering to an analysis of polarimetric radar observations of Saturn's rings. Numerical modeling performed by using the superposition T-matrix method in application to cometary dust in the form of aggregates serves to reproduce the results of polarimetric observations of the distant comet C/2010 S1. On the basis of direct computer solutions of the Maxwell equations, it is demonstrated that all backscattering effects predicted by the low-density theories of radiative transfer and coherent backscattering can also be identified for media with volume packing densities typically encountered in natural and artificial environments. This result implies that spectacular opposition effects observed for some high-albedo atmoshereless Solar system bodies can be attributed to coherent backscattering of sunlight by regolith layers composed of microscopic particles.

Global Regularity of 2D Density Patches for Inhomogeneous Navier-Stokes

NASA Astrophysics Data System (ADS)

Gancedo, Francisco; García-Juárez, Eduardo

2018-07-01

This paper is about Lions' open problem on density patches (Lions in Mathematical topics in fluid mechanics. Vol. 1, volume 3 of Oxford Lecture series in mathematics and its applications, Clarendon Press, Oxford University Press, New York, 1996): whether or not inhomogeneous incompressible Navier-Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev spaces for the velocity, we first establish the propagation of {C^{1+γ}} regularity with {0 < γ < 1} in the case of positive density. Furthermore, we go beyond this to show the persistence of a geometrical quantity such as the curvature. In addition, we obtain a proof for {C^{2+γ}} regularity.

Phase-field-crystal study of solute trapping

NASA Astrophysics Data System (ADS)

Humadi, Harith; Hoyt, Jeffrey J.; Provatas, Nikolas

2013-02-01

In this study we have incorporated two time scales into the phase-field-crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, K as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where K approaches unity in the limit of infinite velocity. However, with the introduction of wavelike dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by Sobolev [Phys. Lett. A10.1016/0375-9601(95)00084-G 199, 383 (1995)], where complete trapping occurs at a finite velocity.

Regularity estimates up to the boundary for elliptic systems of difference equations

NASA Technical Reports Server (NTRS)

Strikwerda, J. C.; Wade, B. A.; Bube, K. P.

1986-01-01

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations.

Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn

NASA Astrophysics Data System (ADS)

Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han

2018-06-01

We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

Applicability of steady models for hot-star winds

NASA Technical Reports Server (NTRS)

Owocki, Stanley P.; Poe, Clint H.; Castor, John I.

1990-01-01

Non-Sobolev models of radiatively driven stellar winds based on a pure-absorption approximation do not have a well-defined steady state. Here the implications of this for flow time-dependence are examined, showing that, under such circumstances, instabilities in the flow attain an absolute character that leads to intrinsic variability. In this case, steady solutions are inherently inapplicable because they do not represent physically realizable states. However, for actual hot-star winds, driving is principally by scattering, not pure absorption. In practice, the relatively weak force associated with slight asymmetries in the diffuse, scattered radiation field may play a crucial role in breaking the solution degeneracy and reducing the instability from an absolute to an advective character.

Calibration of Lévy Processes with American Options

NASA Astrophysics Data System (ADS)

Achdou, Yves

We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

Redescription, generic allocation and synonymy of Decorataria magnilabiata (Molin, 1860) n. comb. (Nematoda: Spirurida: Acuariidae), a parasite of the roseate spoonbill Platalea ajaja L. (Aves: Threskiornithidae) in South America.

PubMed

Mutafchiev, Yasen; Georgiev, Boyko B

2011-09-01

Decorataria magnilabiata (Molin, 1860) n. comb. is proposed for Dispharagus magnilabiatus Molin, 1860 [= Acuaria (Cheilospirura) magnilabiata (Molin, 1860) Railliet, Henry & Sisoff, 1912; Cheilospirura magnilabiata (Molin, 1860) Stiles & Hassall, 1920; Dispharynx magnilabiata (Molin, 1860) Gendre, 1920] (Nematoda, Spirurida, Acuariidae), a parasite of the roseate spoonbill Platalea ajaja L. (Ciconiiformes, Threskiornithidae) known from Brazil, France (bird in captivity), Argentina and Cuba. The species is redescribed and illustrated on the basis of the type-series (from Brazil) in the Helminthological Collection of the Naturhistorisches Museum, Vienna. Syncuaria diacantha Petter, 1961 [= Decorataria diacantha (P.) Skryabin, Sobolev & Ivashkin, 1965], originally described from Platalea ajaja in France (bird in captivity), is recognised as a junior synonym of Decorataria magnilabiata (new synonymy).

Penalized Multi-Way Partial Least Squares for Smooth Trajectory Decoding from Electrocorticographic (ECoG) Recording

PubMed Central

Eliseyev, Andrey; Aksenova, Tetiana

2016-01-01

In the current paper the decoding algorithms for motor-related BCI systems for continuous upper limb trajectory prediction are considered. Two methods for the smooth prediction, namely Sobolev and Polynomial Penalized Multi-Way Partial Least Squares (PLS) regressions, are proposed. The methods are compared to the Multi-Way Partial Least Squares and Kalman Filter approaches. The comparison demonstrated that the proposed methods combined the prediction accuracy of the algorithms of the PLS family and trajectory smoothness of the Kalman Filter. In addition, the prediction delay is significantly lower for the proposed algorithms than for the Kalman Filter approach. The proposed methods could be applied in a wide range of applications beyond neuroscience. PMID:27196417

Global Well-Posedness of the Incompressible Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Cai, Yuan; Lei, Zhen

2018-06-01

This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072-2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597-618, 2001).

Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain

NASA Astrophysics Data System (ADS)

Chae, Myeongju; Choi, Kyudong; Kang, Kyungkeun; Lee, Jihoon

2018-07-01

We consider a simplified model of tumor angiogenesis, described by a Keller-Segel equation on the two dimensional domain (x , y) ∈ R ×Sλ where Sλ is the circle of perimeter λ. It is known that the system allows planar traveling wave solutions of an invading type. In case that λ is sufficiently small, we establish the nonlinear stability of traveling wave solutions in the absence of chemical diffusion if the initial perturbation is sufficiently small in some weighted Sobolev space. When chemical diffusion is present, it can be shown that the system is linearly stable. Lastly, we prove that any solution with our front condition eventually becomes planar under certain regularity conditions.

A large deviations principle for stochastic flows of viscous fluids

NASA Astrophysics Data System (ADS)

Cipriano, Fernanda; Costa, Tiago

2018-04-01

We study the well-posedness of a stochastic differential equation on the two dimensional torus T2, driven by an infinite dimensional Wiener process with drift in the Sobolev space L2 (0 , T ;H1 (T2)) . The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier-Stokes flow approaches the Euler deterministic Lagrangian flow with an exponential rate function.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

NASA Astrophysics Data System (ADS)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Non-LTE line formation in a magnetic field. I. Noncoherent scattering and true absorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Domke, H.; Staude, J.

1973-08-01

The formation of a Zeeman-multiplet by noncoherent scattering and true absorption in a Milne-- Eddington atmosphere is considered assuming a homogeneous magnetic field and complete depolarization of the atomic line levels. The transfer equation for the Stokes parameters is transformed into a scalar integral equation of the Wiener-- Hopf type which is solved by Sobolev's method in closed form. The influence of the magnetic field on the mean scattering number in an infinite medium is discussed. The solution of the line formation problem is obtained for a Planckian source fruction. This solution may be simplified by making the ''finite fieldmore » approximation'', which should be sufficiently accurate for practical purposes. (auth)« less

Distribution-valued initial data for the complex Ginzburg-Landau equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levermore, C.D.; Oliver, M.

1997-11-01

The generalized complex Ginzburg-Landau (CGL) equation with a nonlinearity of order 2{sigma} + 1 in d spatial dimensions has a unique local classical solution for distributional initial data in the Sobolev space H{sup q} provided that q > d/2 - 1/{sigma}. This result directly corresponds to a theorem for the nonlinear Schroedinger (NLS) equation which has been proved by Cazenave and Weissler in 1990. While the proof in the NLS case relies on Besov space techniques, it is shown here that for the CGL equation, the smoothing properties of the linear semigroup can be eased to obtain an almost optimalmore » result by elementary means. 1 fig.« less

Decay estimates of solutions to the bipolar non-isentropic compressible Euler-Maxwell system

NASA Astrophysics Data System (ADS)

Tan, Zhong; Wang, Yong; Tong, Leilei

2017-10-01

We consider the global existence and large time behavior of solutions near a constant equilibrium state to the bipolar non-isentropic compressible Euler-Maxwell system in {R}3 , where the background magnetic field could be non-zero. The global existence is established under the assumption that the H 3 norm of the initial data is small, but its higher order derivatives could be large. Combining the negative Sobolev (or Besov) estimates with the interpolation estimates, we prove the optimal time decay rates of the solution and its higher order spatial derivatives. In this sense, our results improve the similar ones in Wang et al (2012 SIAM J. Math. Anal. 44 3429-57).

Poincare inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces

NASA Astrophysics Data System (ADS)

Bjorn, Jana; Shanmugalingam, Nageswari

2007-08-01

In the setting of metric measure spaces equipped with a doubling measure supporting a weak p-Poincare inequality with 1[less-than-or-equals, slant]p<[infinity], we show that any uniform domain [Omega] is an extension domain for the Newtonian space N1,p([Omega]) and that [Omega], together with the metric and the measure inherited from X, supports a weak p-Poincare inequality. For p>1, we obtain a near characterization of N1,p-extension domains with local estimates for the extension operator.

A Nonlocal Calculation of Circumstellar OH Masers

NASA Astrophysics Data System (ADS)

Collison, A. J.; Nedoluha, G. E.

1993-12-01

We present calculations for circumstellar OH masers which explicitly account for the nonlocal interaction throughout the masing region. Excitation temperatures and observed emission are calculated for all four ground state maser lines. All other transitions are treated using a modified Sobolev approximation. Calculations are performed within the context of a simplified dust/outflow model which provides the pumping conditions and their variation with radius. Total velocity relaxation is implicitly assumed in the calculations. We find general agreement with the qualitative results of earlier work (Collison & Nedoluha, ApJ, 10 Feb 94 issue) and agree with the conclusions of Alcock & Ross (1986, ApJ, 305, 837) who showed that observed profiles can not be produced by a smooth, spherically symmetric wind model of the outflow.

Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations

NASA Astrophysics Data System (ADS)

Phan, Tuoc

2017-12-01

This paper studies the Sobolev regularity for weak solutions of a class of singular quasi-linear parabolic problems of the form ut -div [ A (x , t , u , ∇u) ] =div [ F ] with homogeneous Dirichlet boundary conditions over bounded spatial domains. Our main focus is on the case that the vector coefficients A are discontinuous and singular in (x , t)-variables, and dependent on the solution u. Global and interior weighted W 1 , p (ΩT , ω)-regularity estimates are established for weak solutions of these equations, where ω is a weight function in some Muckenhoupt class of weights. The results obtained are even new for linear equations, and for ω = 1, because of the singularity of the coefficients in (x , t)-variables.

Local existence of solutions to the Euler-Poisson system, including densities without compact support

NASA Astrophysics Data System (ADS)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Peculiarities of the circumstellar envelopes of some Herbig Ae/Be stars

NASA Astrophysics Data System (ADS)

Pogodin, M. A.

1985-10-01

The results of a spectral and photometric investigation of nine Herbig Ae/Be stars in the visible region of the spectrum in the period from 1978 to 1982 are presented. Certain physical and kinematic parameters of the circumstellar envelopes of the investigated objects are determined on the basis of the observational material obtained and Sobolev's (1947) probabilistic method for moving envelopes. It is shown that the observed spectral characteristics of the envelopes of Herbig Ae/Be stars and their variability can be explained by using models of extended isothermal envelopes with varying structural-kinematic parameters. The existence of a correlation between the amount of dust IR excess and the presence of signs of H2O absorption in the spectra of the investigated objects is noted.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

The Thermal Equilibrium Solution of a Generic Bipolar Quantum Hydrodynamic Model

NASA Astrophysics Data System (ADS)

Unterreiter, Andreas

The thermal equilibrium state of a bipolar, isothermic quantum fluid confined to a bounded domain ,d = 1,2 or d = 3 is entirely described by the particle densities n, p, minimizing the energy where G1,2 are strictly convex real valued functions, . It is shown that this variational problem has a unique minimizer in and some regularity results are proven. The semi-classical limit is carried out recovering the minimizer of the limiting functional. The subsequent zero space charge limit leads to extensions of the classical boundary conditions. Due to the lack of regularity the asymptotics can not be settled on Sobolev embedding arguments. The limit is carried out by means of a compactness-by-convexity principle.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Birkhoff Normal Form for Some Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Bambusi, Dario

We consider the problem of extending to PDEs Birkhoff normal form theorem on Hamiltonian systems close to nonresonant elliptic equilibria. As a model problem we take the nonlinear wave equation with Dirichlet boundary conditions on [0,π] g is an analytic skewsymmetric function which vanishes for u=0 and is periodic with period 2π in the x variable. We prove, under a nonresonance condition which is fulfilled for most g's, that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M. The canonical transformation is well defined in a neighbourhood of the origin of a Sobolev type phase space of sufficiently high order. Some dynamical consequences are obtained. The technique of proof is applicable to quite general semilinear equations in one space dimension.

On searching applicants for mechanism of solar-lithosphere relations

NASA Astrophysics Data System (ADS)

Kairatkyzy, Dina; Andreyev, Alexey; Zhumabayeva, Saltanat; Seraliyev, Alibek

2016-04-01

It is actively discussed at present a question on possible influence of solar activity (high-speed solar wind streams bearing the "frozen" magnetic field lines of the Sun) on the stress status of the lithosphere and, consequently, on the Earth's seismic activity (e.g. Zhang, 1998, Acta Seismologica Sinica; Khachikyan et al., EGU2016-2754-1; IUGG2015-3132). There are at least two ideas on possible applicants for physical mechanism of solar-lithosphere relations: (i) - the muons of cosmic rays, which can penetrate the Earth's crust to a depth of at least the first ten kilometers and in tense seismic environment generate nuclear-electromagnetic cascade which energy can be a trigger of earthquake (Tsarev and Chechin, 1988, Preprint № 179, Physical Institute after Lebedev, Moscow); (ii) - the geomagnetic storms (Sobolev et al., 1998, Physics of the Earth #7) when the high-frequency oscillations of the geomagnetic field during the main phase of the storm generate significant induction currents which electric energy entering into the crust can be converted into mechanical energy increasing the stress status of the lithosphere (Sobolev and Demin, Mechano-electric phenomena into the Earth. M . Nauka. 1980). Besides this, among the possible cosmogenic factors changing the stress state of the lithosphere, could be the variation of the angular velocity of rotation of the Earth (e.g. Bostrom, 2000. Tectonic consequence of the Earth's Rotation), if it depends on solar activity variations. More of 50 years ago, Munk and Donald (The Rotation of the Earth, Cambrige University Press, 1960) suggested that the interaction between solar wind and geomagnetic field would probably influence the short period variation of angular velocity of the Earth. In this work, we check up this suggestion on the base of very precise data on the length of day (LOD) from 1986 to the present, which are presented by the International Earth Rotation and Reference Systems Service (IERS). Using the methods

A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian

NASA Astrophysics Data System (ADS)

Quaas, Alexander; Xia, Aliang

2016-08-01

We establish a Liouville type theorem for the fractional Lane-Emden system: {(-Δ)αu=vqin  RN,(-Δ)αv=upin  RN, where α \\in (0,1) , N>2α and p, q are positive real numbers and in an appropriate new range. To prove our result we will use the local realization of fractional Laplacian, which can be constructed as a Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre (2007 Commun. PDE 32 1245-60). Our proof is based on a monotonicity argument for suitable transformed functions and the method of moving planes in a half infinite cylinder ({IR}× S+N , where S+N is the half unit sphere in {{{R}}N+1} ) based on maximum principles which are obtained by barrier functions and a coupling argument using a fractional Sobolev trace inequality.

C1,1 regularity for degenerate elliptic obstacle problems

NASA Astrophysics Data System (ADS)

Daskalopoulos, Panagiota; Feehan, Paul M. N.

2016-03-01

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

A rapid radiative transfer model for reflection of solar radiation

NASA Technical Reports Server (NTRS)

Xiang, X.; Smith, E. A.; Justus, C. G.

1994-01-01

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

G-Strands on symmetric spaces

PubMed Central

2017-01-01

We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa–Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions. PMID:28413343

Lipschitz Metric for the Novikov Equation

NASA Astrophysics Data System (ADS)

Cai, Hong; Chen, Geng; Chen, Robin Ming; Shen, Yannan

2018-03-01

We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport metric which renders the solution map Lipschitz continuous on bounded sets of {H^1(R)\\cap W^{1,4}(R)} , although it is not Lipschitz continuous under the natural Sobolev metric from an energy law due to the finite time gradient blowup. By an application of Thom's transversality theorem, we also prove that when the initial data is in an open dense subset of {H^1(R)\\cap W^{1,4}(R)} , the solution is piecewise smooth. This generic regularity result helps us extend the Lipschitz continuous metric to the general weak solutions. Our method of constructing the metric can be used to treat other kinds of quasi-linear equations, provided a good knowledge about the energy concentration.

Effects of Nongray Opacity on Radiatively Driven Wolf-Rayet Winds

NASA Astrophysics Data System (ADS)

Onifer, A. J.; Gayley, K. G.

2002-05-01

Wolf-Rayet winds are characterized by their large momentum fluxes, and simulations of radiation driving have been increasingly successful in modeling these winds. Simple analytic approaches that help understand the most critical processes for copious momentum deposition already exist in the effectively gray approximation, but these have not been extended to more realistic nongray opacities. With this in mind, we have developed a simplified theory for describing the interaction of the stellar flux with nongray wind opacity. We replace the detailed line list with a set of statistical parameters that are sensitive not only to the strength but also the wavelength distribution of lines, incorporating as a free parameter the rate of photon frequency redistribution. We label the resulting flux-weighted opacity the statistical Sobolev- Rosseland (SSR) mean, and explore how changing these various statistical parameters affects the flux/opacity interaction. We wish to acknowledge NSF grant AST-0098155

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems

NASA Astrophysics Data System (ADS)

Toscani, Giuseppe

2016-10-01

We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.

Solvability of the Initial Value Problem to the Isobe-Kakinuma Model for Water Waves

NASA Astrophysics Data System (ADS)

Nemoto, Ryo; Iguchi, Tatsuo

2017-09-01

We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe-Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t=0 is characteristic for the Isobe-Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh-Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.

A priori Estimates for 3D Incompressible Current-Vortex Sheets

NASA Astrophysics Data System (ADS)

Coulombel, J.-F.; Morando, A.; Secchi, P.; Trebeschi, P.

2012-04-01

We consider the free boundary problem for current-vortex sheets in ideal incompressible magneto-hydrodynamics. It is known that current-vortex sheets may be at most weakly (neutrally) stable due to the existence of surface waves solutions to the linearized equations. The existence of such waves may yield a loss of derivatives in the energy estimate of the solution with respect to the source terms. However, under a suitable stability condition satisfied at each point of the initial discontinuity and a flatness condition on the initial front, we prove an a priori estimate in Sobolev spaces for smooth solutions with no loss of derivatives. The result of this paper gives some hope for proving the local existence of smooth current-vortex sheets without resorting to a Nash-Moser iteration. Such result would be a rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instabilities, which is well known in astrophysics.

Dissipative structure and global existence in critical space for Timoshenko system of memory type

NASA Astrophysics Data System (ADS)

Mori, Naofumi

2018-08-01

In this paper, we consider the initial value problem for the Timoshenko system with a memory term in one dimensional whole space. In the first place, we consider the linearized system: applying the energy method in the Fourier space, we derive the pointwise estimate of the solution in the Fourier space, which first gives the optimal decay estimate of the solution. Next, we give a characterization of the dissipative structure of the system by using the spectral analysis, which confirms our pointwise estimate is optimal. In the second place, we consider the nonlinear system: we show that the global-in-time existence and uniqueness result could be proved in the minimal regularity assumption in the critical Sobolev space H2. In the proof we don't need any time-weighted norm as recent works; we use just an energy method, which is improved to overcome the difficulties caused by regularity-loss property of Timoshenko system.

On Energy Inequality for the Problem on the Evolution of Two Fluids of Different Types Without Surface Tension

NASA Astrophysics Data System (ADS)

Denisova, Irina Vlad.

2015-03-01

The paper deals with the motion of two immiscible viscous fluids in a container, one of the fluids being compressible while another one being incompressible. The interface between the fluids is an unknown closed surface where surface tension is neglected. We assume the compressible fluid to be barotropic, the pressure being given by an arbitrary smooth increasing function. This problem is considered in anisotropic Sobolev-Slobodetskiǐ spaces. We show that the L 2-norms of the velocity and deviation of compressible fluid density from the mean value decay exponentially with respect to time. The proof is based on a local existence theorem (Denisova, Interfaces Free Bound 2:283-312, 2000) and on the idea of constructing a function of generalized energy, proposed by Padula (J Math Fluid Mech 1:62-77, 1999). In addition, we eliminate the restrictions for the viscosities which appeared in Denisova (Interfaces Free Bound 2:283-312, 2000).

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

NASA Astrophysics Data System (ADS)

Lupo, Umberto

2018-04-01

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity H^{1/2+ɛ }_{loc} is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

NASA Astrophysics Data System (ADS)

Alekseev, G.; Tokhtina, A.; Soboleva, O.

2017-10-01

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces

NASA Astrophysics Data System (ADS)

Yang, Qixiang; Yang, Haibo

2018-04-01

For fractional Navier-Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C (R+ , X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y m , β where Y m , β is not contained in C (R+, B˙∞ 1 - 2 β , ∞). Consequently, for 1/2 < β < 1, we establish the global well-posedness of fractional Navier-Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov-Morrey spaces (B˙p,q γ1 ,γ2 (Rn)) n or any Triebel-Lizorkin-Morrey spaces (F˙p,q γ1 ,γ2 (Rn)) n where 1 ≤ p , q ≤ ∞ , 0 ≤γ2 ≤ n/p, γ1 -γ2 = 1 - 2 β. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc.

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Well-posedness of the Cauchy problem for models of large amplitude internal waves

NASA Astrophysics Data System (ADS)

Guyenne, Philippe; Lannes, David; Saut, Jean-Claude

2010-02-01

We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1-36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587-641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538-66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves.

Scattering theory for the defocusing fourth-order Schrödinger equation

NASA Astrophysics Data System (ADS)

Miao, Changxing; Zheng, Jiqiang

2016-02-01

In this paper, we study the global well-posedness and scattering theory for the defocusing fourth-order nonlinear Schrödinger equation (FNLS) \\text{i}{{u}t}+{{Δ }2}u +\\mid u{{\\mid}p}u=0 in dimensions d≥slant 8 . We prove that if the solution u is apriorily bounded in the critical Sobolev space, that is, u\\in Lt∞≤ft(I;\\overset{\\centerdot}{\\mathop{H}} x{{sc}}≤ft({{{R}}d}\\right)\\right) with all {{s}c}:=\\frac{d}{2}-\\frac{4}{p}≥slant 1 if p is an even integer or {{s}c}\\in ≤ft[1,2+p\\right) otherwise, then u is global and scatters. We will give a uniform way to treat the energy-subcritical, energy-critical and energy-supercritical FNLS by making use of the strategy derived from concentration compactness ideas, and we are able to overcome the logarithmic blowup in the double Duhamel trick in dimension eight by exploiting the refined dispersive estimate which is in sharp contrast to the Schrödinger equation.

Winds from accretion disks - Ultraviolet line formation in cataclysmic variables

NASA Technical Reports Server (NTRS)

Shlosman, Isaac; Vitello, Peter

1993-01-01

Winds from accretion disks in cataclysmic variable stars are ubiquitous. Observations by IUE reveal P Cygni-shaped profiles of high-ionization lines which are attributed to these winds. We have studied the formation of UV emission lines in cataclysmic variables by constructing kinematical models of biconical rotating outflows from disks around white dwarfs. The photoionization in the wind is calculated taking into account the radiation fields of the disk, the boundary layer, and the white dwarf. The 3D radiative transfer is solved in the Sobolev approximation. Effects on the line shapes of varying basic physical parameters of the wind are shown explicitly. We identify and map the resonant scattering regions in the wind which have strongly biconical character regardless of the assumed velocity and radiation fields. Rotation at the base of the wind introduces a radial shear which decreases the line optical depth and reduces the line core intensity. We find that it is possible to reproduce the observed P Cygni line shapes and make some predictions to be verified in high-resolution observations.

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.

Raman spectroscopic study of synthesized Na-bearing majoritic garnets

NASA Astrophysics Data System (ADS)

Okamoto, K.

2003-12-01

Majoritic garnets in diamond have been considered as the sample from mantle transition zone (e.g. Moore and Gurney, 1985). For non-destructive, in-situ Raman analysis, Gillet et al. (2002) systematically checked chemistry and Raman peak of various majoritic garnets in diamond. They treated majoritic component as number of excess-silica than 3.0 per formula unit. However, in the basaltic system, majorite garnets also have significant amounts of Na. Na substitution is coupled with Si and Ti as follows; Na +Ti = Ca +Al (Ringwood and Lovering, 1970), Na +Si = Ca + Al (Sobolev and Labrentav, 1971; Ringwood and Major, 1971) or Na + Si = Mg + Al (Gasparik, 1989). Each component in garnet is defined as follows; Mj (majorite) component = ((Si-3)-Na)/2), NaSi (Na2MSi5O12 where M= Ca, Mg, Fe2+) component = (Na-T)/2, and NaTi component = Ti/2. Okamoto and Maruyama (2003) conducted UHP experiments in the MORB + H2O system (KNCFMATSH) at 10-19 GPa. They show that 1) Mj and NaTi component are constant and lower than 0.1 at T = 900 \\deg C, and 2) NaSi component increases drastically above 15 GPa although it is neglibly small at P<15 GPa. Raman spectra was newly analyzed using Okamoto and Maruyama (2003)'s run charges. Above 15 GPa, there is a characteristic sharp peak at 910 cm-1 and broad shoulder between 800 and 900 cm-1 as well as broad band near 960 cm-1. Gillet et at (2002) concluded that the former peak at 910cm-1 is the only reliable signature for the majoritic garnet (Si>3). They also implied that the latter two broad peaks are diagnostic feature for Ti rich garnet (> 1wt% of TiO2) as well as peak at 1030 cm-1. However, in all P range (10-19 GPa) of the present study, TiO2 is higher than 1wt%, and there is a peak at 1030 cm-1. Additional Ti-free experiment at 16 GPa, 1200 \\deg C clearly revealed that Na-bearing majoritic garnet has a significant shoulder at 800-900 cm-1. Ref; Gasparik (1989) CMP, 102,389, Gillet et al. (2002) Am.Min., 87, 312, Moore and Gurney (1985

Do Melt Inclusions Answer Big Questions?

NASA Astrophysics Data System (ADS)

Hofmann, A. W.; Sobolev, A. V.

2009-12-01

In a pioneering paper, Sobolev and Shimizu (1993) demonstrated the existence of ultra-depleted melt inclusions in olivine phenocrysts in MORB. They interpreted these as evidence for the preservation of parental melts formed by progressive near-fractional melting. Subsequently many cases have been described where melt inclusions from single basalt samples display enormous chemical and isotopic heterogeneity. The interpretation of these observations hinges critically on whether such melt inclusions can faithfully preserve primary or parental melt composition. If they do, melt inclusion data can truly answer big questions from small-scale observations. If they do not, they answer rather small questions. Favoring the second possibility, Danyushevsky et al. (2004) have suggested that much of the observed variability of highly incompatible trace elements in melt inclusions “may not represent geologically significant melts, but instead reflect localized, grain-scale reaction processes within the magmatic plumbing system.” We disagree and show that this mechanism cannot, for example, explain isotopic heterogeneity measured in several suites of melt inclusions, nor does it not account for the presence of ultra-depleted melts and "ghost" plagioclase signatures in other inclusions. More recently, Spandler et al. (2007) have suggested on the basis of experimental evidence that diffusion rates for REE in olivine are so rapid that parental melt compositions in melt inclusions are rapidly falsified by diffusional exchange with (evolved) host lava. We show that the very fact that extreme chemical and isotopic heterogeneities are routinely preserved in melt inclusions demonstrates that this conclusion is unwarranted, either because residence times of the olivine phenocrysts are much shorter than assumed by Spandler et al. or because the high experimental diffusion rates are caused by an unknown experimental artifact. Although there is no obvious flaw in design and execution of

Conforming discretizations of boundary element solutions to the electroencephalography forward problem

NASA Astrophysics Data System (ADS)

Rahmouni, Lyes; Adrian, Simon B.; Cools, Kristof; Andriulli, Francesco P.

2018-01-01

In this paper, we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages, in several real case scenarios, in terms of numerical stability and effectiveness when compared with other differential equation based techniques. Unfortunately, however, it is widely reported in literature that the accuracy of standard BEM schemes for the forward EEG problem is often limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required, for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly and classically discretized EEG forward problem operators, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several standardly used discretizations of these formulations are consistent only with an L2-framework, requiring the expansion term to be a square integrable function (i.e., in a Petrov-Galerkin scheme with expansion and testing functions). Instead, those techniques are not consistent when a more appropriate mapping in terms of fractional-order Sobolev spaces is considered. Such a mapping allows the expansion function term to be a less regular function, thus sensibly reducing the need for mesh refinements and low-precisions handling strategies that are currently required. These more favorable mappings, however, require a different and conforming discretization, which must be suitably adapted to them. In order to appropriately fulfill this requirement, we adopt a mixed

Modeling of Red Giant and AGB Stars Atmospheres: Constraints from VLTI and HST Observations

NASA Astrophysics Data System (ADS)

Rau, Gioia

2018-04-01

The chemical enrichment of the Universe is considerably affected by the contributions of low-to-intermediate mass stars through the mass-loss provided via their stellar winds. First, we will present our investigation in the near-IR with VLTI/GRAVITY (Wittkowski, Rau, et al., in prep.). Our aim was to verify at different epochs the model-predicted variability of the visibility spectra. We use CODEX model atmospheres, as well as best-fit 3D radiation hydrodynamic simulations (e.g. Freytag et al., 2017), for comparison with the observations. Our preliminary results on R Peg suggest a decreasing contribution by extended CO layers as the star transitions from maximum to minimum phase. Second, we will show a preliminary modeling of UV spectra obtained with HST/GHRS that contain chromospheric emission lines of, e.g., Mg II and Fe II. Via Sobolev with Exact Integration (SEI) modeling, we determined for the two M-giant stars γ Cru and µ Gem the characteristics of their winds (turbulence, acceleration, and opacity), and their average global mass-loss rates (Rau, Carpenter et al., in prep.). Finally, we briefly discuss the impact of instruments on board JWST in progressing this investigation.

Ultraviolet line diagnostics of accretion disk winds in cataclysmic variables

NASA Technical Reports Server (NTRS)

Vitello, Peter; Shlosman, Isaac

1993-01-01

The IUE data base is used to analyze the UV line shapes of the cataclysmic variables RW Sex, RW Tri, and V Sge. Observed lines are compared to synthetic line profiles computed using a model of rotating biconical winds from accretion disks. The wind model calculates the wind ionization structure self-consistently including photoionization from the disk and boundary layer and treats 3D line radiation transfer in the Sobolev approximation. It is found that winds from accretion disks provide a good fit for reasonable parameters to the observed UV lines which include the P Cygni profiles for low-inclination systems and pure emission at large inclination. Disk winds are preferable to spherical winds which originate on the white dwarf because they: (1) require a much lower ratio of mass-loss rate to accretion rate and are therefore more plausible energetically; (2) provide a natural source for a biconical distribution of mass outflow which produces strong scattering far above the disk leading to P Cygni profiles for low-inclination systems and pure line emission profiles at high inclination with the absence of eclipses in UV lines; and (3) produce rotation-broadened pure emission lines at high inclination.

Line profiles variations from atmospheric eclipses: Constraints on the wind structure in Wolf-Rayet stars

NASA Technical Reports Server (NTRS)

Auer, L. H.; Koenigsberger, G.

1994-01-01

Binary systems in which one of the components has a stellar wind may present a phenomenon known as 'wind' or 'atmospheric eclipse', in which that wind occults the luminous disk of the companion. The enhanced absorption profile, relative to the spectrum at uneclipsed orbital phases, can be be modeled to yield constraints on the spatial structure of the eclipsing wind. A new, very efficient approach to the radiative transfer problem, which makes no requirements with respect to monotonicity of the velocity gradient or size of that gradient, is presented. The technique recovers both the comoving frame calculation and the Sobolev approximation in the appropiate limits. Sample computer simulations of the line profile variations induced by wind eclipses are presented. It is shown that the location of the wind absorption features in frequency is a diagnostic tool for identifying the size of the wind acceleration region. Comparison of the model profile variations with the observed variations in the Wolf-Rayet (W-R)+6 binary system V444 Cyg illustrate how the method can be used to derive information on the structure of the wind of the W-R star constrain the size of the W-R core radius.

UV line diagnostics of accretion disk winds in cataclysmic variables

NASA Technical Reports Server (NTRS)

Vitello, Peter; Shlosman, Isaac

1992-01-01

The IUE data base is used to analyze the UV line shapes of cataclysmic variables RW Sex, RW Tri, and V Sge. Observed lines are compared to synthetic line profiles computed using a model of rotating bi-conical winds from accretion disks. The wind model calculates the wind ionization structure self-consistently including photoionization from the disk and boundary layer and treats 3-D line radiation transfer in the Sobolev approximation. It is found that winds from accretion disks provide a good fit for reasonable parameters to the observed UV lines which include the P Cygni profiles for low inclination systems and pure emission at large inclination. Disk winds are preferable to spherical winds which originate on the white dwarf because they (1) require a much lower ratio of mass loss rate to accretion rate and are therefore more plausible energetically, (2) provide a natural source for a bi-conical distribution of mass outflow which produces strong scattering far above the disk leading to P Cygni profiles for low inclination systems, and pure line emission profiles at high inclination with the absence of eclipses in UV lines, and (3) produce rotation broadened pure emission lines at high inclination.

New Insights into the Puzzling P-Cygni Profiles of Magnetic Massive Stars

NASA Astrophysics Data System (ADS)

Erba, Christiana; David-Uraz, Alexandre; Petit, Véronique; Owocki, Stanley P.

2017-11-01

Magnetic massive stars comprise approximately 10% of the total OB star population. Modern spectropolarimetry shows these stars host strong, stable, large-scale, often nearly dipolar surface magnetic fields of 1 kG or more. These global magnetic fields trap and deflect outflowing stellar wind material, forming an anisotropic magnetosphere that can be probed with wind-sensitive UV resonance lines. Recent HST UV spectra of NGC 1624-2, the most magnetic O star observed to date, show atypically unsaturated P-Cygni profiles in the Civ resonant doublet, as well as a distinct variation with rotational phase. We examine the effect of non-radial, magnetically-channeled wind outflow on P-Cygni line formation, using a Sobolev Exact Integration (SEI) approach for direct comparison with HST UV spectra of NGC 1624-2. We demonstrate that the addition of a magnetic field desaturates the absorption trough of the P-Cygni profiles, but further efforts are needed to fully account for the observed line profile variation. Our study thus provides a first step toward a broader understanding of how strong magnetic fields affect mass loss diagnostics from UV lines.

Time-Parallel Solutions to Ordinary Differential Equations on GPUs with a New Functional Optimization Approach Related to the Sobolev Gradient Method

DTIC Science & Technology

2012-10-01

black and approximations in cyan and magenta. The second ODE is the pendulum equation, given by: This ODE was also implemented using Crank...The drawback of approaches like the one proposed can be observed with a very simple example. Suppose vector is found by applying 4 linear...public release; distribution unlimited Figure 2. A phase space plot of the Pendulum example. Fine solution (black) contains 32768 time steps

Optimal and robust control of a class of nonlinear systems using dynamically re-optimised single network adaptive critic design

NASA Astrophysics Data System (ADS)

Tiwari, Shivendra N.; Padhi, Radhakant

2018-01-01

Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN1) is synthesised offline. However, another linear-in-weight neural network (called as NN2) is trained online and augmented to NN1 in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which is done by synthesising yet another linear-in-weight neural network (called as NN3) online. Training of NN3 is done by utilising the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function. This helps in training NN2 successfully to capture the required optimal relationship. The overall architecture is named as 'Dynamically Re-optimised single network adaptive critic (DR-SNAC)'. Numerical results for two motivating illustrative problems are presented, including comparison studies with closed form solution for one problem, which clearly demonstrate the effectiveness and benefit of the proposed approach.

On Birman's sequence of Hardy-Rellich-type inequalities

NASA Astrophysics Data System (ADS)

Gesztesy, Fritz; Littlejohn, Lance L.; Michael, Isaac; Wellman, Richard

2018-02-01

In 1961, Birman proved a sequence of inequalities {In }, for n ∈ N, valid for functions in C0n ((0 , ∞)) ⊂L2 ((0 , ∞)). In particular, I1 is the classical (integral) Hardy inequality and I2 is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space Hn ([ 0 , ∞)) of functions defined on [ 0 , ∞). Moreover, f ∈Hn ([ 0 , ∞)) implies f‧ ∈Hn-1 ([ 0 , ∞)); as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite b > 0, these inequalities hold on the standard Sobolev space H0n ((0 , b)). Furthermore, in all cases, the Birman constants [ (2 n - 1) ! ! ] 2 /22n in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in L2 ((0 , ∞)) (resp., L2 ((0 , b))). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail.

On the topological stability of continuous functions in certain spaces related to Fourier series

NASA Astrophysics Data System (ADS)

Lebedev, Vladimir V.

2010-04-01

We show that the following properties of a continuous function f on the circle \\mathbb T are equivalent: the sequence \\widehat{f\\circ h} of the Fourier coefficients of the superposition f\\circ h belongs to the weak l^1 for every homeomorphism h of the circle onto itself; f is a function of bounded quadratic variation. We obtain similar results for spaces of functions whose sequence of Fourier coefficients belongs to the weak l^p, 1, for spaces A_p of functions f with \\widehat{f}\\in l^p, for the Sobolev spaces W_2^\\lambda, and for other spaces of functions on \\mathbb T. Under rather general assumptions on a space \\mathbb X of functions on the circle, we give a necessary condition for a given continuous function f to stay in \\mathbb X for every change of variable. We also consider the multidimensional case, which is essentially different from the one-dimensional case. In particular, we show that if p<2 and f is a continuous function on the torus \\mathbb T^d, d\\ge2, such that f\\circ h\\in A_p(\\mathbb T^d) for every homeomorphism h\\colon \\mathbb T^d\\to\\mathbb T^d, then f is constant.

Mappings of Least Dirichlet Energy and their Hopf Differentials

NASA Astrophysics Data System (ADS)

Iwaniec, Tadeusz; Onninen, Jani

2013-08-01

The paper is concerned with mappings {h \\colon {X}} {{begin{array}{ll} onto \\ longrightarrow }} {{Y}} between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in {{X}}) of the energy-minimal mappings is established within the class {overline{fancyscript{H}}_2({X}, {Y})} of strong limits of homeomorphisms in the Sobolev space {fancyscript{W}^{1,2}({X}, {Y})} , a result of considerable interest in the mathematical models of nonlinear elasticity. The inner variation of the independent variable in {{X}} leads to the Hopf differential {hz overline{h_{bar{z}}} dz ⊗ dz} and its trajectories. For a pair of doubly connected domains, in which {{X}} has finite conformal modulus, we establish the following principle: A mapping {h in overline{fancyscript{H}}2 ({X}, {Y})} is energy-minimal if and only if its Hopf-differential is analytic in {{X}} and real along {partial {X}} . In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of slits in {{X}} (cognate with cracks). Slits are triggered by points of concavity of {{Y}} . They originate from {partial {X}} and advance along vertical trajectories of the Hopf differential toward {{X}} where they eventually terminate, so no crosscuts are created.

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

NASA Astrophysics Data System (ADS)

Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric

2016-12-01

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily code various numerical algorithms. Two robust and optimized numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are used to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.

On the Ck-embedding of Lorentzian manifolds in Ricci-flat spaces

NASA Astrophysics Data System (ADS)

Avalos, R.; Dahia, F.; Romero, C.

2018-05-01

In this paper, we investigate the problem of non-analytic embeddings of Lorentzian manifolds in Ricci-flat semi-Riemannian spaces. In order to do this, we first review some relevant results in the area and then motivate both the mathematical and physical interests in this problem. We show that any n-dimensional compact Lorentzian manifold (Mn, g), with g in the Sobolev space Hs+3, s >n/2 , admits an isometric embedding in a (2n + 2)-dimensional Ricci-flat semi-Riemannian manifold. The sharpest result available for these types of embeddings, in the general setting, comes as a corollary of Greene's remarkable embedding theorems R. Greene [Mem. Am. Math. Soc. 97, 1 (1970)], which guarantee the embedding of a compact n-dimensional semi-Riemannian manifold into an n(n + 5)-dimensional semi-Euclidean space, thereby guaranteeing the embedding into a Ricci-flat space with the same dimension. The theorem presented here improves this corollary in n2 + 3n - 2 codimensions by replacing the Riemann-flat condition with the Ricci-flat one from the beginning. Finally, we will present a corollary of this theorem, which shows that a compact strip in an n-dimensional globally hyperbolic space-time can be embedded in a (2n + 2)-dimensional Ricci-flat semi-Riemannian manifold.

Dynamic experiment design regularization approach to adaptive imaging with array radar/SAR sensor systems.

PubMed

Shkvarko, Yuriy; Tuxpan, José; Santos, Stewart

2011-01-01

We consider a problem of high-resolution array radar/SAR imaging formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the random wavefield scattered from a remotely sensed scene observed through a kernel signal formation operator and contaminated with random Gaussian noise. First, the Sobolev-type solution space is constructed to specify the class of consistent kernel SSP estimators with the reproducing kernel structures adapted to the metrics in such the solution space. Next, the "model-free" variational analysis (VA)-based image enhancement approach and the "model-based" descriptive experiment design (DEED) regularization paradigm are unified into a new dynamic experiment design (DYED) regularization framework. Application of the proposed DYED framework to the adaptive array radar/SAR imaging problem leads to a class of two-level (DEED-VA) regularized SSP reconstruction techniques that aggregate the kernel adaptive anisotropic windowing with the projections onto convex sets to enforce the consistency and robustness of the overall iterative SSP estimators. We also show how the proposed DYED regularization method may be considered as a generalization of the MVDR, APES and other high-resolution nonparametric adaptive radar sensing techniques. A family of the DYED-related algorithms is constructed and their effectiveness is finally illustrated via numerical simulations.

On absence of bound states for weakly attractive δ'-interactions supported on non-closed curves in ℝ2

NASA Astrophysics Data System (ADS)

Jex, Michal; Lotoreichik, Vladimir

2016-02-01

Let Λ ⊂ ℝ2 be a non-closed piecewise-C1 curve, which is either bounded with two free endpoints or unbounded with one free endpoint. Let u±|Λ ∈ L2(Λ) be the traces of a function u in the Sobolev space H1(ℝ2∖Λ) onto two faces of Λ. We prove that for a wide class of shapes of Λ the Schrödinger operator Hω Λ with δ'-interaction supported on Λ of strength ω ∈ L∞(Λ; ℝ) associated with the quadratic form H 1 ( R 2 ∖ Λ ) ∋ u ↦ ∫ R 2 |" separators=" ∇ u | 2 d x - ∫ Λ ω |" separators=" u + | Λ - u - | Λ | 2 d s has no negative spectrum provided that ω is pointwise majorized by a strictly positive function explicitly expressed in terms of Λ. If, additionally, the domain ℝ2∖Λ is quasi-conical, we show that σ ( Hω Λ ) = [ 0 , + ∞ ) . For a bounded curve Λ in our class and non-varying interaction strength ω ∈ ℝ, we derive existence of a constant ω∗ > 0 such that σ ( Hω Λ ) = [ 0 , + ∞ ) for all ω ∈ (-∞, ω∗]; informally speaking, bound states are absent in the weak coupling regime.

PREFACE: International Workshop on Multi-Rate processes and Hysterisis

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; O'Malley, Robert E.; Pokrovskii, Alexei V.; Sobolev, Vladimir A.

2006-12-01

with an emphasis on hysteresis and singular perturbations; to learn and to share modern techniques in areas of common interest. The `International Workshop on Multi-Rate Processes and Hysteresis' (University College Cork, Ireland, April 3-8, 2006) brought together more than 50 scientists, actively researching in the areas of dynamical systems with hysteresis and singular perturbations, to analyze these phenomena that occur in many industrial, physical and economic systems. The Workshop has been sponsored by the University College Cork (UCC), the Boole Centre for Research in Informatics, UCC, Cork, the School of Mathematical Sciences UCC, Cork, Science Foundation Ireland and the Irish Mathematical Society. The supportive affiliation of the UK and Republic of Ireland SIAM Section is gratefully acknowledged. The Editors and the Organizers of the Workshop wish to place on record their sincere gratitude to Mr Andrew Zhezherun of University College Cork for both the assistance which he provided to all the presenters at the Workshop, and for the careful formatting of all the manuscripts prior to their being forwarded to the Publisher. More information about the Workshop can be found at http://euclid.ucc.ie/murphys2006.htm Michael P Mortell, Robert E O'Malley, Alexei Pokrovskii and Vladimir Sobolev Editors From left to right: M P Mortell, V Sobolev, R E O'Malley and A Pokrovskii.

Minerals and melt inclusions as keys to understanding magma reservoir processes during formation of volcanic and plutonic mafic-ultramafic complexes in the Maimecha Kotui Province (Polar Siberia)

NASA Astrophysics Data System (ADS)

Simonov, Vladimir; Vasiliev, Yurii; Kotlyarov, Alexey; Stupakov, Sergey

2016-04-01

Magmatic complexes in the Maimecha Kotui Province (Polar Siberia) attract attention of researchers because they contain ultramafic volcanic rocks - meimechites, being products of crystallization of the ultrabasic deep mantle melts (Sobolev et al., 1991, 2009, 2011; Ryabchikov et al., 2002; Vasiliev, Gora, 2014). Effusive meimechites together with intrusive dunites of the Guli massif form ancient (253-246 Ma) volcanic and plutonic association, in which also pyroxenites and alkaline rocks are situated. Conditions of formation of this association were established with the help of minerals and melt inclusions study. The cumulative structure of the Guli massif dunites consists of rather large (2-4 mm) olivine crystals and dividing them zones (0.5-0.7 mm), filled with fine grains of clinopyroxenes and ore minerals (magnetite, ilmenite and chromite). The extended forms of well faceted pyroxene crystals testify to their fast growth from melt between cumulative olivines. Thus, crystallization of clinopyroxenes and ore minerals leads to formation between olivines ore pyroxenites, which are presented in the Guli massif by independent bodies. Analysis of olivine, Cr-spinel and clinopyroxene compositions testify to similarity of conditions of the Guli massif dunites crystallization on the one hand with formation of platinum-bearing Uralian-Alaskan-type mafic-ultramafic complexes and with another - show participation of meimechite magma. Major element composition of melt inclusions in Cr-spinel has shown that dunites of the Guli massif were crystallized with participation of subalkaline picrite magmatic systems, that are relative to melts, responsible of formation of platinum-bearing mafic-ultramafic complexes and meimechites. Peculiarities of trace and rare-earth elements distribution in melt inclusions in Cr-spinel of dunites are actually similar to inclusions in olivine of meimechites. Overall, data on composition of inclusions directly testify to formation of considered

On the Global Regularity of a Helical-Decimated Version of the 3D Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Biferale, Luca; Titi, Edriss S.

2013-06-01

We study the global regularity, for all time and all initial data in H 1/2, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution of Navier-Stokes (NS) equations into the subspace where helicity (the L 2-scalar product of velocity and vorticity) is sign-definite. The presence of a second (beside energy) sign-definite inviscid conserved quadratic quantity, which is equivalent to the H 1/2-Sobolev norm, allows us to demonstrate global existence and uniqueness, of space-periodic solutions, together with continuity with respect to the initial conditions, for this decimated 3D model. This is achieved thanks to the establishment of two new estimates, for this 3D model, which show that the H 1/2 and the time average of the square of the H 3/2 norms of the velocity field remain finite. Such two additional bounds are known, in the spirit of the work of H. Fujita and T. Kato (Arch. Ration. Mech. Anal. 16:269-315, 1964; Rend. Semin. Mat. Univ. Padova 32:243-260, 1962), to be sufficient for showing well-posedness for the 3D NS equations. Furthermore, they are directly linked to the helicity evolution for the dNS model, and therefore with a clear physical meaning and consequences.

A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

2018-04-01

In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

Dynamic Experiment Design Regularization Approach to Adaptive Imaging with Array Radar/SAR Sensor Systems

PubMed Central

Shkvarko, Yuriy; Tuxpan, José; Santos, Stewart

2011-01-01

We consider a problem of high-resolution array radar/SAR imaging formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the random wavefield scattered from a remotely sensed scene observed through a kernel signal formation operator and contaminated with random Gaussian noise. First, the Sobolev-type solution space is constructed to specify the class of consistent kernel SSP estimators with the reproducing kernel structures adapted to the metrics in such the solution space. Next, the “model-free” variational analysis (VA)-based image enhancement approach and the “model-based” descriptive experiment design (DEED) regularization paradigm are unified into a new dynamic experiment design (DYED) regularization framework. Application of the proposed DYED framework to the adaptive array radar/SAR imaging problem leads to a class of two-level (DEED-VA) regularized SSP reconstruction techniques that aggregate the kernel adaptive anisotropic windowing with the projections onto convex sets to enforce the consistency and robustness of the overall iterative SSP estimators. We also show how the proposed DYED regularization method may be considered as a generalization of the MVDR, APES and other high-resolution nonparametric adaptive radar sensing techniques. A family of the DYED-related algorithms is constructed and their effectiveness is finally illustrated via numerical simulations. PMID:22163859

Definition and properties of the libera operator on mixed norm spaces.

PubMed

Pavlovic, Miroslav

2014-01-01

We consider the action of the operator ℒg(z) = (1 - z)(-1)∫ z (1)‍f(ζ)dζ on a class of "mixed norm" spaces of analytic functions on the unit disk, X = H α,ν (p,q) , defined by the requirement g ∈ X ⇔ r ↦ (1 - r) (α) M p (r, g ((ν))) ∈ L (q) ([0,1], dr/(1 - r)), where 1 ≤ p ≤ ∞, 0 < q ≤ ∞, α > 0, and ν is a nonnegative integer. This class contains Besov spaces, weighted Bergman spaces, Dirichlet type spaces, Hardy-Sobolev spaces, and so forth. The expression ℒg need not be defined for g analytic in the unit disk, even for g ∈ X. A sufficient, but not necessary, condition is that Σ(n=0)|(∞)|ĝ(n)/(n + 1) < ∞. We identify the indices p, q, α, and ν for which 1°ℒ is well defined on X, 2 °ℒ acts from X to X, 3° the implication g ∈ X [Symbol: see text] Σ(n = 0)(∞) |/ĝ(n)|(n+1) < ∞ holds. Assertion 2° extends some known results, due to Siskakis and others, and contains some new ones. As an application of 3° we have a generalization of Bernstein's theorem on absolute convergence of power series that belong to a Hölder class.

Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-02-01

In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

Estimation of Mass-Loss Rate for M Giants from UV Emission Line Profiles

NASA Technical Reports Server (NTRS)

Carpenter, Kenneth G.; Robinson, R. D.; Fisher, Richard R. (Technical Monitor)

2001-01-01

The photon-scattering winds of M giants produce absorption features in the strong chromospheric emission lines. These provide us with an opportunity to assess important parameters of the wind, including flow and turbulent velocities, the optical depth of the wind above the region of photon creation, and the star's mass-loss rate. We have used the Lamers et al. (1987) Sobolev with Exact Integration (SET) radiative transfer code, along with simple models of the outer atmospheric structure and wind, to determine the wind characteristics of two M-giant stars, gamma Cru (M3.4) and mu Gem (M3IIIab). The SET code has the advantage of being computationally fast and allows a great number of possible wind models to be examined. The analysis procedure involves specifying wind parameters and then using the program to calculate line profiles for the Mg II (UV1) lines and a range of unblended Fe II lines. These lines have a wide range of wind opacities and therefore probe different heights in the atmosphere. The assumed wind properties are iterated until the predicted profiles match the observations over as many lines as possible. We present estimates of the wind parameters for these stars and offer a comparison to wind properties previously-derived for low-gravity K stars using the same technique.

Self-consistent modelling of line-driven hot-star winds with Monte Carlo radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Noebauer, U. M.; Sim, S. A.

2015-11-01

Radiative pressure exerted by line interactions is a prominent driver of outflows in astrophysical systems, being at work in the outflows emerging from hot stars or from the accretion discs of cataclysmic variables, massive young stars and active galactic nuclei. In this work, a new radiation hydrodynamical approach to model line-driven hot-star winds is presented. By coupling a Monte Carlo radiative transfer scheme with a finite volume fluid dynamical method, line-driven mass outflows may be modelled self-consistently, benefiting from the advantages of Monte Carlo techniques in treating multiline effects, such as multiple scatterings, and in dealing with arbitrary multidimensional configurations. In this work, we introduce our approach in detail by highlighting the key numerical techniques and verifying their operation in a number of simplified applications, specifically in a series of self-consistent, one-dimensional, Sobolev-type, hot-star wind calculations. The utility and accuracy of our approach are demonstrated by comparing the obtained results with the predictions of various formulations of the so-called CAK theory and by confronting the calculations with modern sophisticated techniques of predicting the wind structure. Using these calculations, we also point out some useful diagnostic capabilities our approach provides. Finally, we discuss some of the current limitations of our method, some possible extensions and potential future applications.

Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces

NASA Astrophysics Data System (ADS)

Akagi, Goro; Ôtani, Mitsuharu

The existence of strong solutions of Cauchy problem for the following evolution equation du(t)/dt+∂ϕ1(u(t))-∂ϕ2(u(t))∋f(t) is considered in a real reflexive Banach space V, where ∂ϕ1 and ∂ϕ2 are subdifferential operators from V into its dual V*. The study for this type of problems has been done by several authors in the Hilbert space setting. The scope of our study is extended to the V- V* setting. The main tool employed here is a certain approximation argument in a Hilbert space and for this purpose we need to assume that there exists a Hilbert space H such that V⊂H≡H*⊂V* with densely defined continuous injections. The applicability of our abstract framework will be exemplified in discussing the existence of solutions for the nonlinear heat equation: ut(x,t)-Δpu(x,t)-|u|u(x,t)=f(x,t), x∈Ω, t>0, u|=0, where Ω is a bounded domain in RN. In particular, the existence of local (in time) weak solution is shown under the subcritical growth condition qSobolev's critical exponent) for all initial data u0∈W01,p(Ω). This fact has been conjectured but left as an open problem through many years.

Redescription of Chabaudacuaria multispinosa (Pérez Vigueras, 1938) n. g., n. comb. (Nematoda: Spirurida: Acuariidae) based on specimens from Ardea herodias L. and Nyctanassa violacea (L.) (Ardeidae) in Florida.

PubMed

Mutafchiev, Yasen; Kinsella, John M

2012-10-01

Chabaudacuaria n. g. is erected, as monotypic, for C. multispinosa (Pérez Vigueras, 1938) n. comb. (Spirurida: Acuariidae) [syns Cheilospirura multispinosa Pérez Vigueras, 1938; Acuaria multispinosa (Pérez Vigueras, 1938) Yamaguti, 1961]. This species, a parasite of various ardeid birds, is redescribed by means of light and scanning electron microscopy based on material from great blue herons Ardea herodias L. and yellow-crowned night herons Nyctanassa violacea (L.) in Florida, USA. Chabaudacuaria n. g. resembles Acuaria Bremser, 1811, Cheilospirura Diesing, 1861, Skrjabinocerca Schikhobalova, 1930 and Xenocordon Mawson, 1982 in its straight cordons which do not anastomose. However, it can be distinguished from them by the didelphic-prodelphic uterus and the absence of caudal alae in the males. In the pattern of its cordons (consisting of a row of plates and a longitudinal ridge) and the absence of an area rugosa, the new genus is similar to Chevreuxia Seurat, 1918, Syncuaria Gil'bert, 1927, Aviculariella Wehr, 1931, Skrjabinocara Kurashvili, 1940, Decorataria Sobolev, 1949 and Desportesius Chabaud & Campana, 1949, which are characterised by anastomosing cordons. The didelphic-prodelphic female reproductive system of Chabaudacuaria is intermediate between the didelphic-amphidelphic uterus of Chevreuxia and the monodelphic-prodelphic uterus of Syncuaria, Aviculariella, Skrjabinocara, Desportesius and Decorataria. Therefore, the straight and non-anastomosing cordons are considered to be autapomorphic for Chabaudacuaria.

Soliton Resolution for the Derivative Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine

2018-05-01

We study the derivative nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou (Commun Pure Appl Math 56:1029-1077, 2003) revisited by the {\\overline{partial}} -analysis of McLaughlin and Miller (IMRP Int Math Res Pap 48673:1-77, 2006) and Dieng and McLaughlin (Long-time asymptotics for the NLS equation via dbar methods. Preprint, arXiv:0805.2807, 2008), and complemented by the recent work of Borghese et al. (Ann Inst Henri Poincaré Anal Non Linéaire, https://doi.org/10.1016/j.anihpc.2017.08.006, 2017) on soliton resolution for the focusing nonlinear Schrödinger equation. Our results imply that N-soliton solutions of the derivative nonlinear Schrödinger equation are asymptotically stable.

GHRS observations and theoretical modeling of early type stars in R136a

NASA Astrophysics Data System (ADS)

de Koter, A.; Heap, S.; Hubeny, I.; Lanz, T.; Hutchings, J.; Lamers, H. J. G. L. M.; Maran, S.; Schmutz, W.

1994-05-01

We present the first spectroscopic observations of individual stars in R136a, the most dense part of the starburst cluster 30 Doradus in the LMC. Spectra of two stars are scheduled to be obtained with the GHRS on board the HST: R136a5, the brightest of the complex and R136a2, a Wolf-Rayet star of type WN. The 30 Doradus cluster is the only starburst region in which individual stars can be studied. Therefore, quantitative knowledge of the basic stellar parameters will yield valuable insight into the formation of massive stars in starbursts and into their subsequent evolution. Detailed modeling of the structure of the atmosphere and wind of these stars will also lead to a better understanding of the mechanism(s) that govern their dynamics. We present the first results of our detailed quantitative spectral analysis using state-of-the-art non-LTE model atmospheres for stars with extended and expanding atmospheres. The models are computed using the Improved-Sobolev Approximation wind code (ISA-WIND) of de Koter, Schmutz & Lamers (1993, A&A 277, 561), which has been extended to include C, N and Si. Our model computations are not based on the core-halo approximation, but use a unified treatment of the photosphere and wind. This approach is essential for Wolf-Rayet stars. Our synthetic spectra, dominated by the P Cygni profiles of the UV resonance lines, also account for the numerous weak metal lines of photospheric origin.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu; Salgado, Abner J., E-mail: asalgad1@utk.edu; Wang, Cheng, E-mail: cwang1@umassd.edu

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a generalmore » framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.« less

A New Method for 3D Radiative Transfer with Adaptive Grids

NASA Astrophysics Data System (ADS)

Folini, D.; Walder, R.; Psarros, M.; Desboeufs, A.

2003-01-01

We present a new method for 3D NLTE radiative transfer in moving media, including an adaptive grid, along with some test examples and first applications. The central features of our approach we briefly outline in the following. For the solution of the radiative transfer equation, we make use of a generalized mean intensity approach. In this approach, the transfer eqation is solved directly, instead of using the moments of the transfer equation, thus avoiding the associated closure problem. In a first step, a system of equations for the transfer of each directed intensity is set up, using short characteristics. Next, the entity of systems of equations for each directed intensity is re-formulated in the form of one system of equations for the angle-integrated mean intensity. This system then is solved by a modern, fast BiCGStab iterative solver. An additional advantage of this procedure is that convergence rates barely depend on the spatial discretization. For the solution of the rate equations we use Housholder transformations. Lines are treated by a 3D generalization of the well-known Sobolev-approximation. The two parts, solution of the transfer equation and solution of the rate equations, are iteratively coupled. We recently have implemented an adaptive grid, which allows for recursive refinement on a cell-by-cell basis. The spatial resolution, which is always a problematic issue in 3D simulations, we can thus locally reduce or augment, depending on the problem to be solved.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.

2017-04-01

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.

Estimation of spline function in nonparametric path analysis based on penalized weighted least square (PWLS)

NASA Astrophysics Data System (ADS)

Fernandes, Adji Achmad Rinaldo; Solimun, Arisoesilaningsih, Endang

2017-12-01

The aim of this research is to estimate the spline in Path Analysis-based on Nonparametric Regression using Penalized Weighted Least Square (PWLS) approach. Approach used is Reproducing Kernel Hilbert Space at sobolev space. Nonparametric path analysis model on the equation y1 i=f1.1(x1 i)+ε1 i; y2 i=f1.2(x1 i)+f2.2(y1 i)+ε2 i; i =1 ,2 ,…,n Nonparametric Path Analysis which meet the criteria of minimizing PWLS min fw .k∈W2m[aw .k,bw .k], k =1 ,2 { (2n ) -1(y˜-f ˜ ) TΣ-1(y ˜-f ˜ ) + ∑k =1 2 ∑w =1 2 λw .k ∫aw .k bw .k [fw.k (m )(xi) ] 2d xi } is f ˜^=Ay ˜ with A=T1(T1TU1-1∑-1T1)-1T1TU1-1∑-1+V1U1-1∑-1[I-T1(T1TU1-1∑-1T1)-1T1TU1-1∑-1] columnalign="left">+T2(T2TU2-1∑-1T2)-1T2TU2-1∑-1+V2U2-1∑-1[I1-T2(T2TU2-1∑-1T2) -1T2TU2-1∑-1

Fast Diffusion to Self-Similarity: Complete Spectrum, Long-Time Asymptotics, and Numerology

NASA Astrophysics Data System (ADS)

Denzler, Jochen; McCann, Robert J.

2005-03-01

The complete spectrum is determined for the operator on the Sobolev space W1,2ρ(Rn) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile ρ is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d2. Formally, the operator H=HessρE is the Hessian of this entropy at its minimum ρ, so the spectral gap H≧α:=2-n(1-m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0≦u(0,x) ∈ L1(Rn) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)-nρ(x/R(t)) is always slowest to converge. The higher eigenfunctions which are polynomials with hypergeometric radial parts and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rn and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to ρ with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of ρ.

Optimal Time-decay Estimates for the Compressible Navier-Stokes Equations in the Critical L p Framework

NASA Astrophysics Data System (ADS)

Danchin, Raphaël; Xu, Jiang

2017-04-01

The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework was addressed in Danchin (Invent Math 141(3):579-614, 2000) more than 15 years ago. However, whether (optimal) time-decay rates could be shown in critical spaces has remained an open question. Here we give a positive answer to that issue not only in the L 2 critical framework of Danchin (Invent Math 141(3):579-614, 2000) but also in the general L p critical framework of Charve and Danchin (Arch Ration Mech Anal 198(1):233-271, 2010), Chen et al. (Commun Pure Appl Math 63(9):1173-1224, 2010), Haspot (Arch Ration Mech Anal 202(2):427-460, 2011): we show that under a mild additional decay assumption that is satisfied if, for example, the low frequencies of the initial data are in {L^{p/2}(Rd)}, the L p norm (the slightly stronger dot B^0_{p,1} norm in fact) of the critical global solutions decays like t^{-d(1/p - 1/4} for {tto+∞,} exactly as firstly observed by Matsumura and Nishida in (Proc Jpn Acad Ser A 55:337-342, 1979) in the case p = 2 and d = 3, for solutions with high Sobolev regularity. Our method relies on refined time weighted inequalities in the Fourier space, and is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics.

Inclusion/lamella mineralogy and chemical characteristics of garnets from the Garnet Ridge in the Colorado Plateau, northern Arizona

NASA Astrophysics Data System (ADS)

Sato, Y.; Ogasawara, Y.

2013-12-01

A wide variety of garnets as xenocrysts and those in xenoliths, come from kimberlitic diatreme (Smith et al. 2004), occurs at the Garnet Ridge. Koga and Ogasawara (2012) classified these garnets into 9 groups: (a) Cr and pyrope-rich garnet, (b) pyrope-rich reddish brown garnet, (c) reddish brown garnet, (d) garnet in eclogite, (e) garnet in metasomatized eclogite, (f) garnet aggregate, (g) garnet megacryst, (h) garnet in metasomatic rock I, (i) garnet in metasomatic rock II. They divided genetically these groups into four: mantle peridotite (a, b), subducted oceanic crust (d, e), high-pressure metasomatism (c, f, g), low-pressure metasomatism (h, i).In this study, the following 4 groups (a, b, f, g) were chose for inclusion mineralogy by laser Raman spectroscopy. Groups (a) and (b): pyrope-rich garnets (a: 45-82, b: 61-80 Prp mol%) both Cr-rich and Cr-poor (a: 1.0-5.9, b: 0.0-1.0 wt.% Cr2O3) are Ca-poor (1.5-7.0 wt.% CaO) and single-crystals of 5-15 mm in diameter. Group (a) is identical to chrome-pyrope based on the classification of kimberlitic garnets by Dawson and Stephens (1975). CaO-Cr2O3 ratio of (a, b) indicates lherzorite origin (Turkin and Sobolev 2009). Wang et al. (1999) have reported the detailed inclusion and lamella mineralogy of pyrope-rich garnets from the Garnet Ridge. We identified inclusions of Chl (OH: 3450, 3582, 3679 cm-1), Amp (OH: 3685, 3711 cm-1), Ol, Opx, Cpx, Rt (OH: 3295 cm-1), Mgs, Dol, Cal, sulfides, fluid (OH: 3445 cm-1) and spherical composite inclusions of Amp, Ap, Dol, Mgs, Rt and sulfides, and oriented lamellae (presumable exsolution) of Qz, Ol, Opx, Cpx, Amp, Chl, Rt, Ilm, crichtonite (6-7 Peaks at 120-820 cm-1), carmichaelite (710-782 cm-1, OH: 3340 cm-1), Ap (OH: 3570 cm-1) and Ti-Chn (OH: 3404, 3527, 3564 cm-1) adjacent to the oriented Ol. The mineral assemblages of the inclusion and lamella show a correlation with the host garnet compositions; inclusions: (a, b) Ol + Opx + Cpx × composite, (b, low Mg) Opx + Cpx + Amp

Primitive Melt Inclusions from Multiple Samples from the FAMOUS Zone: Insights into the Mantle Melting Column and the Fractionation Processes

NASA Astrophysics Data System (ADS)

Laubier, M.; Langmuir, C. H.

2008-12-01

On mid-ocean ridges, the influential work by Sobolev and Shimizu (Nature, 1993) and Sobolev (Petrology, 1996) has inferred fractional melting during polybaric upwelling by showing that olivine-hosted inclusions were formed over a range of pressures. However melt inclusion studies have often concerned single MORB samples and may be seen as anecdotal in the sense that they are neither repeated nor globally verified. Recent modeling and experimental results also suggest the importance of post-entrapment processes for major and trace elements. This study presents major and trace element data in 300 olivine-hosted melt inclusions from 11 samples from the FAMOUS segment on the Mid-Atlantic Ridge. Published data from Shimizu (Phys. Earth Planet. Int., 1998) and Kamenetsky (EPSL, 1996; spinel-hosted inclusions) are also reported. In parallel, major and trace element measurements were performed in 150 glasses of the segment in order to have consistent datasets. Melt inclusions, trapped in olivine phenocrysts Mg#85-92, display complex trends in major element plots and can be divided into three groups. Group 1, the largest, is characterized by high MgO (9.4-13.4 wt.%), intermediate SiO2 and Al2O3 contents. Group 2 displays distinctively high Al2O3 (up to 18.4 wt.%), low SiO2 (as low as 46.5 wt.%) and high MgO (10.5-12.8 wt.%) contents, along with low CaO and variable TiO2, K2O and incompatible element concentrations. Group 3 consists of the melt inclusions trapped in less primitive olivines (Mg#<88.5) and displays higher SiO2, CaO and trace element contents. In the lava population, two groups can be distinguished. A small subset, that shares many features with the group 2 melt inclusions, displays high MgO and Al2O3 and low SiO2 and incompatible element contents. This type of lava - high-Al, low-Si and high-Mg - has been previously reported for various mid-ocean ridges (e.g., le Roux et al., Contrib. Min. Petrol., 2002; Eason and Sinton, EPSL, 2008). The second group plots

Petrology and Wavespeeds in Central Tibet Indicate a Partially Melted Mica-Bearing Crust

NASA Astrophysics Data System (ADS)

Hacker, B. R.; Ritzwoller, M. H.; Xie, J.

2013-12-01

Mineralogist, 81, 202-212, 1996. Duret, F., N.M. Shapiro, Z. Cao, V. Levin, P. Molnar, and S. Roecker, Surface wave dispersion across Tibet: Direct evidence for radial anisotropy in the crust, Geophysical Research Letters, 37, doi:10.1029/2010GL043811, 2010. Hacker, B.R., E. Gnos, L. Ratschbacher, M. Grove, M. McWilliams, S.V. Sobolev, W. Jiang, and Z. Wu, Hot and dry xenoliths from the lower crust of Tibet, Science, 287, 2463-2466, 2000. Mechie, J., S.V. Sobolev, L. Ratschbacher, A.Y. Babeyko, G. Bock, A.G. Jones, K.D. Nelson, K.D. Solon, L.D. Brown, and W. Zhao, Precise temperature estimation in the Tibetan crust from seismic detection of the a-b quartz transition, Geology, 32, 601-604, 2004. Xie, J., M.H. Ritzwoller, W. Shen, Y. Yang, Y. Zheng, and L. Zhou, Crustal radial anisotropy across Eastern Tibet and the Western Yangtze Craton, Journal of Geophysical Research, in press, 2013. Xu, Z.J., X. Song, and L. Zhu, Crustal and uppermost mantle S velocity structure under Hi-CLIMB seismic array in central Tibetan Plateau from joint inversion of surface wave dispersion and receiver function data, Tectonophysics, 584, 209-220, 2013. Yang, Y., M.H. Ritzwoller, Y. Zheng, W. Shen, A.L. Levshin, and Z. Xie, A synoptic view of the distribution and connectivity of the mid-crustal low velocity zone beneath Tibet, Journal of Geophysical Research, 117, 10.1029/2011JB008810, 2012.

The importance of being fractional in mixing: optimal choice of the index s in H-s norm

NASA Astrophysics Data System (ADS)

Vermach, Lukas; Caulfield, C. P.

2015-11-01

A natural measure of homogeneity of a mixture is the variance of the concentration field, which in the case of a zero-mean field is the L2-norm. Mathew et al. (Physica D, 2005) introduced a new multi-scale measure to quantify mixing referred to as the mix-norm, which is equivalent to the H - 1 / 2 norm, the Sobolev norm of negative fractional index. Unlike the L2-norm, the mix-norm is not conserved by the advection equation and thus captures mixing even in the non-diffusive systems. Furthermore, the mix-norm is consistent with the ergodic definition of mixing and Lin et al. (JFM, 2011) showed that this property extends to any norm from the class H-s , s > 0 . We consider a zero-mean passive scalar field organised into two layers of different concentrations advected by a flow field in a torus. We solve two non-linear optimisation problems. We identify the optimal initial perturbation of the velocity field with given initial energy as well as the optimal forcing with given total action (the time integral of the kinetic energy of the flow) which both yield maximal mixing by a target time horizon. We analyse sensitivity of the results with respect to s-variation and thus address the importance of the choice of the fractional index This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis.

Wavelet based free-form deformations for nonrigid registration

NASA Astrophysics Data System (ADS)

Sun, Wei; Niessen, Wiro J.; Klein, Stefan

2014-03-01

In nonrigid registration, deformations may take place on the coarse and fine scales. For the conventional B-splines based free-form deformation (FFD) registration, these coarse- and fine-scale deformations are all represented by basis functions of a single scale. Meanwhile, wavelets have been proposed as a signal representation suitable for multi-scale problems. Wavelet analysis leads to a unique decomposition of a signal into its coarse- and fine-scale components. Potentially, this could therefore be useful for image registration. In this work, we investigate whether a wavelet-based FFD model has advantages for nonrigid image registration. We use a B-splines based wavelet, as defined by Cai and Wang.1 This wavelet is expressed as a linear combination of B-spline basis functions. Derived from the original B-spline function, this wavelet is smooth, differentiable, and compactly supported. The basis functions of this wavelet are orthogonal across scales in Sobolev space. This wavelet was previously used for registration in computer vision, in 2D optical flow problems,2 but it was not compared with the conventional B-spline FFD in medical image registration problems. An advantage of choosing this B-splines based wavelet model is that the space of allowable deformation is exactly equivalent to that of the traditional B-spline. The wavelet transformation is essentially a (linear) reparameterization of the B-spline transformation model. Experiments on 10 CT lung and 18 T1-weighted MRI brain datasets show that wavelet based registration leads to smoother deformation fields than traditional B-splines based registration, while achieving better accuracy.

Investigating the origin of cyclical wind variability in hot massive stars - II. Hydrodynamical simulations of corotating interaction regions using realistic spot parameters for the O giant ξ Persei

NASA Astrophysics Data System (ADS)

David-Uraz, A.; Owocki, S. P.; Wade, G. A.; Sundqvist, J. O.; Kee, N. D.

2017-09-01

OB stars exhibit various types of spectral variability historically associated with wind structures, including the apparently ubiquitous discrete absorption components (DACs). These features have been proposed to be caused either by magnetic fields or non-radial pulsations. In this second paper of this series, we revisit the canonical phenomenological hydrodynamical modelling used to explain the formation of DACs by taking into account modern observations and more realistic theoretical predictions. Using constraints on putative bright spots located on the surface of the O giant ξ Persei derived from high precision space-based broad-band optical photometry obtained with the Microvariability and Oscillations of Stars (MOST) space telescope, we generate 2D hydrodynamical simulations of corotating interaction regions in its wind. We then compute synthetic ultraviolet (UV) resonance line profiles using Sobolev Exact Integration and compare them with historical timeseries obtained by the International Ultraviolet Explorer (IUE) to evaluate if the observed behaviour of ξ Persei's DACs is reproduced. Testing three different models of spot size and strength, we find that the classical pattern of variability can be successfully reproduced for two of them: the model with the smallest spots yields absorption features that are incompatible with observations. Furthermore, we test the effect of the radial dependence of ionization levels on line driving, but cannot conclusively assess the importance of this factor. In conclusion, this study self-consistently links optical photometry and UV spectroscopy, paving the way to a better understanding of cyclical wind variability in massive stars in the context of the bright spot paradigm.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garcia, Miriam; Najarro, Francisco; Herrero, Artemio

We present the first quantitative ultraviolet spectroscopic analysis of resolved OB stars in IC 1613. Because of its alleged very low metallicity (≲1/10 Z {sub ☉}, from H II regions), studies in this Local Group dwarf galaxy could become a significant step forward from the Small Magellanic Cloud (SMC) toward the extremely metal-poor massive stars of the early universe. We present HST-COS data covering the ∼1150-1800 Å wavelength range with resolution R ∼ 2500. We find that the targets do exhibit wind features, and these are similar in strength to SMC stars. Wind terminal velocities were derived from the observedmore » P Cygni profiles with the Sobolev plus Exact Integration method. The v {sub ∞}-Z relationship has been revisited. The terminal velocity of IC 1613 O stars is clearly lower than Milky Way counterparts, but there is no clear difference between IC 1613 and SMC or LMC analog stars. We find no clear segregation with host galaxy in the terminal velocities of B-supergiants, nor in the v {sub ∞}/v {sub esc} ratio of the whole OB star sample in any of the studied galaxies. Finally, we present the first evidence that the Fe-abundance of IC 1613 OB stars is similar to the SMC, which is in agreement with previous results on red supergiants. With the confirmed ∼1/10 solar oxygen abundances of B-supergiants, our results indicate that IC 1613's α/Fe ratio is sub-solar.« less

Relaxation limit of a compressible gas-liquid model with well-reservoir interaction

NASA Astrophysics Data System (ADS)

Solem, Susanne; Evje, Steinar

2017-02-01

This paper deals with the relaxation limit of a two-phase compressible gas-liquid model which contains a pressure-dependent well-reservoir interaction term of the form q (P_r - P) where q>0 is the rate of the pressure-dependent influx/efflux of gas, P is the (unknown) wellbore pressure, and P_r is the (known) surrounding reservoir pressure. The model can be used to study gas-kick flow scenarios relevant for various wellbore operations. One extreme case is when the wellbore pressure P is largely dictated by the surrounding reservoir pressure P_r. Formally, this model is obtained by deriving the limiting system as the relaxation parameter q in the full model tends to infinity. The main purpose of this work is to understand to what extent this case can be represented by a well-defined mathematical model for a fixed global time T>0. Well-posedness of the full model has been obtained in Evje (SIAM J Math Anal 45(2):518-546, 2013). However, as the estimates for the full model are dependent on the relaxation parameter q, new estimates must be obtained for the equilibrium model to ensure existence of solutions. By means of appropriate a priori assumptions and some restrictions on the model parameters, necessary estimates (low order and higher order) are obtained. These estimates that depend on the global time T together with smallness assumptions on the initial data are then used to obtain existence of solutions in suitable Sobolev spaces.

Polarization light curve modelling of corotating interaction regions in the wind of the Wolf-Rayet star WR 6

NASA Astrophysics Data System (ADS)

St-Louis, N.; Tremblay, Patrick; Ignace, Richard

2018-02-01

The intriguing WN4b star WR 6 has been known to display epoch-dependent spectroscopic, photometric and polarimetric variability for several decades. In this paper, we set out to verify if a simplified analytical model in which corotating interaction regions (CIRs) threading an otherwise spherical wind is able to reproduce the many broad-band continuum light curves from the literature with a reasonable set of parameters. We modified the optically thin model developed by Ignace, St-Louis & Proulx-Giraldeau to approximately account for multiple scattering and used it to fit 13 separate data sets of this star. By including two CIRs in the wind, we obtained reasonable fits for all data sets with coherent values for the inclination of the rotation axis (i0 = 166°) and for its orientation in the plane of the sky, although in the latter case we obtained two equally acceptable values (ψ = 63° and 152°) from the polarimetry. Additional line profile variation simulations using the Sobolev approximation for the line transfer allowed us to eliminate the ψ = 152° solution. With the adopted configuration (i0 = 166° and ψ = 63°), we were able to reproduce all data sets relatively well with two CIRs located near the stellar equator and always separated by ˜90° in longitude. The epoch dependence comes from the fact that these CIRs migrate along the surface of the star. Density contrasts smaller than a factor of 2 and large opening angles for the CIR (β ⪆ 35°) were found to best reproduce the type of spectroscopic variability reported in the literature.

Estimation of Mass-Loss Rates from Emission Line Profiles in the UV Spectra of Cool Stars

NASA Technical Reports Server (NTRS)

Carpenter, K. G.; Robinson, R. D.; Harper, G. M.

1999-01-01

The photon-scattering winds of cool, low-gravity stars (K-M giants and supergiants) produce absorption features in the strong chromospheric emission lines. This provides us with an opportunity to assess important parameters of the wind, including flow and turbulent velocities, the optical depth of the wind above the region of photon creation, and the star's mass-loss rate. We have used the Lamers et al. Sobolev with Exact Integration (SEI) radiative transfer code along with simple models of the outer atmospheric structure to compute synthetic line profiles for comparison with the observed line profiles. The SEI code has the advantage of being computationally fast and allows a great number of possible wind models to be examined. We therefore use it here to obtain initial first-order estimates of the wind parameters. More sophisticated, but more time-consuming and resource intensive calculations will be performed at a later date, using the SEI-deduced wind parameters as a starting point. A comparison of the profiles over a range of wind velocity laws, turbulence values, and line opacities allows us to constrain the wind parameters, and to estimate the mass-loss rates. We have applied this analysis technique (using lines of Mg II, 0 I, and Fe II) so far to four stars: the normal K5-giant alpha Tau, the hybrid K-giant gamma Dra, the K5 supergiant lambda Vel, and the M-giant gamma Cru. We present in this paper a description of the technique, including the assumptions which go into its use, an assessment of its robustness, and the results of our analysis.

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our

The water concentrations and OH incorporation mechanisms of silicate inclusions in diamonds. What information do they provide?

NASA Astrophysics Data System (ADS)

Tabassum, Nuzhat; Kohn, Simon; Smith, Christopher; Bulanova, Galina

2017-04-01

The water concentrations of nominally anhydrous silicate inclusions in diamonds have the potential to provide information either on the water concentrations of mantle sampled by diamonds, or on the compositions of fluids that precipitate diamonds. In this study we have used FTIR spectroscopy to measure the water concentrations and incorporation mechanisms in inclusions of olivine and pyroxene in diamonds from Australia, Canada, Siberia and India. There are systematic differences in water incorporation mechanism that probably reflect different fluid chemistries and/or oxidation state, but the water concentrations are low, consistent with previous studies [1,2]. Some inclusions also contain phases such as hydrous minerals or fluids, therefore the question arises as to whether the water concentration of the nominally anhydrous minerals (NAMs) are truly representative of the water concentration of the phases at the time of trapping. Is it possible for the NAMs to contain low water concentrations yet coexist with a hydrous fluid under mantle conditions? Or do the NAMs dehydrate in-situ within the inclusions to give a dry NAM + hydrous phase assemblage on ascent and emplacement or during shallow storage in the crust? These questions will be discussed in the light of all data currently available. [1] Novella, D., Bolfan-Casanova, N., Nestola, F. and Harris, J.W., 2015. H 2 O in olivine and garnet inclusions still trapped in diamonds from the Siberian craton: Implications for the water content of cratonic lithosphere peridotites. Lithos, 230, pp.180-183. [2] Taylor, L.A., Logvinova, A.M., Howarth, G.H., Liu, Y., Peslier, A.H., Rossman, G.R., Guan, Y., Chen, Y. and Sobolev, N.V., 2016. Low water contents in diamond mineral inclusions: Proto-genetic origin in a dry cratonic lithosphere.Earth and Planetary Science Letters, 433, pp.125-132.

Melting mode and source lithology inferred from trace element systematic in historical olivine from Lanzarote, Canary Islands

NASA Astrophysics Data System (ADS)

Gómez-Ulla, Alejandra; Sigmarsson, Olgeir; Guðfinnsson, Guðmundur H.

2017-04-01

Trace element concentrations and ratios in olivine phenocrysts, such as fractionation-corrected Ni x (FeO/MgO) and Fe/Mn, have been shown useful as probes of pyroxenite derived component in mixtures of primary mantle melts (e.g. Sobolev et al., 2007). For instance, higher Ni and lower Mn and Ca contents are expected in partial melts of pyroxenite compared to those of lherzolite. We have measured trace element concentrations in olivine from 1730-1736 AD (Timanfaya) and 1824 AD eruptions in Lanzarote (Canary Islands), which erupted mafic and mantle nodule bearing magmas, ranging in composition from highly silica-undersaturated basanite through alkali basalt to tholeiite. The early basanite exhibit the largest olivine trace element variation covering the range of those from MORB and OIB worldwide, whereas later erupted tholeiite have values typical from pyroxenite derived melts. The Fo value decreased systematically with time during the 1730-36 eruption and the proportion of silica-saturated primary melt increased in the parental magma mixture with time. At the end of the eruption, tholeiite magmas crystallized olivine with, increasing concentrations of Mn and Ca and higher Ca/Al at relatively uniform Ni x (FeO/MgO) and Fe/Mn, all of which is readily explained by increased decompression melting at lower temperature. The basanite from the eruption that took place in 1824 AD has olivine with even higher Fo value and trace element variability similar those of the Timanfaya basanite. The fact that the Lanzarote basanite contain olivine with trace element systematic spanning that of MORB and pyroxenite melt can be explained by CO2-flux melting of a lithologically heterogeneous source, generating the diverse compositions. Initial reactive porous flow through depleted oceanic lithosphere and equilibration with dunitic restite of percolating pyroxenite melt may have amplified the observed Ni depletion in olivine of the earliest basanite. The fact that olivine compositions and

How Wolf-Rayet winds are driven by starlight and spectral lines

NASA Astrophysics Data System (ADS)

Onifer, Andrew Joseph, III

Finding the cause of the enormous increase in the mass- loss rate of a Wolf-Rayet (W-R) star, as compared to its O star progenitor, has remained a challenge for many years. This thesis explores the hypothesis that line driving causes the large observed W-R mass-loss rates. Frequency redistribution can cause the photons to filter into gaps in the line spectrum, reducing the efficiency of line driving. Therefore, the role that frequency redistribution plays in lowering the predicted mass-loss rate is explored, both via simple two-domain idealizations of the line list and via a real W-R line list. A simple analytic theory, called the Statistical Sobolev Rosseland (SSR) theory, is developed that calculates the local efficiency of line driving in a completely redistributing wind. In the process a conceptual language is developed to explain the key issues in W-R wind line driving. The results are that with no redistribution, the reduction in radius, and corresponding increase in temperature, of an O star as it evolves into a W-R star causes roughly a six-fold increase in the mass-loss rate. However, with large amounts of redistribution, the efficiency of the wind drops greatly in the presence of spectral gaps. In the most extreme case of SSR, the mass- loss rate drops by a factor of up to an order of magnitude relative to the gray value. To avoid this it is necessary to fill the gaps in the spectrum, and the effect that ionization stratification has in filling the gaps globally over the wind is explored. It is found that with the current line list ionization changes can only fill the gaps sufficiently to cause about a factor of two increase over the SSR value. The conclusion is that in order for line driving to explain the mass-loss rates of W-R winds, more opacity needs to be discovered to fill the gaps, either locally, or globally over a realistic range of ionization strata.

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

NASA Astrophysics Data System (ADS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

global in time existence and uniqueness of a regular solution to the Einstein-Maxwell-Boltzmann system with the cosmological constant. We define and we use the weighted Sobolev separable spaces for the Boltzmann equation; some special spaces for the Einstein equations, then we clearly display all the proofs leading to the global existence theorems.

Experimental Melting Study of Basalt-Peridotite Hybrid Source: Constrains on Chemistry of Recycled Component

NASA Astrophysics Data System (ADS)

Gao, S.; Takahashi, E.; Matsukage, K. N.; Suzuki, T.; Kimura, J. I.

2015-12-01

It is believed that magma genesis of OIB is largely influenced by recycled oceanic crust component involved in the mantle plume (e.g., Hauri et al., 1996; Takahashi & Nakajima., 2002; Sobolev et al., 2007). Mallik & Dasgupta (2012) reported that the wall-rock reaction in MORB-eclogite and peridotite layered experiments produced a spectrum of tholeiitic to alkalic melts. However, the proper eclogite source composition is still under dispute. In order to figure out the geochemistry of recycled component as well as their melting process, we conducted a series of high-P, high-T experiments. Melting experiments (1~10hrs) were performed under 2.9GPa with Boyd-England type piston-cylinder (1460~1540°C for dry experiments, 1400~1500°C for hydrous experiments) and 5GPa with Kawai-type multi-anvil (1550~1650°C for dry experiments, 1350~1550°C for hydrous experiments), at the Magma Factory, Tokyo Tech. Spinel lherzolite KLB-1 (Takahashi 1986) was employed as peridotite component. Two basalts were used as recycled component: Fe-enriched Columbia River basalt (CRB72-180, Takahashi et al., 1998) and N-type MORB (NAM-7, Yasuda et al., 1994). In dry experiments below peridotite dry solidus, melt compositions ranged from basaltic andesite to tholeiite. Opx reaction band generated between basalt and peridotite layer hindered chemical reaction. On the other hand, alkali basalt was formed in hydrous run products because H2O promoted melting process in both layers. Compared with melts formed by N-MORB-peridotite runs, those layered experiments with CRB are enriched in FeO, TiO2, K2O and light REE at given MgO. In other words, melts produced by CRB-peridotite layered experiments are close to alkali basalts in OIB and tholeiite in Hawaii, while those by layered experiments with N-MORB are poor in above elements. Thus we propose that Fe-rich Archean or Proterozoic tholeiite (BVSP 1980) would be a possible candidate for recycled component in OIB source.

Experimental Melting Study of Basalt-Peridotite Hybrid Source: Melting model of Hawaiian plume

NASA Astrophysics Data System (ADS)

Takahashi, E.; Gao, S.

2015-12-01

Eclogite component entrained in ascending plume is considered to be essentially important in producing flood basalts (e.g., Columbia River basalt, Takahashi et al., 1998 EPSL), alkalic OIBs (e.g., Kogiso et al.,2003), ferro-picrites (Tuff et al.,2005) and Hawaiian shield lavas (e.g., Hauri, 1996; Takahashi & Nakajima, 2002, Sobolev et al.,2005). Size of the entrained eclogite, which controls the reaction rates with ambient peridotite, however, is very difficult to constrain using geophysical observation. Among Hawaiian shield volcanoes, Koolau is the most enriched end-member in eclogite component (Frey et al, 1994). Reconstruction of Koolau volcano based on submarine study on Nuuanu landslide (AGU Monograph vol.128, 2002, Takahashi Garcia Lipman eds.) revealed that silica-rich tholeiite appeared only at the last stage (Makapuu stage) of Koolau volcano. Chemical compositions of lavas as well as isotopes change abruptly and coherently across a horizon (Shinozaki et al. and Tanaka et al. ibid.). Based on these observation, Takahashi & Nakajima (2002 ibid) proposed that the Makapuu stage lava in Koolau volcano was supplied from a single large eclogite block. In order to study melting process in Hawaiian plume, high-pressure melting experiments were carried out under dry and hydrous conditions with layered eclogite/peridotite starting materials. Detail of our experiments will be given by Gao et al (2015 AGU). Combined previous field observation with new set of experiments, we propose that variation in SiO2 among Hawaiian tholeiites represent varying degree of wall-rock interaction between eclogite and ambient peridotite. Makapuu stage lavas in Koolau volcano represents eclogite partial melts formed at ~3 GPa with various amount of xenocrystic olivines derived from Pacific plate. In other words, we propose that "primary magma" in the melting column of Hawaiian plume ranges from basaltic andesite to ferro-picrite depending on the lithology of the source. Solidus of

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr; Noutchegueme, Norbert, E-mail: nnoutch@yahoo.fr

. 52] the global in time existence and uniqueness of a regular solution to the Einstein-Maxwell-Boltzmann system with the cosmological constant. We define and we use the weighted Sobolev separable spaces for the Boltzmann equation; some special spaces for the Einstein equations, then we clearly display all the proofs leading to the global existence theorems.« less

Line-driven ablation of circumstellar discs - I. Optically thin decretion discs of classical Oe/Be stars.

PubMed

Kee, Nathaniel Dylan; Owocki, Stanley; Sundqvist, J O

2016-05-21

The extreme luminosities of massive, hot OB stars drive strong stellar winds through line-scattering of the star's UV continuum radiation. For OB stars with an orbiting circumstellar disc, we explore here the effect of such line-scattering in driving an ablation of material from the disc's surface layers, with initial focus on the marginally optically thin decretion discs of classical Oe and Be stars. For this we apply a multidimensional radiation-hydrodynamics code that assumes simple optically thin ray tracing for the stellar continuum, but uses a multiray Sobolev treatment of the line transfer; this fully accounts for the efficient driving by non-radial rays, due to desaturation of line-absorption by velocity gradients associated with the Keplerian shear in the disc. Results show a dense, intermediate-speed surface ablation, consistent with the strong, blueshifted absorption of UV wind lines seen in Be shell stars that are observed from near the disc plane. A key overall result is that, after an initial adjustment to the introduction of the disc, the asymptotic disc destruction rate is typically just an order-unity factor times the stellar wind mass-loss rate. For optically thin Be discs, this leads to a disc destruction time of order months to years, consistent with observationally inferred disc decay times. The much stronger radiative forces of O stars reduce this time to order days, making it more difficult for decretion processes to sustain a disc in earlier spectral types, and so providing a natural explanation for the relative rarity of Oe stars in the Galaxy. Moreover, the decrease in line-driving at lower metallicity implies both a reduction in the winds that help spin-down stars from near-critical rotation, and a reduction in the ablation of any decretion disc; together these provide a natural explanation for the higher fraction of classical Be stars, as well as the presence of Oe stars, in the lower metallicity Magellanic Clouds. We conclude with a

Mg-Fe Isotope Systems of Mantle Xenoliths: Constrains on the Evolution of Siberian Craton

NASA Astrophysics Data System (ADS)

An, Y.; Kiseeva, E. S.; Sobolev, N. V.; Zhang, Z.

2017-12-01

Mantle xenoliths bring to the surface a variety of lithologies (dunites, lherzolites, harzburgites, wehrlites, eclogites, pyroxenites, and websterites) and represent snapshots of the geochemical processes that occur deep within the Earth. Recent improvements in the precision of the MC-ICP-MS measurements have allowed us to expand the amount of data on Mg and Fe isotopes for mantle-derived samples. For instance, to constrain the isotopic composition of the Earth based on the study of spinel and garnet peridotites (An et al., 2017; Teng et al., 2010), to trace the origin and to investigate the isotopic fractionation mechanism during metamorphic process using cratonic or orogenic eclogites (Li et al., 2011; Wang et al., 2012) and to reveal the metasomatism-induced mantle heterogeneity by pyroxenites (Hu et al., 2016). Numerous multi-stage modification events and mantle layering are detected in the subcontinental lithospheric mantle under the Siberian craton (Ashchepkov et al., 2008a; Sobolev et al., 1975, etc). Combined analyses of Mg and Fe isotopic systems could provide new constraints on the formation and evolution of the ancient cratonic mantle. In order to better constrain the magnitude and mechanism of inter-mineral Mg and Fe isotopic fractionations at high temperatures, systematic studies of mantle xenoliths are needed. For example, theoretical calculations and natural samples measurements have shown that large equilibrium Mg isotope fractionations controlled by the difference in coordination number of Mg among minerals could exist (Huang et al., 2013; Li et al., 2011). Thus, the Mg isotope geothermometer could help us trace the evolution history of ancient cratons. In this study we present Mg and Fe isotopic data for whole rocks and separated minerals (clinopyroxene (cpx) and garnet (grt)) from different types of mantle xenoliths (garnet pyroxenites, eclogites, grospydites and garnet peridotites) from a number of kimberlite pipes in Siberian craton (Udachnaya

Line-driven ablation of circumstellar discs – I. Optically thin decretion discs of classical Oe/Be stars

PubMed Central

Kee, Nathaniel Dylan; Owocki, Stanley; Sundqvist, J. O.

2016-01-01

The extreme luminosities of massive, hot OB stars drive strong stellar winds through line-scattering of the star's UV continuum radiation. For OB stars with an orbiting circumstellar disc, we explore here the effect of such line-scattering in driving an ablation of material from the disc's surface layers, with initial focus on the marginally optically thin decretion discs of classical Oe and Be stars. For this we apply a multidimensional radiation-hydrodynamics code that assumes simple optically thin ray tracing for the stellar continuum, but uses a multiray Sobolev treatment of the line transfer; this fully accounts for the efficient driving by non-radial rays, due to desaturation of line-absorption by velocity gradients associated with the Keplerian shear in the disc. Results show a dense, intermediate-speed surface ablation, consistent with the strong, blueshifted absorption of UV wind lines seen in Be shell stars that are observed from near the disc plane. A key overall result is that, after an initial adjustment to the introduction of the disc, the asymptotic disc destruction rate is typically just an order-unity factor times the stellar wind mass-loss rate. For optically thin Be discs, this leads to a disc destruction time of order months to years, consistent with observationally inferred disc decay times. The much stronger radiative forces of O stars reduce this time to order days, making it more difficult for decretion processes to sustain a disc in earlier spectral types, and so providing a natural explanation for the relative rarity of Oe stars in the Galaxy. Moreover, the decrease in line-driving at lower metallicity implies both a reduction in the winds that help spin-down stars from near-critical rotation, and a reduction in the ablation of any decretion disc; together these provide a natural explanation for the higher fraction of classical Be stars, as well as the presence of Oe stars, in the lower metallicity Magellanic Clouds. We conclude with a

Simultaneous Quantification of Temperature, Pyroxenite Abundance, and Upwelling Rates in the Iceland Mantle Source

NASA Astrophysics Data System (ADS)

Brown, E.; Lesher, C. E.

2014-12-01

, which is required to account for much of the observed chemical and isotopic diversity. [1] Langmuir et al, 1992, AGU Geophys. Mono. Ser. 71 [2] Chauvel & Hemond, 2000, G-cubed, v 1 [3] Kokfelt et al, 2003, EPSL, v 214 [4] Sobolev et al, 2007, Science, v 316 [5] Shorttle et al, 2014, EPSL, v 395

Effect of Upper Mantle Heterogeneities on Lithosphere Stresses and Topography

NASA Astrophysics Data System (ADS)

Osei Tutu, A.; Steinberger, B.; Rogozhina, I.; Sobolev, S. V.

2016-12-01

The orientation and magnitude of lithosphere stresses give us knowledge about most of the processes within the Earth that are not easy to observe. It has been established (Steinberger, Schmeling, and Marquart 2001) that large contribution of the forces producing lithosphere stresses have their source origination from the buoyancies of both the upper and lower mantle acting beneath the lithosphere. The contribution of the crustal thickness to the stresses has been estimated to be less than 10% (Steinberger et al. 2001) in most region and increases in areas with high gravitational potential energy like the Himalayas. In most of these studies, the effect of the crust was determined separately by computing the gravitational potential energy from the crust (Ghosh et al. 2013) and applied as correction. (Artyushkov 1973) showed that the inhomogeneous nature of the crust contribute to the stresses observed as against using constant lithosphere thickness in most studies, due to the complexities for implementing a variable lithosphere. We seek extend the approach of Ghosh et al. (2013) by coupling the Crust 1.0 (Laske et al. 2013) to a varaible lithosphere thickness in our numerical method. Using a 3D global lithosphere-asthenosphere model (Popov and Sobolev 2008) with visco-elasto-plastic rheology, coupled at 300 km depth to a mantle modeled with a spectral technique (Hager and O'Connell, 1981), we compute lithosphere stresses and topography. we compare our model with observations; the World Stress Map, Global Strain Rate Map and the observed topgraphy. We use S40RTS seismic tomography below 300 km depth, with radial viscosity distribution (Steinberger et al 2006). To account for all the heterogeneities in the upper mantle (300 km) we used different 3D temperatures models setups. The first model is the thermal lithosphere model (Artemieva and Mooney, 2001) in continental regions and assumes half-space cooling of sea floor with age (Müller et al. 2008) for oceans. For the

Neurons the decision makers, Part I: The firing function of a single neuron.

PubMed

Saaty, Thomas

2017-02-01

This paper is concerned with understanding synthesis of electric signals in the neural system based on making pairwise comparisons. Fundamentally, every person and every animal are born with the talent to compare stimuli from things that share properties in space or over time. Comparisons always need experience to distinguish among things. Pairwise comparisons are numerically reciprocal. If a value is assigned to the larger of two elements that have a given property when compared with the smaller one, then the smaller has the reciprocal of that value when compared with the larger. Because making comparisons requires the reciprocal property, we need mathematics that can cope with division. There are four division algebras that would allow us to use our reciprocals arising from comparisons: The real numbers, the complex numbers, the non-commutative quaternions and the non-associative octonions. Rather than inferring function as from electric flow in a network, in this paper we infer the flow from function. Neurons fire in response to stimuli and their firings vary relative to the intensities of the stimuli. We believe neurons use some kind of pairwise comparison mechanism to determine when to fire based on the stimuli they receive. The ideas we develop here about flows are used to deduce how a system based on this kind of firing determination works and can be described. Furthermore the firing of neurons requires continuous comparisons. To develop a formula describing the output of these pairwise comparisons requires solving Fredholm's equation of the second kind which is satisfied if and only if a simple functional equation has solutions. The Fourier transform of the real solution of this equation leads to inverse square laws like those that are common in physics. The Fourier transform applied to a complex valued solution leads to Dirac type of firings. Such firings are dense in the very general fields of functions known as Sobolev spaces and thus can be used to

The effects of pressure, temperature and composition on olivine-liquid exchange coefficients

NASA Astrophysics Data System (ADS)

Matzen, A. K.; Wood, B. J.

2017-12-01

[4] to calculate Fe3+/Fe2+. We find that the pressure effect should be a significant contributor to the observed systematics of K_{D, Ni-Fe}^{ol-liq} between 1 atm and 3 GPa [2]. [1] Sobolev et al (2007) Science, 316, 412-417, [2] Matzen et al (2017) CMP 172:3, [3] Kegler et al (2008) EPSL 268, 28-40, [4] Kress & Carmichael (1991) CMP 108, 82-92.

Potential Temperatures of Sources of MORB, OIB and LIPs Based on AL Partitioning Between Olivine and Spinel

NASA Astrophysics Data System (ADS)

Sobolev, A. V.; Batanova, V. G.; Krasheninnikov, S.; Borisov, A.; Arndt, N.; Kuzmin, D.; Krivolutskaya, N.; Sushevskaya, N.

2013-12-01

confirm the relatively low temperature of the convecting mantle source of MORB and higher temperatures in the mantle plumes that produce the OIB of Iceland, Hawaii, Gorgona, Archean komatiites and several LIPs (e.g. Siberian, Decan). [1] McKenzie & Bickle, 1988, J. Petr. 29, p 625-679. [2] Wan et al, 2008, Am. Min. 93, p1142-1147. [3] Batanova & Sobolev, 2013, Min. Mag.,p 667, DOI :10.1180/minmag2013.077.5.2 [4] Ford et al, 1983, J. Petr. 24, p 256-265.

Fast Winds and Mass Loss from Metal-Poor Field Giants

NASA Astrophysics Data System (ADS)

Dupree, A. K.; Smith, Graeme H.; Strader, Jay

2009-11-01

Echelle spectra of the infrared He I λ10830 line were obtained with NIRSPEC on the Keck 2 telescope for 41 metal-deficient field giant stars including those on the red giant branch (RGB), asymptotic giant branch (AGB), and red horizontal branch (RHB). The presence of this He I line is ubiquitous in stars with T effgsim 4500 K and MV fainter than -1.5, and reveals the dynamics of the atmosphere. The line strength increases with effective temperature for T effgsim 5300 K in RHB stars. In AGB and RGB stars, the line strength increases with luminosity. Fast outflows (gsim 60 km s-1) are detected from the majority of the stars and about 40% of the outflows have sufficient speed as to allow escape of material from the star as well as from a globular cluster. Outflow speeds and line strengths do not depend on metallicity for our sample ([Fe/H]= -0.7 to -3.0), suggesting the driving mechanism for these winds derives from magnetic and/or hydrodynamic processes. Gas outflows are present in every luminous giant, but are not detected in all stars of lower luminosity indicating possible variability. Mass loss rates ranging from ~3 × 10-10 to ~6 × 10-8 M sun yr-1 estimated from the Sobolev approximation for line formation represent values with evolutionary significance for red giants and RHB stars. We estimate that 0.2 M sun will be lost on the RGB, and the torque of this wind can account for observations of slowly rotating RHB stars in the field. About 0.1-0.2 M sun will be lost on the RHB itself. This first empirical determination of mass loss on the RHB may contribute to the appearance of extended horizontal branches in globular clusters. The spectra appear to resolve the problem of missing intracluster material in globular clusters. Opportunities exist for "wind smothering" of dwarf stars by winds from the evolved population, possibly leading to surface pollution in regions of high stellar density. Data presented herein were obtained at the W. M. Keck Observatory, which

Magma mixing and degassing processes in the magma chamber of Gorely volcano (Kamchatka): evidence from whole-rock and olivine chemistry.

NASA Astrophysics Data System (ADS)

Gavrilenko, M.; Ozerov, A.; Kyle, P. R.; Carr, M. J.; Nikulin, A.

2015-12-01

), Russian Geology and Geophysics, 52(11): p.1353-1367. [6] Selyangin & Ponomareva (1999) J. of Volcanology and Seismology, 2: p.3-23. [7] Sobolev et al. (2007) Science, 316(5823): p.412-417. [8] Zimmer et al. (2010) J. of Petrology, 51(12): p.2411-2444. [9] Wan et al. (2008) American Mineralogist, 93(7), p.1142-1147.

Mass loss from inhomogeneous hot star winds. I. Resonance line formation in 2D models

NASA Astrophysics Data System (ADS)

Sundqvist, J. O.; Puls, J.; Feldmeier, A.

2010-01-01

Context. The mass-loss rate is a key parameter of hot, massive stars. Small-scale inhomogeneities (clumping) in the winds of these stars are conventionally included in spectral analyses by assuming optically thin clumps, a void inter-clump medium, and a smooth velocity field. To reconcile investigations of different diagnostics (in particular, unsaturated UV resonance lines vs. Hα/radio emission) within such models, a highly clumped wind with very low mass-loss rates needs to be invoked, where the resonance lines seem to indicate rates an order of magnitude (or even more) lower than previously accepted values. If found to be realistic, this would challenge the radiative line-driven wind theory and have dramatic consequences for the evolution of massive stars. Aims: We investigate basic properties of the formation of resonance lines in small-scale inhomogeneous hot star winds with non-monotonic velocity fields. Methods: We study inhomogeneous wind structures by means of 2D stochastic and pseudo-2D radiation-hydrodynamic wind models, constructed by assembling 1D snapshots in radially independent slices. A Monte-Carlo radiative transfer code, which treats the resonance line formation in an axially symmetric spherical wind (without resorting to the Sobolev approximation), is presented and used to produce synthetic line spectra. Results: The optically thin clumping limit is only valid for very weak lines. The detailed density structure, the inter-clump medium, and the non-monotonic velocity field are all important for the line formation. We confirm previous findings that radiation-hydrodynamic wind models reproduce observed characteristics of strong lines (e.g., the black troughs) without applying the highly supersonic “microturbulence” needed in smooth models. For intermediate strong lines, the velocity spans of the clumps are of central importance. Current radiation-hydrodynamic models predict spans that are too large to reproduce observed profiles unless a very

High-pressure behaviour of Cr-Fe-Mg-Al spinels: applications to diamond geobarometry

NASA Astrophysics Data System (ADS)

Periotto, Benedetta; Bruschini, Enrico; Nestola, Fabrizio; Lenaz, Davide; Princivalle, Francesco; Andreozzi, Giovanni B.; Bosi, Ferdinando

2014-05-01

Spinels belonging to the chromite - magnesiochromite - hercynite (FeCr2O4-MgCr2O4-FeAl2O4) system are among the most common inclusions found in diamonds (Stachel and Harris 2008). In particular, although FeCr2O4 and MgCr2O4 components sum to between 85 and 88% of spinels found in diamonds, hercynite FeAl2O4 plays a not negligible role in determining their thermo-elastic properties with concentrations reaching 7-9 % (other minor end-members like MgAl2O4, MgFe2O4 and Fe2O3 rarely reach 2-3% in total, see Lenaz et al. 2009). Recent studies were focused on the determination of the diamond formation pressure by the so-called "elastic method" (see for example Nestola et al. 2011 and references therein). It was demonstrated that accurate and precise thermo-elastic parameters are fundamental to minimize the uncertainty of formation pressure. In this work we have determined the equations of state at room temperature of three synthetic spinel end-members chromite - magnesiochromite - hercynite and one natural spinel crystal extracted from a diamond (from Udachnaya mine, Siberia, Russia) by single-crystal X-ray diffraction in situ at high-pressure. A diamond-anvil cell was mounted on a STADI IV diffractometer equipped with a point detector and motorized by SINGLE software (Angel and Finger 2011). The natural crystal was investigated to test (and possibly validate) the "empirical prediction model", capable to provide bulk modulus and its first pressure derivative only knowing the composition of the spinels found in diamonds. Such prediction model could be used to obtain pressure of formation for the diamond-spinel pair through the elastic method. Details and results will be discussed. The research was funded by the ERC Starting Grant to FN (grant agreement n° 307322). References Angel R.J., Finger L.W. (2011) SINGLE A program to control single-crystal diffractometers. Journal of Applied Crystallography, 44, 247-251. Lenaz D., Logvinova A.M., Princivalle F., Sobolev N. (2009

3D Numerical modelling of topography development associated with curved subduction zones

NASA Astrophysics Data System (ADS)

Munch, Jessica; Ueda, Kosuke; Burg, Jean-Pierre; May, Dave; Gerya, Taras

2017-04-01

retreat. Topography associated with slab retreat is curved. Coupling I3ELVIS with SPM yields more accurate topography of the curved subduction zone. This allows balancing the relative importance of surface and deep processes in the evolution of curved subduction zones and the development of their related topography. References: Gerya, T. V., & Yuen, D. A. (2007). Robust characteristics method for modelling multiphase visco-elasto-plastic thermo-mechanical problems. Physics of the Earth and Planetary Interiors, 163(1), 83-105. Gerya, T. V., Stern, R. J., Baes, M., Sobolev, S. V., & Whattam, S. A. (2015). Plate tectonics on the Earth triggered by plume-induced subduction initiation. Nature, 527(7577), 221-225.

PREFACE Preface

NASA Astrophysics Data System (ADS)

Ivanyi, Amalia; Iványi, Péter; Rachinskii, Dmitrii; Sobolev, Vladimir A.

2011-02-01

Engineering, University of Pécs (Hungary), University College Cork (Ireland), University of Pécs (Hungary), The University of Texas at Dallas (USA), and the Cultural Capital of Europe 2010, Pécs (Hungary), is gratefully acknowledged. The Editors and Organizers of the Workshop are sincerely grateful to Dr Géza Várady, Ms Andrea Zseni and Mr Ádám Schiffer of the Pollack Mihály Faculty of Engineering, University of Pécs, and Dr Alexander Pimenov of University College Cork for managing the organization of the conference and for the assistance in formatting of all the manuscripts. More information about the workshop can be found at http://murphys5.pmmk.pte.hu/ Amalia Ivanyi, Péter Iványi, Dmitrii Rachinskii and Vladimir A SobolevEditors MURPHYS 2010, PMMK PTE, 31 May - 3 June 2010 Sponsored by Pollack Mihály logo POLLACK MIHÁLY FACULTY OF ENGINEERING, UNIVERSITY OF PÉCS UCC logo PÉCSI TUDOMÁNYEGYETEM logo PÉCSI TUDOMÁNYEGYETEM UNIVERSITY OF PÉCS UTD logo Cultural capital logo Cultural Capital of Europe 2010, Pécs, Hungary International Steering Committee Z I BalanovIsrael M BrokateGermany R CrossUK K DahmenUSA M DimianRomania G FriedmanUSA A Ivanyi (Co-Chairman)Hungary P Iványi (Co-Chairman)Hungary L KalachevUSA P KrejčíCzech Republic R O'Malley (Co-Chairman)USA A Pokrovskii (Co-Chairman)Ireland N PopovicUK D Rachinskii (Co-Chairman)Ireland S S SazhinUK V Sobolev (Co-Chairman)Russia S SzabóHungary C VisoneItaly International Program Committee G AlmásiHungary Z BalanovIsrael M BrokateGermany R CrossUK K DahmenUSA M DimianRomania G FriedmanUSA A Ivanyi (Co-Chairman)Hungary P Iványi (Co-Chairman)Hungary S JeneiHungary G KádárHungary L KalachevUSA R KersnerHungary G KovácsHungary P KrejčíCzech Republic P M KuczmannHungary P P O'KaneIreland R O'Malley (Co-Chairman)USA A Pokrovskii (Co-Chairman)Ireland N PopovicUK D Rachinskii (Co-Chairman)Ireland B V H ToppingUK V C VisoneItaly

Deep seated inclusions in kimberlites from Kharamai field and some kimberlite fields of Prianabarie.

NASA Astrophysics Data System (ADS)

Ashchepkov, I. V.; Kuligin, S. S.; Afanasiev, V. P.; Vladykin, N. V.; Kostrovitsky, S. I.; Lelyukh, M. I.; Vavilov, M. A.; Nigmatulina, E. N.; Palessky, S. V.

2012-04-01

The problem of the thickness of the lithospheric keel in the northern part of Yakutia is critical for the diamond grade. Reported delamination of the SCLM (Griffin et al., 2005)which is not supported by the geophysical methods (Koulakov et al ., 2011) was checked in number of localities in circum Anabar region. Pyropes, chrome-diopside, omphacites, enstatite, chromites and ilmenites from concentrate three kimberlitic pipes of the Kharamai field revealed compositional variations typical for thick SCLM: pyropes to 13% Of cr2O3 in the association with chromites (to 60% Of cr2O3.) low- Al - Cr diopsides and enstatite, omphacites, Cr-pargasite and K-Na richterite and picroilmenites (to 20% Of MgO). The pyropes belong to lherzolite filed (Sobolev et al., 1973) as those published only in the low-chromium part relate to Ca- Fe to pyroxenite magmatic trend (Tychkov et al., 2008) which is typical for the majority of Mesozoic (especially Jurassic) kimberlitic pipes in Prianabarie and other northern parts of Yakutia. Thermo-barometric reconstructions using four methods of monomineral thermobarometry reveal the thickness of lithospheric keel not less than 200 km which coinsides with the determined thickness of the SCLM beneath nearest Ary- Mastakh filed (Khardakh pipe). Straya Rechka and Kuranakh fields (Universitetskaya, Tudovaya , Los kimberlites etc). But the pipes in Evenkiyskaya kimberlite group (including Malysh and Tuzic pipes) carry material dominantly from the upper part of the SCLM, sub-calcium garnets are rare. Relatively high oxidation state, determined according to chromite, pyroxenes and pyropes are in accord with the rather low diamond grades. However some other Jurassic pipes in northern part of the Siberian craton reveal sufficiently deep mantle roots evidencing about lack of the delamination of mantle keel after Siberian PT superplume. The trace elements determined for the pyropes show variations and belong to the melt metasomatized groups I the middle and

Tectonics of East Siberian Sea Basin and its influence on petroleum systems

NASA Astrophysics Data System (ADS)

Karpov, Yury; Antonina, Stoupakova; Anna, Suslova; Mariia, Agasheva

2016-04-01

saturation in most perspective prospects. Factors of tectonic history, high thickness of sediments in basin, founded possible oil and gas source rocks promise success in future exploration, but in ESSB we also recommend further geophysical investigations (seismic, gravy and magnetic) and well testing of some most perspective prospects, despite of high cost of these activities. We suppose, that investigations of ESSB should be continued to receive positive effects for Russian national economy in the nearest future. References [1] Kirillova (eds) [2013] Geological setting and petroleum potential of sedimentary basins of East Siberian Sea continental margin, v. 1, (in Russian) 249. [2] Sobolev (eds) [2012] Investigation of main sequences of Paleozoic and Meso-Cenozoic sedimentary and magmatic complexes of New Siberian Islands Archipelago, (in Russian), 143. [3] Suprunenko (eds) [2005] Petroleum zoning of Russian East Arctic shelf, Comparative analysis of petroleum potential of this aquatories with definition of perspective prospects and choise of most perspective objects for future projects, v. 1, (in Russian), 264.

Realistic NLTE Radiative Transfer for Modeling Stellar Winds

NASA Technical Reports Server (NTRS)

Bennett, Philip D.

1999-01-01

This NASA grant supported the development of codes to solve the non-LTE multi-level spherical radiative transfer problem in the presence of velocity fields. Much of this work was done in collaboration with Graham Harper (CASA, University of Colorado). These codes were developed for application to the cool, low-velocity winds of evolved late-type stars. Particular emphasis was placed on modeling the wind of lambda Velorum (K4 lb), the brightest K supergiant in the sky, based on extensive observations of the ultraviolet spectrum with the HST/GHRS from GO program 5307. Several solution techniques were examined, including the Eddington factor Approach described in detail by Bennett & Harper (1997). An Eddington factor variant of Harper's S-MULTI code (Harper 1994) for stationary atmospheres was developed and implemented, although full convergence was not realized. The ratio of wind terminal velocity to turbulent velocity is large (approx. 0.3-0.5) in these cool star winds so this assumption of stationarity provides reasonable starting models. Final models, incorporating specified wind laws, were converged using the comoving CRD S-MULTI code. Details of the solution procedure were published by Bennett & Harper (1997). Our analysis of the wind of lambda Vel, based on wind absorption superimposed on chromospheric emission lines in the ultraviolet, can be found in Carpenter et al. (1999). In this paper, we compare observed wind absorption features to an exact CRD calculation in the comoving frame, and also to a much quicker, but approximate, method using the SEI (Sobolev with Exact Integration) code of Lamers, Cerruti-Sola, & Perinotto (1987). Carpenter et al. (1999) provide detailed comparisons of the exact CRD and approximate SEI results and discuss when SEI is adequate to use for computing wind line profiles. Unfortunately, the observational material is insufficient to unambiguously determine the wind acceleration law for lambda Vel. Relatively few unblended Fe II lines

A reconstruction of vegetation and paleohydrologycal changes from peatland in Kansk forest-steppe, Yenisei Siberia

NASA Astrophysics Data System (ADS)

Rodionova, Alexandra

2016-04-01

Peatlands are an important natural archive for past climatic changes. Climatic changes throughout the Holocene have been reconstructed from peat using a wide array of biological and other proxies. Many different proxy indicators can be derived from peat cores allowing for a multi-proxy approach to climatic reconstructions. Peat-based climatic and environmental reconstructions are currently available from many sites in Yenisei Siberia, mainly for its northern territories. The purpose of this paper is to study some features of peatland development and environmental reconstructions from the Holocene period in the south part of Yenisei Siberia (Kansk forest-steppe zone). The main method used in this research is macrofossil analysis. It can be used to reconstruct the development of local vegetation and surface wetness on peatlands. The macrofossil analysis in the peat resulted from the study of the vegetation in a particular place over a period of time, and it allowed the reconstruction of environmental changes that have occurred since the Late Glacial. Then we used ecological scales of moisture and reconstructed surface wetness for the entire period of the bog formation. Radiocarbon dating was carried out at Sobolev Institute of Geology and Mineralogy, Russian Academy of Sciences, Novosibirsk . Peatland "Pinchinskoye" was selected for investigation in Kansk forest-steppe. It is located on the right bank of the Yenisei River in the floodplain of Esaulovka River. Peat cores of 350 cm were selected in the southern part of the peatbog, including 225 cm of peat (with loam layers in the range of 90 to 135 cm), 75 cm of organic and mineral sapropel with the inclusion of fossil shells of mollusks and different plant macrofossils and 50 cm of the loam below. The process of peat accumulation dated back 8400 ± 140 years, which is the oldest date for the forest-steppe zone of Yenisei Siberia. The climate of Boreal period of the Holocene was chilly. Under these conditions, in the

Constraints From the Rock Record, and Complementary Speculation, on Subduction and the Evolution of the Mantle

NASA Astrophysics Data System (ADS)

Kelemen, P.

2006-12-01

process igneous or metamorphic enriches ridge and ophiolite peridotites in Pb relative to U and Th (Godard et al Eos 05). Sequestration of such a low U/Pb and Th/Pb component could help explain global Pb isotope systematics. (c) Some residual peridotites recirculate in the mantle washing machine, emerging as depleted peridotites on the seafloor with little igneous crust. (3) What is the fate of partial melts of subducted basaltic eclogite, when they react with mantle peridotite above subduction zones and beneath ocean islands? Variable time scales, permeability and melt viscosity suggest three possible scenarios: (a) much eclogite melt is trapped within a carapace of pyroxenite, and hydrofracture extracts this melt; (b) eclogite melt reacts to form solid pyroxenite, which then re-melts (Sobolev et al Nature 04); (c) eclogite melt reacts to form pyroxene-rich peridotite plus modified melt in equilibrium with olivine (Kelemen et al EPSL 98).

GHRS Observations of Cool, Low-Gravity Stars. 5; The Outer Atmosphere and Wind of the Nearby K Supergiant Lambda Velorum

NASA Technical Reports Server (NTRS)

Carpenter, Kenneth G.; Robinson, Richard D.; Harper, Graham M.; Bennett, Philip D.; Brown, Alexander; Mullan, Dermott J.

1999-01-01

-absorptions reflect a wind turbulence of approximately equal 9-21 km/s. We further characterize the wind by comparing the observations with synthetic profiles generated with the Lamers et al. Sobolev with Exact Integration (SEI) radiative transfer code, assuming simple models of the outer atmospheric structure. These comparisons indicate that the wind in 1994 can be described by a model with a wind acceleration parameter beta approximately 0.9, a terminal velocity of 29-33 km/s, and a mass-loss rate approximately 3 x 10(exp -9) solar M/yr. Modeling of the 3.6 cm radio flux observed in 1997 suggests a more slowly accelerating wind (higher beta) and/or a higher mass-loss rate than inferred from the UV line profiles. These differences may be due to temporal variations in the wind or from limitations in one or both of the models. The discrepancy is currently under investigation.

Degassing-induced crystallization in silicate melt inclusion: evaluating the role of post-entrapment changes in melt inclusion from the SW volcanic flows of Deccan Large Igneous Province (Deccan LIP) lava.

NASA Astrophysics Data System (ADS)

Rani Choudhary, Babita

2017-04-01

Melt inclusions represent sampling of magma during their growth in magma chambers and during ascent to the surface. Several studies of melt inclusions in Large Igneous Provinces (LIPs) in different parts of the world have been documented in the literature (Sobolev et al. 2011; Kamenetsky et al. 2012). Melt inclusions study from Deccan LIP can provide new insights into the physio-chemical conditions and evolution of this important LIP. The Deccan LIP was fissure eruption mainly emplaced over a very short duration at 66 Ma (Schoene et al. 2015). To better characterize and explain the diversity in geochemical composition, petrogenesis and volatile degassing, melt inclusions studies have been carried out in clinopyroxene and plagioclase feldspar from a suite of samples in the Western Ghats section. Samples were obtained from the upper three formations (the Wai subgroup). The inclusions are primary and range in shape and size varies from a few microns, up to 100 microns. The inclusions are crystalline, and contain daughter phases. Some are glassy, with or without a shrinkage bubble. The melt inclusions show substantial variations in major element composition. Inclusions are significantly enriched in TiO2 (3.68 to 0.08 wt%) and FeO (18.3 to 2.63 wt%). SiO2 ranges from 43.4-66.8 wt% and classification diagrams of total alkali (Na2O+K2O) Vs. silica melt inclusions show that most inclusions are of sub-alkaline to mildly alkaline composition. Al2O3 ranges from 9.7- 22.4wt % and MgO 18.3-1.6. EPMA measurements demonstrated the presence of daughter crystals, such as magnetite and titanomagnetite, and high FeO, TiO2 and CaO within melt inclusions among the silicate daughter crystal clusters. Volatiles are determined have wide range in composition in both plagioclase- and pyroxene-hosted melt inclusions by using FTIR technique, values up to 2wt% H2Ototal and 1808 ppm CO2. Moreover the variability in composition and volatiles the melt from the samples in a single flow suggests

3D-radiative transfer in terrestrial atmosphere: An efficient parallel numerical procedure

NASA Astrophysics Data System (ADS)

Bass, L. P.; Germogenova, T. A.; Nikolaeva, O. V.; Kokhanovsky, A. A.; Kuznetsov, V. S.

2003-04-01

Light propagation and scattering in terrestrial atmosphere is usually studied in the framework of the 1D radiative transfer theory [1]. However, in reality particles (e.g., ice crystals, solid and liquid aerosols, cloud droplets) are randomly distributed in 3D space. In particular, their concentrations vary both in vertical and horizontal directions. Therefore, 3D effects influence modern cloud and aerosol retrieval procedures, which are currently based on the 1D radiative transfer theory. It should be pointed out that the standard radiative transfer equation allows to study these more complex situations as well [2]. In recent year the parallel version of the 2D and 3D RADUGA code has been developed. This version is successfully used in gammas and neutrons transport problems [3]. Applications of this code to radiative transfer in atmosphere problems are contained in [4]. Possibilities of code RADUGA are presented in [5]. The RADUGA code system is an universal solver of radiative transfer problems for complicated models, including 2D and 3D aerosol and cloud fields with arbitrary scattering anisotropy, light absorption, inhomogeneous underlying surface and topography. Both delta type and distributed light sources can be accounted for in the framework of the algorithm developed. The accurate numerical procedure is based on the new discrete ordinate SWDD scheme [6]. The algorithm is specifically designed for parallel supercomputers. The version RADUGA 5.1(P) can run on MBC1000M [7] (768 processors with 10 Gb of hard disc memory for each processor). The peak productivity is equal 1 Tfl. Corresponding scalar version RADUGA 5.1 is working on PC. As a first example of application of the algorithm developed, we have studied the shadowing effects of clouds on neighboring cloudless atmosphere, depending on the cloud optical thickness, surface albedo, and illumination conditions. This is of importance for modern satellite aerosol retrieval algorithms development. [1] Sobolev

Numerical Modeling of Deep Mantle Flow: Thermochemical Convection and Entrainment

NASA Astrophysics Data System (ADS)

Mulyukova, Elvira; Steinberger, Bernhard; Dabrowski, Marcin; Sobolev, Stephan

2013-04-01

One of the most robust results from tomographic studies is the existence of two antipodally located Large Low Shear Velocity Provinces (LLSVPs) at the base of the mantle, which appear to be chemically denser than the ambient mantle. Results from reconstruction studies (Torsvik et al., 2006) infer that the LLSVPs are stable, long-lived, and are sampled by deep mantle plumes that rise predominantly from their margins. The origin of the dense material is debated, but generally falls within three categories: (i) a primitive layer that formed during magma ocean crystallization, (ii) accumulation of a dense eclogitic component from the recycled oceanic crust, and (iii) outer core material leaking into the lower mantle. A dense layer underlying a less dense ambient mantle is gravitationally stable. However, the flow due to thermal density variations, i.e. hot rising plumes and cold downwelling slabs, may deform the layer into piles with higher topography. Further deformation may lead to entrainment of the dense layer, its mixing with the ambient material, and even complete homogenisation with the rest of the mantle. The amount of the anomalous LLSVP-material that gets entrained into the rising plumes poses a constraint on the survival time of the LLSVPs, as well as on the plume buoyancy, on the lithospheric uplift associated with plume interaction and geochemical signature of the erupted lavas observed at the Earth's surface. Recent estimates for the plume responsible for the formation of the Siberian Flood Basalts give about 15% of entrained dense recycled oceanic crust, which made the hot mantle plume almost neutrally buoyant (Sobolev et al., 2011). In this numerical study we investigate the mechanics of entrainment of a dense basal layer by convective mantle flow. We observe that the types of flow that promote entrainment of the dense layer are (i) upwelling of the dense layer when it gets heated enough to overcome its stabilizing chemical density anomaly, (ii

Comparison of publically available Moho depth and crustal thickness grids with newly derived grids by 3D gravity inversion for the High Arctic region.

NASA Astrophysics Data System (ADS)

Lebedeva-Ivanova, Nina; Gaina, Carmen; Minakov, Alexander; Kashubin, Sergey

2016-04-01

deep Arctic Ocean: results of a 3D gravity modeling Russian Geology and Geophysics 54, 247-262. Jakobsson M, Mayer L, Coakley B, Dowdeswell JA, Forbes S, Fridman B, Hodnesdal H, Noormets R, Pedersen R, Rebesco M, Schenke HW, Zarayskaya Y, Accettella D, Armstrong A, Anderson RM, Bienhoff P, Camerlenghi A, Church I, Edwards M, Gardner JV, Hall JK, Hell B, Hestvik O, Krist-offersen Y, Marcussen C, Mohammad R, Mosher D, Nghiem SV, Pedrosa MT, Travaglini PG, Weatherall P (2012). The international bathymetric chart of the Arctic Ocean (IBCAO) version 3.0. Geophys Res Lett 39, L12609. Laske, G., Masters., G., Ma, Z. and Pasyanos, M. (2013). Update on CRUST1.0 - A 1-degree Global Model of Earth's Crust, Geophys. Res. Abstracts, 15, Abstract EGU2013-2658, 2013. Minakov A, Faleide JI, Glebovsky VY, Mjelde R (2012) Structure and evolution of the northern Barents-Kara Sea continental margin from integrated analysis of potential fields, bathymetry and sparse seismic data. Geophys J Int 188, 79-102. Petrov O., Smelror M., Shokalsky S., Morozov A., Kashubin S., Grikurov G., Sobolev N., Petrov E., (2013). A new international tectonic map of the Arctic (TeMAr) at 1:5 M scale and geodynamic evolution in the Arctic region. EGU2013-13481. Reguzzoni, M., & Sampietro, D. (2014). GEMMA: An Earth crustal model based on GOCE satellite data. International Journal of Applied Earth Observation and Geoinformation Spasojevic S. & Gurnis M., (2012). Sea level and vertical motion of continents from dynamic earth models since the late Cretaceous. American Association of Petroleum Geologists Bulletin, 96, pp. 2037-2064.

Group theoretical methods and wavelet theory: coorbit theory and applications

NASA Astrophysics Data System (ADS)

Feichtinger, Hans G.

2013-05-01

Before the invention of orthogonal wavelet systems by Yves Meyer1 in 1986 Gabor expansions (viewed as discretized inversion of the Short-Time Fourier Transform2 using the overlap and add OLA) and (what is now perceived as) wavelet expansions have been treated more or less at an equal footing. The famous paper on painless expansions by Daubechies, Grossman and Meyer3 is a good example for this situation. The description of atomic decompositions for functions in modulation spaces4 (including the classical Sobolev spaces) given by the author5 was directly modeled according to the corresponding atomic characterizations by Frazier and Jawerth,6, 7 more or less with the idea of replacing the dyadic partitions of unity of the Fourier transform side by uniform partitions of unity (so-called BUPU's, first named as such in the early work on Wiener-type spaces by the author in 19808). Watching the literature in the subsequent two decades one can observe that the interest in wavelets "took over", because it became possible to construct orthonormal wavelet systems with compact support and of any given degree of smoothness,9 while in contrast the Balian-Low theorem is prohibiting the existence of corresponding Gabor orthonormal bases, even in the multi-dimensional case and for general symplectic lattices.10 It is an interesting historical fact that* his construction of band-limited orthonormal wavelets (the Meyer wavelet, see11) grew out of an attempt to prove the impossibility of the existence of such systems, and the final insight was that it was not impossible to have such systems, and in fact quite a variety of orthonormal wavelet system can be constructed as we know by now. Meanwhile it is established wisdom that wavelet theory and time-frequency analysis are two different ways of decomposing signals in orthogonal resp. non-orthogonal ways. The unifying theory, covering both cases, distilling from these two situations the common group theoretical background lead to the

The ophiolite of the Eohellenic nappe in the island of Skyros, Greece: Geotectonic environment of formation and metamorphic conditions inferred by mineralogical and geochemical data

NASA Astrophysics Data System (ADS)

Karkalis, Christos; Magganas, Andreas; Koutsovitis, Petros

2014-05-01

, the occurrence of rodingites and ophicalcites clearly point to interaction of the gabbroic rocks and serpentinites with hydrothermal fluids, which most probably took place during the stage of exhumation and tectonic emplacement. Ophicalcites contain serpentine, calcite, magnetite, as well as rare pyroxene and spinel. Rodingites on their behalf include hydroandradite (Alm0.00Adr61.33-67.43Grs28.25-35.18Prp0.10-2.49Sps0.00-0.33Uv0.41-2.75), vesuvianite (MgO=2.78-3.33 wt.%; TiO2=0.02-0.59 wt.%) diopside neoblasts (En48.53-49.89Wo47.56-48.10Fs2.32-3.33; Mg#=93.96-96.28), chlorite and also accessory prehnite. Some small-sized Cr-bearing hydrogarnet crystals (Cr2O3=10.34 wt.%) were most likely formed at the expense of spinel. The types of hydrogarnet and vesuvianite crystals are highly indicative for the involvement of subduction-related fluids during the formation of the rodingites [6]. References: [1] Jacobshagen & Wallbrecher 1984: Geol. Soc., London, Sp. Pub. 17, 591-602, [2] Pe-Piper 1991: Ofioliti, 16, 111 - 120, [3] Kamenetsky Sobolev, Joron & Semet 2001: J Petrol 42, 655-671, [4] Agrawal, Guevara & Verma 2008: Intern. Geol. Rev. 50, 1057-1079, [5] Pearce & Cann 1973: Earth Plan. Sci. Lett. 19, 290-300, [6] Koutsovitis, Magganas, Pomonis & Ntaflos 2013. Lithos 172-173, 139-157.

Limitations on the Estimation of Parental Magma Temperature Using Olivine-melt Equilibria: Hotspots Not So Hot

NASA Astrophysics Data System (ADS)

Natland, J. H.

2004-12-01

from melt strains produced by partial melting of both depleted and enriched pyroxenite or recycled ocean-crust (eclogite) (e.g., refs.1 and 2). Some Icelandic picrites also contain large phenocrysts of plagioclase and clinopyroxene; their abundant olivine evidently resulted from mechanical processes of concentration of olivine such as flowage differentiation. Using compositions of low-Al2O3 melt inclusions and host liquids to estimate spinel compositions (ref. 3) reveals many instances of crystallization at higher oxidation states than occur during MORB crystallization, and successfully predicts presence of spinel with Cr/(Cr+Al) = 60-75 actually found in picrites from Hawaii, Iceland, elsewhere in the North Atlantic Igneous Province, and the komatiites of Gorgona, but not in MORB. Where fresh glass is lacking (e.g., Gorgona), bulk-rock compositions have been used to reconstruct conditions of crystallization of parental liquids; but this is greatly complicated by the type and extent of alteration of the rocks. The consequence of all of these factors is that FeO in presumed olivine-controlled liquids is often overestimated, thus many estimated temperatures of crystallization of primitive magnesian liquids are too high by as much as 50-100o absolute, and derived potential temperatures consequently are too high by more than this. (1) Hansteen, T., 1991. Contrib. Mineral. Petrol. 109, 225. (2) Sobolev, A., Hofmann, A., and Nikogosian, I., 2000. Nature, 404, 986. (3) Poustovetov, A., and Roeder, P., 2001, Canad. Mineral. 39, 309.

Multistage metasomatism in lithospheric mantle beneath V. Grib pipe (Arkhangelsk diamondiferous province, Russia): evidence from REE patterns in garnet xenocrysts.

NASA Astrophysics Data System (ADS)

Shchukina, Elena; Alexei, Agashev; Nikolai, Pokhilenko

2015-04-01

150 garnet xenocrysts from V. Grib kimberlite pipe were analyzed for major and trace elements compositions. 70 % of garnet belong to lherzolite field; 14 % - megacrysts and pyroxenites; 11 % - eclogites; 4 % - harzburgite; 1 % (1- wehrlite defined by Sobolev (1973). Harzburgite garnets: sinusoidal REE patterns Smn/Ern > 5 (5.2 - 19.8). low Y (0.5 - 3.9 ppm), Zr (1.1 - 44.6 ppm), Ti (54 - 1322 ppm). Wehrlite garnetd: close to sinusoidal REE patterns, Smn/Ern - 1.8. Megacrysts and pyroxenites garnets: normal REE patterns Smn/Ern < 1 (0.2 - 0.6), high TiO2 (0.9 - 1.3 wt %). Lherzolite garnets 70 % show four groups of REE patterns similar to peridotite xenoliths (Shchukina et al., 2013, 2015). 1-st contains MREE at С1 level, Sm/Ern - 0.03, La/Ybn - 0.002. increasing La -Yb range, low Y, Zr, Ti indicating residual nature. 2-nd: MREE at 2 - 13 chondrite units, Smn/Ern (0.16 - 0.98), La/Ybn - 0.001 - 0.040 and flat pattern from MREE to HREE. 3-rd -MREE at 5 - 14 chondrite units, Sm/Ern > 1 (1.05 - 4.81) La/Ybn - 0.010-0.051 increasing an hump at MREE decreasing to HREE. 4-th: sinusoidal REE, Sm/Ern 4.2 - 27.2. and harzburgite Y, Zr, Ti . Average Cr2O3 content increases from 2-nd to the 3-rd group (3.3 to 5.7 wt%) and 4th (7.9 wt %). Average Y/Zr decreases from 2-nd (0.6) to 3rd (0.2) and 4th group (0.08). REE and Y, Zr, Ti indicate the metasomatic origin of garnets of 2, 3. 4 groups. Modeling of TREfor equilibrated melts and fractional crystallization 2nd group close to Turyino field basalts and 3-rd - to Izmozero field picrites of Arkhangelsk diamondiferous province (ADP). Basing on geochemical data of garnet xenocrysts and garnets and clinopyroxenes in peridotites (Shchukina et al., 2013, 2015) we suppose at least 3 stage of high-temperature metasomatic enrichment. 1st stage - is enrichment of residual garnets (found only in peridotite garnets) in LREE by the influence of carbonatite melt close to the Mela field carbonatites of ADP. REE patterns in clinopyroxenes from

Formation and metasomatism of continental lithospheric mantle in intra-plate and subduction-related tectonic settings

NASA Astrophysics Data System (ADS)

Ionov, Dmitri

2010-05-01

, major and trace element and isotope compositions of fertile lherzolites and thus cannot provide viable alternatives to the concept of melt extraction from pristine mantle as the major mechanism of CLM formation. Published data on xenoliths from andesitic volcanoes and on supra-subduction oceanic peridotites [4] show that the most common rocks in mantle wedge lithosphere are highly refractory harzburgites characterized by a combination of variable but generally high modal opx (18-30%) with very low modal cpx (1.5-3%). At a given olivine (or MgO) content, they have higher opx and silica, and lower cpx, Al and Ca contents than normal refractory peridotite xenoliths in continental basalts; the Mg-Si and Al-Si trends in those rocks resemble those in cratonic peridotites. These features may indicate either fluid fluxing during melting in the mantle wedge or selective post-melting metasomatic enrichments in silica to transform some olivine to opx. High oxygen fugacities and radiogenic Os-isotope compositions in those rocks may be related to enrichments by slab-derived fluids, but these features are not always coupled with trace element enrichments or patterns commonly attributed to "subduction zone metasomatism" deduced from studies of arc volcanic rocks and experiments. The valuable insights provided by experimental work and xenolith case studies are difficult to apply to many natural peridotite series because late-stage processes commonly overlap the evidence for initial melting. References: [1] Herzberg C., J. Petrol. 45: 2507 (2004). [2] Ionov D. & Sobolev A., GCA 72 (S1): A410 (2008). [3] Ionov D., Contrib. Miner. Petrol. (2007) [4] Ionov D., J. Petrol. doi: 10.1093/petrology/egp090 (2010)

H2O Paradox and its Implications on H2O in Moon

NASA Astrophysics Data System (ADS)

Zhang, Youxue

2017-04-01

second scenario is unlikely on Moon because there was unlikely plate tectonics, and because there is no similar H2O-rich transition zone or D" layer due to the much lower maximum pressure in Moon. In the third scenario, volatiles from an extralunar source would likely be lost from the high vacuum environment of the lunar surface, meaning that it would not impact on the H2O content estimation. [1] McDonough & Sun (1995) Chem. Geol. 120, 223. [2] Palme & O'Neill (2014) Treatise on Geochemistry 3, 1. [3] Zhang (2014) Treatise on Geochemistry 6, 37. [4] Zhang & Zindler (1989) JGR 94, 13719. [5] Hui et al. (2013) Nature Geosci. 6, 177. [6] Chen et al. (2015) EPSL 427, 37. [7] Albarede et al. (2015) MPS 50, 568. [8] Sobolev et al. (2016) Nature 531, 628. [9] Chyba (1987) Nature 330, 632. [10] Hartogh et al. (2011) Nature 478, 218. [11] Hui et al. (2016) Goldschmidt Conf. Abstr.

On the adaptive daily forecasting of seismic aftershock hazard

NASA Astrophysics Data System (ADS)

Ebrahimian, Hossein; Jalayer, Fatemeh; Asprone, Domenico; Lombardi, Anna Maria; Marzocchi, Warner; Prota, Andrea; Manfredi, Gaetano

2013-04-01

aftershock catalog. The parameters of the modified Omori model are estimated in an adaptive manner using the Bayesian updating based on the aftershock events that had already taken place at each day elapsed and using the Italian generic sequence (Lolli and Gasperini 2003) as prior information. For the ETAS model, the real-time daily forecast of the spatio-temporal evolution of the L'Aquila sequence provided for the Italian Civil Protection for managing the emergency (Marzocchi and Lombardi, 2009) is utilized. Moreover, the parameters of the ground motion prediction relation proposed by Sabetta and Pugliese (1996) are updated adaptively and on a daily basis using Bayesian updating based on the ongoing aftershock sequence. Finally, the forecasted daily rates of exceeding (first-mode) spectral acceleration values are compared with observed rates of exceedance calculated based on the wave-forms that have actually taken place. References Jalayer, F., Asprone, D., Prota, A., Manfredi, G. (2011). A decision support system for post-earthquake reliability assessment of structures subjected to after-shocks: an application to L'Aquila earthquake, 2009. Bull. Earthquake Eng. 9(4) 997-1014. Jordan, T.H., Chen Y-T., Gasparini P., Madariaga R., Main I., Marzocchi W., Papadopoulos G., Sobolev G., Yamaoka K., and J. Zschau (2011). Operational earthquake forecasting: State of knowledge and guidelines for implementation, Ann. Geophys. 54(4) 315-391, doi 10.4401/ag-5350. Lolli, B., and P. Gasperini (2003). Aftershocks hazard in Italy part I: estimation of time-magnitude distribution model parameters and computation of probabilities of occurrence. Journal of Seismology 7(2) 235-257. Marzocchi, W., and A.M. Lombardi (2009). Real-time forecasting following a damaging earthquake, Geophys. Res. Lett. 36, L21302, doi: 10.1029/2009GL040233. Sabetta F., A. Pugliese (1996) Estimation of response spectra and simulation of nonstationary earthquake ground motions. Bull Seismol Soc Am 86(2) 337-352.

NiO and Fe/Mn in Fo-rich olivines from OIB, MORB, and mantle peridotites

NASA Astrophysics Data System (ADS)

Li, H.; Baker, M.; Hofmann, A. E.; Clague, D.; Stolper, E.

2006-12-01

regular trend from MORB/Iceland, to Baffin Isl, to mantle peridotites/Juan Fernandez, to Reunion/Hawaii. This array can't be explained by simple crystallization (all have similar Fo) or by variable degrees of partial melting of a single source. The NiO-Fe/Mn correlation can be modeled by quantitative addition of 1-2% oxidized core to depleted mantle and thus is consistent with the core-addition hypothesis. However, more complex core-mantle interactions/fractionations would still be required to explain trace siderophile and chalcophile elements and isotopes. Moreover, other hypotheses to explain the observed trend (including addition of silicic melts to peridotite) cannot be ruled out. (2) The Hawaiian data, although clearly defining with Reunion the upper end of the overall NiO-Fe/Mn array, are more complex. For example, a single Mauna Kea sample has ~Fo90 phenocrysts with NiO from 0.30 to 0.54%, all with Fe/Mn=72-80, and North Arch and Loihi olivines have relatively low NiO at Fe/Mn ratios comparable to other Hawaiian olivines. Although Loihi and North Arch lavas are low in SiO2, in detail the NiO of Hawaiian olivines are not well predicted by SiO2 contents of the host lavas. (3) The Gorgona Isl komatiites fall off the overall trend, extending to NiO >0.5 wt% at Fe/Mn ~62, perhaps reflecting different sources, processes, or anomalous degrees of melting. [1] Kelemen et al (1998) EPSL 164, 387-406 [2] Sobolev et al (2005) Nature 434, 590-597 [3] Ryabchikov (2003) Doklady Earth Sci. 389A, 437-439 [4] Humayun et al (2004) Science 306, 91-94

Proterozoic Eastern Sayan ophiolites (Central Asian Orogenic Belt) record subduction initiation in vicinity of continental block

NASA Astrophysics Data System (ADS)

Belyaev, Vasilii; Gornova, Marina; Medvedev, Alexander; Dril, Sergey; Karimov, Anas

2017-04-01

volcanics and dikes are low-Ca and intermediate-Ca boninites, andesite-basalts, andesites, dacites of calc-alkaline (CA) affinity with rare evolved island-arc tholeiitic (IAT) andesite-basalts. They resemble appropriate rocks of intraoceanic island arcs, forearcs, and ophiolites. Boninites and CA-andesites are LREE-enriched (La/SmPM 1.2-3.8) at low HREE (0.5-1.6 ppm Yb) contents while evolved IAT show flat REE (La/SmPM = 1.1) and higher abundances (2.4-2.8 ppm Yb), and both have negative Nb anomalies. Nd-isotopic data expressed as epsilon Nd(1020Ma) values are -2.3 to +4.1 in cumulates, -2.8 to +0.4 in boninites and andesites, and +2.3 to +2.7 in IAT (compared to epsilon Nd(1020Ma) +7.8 in depleted mantle). The ophiolites obducted on the Gargan continental block, which contains Archean gneisses with epsilon Nd(1020) = -20 to -281. Subduction and recycling of sediments derived from these gneisses could explain enriched Nd isotopic characteristics of the studied ophiolitic rocks. The boninite-andesite-IAT association is usually found in subduction initiation settings recorded by modern forearc regions and forearc ophiolites. The difference of the Eastern Sayan ophiolites is their supposed formation close to ancient continental block which supplied recycled material into newly formed subduction zone. 1. Sklyarov et al (2016) Russ Geol Geophys 57, 127-140 2. Sobolev et al (1996) Petrology 3, 326-336.

Instabilities in free-surface Hartmann flow at low magnetic Prandtl numbers

NASA Astrophysics Data System (ADS)

Giannakis, Dimitrios

2009-06-01

order of the Sobolev spaces of the continuous problem. The orthogonality properties of the bases solve the matrix-coefficient growth problem of the discrete stability operators, and eigenvalue-eigenfunction pairs can be computed stably at spectral orders at least as large as p =3000 with p -independent roundoff error. We find that, because it is a critical-layer instability (moderately modified by the presence of the free surface), the hard mode exhibits similar behavior to the even unstable mode in the corresponding closed-channel flow, in terms of both the weak influence of Pm on its neutral-stability curve and the monotonic increase of its critical Reynolds number, Re c , with the Hartmann number. In contrast, the soft mode's stability properties exhibit the novel behavior of differing markedly between problems with small, but nonzero, Pm and their counterparts in the inductionless limit. Notably, the critical Reynolds number of the soft mode grows exponentially with Ha in inductionless problems, but when Pm is nonzero that growth is suppressed to either a sublinearly increasing, or a decreasing function of Ha (respectively when the lower wall is an electrical insulator or a perfect conductor). In the insulating-wall case, we also observe pairs of counter-propagating Alfvén waves, the upstream- propagating wave undergoing an instability at high Alfvén numbers. We attribute the observed Pm -sensitivity of the soft instability to the strong-field behavior of the participating inductionless mode, which, even though stabilized by the magnetic field, approaches neutral stability as Ha grows. This near-equilibrium is consistent with a balance between Lorentz and gravitational forces, and renders the mode susceptible to effects associated with the dynamical response of the magnetic field to the flow (which vanishes in the inductionless limit), even when the magnetic diffusivity is large. The boundary conditions play a major role in the magnetic field response to the flow

PREFACE: International Workshop on Multi-Rate Processes and Hysteresis

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; O'Malley, Robert E.; Pokrovskii, Alexei; Rachinskii, Dmitrii; Sobolev, Vladimir A.

2008-07-01

, International Association of Hydrological Sciences, and Laboratoire Poncelet is gratefully acknowledged. The Editors and the Organizers of the Workshop wish to place on record their sincere gratitude to Mr Andrew Zhezherun and Mr Alexander Pimenov of University College Cork for both the assistance which he provided to all the presenters at the Workshop, and for the careful formatting of all the manuscripts prior to their being forwarded to the Publisher. More information about the Workshop can be found at http://euclid.ucc.ie/murphys2006.htm Michael P Mortell, Robert E O'Malley Jr, Alexei Pokrovskii, Dmitrii Rachinskii and Vladimir Sobolev Editors

Verochka Zingan or recollections from the Physics Department of the Moscow University

NASA Astrophysics Data System (ADS)

Gaina, Alex

. Laufer, Yu. El'nitskii, Gh. Nemtoi, Yu. Oprunenko, N.N. Semenov, Varun Sahni, A.A. Starobinskii, Liusea Burca, Serge Rollet, Tatyana Davydova, Zinaida Uglichina (Khafizova), T.Filippova, V.S. Filippov, Vera Zingan (Stefanovici), B.A. Gaina, E.F. Gaina, Valeri Gaina, A. Kirnitskii, M. Kavalerchik, Margarita Kavalerchik, Mark Rainis, L.I. Sedov, D. Mangeron, S. Taltu (Coanda), Z. Sali(Chitoroaga, Kitoroage), Raisa M. Gorbachova, Maria Bulgaru, S. Pavlichenko, Nadezhda Shishkan, A.N. Matveev, N.Ya. Tyapunina, D.F. Kiselev, V.A. Petukhov, N.Ch. Krutitskaya, G.N. Medvedev, A.A. Shishkin,I.A. Shishmarev,A.G. Sveshnikov, A.B. Vasil'eva, A.G. Yagola, I.I. Ol'hovskii, V.V. Kravtsov, V.V.Petkevich, V.I. Grigor'ev, V.S. Rostovskii, V.V. Balashov, B.I. Spasskii, V.D. Krivchenkov, M.B. Menskii, V.Ya. Fainberg, V.G. Kadyshevskii, B.K. Kerimov, V.A. Matveev, I.A. Kvasnikov, D.V. Gal'tsov, V.R. Khalilov, G.A. Chizhov,I.A. Obukhov, V.N. Melnikov, A.A. Logunov, A.N. Tavkhelidze,Yu.S. Vladimirov, N.F. Florea (Floria), B.A. Lysov, V.D. Kukin, 601-academic group (1977), A.R. Khokhlov, P.L. Kapitza, S.P. Kapitza, Ion C. Inculet, Ion I. Inculet,W. Bittner, Nikolay Florea (Floria), M.M. Heraskov, N.V. Sklifosovskii, N.N. Bantysh-Kamenskii, N.D. Zelinskii, Olga Crusevan (Krushevan), Eugenia Crusevan (Krushevan),L.S. Berg, I. Buzdugan (Buzdyga),S.G. Lazo, M.K. Grebenchya (Grebencea), V.T. Kondurar (Conduraru), E.A. Grebenikov, K.F. Teodorchik, V.A. Albitzky, M.V. Nazarov, Tatiana Nazarova, V. P. Oleinikov, O.V. Bolshakov, D.M. Nikolaev, V. Afanas'ev, Olga Tatarinskaya, Yu.V. Karaganchou, B.A. Volkov, V.K. Turta, S. Varzar, C. Sochichiu, V.B. Braginsky, V.S. Fursov, L.I. Brezhnev, V.I. Sobolev (INP MSU), V.A. Smirnov (INP MSU), L.D. Landau, M.A. Leontovich, A.G. Loskutova, Yu.M. Loskutov, N.S. Akulov, V.B. Gostev, A.R. Frenkin, N.N. Kolesnikov, A. Vasil'ev, V.N. Tsytovich, Ya.A. Frenkel, N.V. Mitskievich, E.A. Grebenikov, A.N. Prokopenya, A. Einstein, L.I. Sedov, A.N. Kolmogorov, V.I. Arnold, G

Developpement de techniques de diagnostic non intrusif par tomographie optique

NASA Astrophysics Data System (ADS)

Dubot, Fabien

pour l'algorithme de Gauss-Newton amorti, et les regularisations basees sur le maillage et l'utilisation des gradients de Sobolev, uniformes ou spatialement dependants, lors de l'extraction du gradient de la fonction cout, pour la methode BFGS. Les resultats numeriques indiquent que l'algorithme de BFGS surpasse celui de Gauss-Newton amorti en ce qui concerne la qualite des reconstructions obtenues, le temps de calcul ou encore la facilite de selection du parametre de regularisation. Deuxiemement, une etude sur la quasi-independance du parametre de penalisation de Tikhonov optimal par rapport a la dimension de l'espace de controle dans les problemes inverses d'estimation de fonctions spatialement dependantes est menee. Cette etude fait suite a une observation realisee lors de la premiere partie de ce travail ou le parametre de Tikhonov, determine par la methode " L-curve ", se trouve etre independant de la dimension de l'espace de controle dans le cas sous-determine. Cette hypothese est demontree theoriquement puis verifiee numeriquement sur un probleme inverse lineaire de conduction de la chaleur puis sur le probleme inverse non-lineaire de TOD. La verification numerique repose sur la determination d'un parametre de Tikhonov optimal, defini comme etant celui qui minimise les ecarts entre les cibles et les reconstructions. La demonstration theorique repose sur le principe de Morozov (discrepancy principle) dans le cas lineaire, tandis qu'elle repose essentiellement sur l'hypothese que les fonctions radiatives a reconstruire sont des variables aleatoires suivant une loi normale dans le cas non-lineaire. En conclusion, la these demontre que le parametre de Tikhonov peut etre determine en utilisant une parametrisation des variables de controle associee a un maillage lâche afin de reduire les temps de calcul. Troisiemement, une methode inverse multi-echelle basee sur les ondelettes associee a l'algorithme de BFGS est developpee. Cette methode, qui s'appuie sur une

PREFACE: International Conference on Inverse Problems 2010

NASA Astrophysics Data System (ADS)

Hon, Yiu-Chung; Ling, Leevan

2011-03-01

Sciences, South KoreaYu Jiang, Hokkaido University, JapanDe-Xing Kong, Zhejiang University, ChinaOlga Krivorotko, Novosibirsk State University, RussiaPhilipp Küegler, Austrian Academy of Sciences, AustriaKiwoon Kwon, Dongguk University, South KoreaChun-Kong Law, National Sun Yat-sen University, TaiwanJune-Yub Lee, Ewha Womans University, South KoreaMing Li, City University of Hong Kong, HKSARMikyoung Lim, Korea Advanced Institute of Science and Technology (KAIST), South KoreaJijun Liu, Southeast University, ChinaXiaodong Liu, Chinese Academy of Sciences, ChinaFuming Ma, Jilin University, ChinaHang Ma, Shanghai University, ChinaValdemar Melicher, Ghent University, BelgiumGen Nakamura, Hokkaido University, JapanLong Tuan Nguyen, Ruhr-Universitat Bochum, GermanyEtibar Panakhov, Firat University, TurkeyRobert Plato, University of Siegen, GermanyJean-Pierre Puel, The University of Tokyo, JapanHans-Jürgen Reinhardt, University of Siegen, GermanyMaxim Shishlenin, Sobolev Institute of Mathematics, RussiaIlya Silvestrov, Institute of Petroleum Geology and Geophysics SB RAS, RussiaMourad Sini, Austrian Academy of Sciences, AustriaJán Sládek, Slovak Academy of Sciences, SlovakiaZhijun Tan, Sun Yat-sen University, ChinaQuan-Fang Wang, The Chinese University of Hong Kong, HKSARWenyan Wang, The University of Tokyo, JapanPihua Wen, Queen Mary, University of London, UKZhihai Xiang, Tsinghua University, ChinaXiang-Tuan Xiong, Northwest Normal University, ChinaDinghua Xu, Zhejiang Sci-Tech University, ChinaYongzhi Steve Xu, University of Louisville, USAJiaqing Yang, Chinese Academy of Sciences, ChinaJian Zhang, Sichuan Normal University, ChinaYing Zhang, Fudan University, ChinaTing Zhou, University of Washington, USAJianxin Zhu, Zhejiang University, China Advisory BoardH Thomas Banks, North Carolina State University, USATony F Chan, The Hong Kong University of Science and Technology, HKSARHeinz W Engl, Johannes Kepler Universitát Linz, AustriaRainer Kress, Georg-August-Universitát G�

Detecting of the processes of the diamond formation using the monomineral thermobarometry .

NASA Astrophysics Data System (ADS)

Ashchepkov, Igor; Afanasiev, Valentin; Pokhilenko, Lyudmila; Logvinova, Alla; Vladykin, Nikolai

2010-05-01

The methods of the monomineral thermobarometry used for the reconstruction of the mantle sections beneath the kimberlite pipes (Ashchepkov et al., 2009) allow to determined PT range for the diamond inclusions (DI) and diamond bearing associations. They show various conditions for the crystallization of diamond for in mantle lithosphere beneath the Yakutia, Africa, and North America. In Yakutia most DI (Sobolev ea 1997, 2004; Logvinova ea., 2005 and ref their in) (Cr-pyropes, Mg -opx) form Mir and Udachnaya pipes are referred to the cold geotherms 35 (partly 33 mvm-2) at the pressure range from 35 to 80 kbar. Cr- pyropes (Ti-bearing) partly drops the on the heated area near convective branches 40-45 mvm-2 convective geotherms. Most Cr- rich pyroxenes refer to the coldest or heated (metasomatic type) at the deeper parts of the mantle columns while mildly Cr-rich varieties refer to the conditions of the crystallization from the melts related to the protokimberlites and associated carbonatites near the Graphite-Diamond boundary (G-D). They are more widely distributed in mantle beneath the Mir pipe where the essential part of mantle column from 50 to 35kbar was subjected to the refertilization. But chromite PT estimates mostly refer the heated conditions of the convective branch at the lithosphere base (~70-60kbar). They are most typical for the Alakite pipes. Diamond bearing eclogites show the some separate levels of crystallization with the high T-range reflecting conditions 35 to 45 mvm-2 mostly in the 60-50 kbar interval. They coincide with the levels of the intensive heating in the mantle columns. For the South Africa in the Mesozoic pipes beneath Lesotho - Jagersfontein (Viljoen ea. 2005), Finsch (Appleyard ea., 2004; Gurney, Switzer, 1973; She ea., 1983), Koffiefontein (Rickard ea., 1986), diamond bearing associations refer to three geotherm branches. The coldest (Cr-pyropes and Mg-Opx) is related to ancient subduction with the heating at 60 and 75 kbars. The 40

PREFACE: 6th International Conference on Inverse Problems in Engineering: Theory and Practice

NASA Astrophysics Data System (ADS)

Bonnet, Marc

2008-07-01

. Lionheart (U. Manchester, UK) M. Bertero (U. Genova, Italy) D. Maillet (Nancy-U., France) J. Blum (U. Nice, France) W. Marquardt (RWTH Aachen, Germany) H. D. Bui (Ecole Polytech., France) P. A. Martin (Col. School of Mines, USA) T. Burczynski (Silesian Tech. U., Gliwice, Poland) A. Michalak (U. of Michigan, USA) G. Dassios (U. Patras, Greece) A. Nenarokomov (Moscow Aviation Inst., Russia) D. Delaunay (U. Nantes, France) D. Murio (U. Cincinnati, USA) H. Dinh Nho (Hanoi Inst. Maths, Vietnam) A. J. Nowak (Silesian Tech. U. Gliwice, Poland) A. El Badia (U. Tech. Compiègne, France) H. R. B. Orlande (Federal U. Rio de Janeiro, Brazil) J. Frankel (U. Tennessee, USA) L. Päivärinta (U. Helsinki, Finland) O. Ghattas (Carnegie Mellon U., USA) D. Petit (U. Poitiers, France) B. Guzina (U. Minnesota, USA) L. Pronzato (U. Nice, France) A. Hasanov (Kocaeli U., Turkey) M. Prud'homme (Ecole Polytech. Montréal, Canada) F. Hild (ENS Cachan, France) O. Scherzer (U. Innsbruck, Austria) C.-H. Huang (National Cheng Kung U., Taiwan) V. Shutyaev (Inst. Num. Maths, Russia) M. Ikehata (Gunma U., Japan) A. J. Silva Neto (U. Estado Rio de Janeiro, Brazil) M. Jaoua (Ecole Nat. Ingé. Tunis, Tunisia) V. Steffen Jr (U. Federal Uberlandia, Brazil) Y. Jarny (U. Nantes, France) G. Uhlmann (U. Washington, USA) S. Kabanikhin (Sobolev Inst. Maths., Russia) K. A. Woodbury (U. Alabama, USA) J. Kaipio (U. Kuopio, Finland) A. Yagola (Moscow State U., Russia) Kyung Youn Kim (Cheju National U., South Korea) E. Zuazua (U. Complutense Madrid, Spain) Additional Reviewers H. Ammari (ESPCI and Ecole Polytech., France) Y. Favennec (U. Poitiers, France) S. Avril (Ecole Mines St. Etienne, France) O. Fudym (Ecole Mines Albi, France) G. Bal (U. Columbia, USA) M. Girault (U. Poitiers, France) J.-L. Battaglia (U. Bordeaux, France) F. Hemez (Los Alamos Natl. Lab., USA) F. Bauer (Johannes Kepler U., Linz, Austria) M. Janicki (RICAM, Linz, Austria & T.U. Lodz, Poland) C. Bissieux (U. Reims, France) N. Laraqi (U. Paris X, France

Physico-chemical transition from peridotite assemblage to the eclogite one (experimental data at 7.0 GPa).

NASA Astrophysics Data System (ADS)

Butvina, Valentina; Litvin, Yurii

2010-05-01

Peridotites and eclogites, including diamond-bearing ones, are the basic ultra-basic and basic rocks of the upper mantle (Ringwood, 1969, 1975; Sobolev, 1974; Marakushev, 1985; Taylor & Anand, 2004). These rocks are presented in the assemblage of mantle xenolyths in kimberlites, but the basic minerals of peridotite paragenesis, olivine, orthopyroxene, garnet and clinopyroxene as well as of an eclogite paragenesis, garnet and omphacite are wide-spread synthetic inclusions in diamonds. The cases of finding minerals and peridotite and eclogite parageneses in diamond are described. It implies that these parageneses can have a single mantle source. However, the formation of peridotite and eclogite mineral parageneses at differentiation of the primary ultrabasite melt during physico-chemical single process is possible only at overcoming the 'eclogite' thermal barrier (O'Hara, 1968; Litvin, 1991). Eclogite genesis is one of the most difficult and discussional problems of modern petrology. Among investigators there is an opinion about eclogite heterogeneity not only on conditions of formation (crust, mantle), but also by composition of the initial rocks (para-, orthoeclogites) as well as by the way of their formation (magmatic, metamorphic, metasomatic). In literature diamond-bearing eclogite nodules of kimberlite pipes are often considered as metamorphic, which are formed at subduction of the Archean or of the Proterozoic oceanic crust (MacGregor & Manton, 1986; McCandless & Gurney, 1986, 1997 et al.). Only the presence of Na2O in garnet and K2O in clinopyroxene is a criterion of their participation in mantle magmatic processes. Together with the hypotheses considered on eclogite origin there exists a version suggested in papers (Kushiro, 1972; Kushiro & Yoder, 1974), according to which mantle eclogites could be formed due to peridotite substance in the processes of fractional crystallization of ultrabasite magmas. The present paper is devoted to the experimental study of