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[en] A spherical Radon transform that averages a function over all spheres centered on a given sphere is related to not only pure but also applied mathematics topics. Especially, the problem of inverting this spherical Radon transform arising in photoacoustic tomography and sonar has been studied in many articles. We provide two series formulas for inversion: one does not require the compact support of the source function unlike most inversion formulas and the other is singular value decomposition type, i.e., the series formula is based on the complete orthogonal system. Last, we discuss its continuity. (paper)
[en] We consider spherically symmetric stellar systems with distribution function F depending only on the energy epsilon. Using the second variation of energy and the corresponding eigenvalue equation, we show that the condition dF/d epsilon<0 is a sufficient condition of stability for aspherical modes. This gives a new demonstration of the result obtained by Antonov with his functional
[fr]Nous considerons des systemes stellaires spheriques dont la fonction de distribution F depend uniquement de l'energie epsilon. En utilisant la seconde variation de l'energie et l'equation aux valeurs propres associee, nous montrons que la condition dF/d epsilon<0 est une condition suffisante de stabilite vis-a-vis des modes aspheriques. Ceci donne une nouvelle demonstration du resultat obtenu pour les polytropes par Antonov a l'aide de sa fonctionnelle
[en] Full text: There is a longstanding issue on the physical nature of a low frequency (< 50 kHz) MHD instability observed at the early phase of the discharges of a spherical tokamak (ST) - the National Spherical Torus Experiment (NSTX). This work provides evidence that low frequency modes in spherical tokamaks are often driven by the rapid plasma flow. The centrifugal force associated with toroidal plasma flow is identified as the key physics mechanism for generating this instability located in the plasma core region. Positive mode identification between toroidal modelling and experiments is achieved for the mode frequency, the mode internal structure, as well as the threshold flow value for the mode onset. The threshold flow value weakly depends on the precise value of safety factor and the mode is located around the location of sharp density gradient. More important, since the achievable rotation value on NSTX is comparable with that for future component test facilities (CTF) based on ST, the presented results in this work are helpful for the conceptual design of ST-CTF to avoid the instability driven by fast plasma flow. (author)
[en] The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. Affine homogeneous spaces G/H of complexity 1 are classified in this paper. These results are the natural continuation of the earlier classification of spherical affine homogeneous spaces, that is, spaces of complexity 0.
[en] Seismic ray-tracing methods are widely used in seismology, with most such algorithms being executed in Cartesian or spherical coordinate systems. However, the actual Earth is not a perfect sphere but rather an ellipsoid, meaning that results calculated in spherical coordinates may be different from the actual situation. The general approach is to first calculate traveltimes in a spherical Earth model, then apply ellipsoidal time corrections to obtain more accurate traveltime data. Alternatively, one may directly conduct the ray tracing in the ellipsoidal Earth model without any time corrections. In this paper, we extend the functional of the multistage irregular shortest-path method, previously formulated for a spherical Earth model, to an ellipsoidal Earth model in order to trace multiphase global seismic arrivals. The results of two models indicate that the proposed algorithm has high computational accuracy, which can be further tuned by decreasing the secondary node spacing. Comparison tests indicate that the traveltime differences between the ellipsoidal and spherical coordinate ray-tracing methods cannot be ignored for direct P and S arrivals, reflected PcP and ScS arrivals, and reflected and converted PcS and ScP arrivals. The traveltime differences (TE − TS) computed by the ellipsoidal and spherical ray-tracing methods have different distribution patterns, being dependent on the source locations. However, in general, these traveltime differences (TE − TS) have relatively large negative values near the polar region and positive values near the equatorial region, except for sources located near the polar region. For ellipsoidal time correction in a specific case, the maximum differences between the traveltimes computed by the ellipsoidal coordinate ray-tracing method and the AK135 Traveltime Table after application of ellipsoidal time corrections are less than 0.1 s. Meanwhile, the maximum differences between the traveltimes predicted by the ellipsoidal coordinate ray-tracing method and by the spherical coordinate ray-tracing method after application of ellipsoidal time corrections are only 0.075 s for the six stated phases. These results indicating that ray tracing could be conducted directly in the ellipsoidal Earth model.
[en] Microcapsules containing water-soluble ammonium persulfate (APS) cores as gel breakers that offer controlled burst release, are become increasingly important in improving the gel breaking efficiency of fracturing fluids in oil fields. To date, microcapsules with various control slow release behaviors have been thoroughly investigated, but microcapsules with burst release properties are rarely studied. Here, we reported a novel inverse emulsion polymerization method to exploit this new type of microcapsule. The microcapsules were composed of APS cores and stimuli-responsive P(MMA-co-AA) copolymer shells. The microcapsules have spherical structures with diameters of 10 to 16 μm. The encapsulated cores offer controlled burst release from the microcapsules and their beginning time of burst release could be delayed up to 42 h. Moreover, all of the cores could be completely released within 1 h from the microcapsules. The temperature, pH, and salt concentration change could stimulate the release. These novel microcapsules might have promising applications in oil exploration, batteries, monomer polymerization, fiber printing, and grease. (paper)
[en] The problem of normal collision of a spherical particle with a half-space is considered with allowance for nonlocal plastic deformation in the case where the strength limit depends on the contact radius, as well as for the strengthening effect in the deformed material. The dimensionless coefficient of normal velocity restitution has been calculated numerically as a function of the initial velocity of the spherical particle. The obtained data coincide well with experimental results available in the literature.
[en] The cone-beam transform consists of integrating a function defined on the three-dimensional space along every ray that starts on a certain scanning set. Based on Grangeat’s formula, Louis (2016 Inverse Problems 32 115005) states reconstruction formulas based on a new generalized Funk–Radon transform on the sphere. In this article, we give a singular value decomposition of this generalized Funk–Radon transform. We use this result to derive a singular value decomposition of the cone-beam transform with sources on the sphere thus generalizing a result of Kazantsev (2015 J. Inverse Ill-Posed Problems 23 173–85). (paper)
[en] Highlights: • Anionic polyacrylamide-assisted hydrothermal route was used as novel surface inhibitor to produce carbon spheres. • Monodispersed and uniform carbonaceous spheres with high starting glucose concentration were obtained. • Surface modification with alkaline can enhance the adsorptive capability of spheres.