Determination of time dependent factors of coefficients in fractional diffusion equations

We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in a bounded domain

Universal Phase Diagram for High-Piezoelectric Perovskite Systems

Strong piezoelectricity in the perovskite-type PbZr(1-x)TixO3 (PZT) and Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) systems is generally associated with the existence of a morphotropic phase boundary (MPB) separating regions with rhombohedral and tetragonal symmetry. An x-ray study of PZN-9%PT has revealed the presence of a new orthorhombic phase at the MPB, and a near-vertical boundary between the rhombohedral and orthorhombic phases, similar to that found for PZT between the rhombohedral and monoclinic phases. We discuss the results in the light of a recent theoretical paper by Vanderbilt and Cohen, which attributes these low-symmetry phases to the high anharmonicity in these oxide systems.Comment: REVTeX file. 4 pages,=A0 4 figures embedde

Phase transition in Pr0.5Ca0.5CoO3 and related cobaltites

We present an extensive investigation (magnetic, electric and thermal measurements and X-ray absorption spectroscopy) of the Pr0.5Ca0.5CoO3 and (Pr1-yYy)0.7Ca0.3CoO3 (y=0.0625-0.15) perovskites, in which a peculiar metal-insulator (M-I) transition, accompanied with pronounced structural and magnetic anomalies, occurs at 76 K and 40-132 K, respectively. The inspection of the M-I transition using the XANES data of Pr L3-edge and Co K-edge proofs the presence of Pr4+ ions at low temperatures and indicates simultaneously the intermediate spin to low spin crossover of Co species on lowering the temperature. The study thus definitively confirms the synchronicity of the electron transfer between Pr3+ ions and Co^(3+/4+)O3 subsystem and the transition to the low-spin, less electrically conducting phase. The large extent of the transfer is evidenced by the good quantitative agreement of the determined amount of the Pr4+ species, obtained either from the temperature dependence of the XANES spectra or via integration of the magnetic entropy change over the Pr4+ related Schottky peak in the low-temperature specific heat. These results show that the average valence of Pr3+/Pr4+ ions increases (in concomitance with the decrease of the formal Co valence) below TMI for (Pr0.925Y0.075)0.7Ca0.3CoO3 up to 3.16+ (the doping level of the CoO3 subsystem decreases from 3.30+ to 3.20+), for (Pr0.85Y0.15)0.7Ca0.3CoO3 up to 3.28+ (the decrease of doping level from 3.30+ to 3.13+) and for Pr0.5Ca0.5CoO3 up to 3.46+ (the decrease of doping level from 3.50+ to 3.27+).Comment: 19 pages, 11 figure

The ground state properties of the mixed-valence cobaltites Nd0.7_{0.7}Sr0.3_{0.3}CoO3_3, Nd0.7_{0.7}Ca0.3_{0.3}CoO3_3 and Pr0.7_{0.7}Ca0.3_{0.3}CoO3_3

The electric, magnetic, and thermal properties of three perovskite cobaltites with the same 30% hole doping and ferromagnetic ground state were investigated down to very low temperatures. With decreasing size of large cations, the ferromagnetic Curie temperature and spontaneous moments of cobalt are gradually suppressed - $T_C=130$ K, 55 K and 25 K and $m = 0.68 \mu_B$, 0.34 $\mu_B$ and 0.23 $\mu_B$ for Nd$_{0.7}$Sr$_{0.3}$CoO$_3$, Pr$_{0.7}$Ca$_{0.3}$CoO$_3$ and Nd$_{0.7}$Ca$_{0.3}$CoO$_3$, respectively. The moment reduction with respect to moment of the conventional ferromagnet La$_{0.7}$Sr$_{0.3}$CoO$_3$ ($T_C=230$ K, $m = 1.71 \mu_B$) in so-called IS/LS state for Co$^{3+}$/Co$^{4+}$, was originally interpreted using phase-separation scenario. Based on the present results, mainly the analysis of Schottky peak originating in Zeeman splitting of the ground state Kramers doublet of Nd$^{3+}$, we find, however, that ferromagnetic phase in Nd$_{0.7}$Ca$_{0.3}$CoO$_3$ and likely also Pr$_{0.7}$Ca$_{0.3}$CoO$_3$ is uniformly distributed over all sample volume, despite the severe drop of moments. The ground state of these compounds is identified with the LS/LS-related phase derived theoretically by Sboychakov \textit{et al.} [Phys. Rev. B \textbf{80}, 024423 (2009)]. The ground state of Nd$_{0.7}$Sr$_{0.3}$CoO$_3$ with an intermediate cobalt moment is inhomogeneous due to competing of LS/LS and IS/LS phases. In the theoretical part of the study, the crystal field split levels for $4f^3$ (Nd$^{3+}$), $4f^2$ (Pr$^{3+}$) and $4f^1$ (Ce$^{3+}$ or Pr$^{4+}$) are calculated and their magnetic characteristics are presented.Comment: 32 pages, 11 figure

Physical Properties, Star Formation, and Active Galactic Nucleus Activity in Balmer Break Galaxies at 0 < z < 1

We present a spectroscopic study with the derivation of the physical properties of 37 Balmer break galaxies, which have the necessary lines to locate them in star-forming-AGN diagnostic diagrams. These galaxies span a redshift range from 0.045 to 0.93 and are somewhat less massive than similar samples of previous works. The studied sample has multiwavelength photometric data coverage from the ultraviolet to MIR Spitzer bands. We investigate the connection between star formation and AGN activity via optical, mass-excitation (MEx) and MIR diagnostic diagrams. Through optical diagrams, 31 (84%) star-forming galaxies, 2 (5%) composite galaxies and 3 (8%) AGNs were classified, whereas from the MEx diagram only one galaxy was classified as AGN. A total of 19 galaxies have photometry available in all the IRAC/Spitzer bands. Of these, 3 AGN candidates were not classified as AGN in the optical diagrams, suggesting they are dusty/obscured AGNs, or that nuclear star formation has diluted their contributions. Furthermore, the relationship between SFR surface density (\Sigma_{SFR}) and stellar mass surface density per time unit (\Sigma_{M_{\ast}/\tau}) as a function of redshift was investigated using the [OII] \lambda3727, 3729, H\alpha \lambda6563 luminosities, which revealed that both quantities are larger for higher redshift galaxies. We also studied the SFR and SSFR versus stellar mass and color relations, with the more massive galaxies having higher SFR values but lower SSFR values than less massive galaxies. These results are consistent with previous ones showing that, at a given mass, high-redshift galaxies have on average larger SFR and SSFR values than low-redshift galaxies. Finally, bluer galaxies have larger SSFR values than redder galaxies and for a given color the SSFR is larger for higher redshift galaxies.Comment: preprint version, 36 pages, 17 figures, 3 tables, accepted for publication in the Astrophysical Journa

Simultaneous valence shift of Pr and Tb ions at the spin-state transition in ((Pr1−y_{1-y}Tby)0.7_{y})_{0.7}Ca0.3_{0.3}CoO3_{3}

Temperature dependence of the X-ray absorption near-edge structure (XANES) spectra at the Pr $L_{3}$- and Tb $L_{3}$-edges was measured for the (Pr$_{1-y}$Tb$_{y})_{0.7}$Ca$_{0.3}$CoO$_{3}$ system, in which a metal-insulator (MI) and spin-state (SS) transition took place simultaneously at a critical temperature $T_{\rm MI}$. A small increase in the valence of the terbium ion was found below $T_{\rm MI}$, besides the enhancement of the praseodymium valence; the trivalent states, which are stable at room temperature, change to a 3+/4+ ionic mixture at low temperatures. In particular for the $y$=0.2 sample, the average valence determined at 8 K amounts to 3.03+ and 3.25+ for the Tb and Pr ion, respectively. In analogous (Pr$_{1-y}$RE$_{y})_{0.7}$Ca$_{0.3}$CoO$_{3}$ samples (RE=Sm and Eu), in which the MI-SS transition also took place, no valence shift of the RE ion was detected in the XANES spectra at the RE ion $L_{3}$-edge. The role of the substituted RE ion for the Pr-site on the MI-SS transition is discussed

A new concept of a hybrid trapped field magnet lens

In this paper, a new concept of a hybrid trapped field magnet lens (HTFML) is proposed. The HTMFL exploits the “vortex pinning effect” of an outer superconducting bulk cylinder, which is magnetized as a trapped field magnet (TFM) using field-cooled magnetization (FCM), and the “diamagnetic shielding effect” of an inner bulk magnetic lens to generate a concentrated magnetic field higher than the trapped field from the TFM in the bore of the magnetic lens. This requires that, during the FCM process, the outer cylinder is in the normal state (T > superconducting transition temperature, Tc) and the inner lens is in the superconducting state (T < Tc) when the external magnetizing field is applied, followed by cooling to an appropriate operating temperature, then removing the external field. This is explored for two potential cases: 1) exploiting the difference in Tc of two different bulk materials (“case-1”), e.g. MgB2 (Tc = 39 K) and GdBaCuO (Tc = 92 K) or 2) using the same material for the whole HTFML, e.g., GdBaCuO, but utilizing individually-controlled cryostats, the same cryostat with different cooling loops or coolants, or heaters that keep the outer bulk cylinder at a temperature above Tc to achieve the same desired effect. The HTFML is verified using numerical simulations for “case-1” using an MgB2 cylinder and GdBaCuO lens pair and for “case-2” using a GdBaCuO cylinder and GdBaCuO lens pair. As a result, the HTFML could reliably generate a concentrated magnetic field Bc = 4.73 T with the external magnetizing field Bapp = 3 T in the “case-1, and a higher Bc = 13.49 T with higher Bapp = 10 T in the “case-2,” respectively. This could, for example, be used to enhance the magnetic field in the bore of a bulk superconducting NMR/MRI system to improve its resolution