Oscillation of a time fractional partial differential equation

We consider a time fractional partial differential equation subject to the Neumann boundary condition. Several sufficient conditions are established for oscillation of solutions of such equation by using the integral averaging method and a generalized Riccati technique. The main results are illustrated by examples

Approaching the Ground State of Frustrated A-site Spinels: A Combined Magnetization and Polarized Neutron Scattering Study

We re-investigate the magnetically frustrated, {\it diamond-lattice-antiferromagnet} spinels FeAl$_2$O$_4$ and MnAl$_2$O$_4$ using magnetization measurements and diffuse scattering of polarized neutrons. In FeAl$_2$O$_4$, macroscopic measurements evidence a "cusp" in zero field-cooled susceptibility around 13~K. Dynamic magnetic susceptibility and {\it memory effect} experiments provide results that do not conform with a canonical spin-glass scenario in this material. Through polarized neutron scattering studies, absence of long-range magnetic order down to 4~K is confirmed in FeAl$_2$O$_4$. By modeling the powder averaged differential magnetic neutron scattering cross-section, we estimate that the spin-spin correlations in this compound extend up to the third nearest-neighbour shell. The estimated value of the Land\'{e} $g$ factor points towards orbital contributions from Fe$^{2+}$. This is also supported by a Curie-Weiss analysis of the magnetic susceptibility. MnAl$_2$O$_4$, on the contrary, undergoes a magnetic phase transition into a long-range ordered state below $\approx$ 40~K, which is confirmed by macroscopic measurements and polarized neutron diffraction. However, the polarized neutron studies reveal the existence of prominent spin-fluctuations co-existing with long-range antiferromagnetic order. The magnetic diffuse intensity suggests a similar short range order as in FeAl$_2$O$_4$. Results of the present work supports the importance of spin-spin correlations in understanding magnetic response of frustrated magnets like $A$-site spinels which have predominant short-range spin correlations reminiscent of the "spin liquid" state.Comment: 10 pages, 10 figures, double-column, accepted in Phys. Rev. B, 201

Solvent Uptake of Liquid Rubber Toughened Epoxy/Clay Nanocomposites

Carboxyl-terminated poly (butadiene-co-acrylonitrile) (CTBN) liquid rubber toughened epoxy (epoxy/CTBN blend) and CTBN-toughened epoxy/clay nanocomposites (epoxy/clay/CTBN nanocomposites) were prepared, and solvent (acetone) uptake was studied as a function of CTBN content. It was found that in both epoxy/CTBN blend and epoxy/clay/CTBN nanocomposites, the diffusion coefficient initially increased with an increase in CTBN content, with a maximum value registered for the systems containing 15 phr of CTBN. With a further increase of CTBN, the diffusion coefficient was found to decrease. The variation of solvent uptake with CTBN content depends on both the amount of dissolved rubber in the epoxy phase and the phase morphology associated with each composition. The high acetone uptake in 15 and 20 phr CTBN-loaded system was found to be reduced dramatically by the incorporation of 3 phr nanoclay. Owing to the presence of high aspect ratio clay platelets, the diffusion of acetone undergoes a more tortuous path in epoxy/clay/CTBN nanocomposites than in epoxy/CTBN blends. A diffusion mechanism correlated to composition for epoxy/CTBN blend and epoxy/clay/CTBN nanocomposites was proposed.Scopu

Associative N2-fixation in pearl millet and sorghum: levels and response to inoculation.

N2-fixation was compared in pearl millet (Pennisetum glaucum), sorghum, pigeonpeas, chickpeas, and groundnuts and the responses of the two cereal crops to inoculation with N2-fixing bacteria was examined. The overall mean nitrogenase activity (C2H2 reduction) in pearl millet throughout the growing period was less than 0.1% of that in pigeonpeas and the activity in sorghum was only 1.3% of that in chickpeas. Whether assessed by the determination of the N balance in pots, using pigeonpeas as reference, or by the measurement of the natural abundance of 15N (δ15N) using groundnuts as reference, N gain by these cereals, even when they were inoculated with N2-fixing bacteria was not observed. Inoculation trials were conducted in pots and in the field with Azospirillum lipoferum and Azotobacter chroococcum. Only one trial with sterilized soil in pots showed a significant response to inoculation. It is concluded that associative N2-fixing systems in pearl millet and sorghum do not exert an agronomically significant impact through N input on the production of these crops

Observation of spin glass state in weakly ferromagnetic Sr2_2FeCoO6_6 double perovskite

We report the observation of spin glass state in the double perovskite oxide Sr$_{2}$FeCoO$_{6}$ prepared through sol-gel technique. Initial structural studies using x rays reveal that the compound crystallizes in tetragonal $I 4/m$ structure with lattice parameters, $a$ = 5.4609(2) \AA and $c$ = 7.7113(7) \AA. The temperature dependent powder x ray studies reveal no structural phase transition in the temperature range 10 -- 300 K. However, the unit cell volume shows an anomaly coinciding with the magnetic transition temperature thereby suggesting a close connection between lattice and magnetism. Neutron diffraction studies and subsequent bond valence sums analysis show that in Sr$_{2}$FeCoO$_{6}$, the $B$ site is randomly occupied by Fe and Co in the mixed valence states of Fe$^{3+}$/Fe$^{4+}$ and Co$^{3+}$/Co$^{4+}$. The random occupancy and mixed valence sets the stage for inhomogeneous magnetic exchange interactions and in turn, for the spin glass like state in this double perovskite which is observed as an irreversibility in temperature dependent dc magnetization at $T_f\sim$ 75 K. Thermal hysteresis observed in the magnetization profile of Sr$_{2}$FeCoO$_{6}$ is indicative of the mixed magnetic phases present. The dynamic magnetic susceptibility displays characteristic frequency dependence and confirms the spin glass nature of this material. Dynamical scaling analysis of $\chi'(T)$ yields a critical temperature $T_{ct}$ = 75.14(8) K and an exponent $z\nu$ = 6.2(2) typical for spin glasses. The signature of presence of mixed magnetic interactions is obtained from the thermal hysteresis in magnetization of Sr$_{2}$FeCoO$_{6}$. Combining the neutron and magnetization results of Sr$_2$FeCoO$_6$, we deduce the spin states of Fe to be in low spin while that of Co to be in low spin and intermediate spin.Comment: 23 pages, 6 figures, accepted in J. Appl. Phy

Optimization and fabrication of customized scaffold using additive manufacturing to match the property of human bone

Additive manufacturing plays a major role in medical science. One of the applications is the development of bone scaffolds. During scaffold fabrication, obtaining the properties of the polyamide scaffolds to mimic the elastic properties of human subchondral bone is a challenging task. In order to overcome this challenge, the present numerical study validated by experimental routine allows optimizing, fabricating and automating the generation of open porous polyamide scaffolds. Human subchondral bone has an elastic modulus of 1.15 GPa and pore size of 800 μm which helps for cell ingrowth. The design parameters such as strut diameter (0.6-3 mm) and unit cell size (1.4-5 mm) were considered for this investigation. The optimized scaffold structure was fabricated using selective laser sintering method, one of the additive manufacturing (AM) processes and the structure was validated through uniaxial compression. Experimental test revealed a deviation in structural modulus of about 14, 10 and 17% for circular, square and hexagonal cross section, respectively. Optimized unit cell dimensions were found. The preliminary MTT (Methyl Thiazolyl diphenyl-Tetrazolium bromide) assay tests to evaluate the distributions of cells were performed, using in vitro perfusion culture experiments. It was found that the scaffold structure with square cross section has the maximum percentage of cell viability of 58.33%. A computer-aided design tool was developed using CATIA V5 Visual Basic program for modelling the bone scaffolds with better interconnectivity of unit blocks, porosity and compressive strength. This program facilitates automatic generation of optimized scaffold structure by providing necessary input parameters. The developed CAD tool was efficient enough to model the customized scaffold