On the SL(2) period integral

Let E/F be a quadratic extension of number fields. For a cuspidal representation $\pi$ of SL(2,A_E), we study the non-vanishing of the period integral on SL(2,F)\SL(2,A_F). We characterise the non-vanishing of the period integral of $\pi$ in terms of $\pi$ being generic with respect to characters of E\A_E which are trivial on A_F. We show that the period integral in general is not a product of local invariant functionals, and find a necessary and sufficient condition when it is. We exhibit cuspidal representations of SL(2,A_E) whose period integral vanishes identically while each local constituent admits an SL(2)-invariant linear functional. Finally, we construct an automorphic representation $\pi$ on SL(2,A_E) which is abstractly SL(2,A_F) distinguished but none of the elements in the global L-packet determined by $\pi$ is distinguished by SL(2,A_F)

A local global question in automorphic forms

In this paper, we consider the \SL(2) analogue of two well-known theorems about period integrals of automorphic forms on \GL(2): one due to Harder-Langlands-Rapoport, and the other due to Waldspurger.Comment: 28 page

Valence Fluctuation in CeMo2Si2C

We report on the valence fluctuation of Ce in CeMo$_{2}$Si$_{2}$C as studied by means of magnetic susceptibility $\chi(T)$, specific heat $C(T)$, electrical resistivity $\rho(T)$ and x-ray absorption spectroscopy. Powder x-ray diffraction revealed that CeMo$_{2}$Si$_{2}$C crystallizes in CeCr$_{2}$Si$_{2}$C-type layered tetragonal crystal structure (space group \textit{P4/mmm}). The unit cell volume of CeMo$_{2}$Si$_{2}$C deviates from the expected lanthanide contraction, indicating non-trivalent state of Ce ions in this compound. The observed weak temperature dependence of the magnetic susceptibility and its low value indicate that Ce ions are in valence fluctuating state. The formal $L_{III}$ Ce valence in CeMo$_{2}$Si$_{2}$C $$ = 3.11 as determined from x-ray absorption spectroscopy measurement is well bellow the value $\simeq$ 3.4 in tetravalent Ce compound CeO$_{2}$. The temperature dependence of specific heat does not show any anomaly down to 1.8 K which rules out any magnetic ordering in the system. The Sommerfeld coefficient obtained from the specific heat data is $\gamma$ = 23.4 mJ/mol\,K$^{2}$. The electrical resistivity follows the $T{^2}$ behavior in the low temperature range below 35 K confirming a Fermi liquid behavior. Accordingly both the Kadowaki Wood ratio $A/\gamma^{2}$ and the Sommerfeld Wilson ratio $\chi(0)/\gamma$ are in the range expected for Fermi-liquid systems. In order to get some information on the electronic states, we calculated the band structure within the density functional theory, eventhough this approach is not able to treat 4f electrons accurately. The non-$f$ electron states crossing the Fermi level have mostly Mo 4d character. They provide the states with which the 4f sates are strongly hybridized, leading to the intermediate valent state.Comment: 18 pages, 10 figures Submitted to Journal of Alloys and Compound

PARS: Programs for Analysis and Resizing of Structures, user manual

PARS processors and their use, flutter analysis, sensitivity analysis for stresses, and resizing are presented. Design variable definition and interface with finite element model, static constraints and their derivatives, flutter derivatives, and optimization are discussed

Itinerant and local-moment magnetism in EuCr2As2 single crystals

We report on the crystal structure, physical properties, and electronic structure calculations for the ternary pnictide compound EuCr2As2. X-ray diffraction studies confirmed that EuCr2As2 crystalizes in the ThCr2Si2-type tetragonal structure (space group I4/mmm). The Eu ions are in a stable divalent state in this compound. Eu moments in EuCr2As2 order magnetically below Tm = 21 K. A sharp increase in the magnetic susceptibility below Tm and the positive value of the paramagnetic Curie temperature obtained from the Curie-Weiss fit suggest dominant ferromagnetic interactions. The heat capacity exhibits a sharp {\lambda}-shape anomaly at Tm, confirming the bulk nature of the magnetic transition. The extracted magnetic entropy at the magnetic transition temperature is consistent with the theoretical value Rln(2S+1) for S = 7/2 of the Eu2+ ion. The temperature dependence of the electrical resistivity \r{ho}(T) shows metallic behavior along with an anomaly at 21 K. In addition, we observe a reasonably large negative magneto-resistance (~ -24%) at lower temperature. Electronic structure calculations for EuCr2As2 reveal a moderately high density of states of Cr-3d orbitals at the Fermi energy, indicating that the nonmagnetic state of Cr is unstable against magnetic order. Our density functional calculations for EuCr2As2 predict a G-type AFM order in the Cr sublattice. The electronic structure calculations suggest a weak interlayer coupling of the Eu moments.Comment: 9 pages, 7 figure

The use of remote sensing data for drought assessment and monitoring in southwest Asia

Drought / Monitoring / Indicators / Assessment / Remote sensing / Asia

Distinguished representations for SL(2)

Let E/F be a quadratic extension of p-adic fields. We compute the multiplicity of the space of SL2(F)-invariant linear forms on a representation of SL2(E). This multiplicity varies inside an L-packet similar in spirit to the multiplicity formula for automorphic representations due to Labesse and Langlands

Valence fuctuation and magnetic ordering in EuNi2(P1-xGex)2 single crystals

Unusual phases and phase transitions are seen at the magnetic-nonmagnetic boundary in Ce, Eu and Yb-based compounds. EuNi$_2$P$_{2}$ is a very unusual valence fluctuating Eu system, because at low temperatures the Eu valence stays close to 2.5 instead of approaching an integer value. Eu valence and thus the magnetic property in this system can be tuned by Ge substitution in P site as EuNi$_2$Ge$_{2}$ is known to exhibit antiferromagnetc (AFM) ordering of divalent Eu moments with $T_N$ = 30 K. We have grown EuNi$_2$(P$_{1-x}$Ge$_x$)$_2$ (0.0 $\leq$ $x$ $\leq$ 0.5) single crystals and studied their magnetic, thermodynamic and transport properties. Increasing Ge doping to $x >$ 0.4 results in a well-defined AFM ordered state with $T_N$ = 12 K for $x$ = 0.5. Moreover, the reduced value of magnetic entropy for $x$ = 0.5 at $T_N$ suggests the presence of valance fluctuation/ Kondo effect in this compound. Interestingly, the specific heat exhibits an enhanced Sommerfeld coefficient upon Ge doping. Subsequently, electronic structure calculations lead to a non-integral valence in EuNi$_2$P$_{2}$ but a stable divalent Eu state in EuNi$_2$Ge$_{2}$ which is in good agreement with experimental results.Comment: 7 pages, 8 figure

Droplet size distribution in homogeneous isotropic turbulence

We study the physics of droplet breakup in a statistically stationary homogeneous and isotropic turbulent flow by means of high resolution numerical investigations based on the multicomponent lattice Boltzmann method. We verified the validity of the criterion proposed by Hinze (1955) for droplet breakup and we measured the full probability distribution function (pdf) of droplets radii at different Reynolds numbers and for different volume fraction. By means of a Lagrangian tracking we could follow individual droplets along their trajectories, define a local Weber number based on the velocity gradients and study its cross-correlation with droplet deformation.Comment: 10 pages, 6 figure