Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

A Global Photoionization Response to Prompt Emission and Outliers: Different Origin of Long Gamma-ray Bursts?

By using the line ratio \ion{C}{4}$\lambda1549$/\ion{C}{2}$\lambda1335$ as a tracer of ionization ratio of the interstellar medium (ISM) illuminated by a long gamma-ray burst (LGRB), we identify a global photoionization response of the ionization ratio to the photon luminosity of the prompt emission assessed by either $L_{\mathrm{iso}}/E_{\mathrm{peak}}$ or $L_{\mathrm{iso}}/E^2_{\mathrm{peak}}$. The ionization ratio increases with both $L_{\mathrm{iso}}/E_{\mathrm{peak}}$ and $L_{\mathrm{iso}}/E^2_{\mathrm{peak}}$ for a majority of the LGRBs in our sample, although there are a few outliers. The identified dependence of \ion{C}{4}/\ion{C}{2} on $L_{\mathrm{iso}}/E^2_{\mathrm{peak}}$ suggests that the scatter of the widely accepted Amati relation is related with the ionization ratio in ISM. The outliers tend to have relatively high \ion{C}{4}/\ion{C}{2} values as well as relatively high \ion{C}{4}$\lambda1549$/\ion{Si}{4}$\lambda1403$ ratios, which suggests an existence of Wolf-Rayet stars in the environment of these LGRBs. We finally argue that the outliers and the LGRBs following the identified \ion{C}{4}/\ion{C}{2}$-L_{\mathrm{iso}}/E_{\mathrm{peak}}$ ($L_{\mathrm{iso}}/E^2_{\mathrm{peak}}$) correlation might come from different progenitors with different local environments.Comment: 7 pages, 3 figures and 2 tables, to be published in Ap

The fractional quantum Hall effect in infinite layer systems

Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases host ``one and a half'' dimensional surface phases in which motion in one direction is chiral. We offer a general analysis of conduction in the latter by combining sum rule and renormalization group arguments, and find that when interlayer tunneling is marginal or irrelevant they are chiral semi-metals that conduct only at T > 0 or with disorder.Comment: RevTeX 3.0, 4p., 2 figs with epsf; reference to the detailed companion paper cond-mat/0006506 adde

Single transverse-spin asymmetry in Drell-Yan lepton angular distribution

We calculate a single transverse-spin asymmetry for the Drell-Yan lepton-pair's angular distribution in perturbative QCD. At leading order in the strong coupling constant, the asymmetry is expressed in terms of a twist-3 quark-gluon correlation function T_F^{(V)}(x_1,x_2). In our calculation, the same result was obtained in both light-cone and covariant gauge in QCD, while keeping explicit electromagnetic current conservation for the virtual photon that decays into the lepton pair. We also present a numerical estimate of the asymmetry and compare the result to an existing other prediction.Comment: 15 pages, Revtex, 5 Postscript figures, uses aps.sty, epsfig.st

Phenomenology of single spin asymmetries in p(transv. polarized)-p -> pion + X

A phenomenological description of single transverse spin effects in hadron-hadron inclusive processes is proposed, assuming a generalized factorization scheme and pQCD hard interactions. The transverse momentum, k_T, of the quarks inside the hadrons and of the hadrons relatively to the fragmenting quark, is taken into account in distribution and fragmentation functions, and leads to possible non zero single spin asymmetries. The role of k_T and spin dependent quark fragmentations -- the so-called Collins effect -- is investigated in details in p(transv. polarized)-p -> pion + X processes: it is shown how the experimental data could be described, obtaining an explicit expression for the spin asymmetry of a polarized fragmenting quark, on which some comments are made. Predictions for other processes, possible further applications and experimental tests are discussed.Comment: 20+1 pages, LaTeX, 6 eps figures, uses epsfig.sty. Version v2: Some sentences rephrased and comments added throughout the paper; one reference added; no changes in results and figures. Final version to be published in Phys. Rev.

Two-hadron interference fragmentation functions. Part I: general framework

We investigate the properties of interference fragmentation functions measurable from the distribution of two hadrons produced in the same jet in the current fragmentation region of a hard process. We discuss the azimuthal angular dependences in the leading order cross section of two-hadron inclusive lepton-nucleon scattering as an example how these interference fragmentation functions can be addressed separately.Comment: RevTeX, 7 figures, first part of a work split in two, second part forthcoming in few day

High-temperature electrical and thermal transport properties of fully filled skutterudites RFe_(4)Sb_(12) (R = Ca, Sr, Ba, La, Ce, Pr, Nd, Eu, and Yb)

Fully filled skutterudites RFe_(4)Sb_(12) (R = Ca, Sr, Ba, La, Ce, Pr, Nd, Eu, and Yb) have been prepared and the high-temperature electrical and thermal transport properties are investigated systematically. Lattice constants of RFe_(4)Sb_(12) increase almost linearly with increasing the ionic radii of the fillers, while the lattice expansion in filled structure is weakly influenced by the filler valence charge states. Using simple charge counting, the hole concentration in RFe_(4)Sb_(12) with divalent fillers (R = Ca, Sr, Ba, Eu, and Yb) is much higher than that in RFe4Sb12 with trivalent fillers (R = La, Ce, Pr, and Nd), resulting in relatively high electrical conductivity and low Seebeck coefficient. It is also found that RFe_(4)Sb_(12) filled skutterudites having similar filler valence charge states exhibit comparable electrical conductivity and Seebeck coefficient, and the behavior of the temperature dependence, thereby leading to comparable power factor values in the temperature range from 300 to 800 K. All RFe_(4)Sb_(12) samples possess low lattice thermal conductivity. The correlation between the lattice thermal resistivity WL and ionic radii of the fillers is discussed and a good relationship of W_L ~ (r_(cage)−r_(ion))^3 is observed in lanthanide metal filled skutterudites. CeFe_(4)Sb_(12), PrFe_(4)Sb_(12), and NdFe_(4)Sb_(12) show the highest thermoelectric figure of merit around 0.87 at 750 K among all the filled skutterudites studied in this work

Broad-lined type Ic supernova iPTF16asu: A challenge to all popular models

It is well-known that ordinary supernovae (SNe) are powered by 56Ni cascade decay. Broad-lined type Ic SNe (SNe Ic-BL) are a subclass of SNe that are not all exclusively powered by 56Ni decay. It was suggested that some SNe Ic-BL are powered by magnetar spin-down. iPTF16asu is a peculiar broad-lined type Ic supernova discovered by the intermediate Palomar Transient Factory. With a rest-frame rise time of only 4 days, iPTF16asu challenges the existing popular models, for example, the radioactive heating (56Ni-only) and the magnetar+56Ni models. Here we show that this rapid rise could be attributed to interaction between the SN ejecta and a pre-existing circumstellar medium ejected by the progenitor during its final stages of evolution, while the late-time light curve can be better explained by energy input from a rapidly spinning magnetar. This model is a natural extension to the previous magnetar model. The mass-loss rate of the progenitor and ejecta mass are consistent with a progenitor that experienced a common envelope evolution in a binary. An alternative model for the early rapid rise of the light curve is the cooling of a shock propagating into an extended envelope of the progenitor. It is difficult at this stage to tell which model (interaction+magnetar+56Ni or cooling+magnetar+56Ni) is better for iPTF16asu. However, it is worth noting that the inferred envelope mass in the cooling+magnetar+56Ni is very high.Comment: 11 pages, 4 figures, 3 table