Explicit birational geometry of 3-folds of general type, I

Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12}(V):=\text{dim} H^0(V, 12K_V)>0$ and $P_{m_0}(V)>1$ for some positive integer $m_0\leq 24$. A direct consequence is the birationality of the pluricanonical map $\varphi_m$ for all $m\geq 126$. Besides, the canonical volume $\text{Vol}(V)$ has a universal lower bound $\nu(3)\geq \frac{1}{63\cdot 126^2}$.Comment: 29 pages, Ann Sci Ecole Norm Sup (to appear

Phonological similarity effects in Cantonese word recognition

Two lexical decision experiments in Cantonese are described in which the recognition of spoken target words as a function of phonological similarity to a preceding prime is investigated. Phonological similaritv in first syllables produced inhibition, while similarity in second syllables led to facilitation. Differences between syllables in tonal and segmental structure had generally similar effects

Anti-ferrodistortive Nanodomains in PMN Relaxor

Temperature dependent studies of the 1/2(hk0) superlattice reflections \alpha spots by synchrotron x-ray scattering measurements were performed in (PMN) and (PMN-xPT) with Ti doping x<0.32 single crystals. Separation of the \alpha spots from the underlying diffuse scattering background allowed studying them as separate entities for the first time. Structure factor calculations have shown that alpha spots constitute the presence of a new kind of anti-ferrodistortive nanoregions (AFR) in the form of fluctuations produced by anti-parallel short-range correlated Pb^2+ displacements. AFR appear to be different and unrelated to the chemical nanodomains (CND) and ferroelectric polar nanoregions (PNR). Simultaneous presence of AFR and PNR can explain relaxor behavior as a result of competition between randomly occurring ferroelectric and anti-ferroelectric fluctuations. Temperature dependence of the \alpha spots in PMN showed a direct correlation with the freezing phase transition near Tf~220 K.Comment: 10 pages, 7 figures, Conference-Fundamental Physics of Ferroelectrics 200

Evolutionary Analysis of Gaseous Sub-Neptune-Mass Planets with MESA

Sub-Neptune-sized exoplanets represent one of the most common types of planets in the Milky Way, yet many of their properties are unknown. Here, we present a prescription to adapt the capabilities of the stellar evolution toolkit Modules for Experiments in Stellar Astrophysics (MESA) to model sub-Neptune mass planets with H/He envelopes. With the addition of routines treating the planet core luminosity, heavy element enrichment, atmospheric boundary condition, and mass loss due to hydrodynamic winds, the evolutionary pathways of planets with diverse starting conditions are more accurately constrained. Using these dynamical models, we construct mass-composition relationships of planets from 1 to 400 $M_{\oplus}$ and investigate how mass-loss impacts their composition and evolution history. We demonstrate that planet radii are typically insensitive to the evolution pathway that brought the planet to its instantaneous mass, composition and age, with variations from hysteresis. We find that planet envelope mass loss timescales, $\tau_{\rm env}$, vary non-monotonically with H/He envelope mass fractions (at fixed planet mass). In our simulations of young (100~Myr) low-mass ($M_p\lesssim10~M_\oplus$) planets with rocky cores, $\tau_{\rm env}$ is maximized at $M_{\rm env}/M_p=1\%$ to $3\%$. The resulting convergent mass loss evolution could potentially imprint itself on the close-in planet population as a preferred H/He mass fraction of ${\sim}1\%$. Looking ahead, we anticipate that this numerical code will see widespread applications complementing both 3-D models and observational exoplanet surveys.Comment: 18 pages, 9 figures, and 4 tables. Accepted to the Astrophysical Journal on August 29th, 201

Frustrated double ionization in two-electron triatomic molecules

Using a semi-classical model, we investigate frustrated double ionization (FDI) in $\mathrm{D_3^+}$, a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We compute the kinetic energy release of the nuclei and find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a feature that can potentially be observed experimentally and is a signature of only one of the two pathways of FDI.Comment: 5 pages, 4 figure