A Generalization of Mathieu Subspaces to Modules of Associative Algebras

We first propose a generalization of the notion of Mathieu subspaces of associative algebras $\mathcal A$, which was introduced recently in [Z4] and [Z6], to $\mathcal A$-modules $\mathcal M$. The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets $\sigma(N)$ and $\tau(N)$ of stable elements and quasi-stable elements, respectively, for all $R$-subspaces $N$ of $\mathcal A$-modules $\mathcal M$, where $R$ is the base ring of $\mathcal A$. We then prove some general properties of the sets $\sigma(N)$ and $\tau(N)$. Furthermore, examples from certain modules of the quasi-stable algebras [Z6], matrix algebras over fields and polynomial algebras are also studied.Comment: A new case has been added; some mistakes and misprints have been corrected. Latex, 31 page

Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD

At small transverse momentum $q_T$, transverse-momentum dependent parton distribution functions (TMDPDFs) arise as genuinely nonperturbative objects that describe Drell-Yan like processes in hadron collisions as well as semi-inclusive deep-inelastic scattering. TMDPDFs naturally depend on the hadron momentum, and the associated evolution is determined by the Collins-Soper equation. For $q_T \sim \Lambda_\mathrm{QCD}$ the corresponding evolution kernel (or anomalous dimension) is nonperturbative and must be determined as an independent ingredient in order to relate TMDPDFs at different scales. We propose a method to extract this kernel using lattice QCD and the Large-Momentum Effective Theory, where the physical TMD correlation involving light-like paths is approximated by a quasi TMDPDF, defined using equal-time correlation functions with a large-momentum hadron state. The kernel is determined from a ratio of quasi TMDPDFs extracted at different hadron momenta.Comment: 9 pages, 2 figures; v2: extended the review of TMDPDF commonalities, version submitted to PRD; v3: minor changes, journal versio

Many-core compiler fuzzing

We address the compiler correctness problem for many-core systems through novel applications of fuzz testing to OpenCL compilers. Focusing on two methods from prior work, random differential testing and testing via equivalence modulo inputs (EMI), we present several strategies for random generation of deterministic, communicating OpenCL kernels, and an injection mechanism that allows EMI testing to be applied to kernels that otherwise exhibit little or no dynamically-dead code. We use these methods to conduct a large, controlled testing campaign with respect to 21 OpenCL (device, compiler) configurations, covering a range of CPU, GPU, accelerator, FPGA and emulator implementations. Our study provides independent validation of claims in prior work related to the effectiveness of random differential testing and EMI testing, proposes novel methods for lifting these techniques to the many-core setting and reveals a significant number of OpenCL compiler bugs in commercial implementations

Correlation between the cohesive energy and the onset of radiation-enhanced diffusion in ion mixing

A correlation between the cohesive energy of elemental solids and the characteristic temperature Tc for the onset of radiation-enhanced diffusion during ion mixing is established. This correlation enables one to predict the onset of radiation-enhanced diffusion for systems which have not yet been investigated. A theoretical argument based on the current models of cascade mixing and radiation-enhanced diffusion is provided as a basis for understanding this observation

Relations Between Low-lying Quantum Wave Functions and Solutions of the Hamilton-Jacobi Equation

We discuss a new relation between the low lying Schroedinger wave function of a particle in a one-dimentional potential V and the solution of the corresponding Hamilton-Jacobi equation with -V as its potential. The function V is $\geq 0$, and can have several minina (V=0). We assume the problem to be characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller quantum tunneling parameter $\epsilon$ between these different minima. Expanding either the wave function or its energy as a formal double power series in $g^{-1}$ and $\epsilon$, we show how the coefficients of $g^{-m}\epsilon^n$ in such an expansion can be expressed in terms of definite integrals, with leading order term determined by the classical solution of the Hamilton-Jacobi equation. A detailed analysis is given for the particular example of quartic potential $V={1/2}g^2(x^2-a^2)^2$.Comment: LaTex, 48 pages, no figur

Radio Variability of Sagittarius A* - A 106 Day Cycle

We report the presence of a 106-day cycle in the radio variability of Sgr A* based on an analysis of data observed with the Very Large Array (VLA) over the past 20 years. The pulsed signal is most clearly seen at 1.3 cm with a ratio of cycle frequency to frequency width f/Delta_f= 2.2+/-0.3. The periodic signal is also clearly observed at 2 cm. At 3.6 cm the detection of a periodic signal is marginal. No significant periodicity is detected at both 6 and 20 cm. Since the sampling function is irregular we performed a number of tests to insure that the observed periodicity is not the result of noise. Similar results were found for a maximum entropy method and periodogram with CLEAN method. The probability of false detection for several different noise distributions is less than 5% based on Monte Carlo tests. The radio properties of the pulsed component at 1.3 cm are spectral index alpha ~ 1.0+/- 0.1 (for S nu^alpha), amplitude Delta S=0.42 +/- 0.04 Jy and characteristic time scale Delta t_FWHM ~ 25 +/- 5 days. The lack of VLBI detection of a secondary component suggests that the variability occurs within Sgr A* on a scale of ~5 AU, suggesting an instability of the accretion disk.Comment: 14 Pages, 3 figures. ApJ Lett 2000 accepte

Mapping the Dirac point in gated bilayer graphene

We have performed low temperature scanning tunneling spectroscopy measurements on exfoliated bilayer graphene on SiO2. By varying the back gate voltage we observed a linear shift of the Dirac point and an opening of a band gap due to the perpendicular electric field. In addition to observing a shift in the Dirac point, we also measured its spatial dependence using spatially resolved scanning tunneling spectroscopy. The spatial variation of the Dirac point was not correlated with topographic features and therefore we attribute its shift to random charged impurities.Comment: 3 pages, 3 figure

The Friedberg-Lee model at finite temperature and density

The Friedberg-Lee model is studied at finite temperature and density. By using the finite temperature field theory, the effective potential of the Friedberg-Lee model and the bag constant $B(T)$ and $B(T,\mu)$ have been calculated at different temperatures and densities. It is shown that there is a critical temperature $T_{C}\simeq 106.6 \mathrm{MeV}$ when $\mu=0 \mathrm{MeV}$ and a critical chemical potential $\mu \simeq 223.1 \mathrm{MeV}$ for fixing the temperature at $T=50 \mathrm{MeV}$. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when $T\leq T_{C}$ (or $\mu \leq \mu_C$), there is a bag constant $B(T)$ (or $B(T,\mu)$) and the soliton solutions are stable. However, when $T>T_{C}$ (or $\mu>\mu_C$) the bag constant $B(T)=0 \mathrm{MeV}$ (or $B(T,\mu)=0 \mathrm{MeV}$) and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.Comment: 12 pages, 11 figures; version accepted for publication in Phys. Rev.

Optimal trajectories for the aeroassisted flight experiment

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous earth orbit and LEO denotes a low earth orbit. The trajectories of an AFE spacecraft are analyzed in a 3D-space, employing the full system of 6 ordinary differential equations (ODEs) describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted. Two possible transfers are considered: (1) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (2) direct ascent to a 178 NM apogee