Loop-Erasure of Plane Brownian Motion

We use the coupling technique to prove that there exists a loop-erasure of a plane Brownian motion stopped on exiting a simply connected domain, and the loop-erased curve is the reversal of a radial SLE$_2$ curve.Comment: 10 page

Automated approaches for band gap mapping in STEM-EELS

Band gap variations in thin film structures, across grain boundaries, and in embedded nanoparticles are of increasing interest in the materials science community. As many common experimental techniques for measuring band gaps do not have the spatial resolution needed to observe these variations directly, probe-corrected Scanning Transmission Electron Microscope (STEM) with monochromated Electron Energy-Loss Spectroscopy (EELS) is a promising method for studying band gaps of such features. However, extraction of band gaps from EELS data sets usually requires heavy user involvement, and makes the analysis of large data sets challenging. Here we develop and present methods for automated extraction of band gap maps from large STEM-EELS data sets with high spatial resolution while preserving high accuracy and precision

Nucleosynthesis in the terrestrial and solar atmospheres

Variations of Delta D, delta C-13, Delta C-14 and Delta O-18 with time were measured by a lot of experiments. Many abnormalities of isotope abundances in cosmic rays were found by balloons and satellites. It is suggested that these abnormalities are related to nuclearsynthesis in the terrestrial and solar atmospheres and are closely related to solar activities

Restriction Properties of Annulus SLE

For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a restriction property, which is similar to that for chordal SLE$(\kappa)$. Using this property, we construct $n\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\kappa)$ trace.Comment: 37 page

A very important process of nucleosynthesis in stars

When some nuclei are free from strong gravitational field, they are unstable and will become stable nuclei by competitions of following processes: (1) neutron-evaporation; (2) spontaneous fission; and (3) beta prime 3-decay. At the initial stage, (1) and (2) are important and (3) can be ignored. The qualitative results are as follows: (1) it seems that nuclei with A 100 come from the spontaneous fission and beta prime decay of neutron-evaporated nuclei with A similiar to 140-440, which can replace the r-process; (2) the super-heavy elements with Z=114--126 (A similiar to 330--360) can be formed. They can be observed in cosmic rage if they have the halftime T 10 to the 7th poweer years; (3) the peak in the rare-earth elements comes from the symmetric fission of super-heavy elements; (4) there are more neutron-rich nuclei in the fragments; and (5) the abundances of a 83 elements in cosmic rays are one order of magnitude higher than that in the solar system

Perfect State Transfer in Laplacian Quantum Walk

For a graph $G$ and a related symmetric matrix $M$, the continuous-time quantum walk on $G$ relative to $M$ is defined as the unitary matrix $U(t) = \exp(-itM)$, where $t$ varies over the reals. Perfect state transfer occurs between vertices $u$ and $v$ at time $\tau$ if the $(u,v)$-entry of $U(\tau)$ has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer: (1) If a $n$-vertex graph has perfect state transfer at time $\tau$ relative to the Laplacian, then so does its complement if $n\tau$ is an integer multiple of $2\pi$. As a corollary, the double cone over any $m$-vertex graph has perfect state transfer relative to the Laplacian if and only if $m \equiv 2 \pmod{4}$. This was previously known for a double cone over a clique (S. Bose, A. Casaccino, S. Mancini, S. Severini, Int. J. Quant. Inf., 7:11, 2009). (2) If a graph $G$ has perfect state transfer at time $\tau$ relative to the normalized Laplacian, then so does the weak product $G \times H$ if for any normalized Laplacian eigenvalues $\lambda$ of $G$ and $\mu$ of $H$, we have $\mu(\lambda-1)\tau$ is an integer multiple of $2\pi$. As a corollary, a weak product of $P_{3}$ with an even clique or an odd cube has perfect state transfer relative to the normalized Laplacian. It was known earlier that a weak product of a circulant with odd integer eigenvalues and an even cube or a Cartesian power of $P_{3}$ has perfect state transfer relative to the adjacency matrix. As for negative results, no path with four vertices or more has antipodal perfect state transfer relative to the normalized Laplacian. This almost matches the state of affairs under the adjacency matrix (C. Godsil, Discrete Math., 312:1, 2011).Comment: 26 pages, 5 figures, 1 tabl

Quantum ratchet transport with minimal dispersion rate

We analyze the performance of quantum ratchets by considering the dynamics of an initially localized wave packet loaded into a flashing periodic potential. The directed center-of-mass motion can be initiated by the uniform modulation of the potential height, provided that the modulation protocol breaks all relevant time- and spatial reflection symmetries. A poor performance of quantum ratchet transport is characterized by a slow net motion and a fast diffusive spreading of the wave packet, while the desirable optimal performance is the contrary. By invoking a quantum analog of the classical P\'eclet number, namely the quotient of the group velocity and the dispersion of the propagating wave packet, we calibrate the transport properties of flashing quantum ratchets and discuss the mechanisms that yield low-dispersive directed transport.Comment: 6 pages; 3 figures; 1 tabl