New Results for Diffusion in Lorentz Lattice Gas Cellular Automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported, of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the super diffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits with {\em universal} exponents ${\displaystyle{d_f = \frac{7}{4}}}$ and ${\displaystyle{\tau = \frac{15}{7}}}$. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem, and of the dynamical significance of hyperscaling.Comment: 52 pages, including 18 figures on the last 22 pages, email: [email protected]

Squamous Cell Carcinoma in a Heel Ulcer in a Patient With Diabetes

A technique for measuring B-H curves of grain-oriented silicon steel along arbitrary directions has been developed. As the control of waveform is not necessary in this technique, it is possible to measure B-H curves up to high flux densities which are required for calculating flux distribution using the finite element method</p

Anisotropy Reversal of the Upper Critical Field at Low Temperatures and Spin-Locked Superconductivity in K2Cr3As3

We report the first measurements of the anisotropic upper critical field $H_{c2}(T)$ for K$_{2}$Cr$_{3}$As$_{3}$ single crystals up to 60 T and $T > 0.6$ K. Our results show that the upper critical field parallel to the Cr chains, $H_{c2}^\parallel (T)$, exhibits a paramagnetically-limited behavior, whereas the shape of the $H_{c2}^\perp (T)$ curve (perpendicular to the Cr chains) has no evidence of paramagnetic effects. As a result, the curves $H_{c2}^\perp (T)$ and $H_{c2}^\parallel(T)$ cross at $T\approx 4$ K, so that the anisotropy parameter $\gamma_H(T)=H_{c2}^\perp/H_{c2}^\parallel (T)$ increases from $\gamma_H(T_c)\approx 0.35$ near $T_c$ to $\gamma_H(0)\approx 1.7$ at 0.6 K. This behavior of $H_{c2}^\|(T)$ is inconsistent with triplet superconductivity but suggests a form of singlet superconductivity with the electron spins locked onto the direction of Cr chains

Discovery of Radio/X-ray/Optical Resolved Supernova Remnants in the Center of the Andromeda Galaxy

We have detected a spatially resolved supernova remnant (SNR) in the center of the Andromeda Galaxy, in radio, X-ray, and optical wavelengths. These observations provide the highest spatial resolution imaging of a radio/X-ray/optical SNR in that galaxy to date. The multi-wavelength morphology, radio spectral index, X-ray colors, and narrow-band optical imaging are consistent with a shell-type SNR. A second SNR is also seen resolved in both radio and X-ray. By comparing the morphological sturcture of the SNRs in different wavelengths and with that in our own Galaxy, we can study the shock morphologies of SNRs in the Andromeda Galaxy. The proximity of the SNRs to the core suggests high interstellar medium density in the vicinity of the SNRs in the center of the Andromeda Galaxy.Comment: 5 pages, 3 figures, accepted for publication in ApJ

The Discovery of a Spatially-Resolved Supernova Remnant in M31 with Chandra

Chandra observations of M31 allow the first spatially resolved X-ray image of a supernova remnant (SNR) in an external spiral galaxy. CXOM31 J004327.7+411829 is a slightly elongated ring-shaped object with a diameter of ~11'' (42 pc). In addition, the X-ray image hints that the chemical composition of the SNR is spatial dependent. The X-ray spectrum of the SNR can be well fitted with a Raymond-Smith model or a non-equilibrium ionization model. Depending on the spectral model, the 0.3-7 keV luminosity is between 3.2x10^36 erg/s and 4.5x10^37 erg/s. The age of the SNR is estimated to be 3210-22300 years and the number density of ambient gas is ~0.003-0.3 cm^-3. This suggests that the local interstellar medium around the SNR is low.Comment: 5 pages, 3 figures; accepted for publication in ApJ