Newly Determined Explosion Center of Tycho's Supernova and the Implications for Proposed Ex-Companion Stars of the Progenitor

`Star G', near the center of the supernova remnant of Tycho's SN1572, has been claimed to be the ex-companion star of the exploding white dwarf, thus pointing to the progenitor being like a recurrent nova. This claim has been controversial, but there have been no confident proofs or disproofs. Previously, no has seriously addressed the question as to the exact explosion site in 1572. We now provide accurate measures of the supernova position by two radically different methods. Our first method is to use the 42 measured angular distances between the supernova in 1572 and bright nearby stars, with individual measures being as good as 84 arc-seconds, and all resulting in a position with a 1-$\sigma$ error radius of 39 arc-seconds (including systematic uncertainties). Our second method is to use a detailed and realistic expansion model for 19 positions around the edge of the remnant, where the swept-up material has measured densities, and we determine the center of expansion with a chi-square fit to the 19 measured radii and velocities. This method has a 1-$\sigma$ error radius of 7.5 arc-seconds. Both measures are substantially offset from the geometric center, and both agree closely, proving that neither has any significant systematic errors. Our final combined position for the site of the 1572 explosion is J2000 $\alpha$=0h 25m 15.36s, $\delta=64^{\circ} 8' 40.2"$, with a 7.3 arc-second 1-sigma uncertainty. Star G is rejected at the 8.2-$\sigma$ confidence level. Our new position lies mostly outside the region previously searched for ex-companion stars.Comment: to be published in Ap

The (11112) model on a 1+1 dimensional lattice

We study the chiral gauge model (11112) of four left-movers and one right-mover with strong interactions in the 1+1 dimensional lattice. Exact computations of relevant $S$-matrix elements demonstrate a loophole that so constructed model and its dynamics can possibly evade the ``no-go'' theorem of Nielsen and Ninomiya.Comment: 15 pages, 1 fig. to appear in Phys. Rev.

Environmental governance in China

--

The relationship between amyloid structure and cytotoxicity

Self-assembly of proteins and peptides into amyloid structures has been the subject of intense and focused research due to their association with neurodegenerative, age-related human diseases and transmissible prion diseases in humans and mammals. Of the disease associated amyloid assemblies, a diverse array of species, ranging from small oligomeric assembly intermediates to fibrillar structures, have been shown to have toxic potential. Equally, a range of species formed by the same disease associated amyloid sequences have been found to be relatively benign under comparable monomer equivalent concentrations and conditions. In recent years, an increasing number of functional amyloid systems have also been found. These developments show that not all amyloid structures are generically toxic to cells. Given these observations, it is important to understand why amyloid structures may encode such varied toxic potential despite sharing a common core molecular architecture. Here, we discuss possible links between different aspects of amyloidogenic structures and assembly mechanisms with their varied functional effects. We propose testable hypotheses for the relationship between amyloid structure and its toxic potential in the context of recent reports on amyloid sequence, structure, and toxicity relationships

Power grids vulnerability: a complex network approach

Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.Comment: 16 pages, 3 figures. Figure 2 and table II modified. Typos corrected. Version accepted for publication in Chao

Boundary between the thermal and statistical polarization regimes in a nuclear spin ensemble

As the number of spins in an ensemble is reduced, the statistical uctuations in its polarization eventually exceed the mean thermal polarization. This transition has now been surpassed in a number of recent nuclear magnetic resonance experiments, which achieve nanometer-scale detection volumes. Here, we measure nanometer- scale ensembles of nuclear spins in a KPF6 sample using magnetic resonance force microscopy. In particular, we investigate the transition between regimes dominated by thermal and statistical nuclear polarization. The ratio between the two types of polarization provides a measure of the number of spins in the detected ensemble

Theory for transport through a single magnetic molecule: Endohedral N@C60

We consider transport through a single N@C60 molecule, weakly coupled to metallic leads. Employing a density-matrix formalism we derive rate equations for the occupation probabilities of many-particle states of the molecule. We calculate the current-voltage characteristics and the differential conductance for N@C60 in a break junction. Our results reveal Coulomb-blockade behavior as well as a fine structure of the Coulomb-blockade peaks due to the exchange coupling of the C60 spin to the spin of the encapsulated nitrogen atom.Comment: 5 pages, 4 figures, v2: version as publishe

Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation

In this paper we discuss a new type of 4-dimensional representation of the braid group. The matrices of braid operations are constructed by q-deformation of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m, the other, which we find, is related to the Bogoliubov Hamiltonian for quasiparticles in $^3$He-B with the same free energy and mass being m/2. In the process, we choose the free q-deformation parameter as a special value in order to be consistent with the anyon description for fractional quantum Hall effect with $\nu = 1/2$.Comment: 3 pages, 5 figure