The breakage prediction for hydromechanical deep drawing based on local bifurcation theory

A criterion of sheet metal localized necking under plane stress was established based on the bifurcation theory and the characteristics theory of differential equation. In order to be capable to incorporate the directional dependence of the plastic strain rate on stress rate, Ito-Goya’s constitutive equation which gave a one to one relationship between stress rate component and plastic strain rate component was employed. The hydromechanical deep drawing process of a cylindrical cup part was simulated using the commercial software ABAQUS IMPLICIT. The onset of breakage of the part during the forming process was predicted by combining the simulation results with the local necking criterion. The proposed method is applied to the hydro-mechanical deep drawing process for A2219 aluminum alloy sheet metal to predict the breakage of the cylindrical cup part. The proposed method can be applied to the prediction of breakage in the forming of the automotive bodies

Quantum Field Effects on Cosmological Phase Transition in Anisotropic Spacetimes

The one-loop renormalized effective potentials for the massive $\phi^4$ theory on the spatially homogeneous models of Bianchi type I and Kantowski-Sachs type are evaluated. It is used to see how the quantum field affects the cosmological phase transition in the anisotropic spacetimes. For reasons of the mathematical technique it is assumed that the spacetimes are slowly varying or have specially metric forms. We obtain the analytic results and present detailed discussions about the quantum field corrections to the symmetry breaking or symmetry restoration in the model spacetimes.Comment: Latex 17 page

A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

Remark on approximation in the calculation of the primordial spectrum generated during inflation

We re-examine approximations in the analytical calculation of the primordial spectrum of cosmological perturbation produced during inflation. Taking two inflation models (chaotic inflation and natural inflation) as examples, we numerically verify the accuracy of these approximations.Comment: 10 pages, 6 figures, to appear in PR

A Study of Anyon Statistics by Breit Hamiltonian Formalism

We study the anyon statistics of a $2 + 1$ dimensional Maxwell-Chern-Simons (MCS) gauge theory by using a systemmetic metheod, the Breit Hamiltonian formalism.Comment: 25 pages, LATE

Non-Thermal Production of WIMPs and the Sub-Galactic Structure of the Universe

There is increasing evidence that conventional cold dark matter (CDM) models lead to conflicts between observations and numerical simulations of dark matter halos on sub-galactic scales. Spergel and Steinhardt showed that if the CDM is strongly self-interacting, then the conflicts disappear. However, the assumption of strong self-interaction would rule out the favored candidates for CDM, namely weakly interacting massive particles (WIMPs), such as the neutralino. In this paper we propose a mechanism of non-thermal production of WIMPs and study its implications on the power spectrum. We find that the non-vanishing velocity of the WIMPs suppresses the power spectrum on small scales compared to what it obtained in the conventional CDM model. Our results show that, in this context, WIMPs as candidates for dark matter can work well both on large scales and on sub-galactic scales.Comment: 6 pages, 2 figures; typo corrected; to appear in PR

A three dimensional extinction map of the Galactic Anticentre from multi-band photometry

We present a three dimensional extinction map in $r$ band. The map has a spatial angular resolution, depending on latitude, between 3 -- 9\,arcmin and covers the entire XSTPS-GAC survey area of over 6,000\,$\rm deg^2$ for Galactic longitude $\rm 140 \leq$ $l$ $\leq 220\deg$ and latitude $\rm -40\leq$ $b$ $\leq 40\deg$. By cross-matching the photometric catalog of the Xuyi Schmidt Telescope Photometric Survey of the Galactic Anticentre (XSTPS-GAC) with those of 2MASS and WISE, we have built a multi-band photometric stellar sample of about 30 million stars and applied spectral energy distribution (SED) fitting to the sample. By combining photometric data from the optical to the near-infrared, we are able to break the degeneracy between the intrinsic stellar colours and the amounts of extinction by dust grains for stars with high photometric accuracy, and trace the extinction as a function of distance for low Galactic latitude and thus highly extincted regions. This has allowed us to derive the best-fit extinction and distance information of more than 13 million stars, which are used to construct the three dimensional extinction map. We have also applied a Rayleigh-Jeans colour excess (RJCE) method to the data using the 2MASS and WISE colour $(H-W2)$. The resulting RJCE extinction map is consistent with the integrated two dimensional map deduced using the best-fit SED algorithm. However for individual stars, the amounts of extinction yielded by the RJCE method suffer from larger errors than those given by the best-fit SED algorithm.Comment: 20 pages, 18 figures, accepted in MNRA

Dust-to-gas ratio, XCOX_{\rm CO} factor and CO-dark gas in the Galactic anticentre: an observational study

We investigate the correlation between extinction and H~{\sc i} and CO emission at intermediate and high Galactic latitudes (|b|>10\degr) within the footprint of the Xuyi Schmidt Telescope Photometric Survey of the Galactic anticentre (XSTPS-GAC) on small and large scales. In Paper I (Chen et al. 2014), we present a three-dimensional dust extinction map within the footprint of XSTPS-GAC, covering a sky area of over 6,000\,deg$^2$ at a spatial angular resolution of 6\,arcmin. In the current work, the map is combined with data from gas tracers, including H~{\sc i} data from the Galactic Arecibo L-band Feed Array H~{\sc i} survey and CO data from the Planck mission, to constrain the values of dust-to-gas ratio $DGR=A_V/N({\rm H})$ and CO-to-$\rm H_2$ conversion factor $X_{\rm CO}=N({\rm H_2})/W_{\rm CO}$ for the entire GAC footprint excluding the Galactic plane, as well as for selected star-forming regions (such as the Orion, Taurus and Perseus clouds) and a region of diffuse gas in the northern Galactic hemisphere. For the whole GAC footprint, we find $DGR=(4.15\pm0.01) \times 10^{-22}$\,$\rm mag\,cm^{2}$ and $X_{\rm CO}=(1.72 \pm 0.03) \times 10^{20}$\,$\rm cm^{-2}\,(K\,km\,s^{-1})^{-1}$. We have also investigated the distribution of "CO-dark" gas (DG) within the footprint of GAC and found a linear correlation between the DG column density and the $V$-band extinction: $N({\rm DG}) \simeq 2.2 \times 10^{21} (A_V - A^{c}_{V})\,\rm cm^{-2}$. The mass fraction of DG is found to be $f_{\rm DG}\sim 0.55$ toward the Galactic anticentre, which is respectively about 23 and 124 per cent of the atomic and CO-traced molecular gas in the same region. This result is consistent with the theoretical work of Papadopoulos et al. but much larger than that expected in the $\rm H_2$ cloud models by Wolfire et al.Comment: 11 pages, 7 figures, accepted for publication in MNRA