Fitting functions for dark matter density profiles

We present a unified parameterization of the fitting functions suitable for density profiles of dark matter haloes or elliptical galaxies. A notable feature is that the classical Einasto profile appears naturally as the continuous limiting case of the cored subfamily amongst the double power-law profiles of Zhao (1996). Based on this, we also argue that there is basically no qualitative difference between halo models well-fitted by the Einasto profile and the standard NFW model. This may even be the case quantitatively unless the resolutions of simulations and the precisions of fittings are sufficiently high to make meaningful distinction possible.Comment: 13 pages (6 pages main text + 5 pages appendices + 2 pages full tables) including 5 figures and 7 tables. submitted to MNRA

Newly discovered brown dwarfs not seen in microlensing time scale frequency distribution?

The 2-Micron All Sky Survey (2MASS) (Skrutskie et al. 1997) and the DEep Near Infrared Survey of the southern sky (DENIS) (Epchtein et al. 1997) have revealed a heretofore unknown population of free brown dwarfs that has extended the local mass function down to as small as 0.01M_sun (Reid et al. 1999). If this local proportion of brown dwarfs extends throughout the Galaxy---in particular in the Galactic bulge---one expects an increase in the predicted fraction of short time scale microlensing events in directions toward the Galactic bulge. Zhao et al.(1996) have indicated that a mass function with 30-60% of the lens mass in brown dwarfs is not consistent with empirical microlensing data. Here we show that even the much lower mass fraction (~ 10%) of brown dwarfs inferred from the new discoveries appears inconsistent with the data. The added brown dwarfs do indeed increase the expected number of short time scale events, but they appear to drive the peak in the time scale frequency distribution to time scales smaller than that observed, and do not otherwise match the observed distribution. A reasonably good match to the empirical data (Alcock et al. 1996) is obtained by increasing the fraction of stars in the range 0.08<m<0.7M_sun considerably above that deduced from several star counts. However, all inferences from microlensing about the appropriate stellar mass function must be qualified by the meagerness of the microlensing data and the uncertainties in the Galactic model.Comment: 5 pages, 1 figure. PS file using aas2pp4.sty. To appear in ApJ Letter

Investigation of transition between spark ignition and controlled auto-ignition combustion in a V6 direct-injection engine with cam profile switching

Controlled auto-ignition (CAI) combustion, also known as Homogeneous Charge Compression Ignition (HCCI) can be achieved by trapping residuals with early exhaust valve closure in a direct fuel injection in-cylinder four-stroke gasoline engines (through the employment of low-lift cam profiles). Due to the operating region being limited to low and mid-load operation for CAI combustion with a low-lift cam profile, it is important to be able to operate SI combustion at high-load with a normal cam profile. A 3.0L prototype engine was modified to achieve CAI combustion, using a Cam Profile Switching mechanism which has the capability to switch between high and low-lift cam-profiles. A strategy was used where a high-profile could be used for SI combustion and a low-lift profile was used for CAI combustion. Initial analysis showed that for transitioning from SI to CAI combustion, misfire occurred on the first CAI transitional cycle. Subsequent experiments showed that the throttle opening position and switching time could be controlled avoiding misfire. Further work investigated transitioning at different loads and from CAI to SI combustion

Ferromagnetic Type-II Weyl Semimetal in Pyrite Chromium Dioxide

Magnetic topological materials have recently drawn significant importance and interest, due to their topologically nontrivial electronic structure within spontaneous magnetic moments and band inversion. Based on first-principles calculations, we propose that chromium dioxide, in its ferromagnetic pyrite structure, can realize one pair of type-II Weyl points between the $N$th and $(N+1)$th bands, where $N$ is the total number of valence electrons per unit cell. Other Weyl points between the $(N-1)$th and $N$th bands also appear close to the Fermi level due to the complex topological electronic band structure. The symmetry analysis elucidates that the Weyl points arise from a triply-degenerate point splitting due to the mirror reflection symmetry broken in the presence of spin-orbital coupling, which is equivalent to an applied magnetic field along the direction of magnetization. The Weyl points located on the magnetic axis are protected by the three-fold rotational symmetry. The corresponding Fermi arcs projected on both (001) and (110) surfaces are calculated as well and observed clearly. This finding opens a wide range of possible experimental realizations of type-II Weyl fermions in a system with time-reversal breaking.Comment: 8 pages, 5 figure

New families of weighted sum formulas for multiple zeta values

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Energy transfer process in gas models of Lennard-Jones interactions

We perform simulations to investigate how the energy carried by a molecule transfers to others in an equilibrium gas model. For this purpose we consider a microcanonical ensemble of equilibrium gas systems, each of them contains a tagged molecule located at the same position initially. The ensuing transfer process of the energy initially carried by the tagged molecule is then exposed in terms of the ensemble-averaged energy density distribution. In both a 2D and a 3D gas model with Lennard-Jones interactions at room temperature, it is found that the energy carried by a molecule propagates in the gas ballistically, in clear contrast with the Gaussian diffusion widely assumed in previous studies. A possible scheme of experimental study of this issue is also proposedComment: 5 pages,3 figur

Killing Spinors for the Bosonic String

We obtain the effective action for the bosonic string with arbitrary Yang-Mills fields, up to the \alpha' order, in general dimensions. The form of the action is determined by the requirement that the action admit well-defined Killing spinor equations, whose projected integrability conditions give rise to the full set of equations of motion. The success of the construction suggests that the hidden "pseudo-supersymmetry" associated with the Killing spinor equations may be a property of the bosonic string itself.Comment: 9 page