Mass Dependence of the Entropy Product and Sum

For black holes with multiple horizons, the area product of all horizons has been proven to be mass independent in many cases. Counterexamples were also found in some occasions. In this paper, we first prove a theorem derived from the first law of black hole thermodynamics and a mathematical lemma related to the Vandermonde determinant. With these arguments, we develop some general criterion for the mass independence of the entropy product as well as the entropy sum. In particular, if a $d$-dimensional spacetime is spherically symmetric and its radial metric function $f(r)$ is a Laurent series in $r$ with the lowest power $-m$ and the highest power $n$, we find the criteria is extremely simple: The entropy product is mass independent if and only if $m\geq d-2$ and $n\geq4-d$. The entropy sum is mass independent if and only if $m\geq d-2$ and $n\geq 2$. Compared to previous works, our method does not require an exact expression of the metric. Our arguments turn out to be useful even for rotating black holes. By applying our theorem and lemma to a Myers-Perry black hole with spacetime dimension $d$, we show that the entropy product/sum is mass independent for all $d>4$, while it is mass dependent only for $d=4$, i.e., the Kerr solution.Comment: 12 page

Modelling of organic magnetoresistance in aluminium tris(8-hydroxyquinolinate) light emitting diodes

PhDThis thesis concerns itself with the scientific study of the modelling of organic magnetoresitance (OMR). This can be divided into two parts: the magnetic field effects on the intersystem crossing (ISC) in organic semiconductors, and the modelling of OMR, including triplet polaron interactions (TPI). In my studies of the magnetic field effect on photoluminescence (PL), the ISC rate, kISC, is estimated by modelling the dependence of the PL under high excitation intensity. Using a modified rate model, a kISC of 2.3 x 104s-1 is derived at a temperature of 80K in Alq3. An excited state absorption (ESA) mechanism was also proposed to help understand how the ISC can occur from higher excited triplet states to the singlet state, rather than just from the singlet to a lower lying triplet state. This is necessary as the measured activation energy from the transfer from T1 to S1 is only 15±5meV. In addition, the effect of a magnetic field on photoluminescence intensity for Alq3 is reported, in order to explain the change in the kISC caused by an applied magnetic field. The magnetic field may affect the mixing of a pair state prior to exciton formation as well as the exciton itself. I then present the modelling of OMR as a function of device thickness. Here, a TPI model is proposed to fit the OMR data. For all Alq3 devices of any thickness, the OMR data can be modelled using just three processes: triplet dissociation, polaron trapping and TPI. Both the sum of prefactors for dissociation and trapping (ad+ at), and the prefactor for TPI, ai, are proportional to the exciton concentration within the device, over the full range of operating conditions. This is the first time that a predictive model of OMR has been developed. This model is then extended to fit the OMR data as a function of temperature. In addition, I discuss some surprising phenomena at low temperature, such as a delay between the onset of light emission and the onset of OMR, and the decrease in the percentage efficiency change with the effect of a magnetic field

Can gravitational dynamics be obtained by diffeomorphism invariance of action?

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in usual way is automatically diffeomorphism invariant in nature, which thus invalidates this alternative perspective to obtain gravitational dynamics. Especially, we also show what is wrong with the technical derivation of gravitational dynamics in the alternative approach.Comment: version published in PR

Laser-assisted microchanneling on PMMA substrate utilizing two-pass fabrication method

Microchannel is widely used in microfluidic devices for mixing, chemical reaction, detection, particle separation and etc. CO2 laser-based microchanneling of PMMA as a low cost, rapid, noncontact fabrication method has attracted the attention of industry. However, the typical V-shape grooves fabricated by CO2 laser microchanneling have limitations since the V-shape grooves will affect the flow behavior and heat transfer of the fluid, which are important to the performance of microfluidic devices. A two-pass fabrication method is proposed and investigated in this paper to improve the quality of the PMMA microchannel fabricated by CO2 laser. It was found that by using this method, a trapezoidal shape groove can be formed. Such a microchannel is of higher quality compared with the V-shape groove microchannel

On Newman-Penrose constants of stationary electrovacuum spacetimes

A theorem related to the Newman-Penrose constants is proven. The theorem states that all the Newman-Penrose constants of asymptotically flat, stationary, asymptotically algebraically special electrovacuum spacetimes are zero. Straightforward application of this theorem shows that all the Newman-Penrose constants of the Kerr-Newman spacetime must vanish.Comment: 11pages, no figures accepted by PR