A4A_4 Group and Tri-bimaximal Neutrino Mixing -- A Renormalizable Model

The tetrahedron $A_4$ group has been widely used in studying neutrino mixing matrix. It provides a natural framework of model building for the tri-bimaximal mixing matrix. In this class of models, it is necessary to have two Higgs fields, $\chi$ and $\chi'$, transforming under $A_4$ as 3 with one of them having vacuum expectation values for the three components to be equal and another having only one of the components to be non-zero. These specific vev structures require separating $\chi$ and $\chi'$ from communicating with each other. The clash of the different vev structures for $\chi$ and $\chi'$ is the so called sequestering problem. In this work, I show that it is possible to construct renormalizable supersymmetric models producing the tri-bimaximal neutrino mixing with no sequestering problem.Comment: 4 page

(2+1)(2+1)-dimensional regular black holes with nonlinear electrodynamics sources

On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of $(2+1)$-dimensional regular black hole in general relativity coupled with nonlinear electrodynamics sources. By the use of the two conditions, we obtain a general approach to construct $(2+1)$-dimensional regular black holes. In this manner, we construct four $(2+1)$-dimensional regular black holes as examples. We also study the thermodynamic properties of the regular black holes and verify the first law of black hole thermodynamics.Comment: 13 pages, 4 figures. in press in PL

Quantization of Black Holes

We show that black holes can be quantized in an intuitive and elegant way with results in agreement with conventional knowledge of black holes by using Bohr's idea of quantizing the motion of an electron inside the atom in quantum mechanics. We find that properties of black holes can be also derived from an Ansatz of quantized entropy \Delta S=4\pi k {\Delta R / \lambdabar}, which was suggested in a previous work to unify the black hole entropy formula and Verlinde's conjecture to explain gravity as an entropic force. Such an Ansatz also explains gravity as an entropic force from quantum effect. This suggests a way to unify gravity with quantum theory. Several interesting and surprising results of black holes are given from which we predict the existence of primordial black holes ranging from Planck scale both in size and energy to big ones in size but with low energy behaviors.Comment: Latex 7 pages, no figure

Effects of Initial Stance of Quadruped Trotting on Walking Stability

It is very important for quadruped walking machine to keep its stability in high speed walking. It has been indicated that moment around the supporting diagonal line of quadruped in trotting gait largely influences walking stability. In this paper, moment around the supporting diagonal line of quadruped in trotting gait is modeled and its effects on body attitude are analyzed. The degree of influence varies with different initial stances of quadruped and we get the optimal initial stance of quadruped in trotting gait with maximal walking stability. Simulation results are presented. Keywords: quadruped, trotting, attitude, walking stability

An efficient plate heater with uniform surface temperature engineered with effective thermal materials

Extended from its electromagnetic counterpart, transformation thermodynamics applied to thermal conduction equations can map a virtual geometry into a physical thermal medium, realizing the manipulation of heat flux with almost arbitrarily desired diffusion paths, which provides unprecedented opportunities to create thermal devices unconceivable or deemed impossible before. In this work we employ this technique to design an efficient plate heater that can transiently achieve a large surface of uniform temperature powered by a small thermal source. As opposed to the traditional approach of relying on the deployment of a resistor network, our approach fully takes advantage of an advanced functional material system to guide the heat flux to achieve the desired temperature heating profile. A different set of material parameters for the transformed device has been developed, offering the parametric freedom for practical applications. As a proof of concept, the proposed devices are implemented with engineered thermal materials and show desired heating behaviors consistent with numerical simulations. Unique applications for these devices can be envisioned where stringent temperature uniformity and a compact heat source are both demanded.Comment: 14 pages, 5 figure