Competing edge networks

We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, subject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the other?s growth and encourage the other?s demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails.     

Improvement of breakdown characteristics of an A1GaN/GaN HEMT with a U-type gate foot for millimeter-wave power application

<正>In this study,the physics-based device simulation tool Silvaco ATLAS is used to characterize the electrical properties of an AlGaN/GaN high electron mobility transistor(HEMT) with a U-type gate foot.The U-gate AlGaN/GaN HEMT mainly features a gradually changed sidewall angle,which effectively mitigates the electric field in the channel, thus obtaining enhanced off-state breakdown characteristics.At the same time,only a small additional gate capacitance and decreased gate resistance ensure excellent RF characteristics for the U-gate device.U-gate AlGaN/GaN HEMTs are feasible through adjusting the etching conditions of an inductively coupled plasma system,without introducing any extra process steps.The simulation results are confirmed by experimental measurements.These features indicate that U-gate AlGaN/GaN HEMTs might be promising candidates for use in miltimeter-wave power applications.     

Comparative study of heterogeneous magnetic state above TC in La0.82Sr0.18CoO3 cobaltite and La0.83Sr0.17MnO3 manganite

The magnetic, transport and structural properties are studied for La_0.83Sr_0.17MnO₃ and La_0.82Sr_0.18CoO₃ single crystals with nearly the same doping and the metallic ground state. Their comparisons have shown that ferromagnetic clusters originate in the paramagnetic matrix below Т^?>T_C in both samples and exhibit similar properties. This suggests the possible universality of such phenomena in doped mixed-valence oxides of transition metals with the perovskite-type structure. The cluster density increases on cooling and plays an important role on the physical properties of these systems. The differences in cluster evolutions and scenarios of their insulator–metal transitions are related to different magnetic behaviors of the matrixes in these crystals that is mainly due to distinct spin states of the Mn³⁺ and Co³⁺ ions.     

Affine holomorphic quantization

We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation, allowing to implement manifest locality without the necessity for metric or causal background structures. The quantization combines the holomorphic version of geometric quantization for state spaces with the Feynman path integral quantization for amplitudes. We also develop an adapted notion of coherent states, discuss vacuum states, and consider observables and their Berezin–Toeplitz quantization. Moreover, we derive a factorization identity for the amplitude in the special case of a linear field theory modified by a source-like term and comment on its use as a generating functional for a generalized S$S$-matrix.     

Conformal field theories in six-dimensional twistor space

This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space–time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the six-dimensional case in which twistor space is the 6-quadric Q$Q$ in CP⁷${\mathbb{C}\mathbb{P}}^7$ with a view to applications to the self-dual (0,2)$(0,2)$-theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These yield an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space (H²$H^2$ and H³$H^3$) in which the H³$H^3$s arise as obstructions to extending the H²$H^2$s off Q$Q$ into CP⁷${\mathbb{C}\mathbb{P}}^7$.     

Solving Toda field theories and related algebraic and differential properties

Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld–Sokolov gauge is used. The main objective of this paper is to carry out this approach of solving the Toda field theories for the classical Lie algebras, following Balog et al. (1990) [5]. In this process, we discover and prove some algebraic identities for principal minors of special matrices. The known elegant solutions of Leznov (1980) [10] fit in our scheme in the sense that they are the general solutions to our conditions discovered in this solving process. To prove this, we find and prove some differential identities for iterated integrals. It can be said that altogether our paper gives complete mathematical proofs for Leznov’s solutions.     

Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Let {(ξni, ηni), 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as(S_1, ρ_n S_1 +(1-ρ_n~2S_2)~(1/2)), ρn∈(0, 1), where(S1, S2) is a bivariate spherical random vector. For the distribution function of radius (S_1~2+ S_2~2)~(1/2) belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of ρn to 1 is given. In this paper,under the refinement of the rate of convergence of ρn to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.     

EPR and photoluminescence properties of green light emitting LaAl11O18:Mn phosphors

The LaAl₁₁O₁₈:Mn²⁺ powder phosphor has been prepared using a self-propagating synthesis. Formation and homogeneity of the LaAl₁₁O₁₈:Mn²⁺ phosphor has been verified by X-ray diffraction and energy dispersive X-ray analysis respectively. The EPR spectra of Mn²⁺ ions exhibit resonance signals with effective g values at g≈4.8 and g≈1.978. The signal at g≈1.978 exhibits six-line hyperfine structure and is due to Mn²⁺ ions in an environment close to tetrahedral symmetry, whereas the resonance at g≈4.8 is attributed to the rhombic surroundings of the Mn²⁺ ions. It is observed that the number of spins participating in resonance for g≈1.978 increases with decreasing temperature obeying the Boltzmann law. Upon 451 nm excitation, the photoluminescence spectrum exhibits a green emission peak at 514 nm due to ⁴T₁ (G)→⁶A₁ (S) transition of Mn²⁺ ions. The crystal field parameter Dq and Racah inter-electronic repulsion parameters B and C have been evaluated from the excitation spectrum.     

Theoretical study on the dislocations in the bubble rafts

The core structure of the dislocation in a bubble raft has been evaluated by using the improved P–N equation. The dislocation profile has been obtained explicitly for the bubble radius R=0.296, 0.592, 0.650, 0.888 mm. The results show that the core width of dislocation will increase rapidly when the bubble radius decreases, especially, this trend will become more significant as the radius is more smaller. Our calculated results agree well with the experimental data, and our method can be used to predict the core structure of the dislocation in a bubble raft where bubble-radius is given arbitrarily.