Electronic structure and optical properties of ABP2O7 double phosphates

Luminescence and luminescence excitation under VUV radiation of ${\mathrm{ABP}}_2{\mathrm{O}}_7$ ($\mathrm{A}=\mathrm{Na}$, K, Cs; $\mathrm{B}=\mathrm{Al}$, In) double phosphates are studied. Two emission bands peaking near 330 and 420 nm are common for investigated ${\mathrm{ABP}}_2{\mathrm{O}}_7$ crystals. The band structure and partial densities of electronic states of perfect ${\mathrm{KAlP}}_2{\mathrm{O}}_7$, ${\mathrm{LiInP}}_2{\mathrm{O}}_7$ and ${\mathrm{NaTiP}}_2{\mathrm{O}}_7$ crystals are calculated by the full-potential linear-augmented-plane-wave (FLAPW) method. It is found that the structures of the conduction bands of ${\mathrm{ABP}}_2{\mathrm{O}}_7$ crystals, which have different B cations, are appreciably different. Experimental results are compared with results of calculations of the electronic structure. Assumptions concerning the origin of luminescence in double phosphates are made.     

Traffic flow behavior at un-signalized intersection with crossings pedestrians

Mixed traffic flux composed of crossing pedestrians and vehicles extensively exists in cities. To study the characteristics of the interference traffic flux, we develop a pedestrian-vehicle cellular automata model to present the interaction behaviors on a simple cross road. By realizing the fundamental parameters (i.e. injecting rates ${\alpha }_1$, ${\alpha }_2$, the extracting rate β and the pedestrian arrival rate ${\alpha }_P$), simulations are carried out. The vehicular traffic flux is calculated in terms of rates. The effect of the crosswalk can be regarded as a dynamic impurity. The system phase diagrams in the $({\alpha }_1,{\alpha }_P)$ plane are built. It is found that the phase diagrams consist essentially of four phases namely Free Flow, Congested, Maximal Current and Gridlock. The value of the Maximal current phase depends on the extracting rate β, while the Gridlock phase is achieved only when the pedestrians generating rate is higher than a critical value. Furthermore, the effect of vehicles changing lane ($P_{\mathrm{ch}1},P_{\mathrm{ch}2}$) and the location of the crosswalk $X_P$ on the dynamic characteristics of vehicles flow are investigated. It is found that traffic situation in the system is slightly enhanced if the location of the crosswalks $X_P$ is far from the intersection. However, when $P_{\mathrm{ch}1}$, $P_{\mathrm{ch}2}$ increase, the traffic becomes congested and the Gridlock phase enlarges.     

Persistent luminescence and synchrotron radiation study of the Ca2MgSi2O7:Eu2+,R3+ materials

The tetragonal ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+},{\mathrm{R}}^{3+}$ persistent luminescence materials were prepared by a solid state reaction. The UV excited and persistent luminescence was observed in the green region centred at 535 nm. Both luminescence phenomena are due to the same ${\mathrm{Eu}}^{2+}$ ion occupying the single ${\mathrm{Ca}}^{2+}$ site in the host lattice. The ${\mathrm{R}}^{3+}$ codoping usually reduced the persistent luminescence of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$, which differs from the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ and ${\mathrm{MAl}}_2{\mathrm{O}}_4$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Ca},\mathrm{Sr})$ materials. Only the ${\mathrm{Tb}}^{3+}$ ion enhanced slightly the persistent luminescence. With the aid of synchrotron radiation, the band gap energy of ${\mathrm{Ca}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ was found to be about 7 eV that is very similar to those of the ${\mathrm{M}}_2{\mathrm{MgSi}}_2{\mathrm{O}}_7$:${\mathrm{Eu}}^{2+}$ $(\mathrm{M}=\mathrm{Sr},\mathrm{Ba})$ materials. Thermoluminescence results suggested that the ${\mathrm{R}}^{3+}$ ions might act as electron traps, but only the TL peaks created by ${\mathrm{Tm}}^{3+}$ and ${\mathrm{Sm}}^{3+}$ can be found in the temperature range accessible. Lattice defects (e.g. oxygen vacancies) are also important, since the same main thermoluminescence peak was observed at about $100{}^{\circ }\mathrm{C}$ with and without ${\mathrm{R}}^{3+}$ codoping.     

On the non-integrability of a generalized Darboux Halphen system

In this paper we study a generalized Darboux Halphen system given by ${\dot{x}}_1=x_2{x}_3-x_1(x_2+x_3)+{\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)\text{,}$${\dot{x}}_2=x_3{x}_1-x_2(x_3+x_1)+{\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)\text{,}$${\dot{x}}_3=x_1{x}_2-x_3(x_1+x_2)+{\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)\text{,}$ where $x_1$, $x_2$, $x_3$ are real variables, ${\alpha }_1,{\alpha }_2,{\alpha }_3$ are real constants and ${\tau }^2({\alpha }_1,{\alpha }_2,{\alpha }_3,x_1,x_2,x_3)={\alpha }_1^2(x_1-x_2)(x_3-x_1)+{\alpha }_2^2(x_2-x_3)(x_1-x_2)+{\alpha }_3^2(x_3-x_1)(x_2-x_3)\text{.}$ We prove that, for any $({\alpha }_1,{\alpha }_2,{\alpha }_3)\in {\mathbb{R}}^3\setminus \left\{(0,0,0)\right\}$, this system does not admit any non-constant global first integral that can be described by a formal power series. Furthermore, restricting the values of $({\alpha }_1,{\alpha }_2,{\alpha }_3)$ to a full Lebesgue measure set, we prove that this system does not admit any non-constant rational or Darbouxian global first integral. This is a first step toward proving that this system is chaotic.