Electrostatic characterisation of corona-wire aerosol chargers

This paper investigates the electrostatic properties of aerosol corona-wire diffusion chargers. The most important parameters that determine charging levels of particles at the outlet of such devices are the ion concentration, $N_{\mathrm{i}}$, and the mean residence time of the aerosol in the charging zone, t. A method to determine the exact $N_{\mathrm{i}}t$ product is presented and used for the characterization of a Hewitt-type corona charger. It is shown that ignoring the space charge effect leads to significant errors when the ion concentration is greater than $5\times {10}^{13}\mathrm{ions}/{\mathrm{m}}^3$. A numerical model developed to describe the performance of the device in more detail is used to predict the behavior of the charger when some geometric characteristics are changed. Estimations of ion penetration levels through the inner electrode based on the numerical model show better agreement with the experimental results at sub-atmospheric pressures. Finally, calculations of the average $N_{\mathrm{i}}t$ product appear to increase with pressure despite the fact that the ionic concentration is significantly lower.     

The pentagram integrals for Poncelet families

The pentagram map is now known to be a discrete integrable system. We show that the integrals for the pentagram map are constant along Poncelet families. That is, if $P_1$ and $P_2$ are two polygons in the same Poncelet family, and $f$ is a monodromy invariant for the pentagram map, then $f\left(P_1\right)=f\left(P_2\right)$. Our proof combines complex analysis with an analysis of the geometry of a degenerating sequence of Poncelet polygons.     

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.     

Effect of hydrostatic pressure on diamagnetic susceptibility of hydrogenic donor impurity in core/shell/shell spherical quantum dot with Kratzer confining potential

Dependencies of diamagnetic susceptibility ${\chi }_{dia}$ on parameter $r_0$ for different values of hydrostatic pressure for 1s state.Dependence of diamagnetic susceptibility ${\chi }_{dia}$ on hydrostatic pressure $P$ for different values of $r_0$ for 1s state.

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ESR in a gapped Anderson model

We applied the numerical renormalization group method to study the electron spin resonance (ESR) of a single-impurity Anderson model with a gap $\Delta$ in the conduction electron density of states, centered at the Fermi level. We analyzed the relaxation rate $1/T_1$ of a magnetic probe located at a position $\overrightarrow{R}$ around the Anderson impurity. It presents different behaviors for the symmetric and the asymmetric case. For the symmetric case and any $\Delta >0$, $1/T_1$ goes to a constant for $T?{\Gamma }_{\text{k}}$ (Kondo resonance). $1/T_1$ decreases monotonically to zero only for $\Delta =0$. For the asymmetric case, there is a $\Delta$ under which $1/T_1$ decreases monotonically to zero as $T\to 0$, and above which $1/T_1$ saturates, as occurs in the symmetric case for $\Delta >0$. This behavior indicates a quantum phase transition from the quenched to the unquenched magnetic moment in the ground state of the Anderson ion.     

Lagrangian surfaces in the complex hyperquadric Q2

In this paper, we introduce a one-form $\Phi$ associated to a Lagrangian immersion $f$ from Riemann surface $M$ into the complex hyperquadric $Q_2$. It is proved that $f$ is minimal if and only if $\Phi$ is vanishing and $f$ is H-minimal if and only if $\Phi$ is holomorphic. As an application, a family of $S^1$-equivariant minimal Lagrangian tori in $Q_2$ are obtained.