Experimental and theoretical studies on X-ray induced secondary electron yields in Ti and TiO2

Generation of X-ray induced secondary electrons in Ti and TiO₂ was studied from both experimental and theoretical approaches, using X-ray photoelectron spectroscopy (XPS) attached to a synchrotron radiation facility and Monte Carlo simulation, respectively.The experiment revealed that the yields of secondary electrons induced by X-rays (electrons/photon) at photon energies to 4950 and 5000 eV for Ti and TiO₂ are δ_Ti(4950 eV) = 0.002 and δ_Ti(5000 eV) = 0.014 while those for TiO₂ are δTiO₂(4950 eV)=0.003 and δTiO₂(5000 eV)=0.018.A novel approach to obtain the escape depth of secondary electrons has been proposed and applied to Ti and TiO₂. The approach agreed very well with the experimental data reported so far. The Monte Carlo simulation predicted; and while and .An experimental examination on the contribution of X-ray induced secondary electrons to photocatalysis in TiO₂ has also been proposed.     

The heat equation with time-independent multiplicative stable Lévy noise

We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the Skorokhod integral or Wick product. We give a criterion for existence based on the dimension of the space variable, and the parameter p$p$ of the stable noise. Our arguments are different for p<1$p<1$ and p?1$p?1$.     

A CLT for renewal processes with a finite set of interarrival distributions

We prove a central limit theorem for a renewal process based on a sequence of independent non-negative interarrival times whose distributions are taken from a finite set. The result extends the classical central limit theorem obtained by Takács (1956).     

The Law of the Iterated Logarithm for Finitely Inhomogeneous Random Walks

The Hartman–Wintner–Strassen law of the iterated logarithm states that if X ₁, X ₂,… are independent identically distributed random variables and S _n =X ₁+???+X _n , then

$\limsup_{n}S_{n}/\sqrt{2n\log \log n}=1\quad \text{a.s.},\qquad \liminf_{n}S_{n}/\sqrt{2n\log \log n}=-1\quad \text{a.s.}$

if and only if EX ₁ ² =1 and EX ₁=0. We extend this to the case where the X _n are no longer identically distributed, but rather their distributions come from a finite set of distributions.

     

Compact eye-safe laser sources based on OPOs with KTP or PPKTP crystals

We report on compact eye-safe nanosecond laser sources emitting in the 1.5 μm wavelength range based on non-critically phase-matched parametric interaction in optical parametric oscillators (OPOs) with KTP and periodically poled KTP (PPKTP) crystals, pumped by the fundamental frequency of Nd:YAG lasers. As much as 250 μJ signal pulse energy at 1.5 μm wavelength, 6.5 ns FWHM pulse-width, has been obtained in a PPKTP-OPO, extracavity pumped by a Nd:YAG microlaser oscillator–amplifier at 650 μJ pump pulse energy, 8 ns pulse-width. A single signal pulse of 2.7-mJ output energy at 1.57 μm wavelength, less than 5 ns pulse-width, was generated in a KTP-OPO, intracavity pumped by a passively Q-switched Nd:YAG laser.     

Specific heat of a fermionic atomic cloud in the unitary regime

In the unitary regime, when the scattering amplitude greatly exceeds in magnitude the average interparticle separation, and below the critical temperature thermal properties of an atomic fermionic cloud are governed by the collective modes, specifically the Bogoliubov-Anderson sound modes. The specific heat of an atomic cloud in an elongated trap, in particular, has a rather complex temperature dependence, which changes from an exponential behavior at very low temperatures (T < h omega(parallel)), to proportional T for h omega(parallel) < T < h omega(perpendicular) and then continuously to proportional T4 at temperatures just below the critical temperature, when the surface modes play a dominant role. Only the low (h omega(parallel) < T < h omega(perpendicular)) and high (h omega(perpendicular) < T < T(c)) temperature power laws are well defined. For the intermediate temperatures one can introduce at most a gradually increasing with temperature exponent.