Decay kinetics of the green emission in tungstates and molybdates

Luminescence characteristics of a number of undoped and variously doped PbWO₄ crystals were studied at 0.4–400 K by the time-resolved spectroscopy and compared with those of ZnWO₄,CdWO₄ and PbMoO₄ crystals. Two types of green emission centres are detected in PbWO₄ crystals. The centres of the first type are responsible for the low-temperature 2.3–2.4 eV emission observed under excitation around 3.90–3.95 eV. The structure and parameters of their relaxed excited states were determined. It was concluded that the origin of defects responsible for the green emission of the first type could vary for different crystals. The centres of the second type with the emission around 2.5 eV appear in crystals containing oxygen vacancies after the thermal destruction of Pb⁺-WO₃ centres at T>180 K. Decomposition of the exciton and various defect-related states was also studied, and activation energies of this process were calculated.     

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Activation and Afterheat Calculation Analysis for TBM

Safety considerations of TBM are part of the design process to ensure that the TBM do not adversely affect the safety of ITER. So accurate calculations of all radioactivity and potential harmfulness are very important for designing of device, selecting of blanket and shield material, analyzing of the safety and environment, disposing of nuclear waste and operation of the reactor.     

Diffusion on the torus for Hamiltonian maps

For a mapping of the torusT ² we propose a definition of the diffusion coefficientD suggested by the solution of the diffusion equation ofT ². The definition ofD, based on the limit of moments of the invariant measure, depends on the set where an initial uniform distribution is assigned. For the algebraic automorphism of the torus the limit is proved to exist and to have the same value for almost all initial sets in the subfamily of parallelograms. Numerical results show that it has the same value for arbitrary polygons and for arbitrary moments.     

Modified Kramers formulas for the decay rate in agreement with dynamical modeling

Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.     

Optical and luminescence properties of Dy3+ ions in phosphate based glasses

Phosphate glasses with compositions of 44P₂O₅ + 17K₂O + 9Al₂O₃ + (30 − x)CaF₂ + xDy₂O₃ (x = 0.05, 0.1, 0.5, 1.0, 2.0, 3.0 and 4.0 mol %) were prepared and characterized by X-ray diffraction (XRD), differential thermal analysis (DTA), Fourier transform infrared (FTIR), optical absorption, emission and decay measurements. The observed absorption bands were analyzed by using the free-ion Hamiltonian (H_FI) model. The Judd–Ofelt (JO) analysis has been performed and the intensity parameters (Ω_λ, λ = 2, 4, 6) were evaluated in order to predict the radiative properties of the excited states. From the emission spectra, the effective band widths (Δλ_eff), stimulated emission cross-sections (σ(λ_p)), yellow to blue (Y/B) intensity ratios and chromaticity color coordinates (x, y) have been determined. The fluorescence decays from the ⁴F_9/2 level of Dy³⁺ ions were measured by monitoring the intense ⁴F_9/2 → ⁶H_15/2 transition (486 nm). The experimental lifetimes (τ_exp) are found to decrease with the increase of Dy³⁺ ions concentration due to the quenching process. The decay curves are perfectly single exponential at lower concentrations and gradually changes to non-exponential for higher concentrations. The non-exponential decay curves are well fitted to the Inokuti–Hirayama (IH) model for S = 6, which indicates that the energy transfer between the donor and acceptor is of dipole–dipole type. The systematic analysis of revealed that the energy transfer mechanism strongly depends on Dy³⁺ ions concentration and the host glass composition.     

On strong solutions to the compressible Hall-magnetohydrodynamic system

In this paper, we consider strong/classical solutions to the 3D compressible Hall-magnetohydrodynamic system. First, we prove the existence of local strong solutions with positive density. Then the existence of global small solutions with small initial data is proved. Optimal time decay rate is also established.     

Quantitative Time-Resolved Fluorescence Spectrum of the Cortical Sarcoma and the Adjacent Normal Tissue

The difference in time-resolved fluorescence spectrum between the cortical sarcoma and the adjacent normal tissue was studied in both experimental and theoretical ways. The Clinical data were obtained in vivo using a time-resolved fluorescence spectrometer employing a single fiber-optic probe for excitation and detection. Tissue was modeled as s-180 sarcoma tumor surrounded with normal muscle and was mediated by the Palladium-porphyrin photosensitizer (Pd-TCPP). The emitted fluorescence was considered as arising from the tumor tissue or the normal muscle, due to the presence of the photosensitizer. A computational code which could simulating time-resolved fluorescence emission was presented and applied to comparing fluorescence decay of photosensitizer in different stages of tumor growth. In this code the different stages of the tumor was modeled through changing the time τ, the delay of the fluorescence photon emission and z _max, the thickness of the tumor. It was found in the in vivo experiment that the fluorescence from tumor tissue decayed more quickly than from the adjacent normal muscle. For the ten rats in the first experiment day, the mean decay constant of tumor T _s and normal tissue T _n were 554 and 526 μs, respectively. And T _s increased with the tumor growth, from 554 μs in the first day to 634 μs in the eighth day while T _s kept steady. It was believed that the more adequate oxygen supplied by the normal tissue can more effectively quench the fluorescence and in the normal tissue the photosensitizer lifetime is smaller. As a result the simulated time-resolved fluorescence spectrum of normal tissue showed more quickly decay. And the thickness of the tumor can also delay the fluorescence decay. Both the experimental and simulated results indicated that the germination of the tumor would increase the decay constant of the time-resolved fluorescence spectrum. So decay constant of the tumor tissue spectrum should be larger than that of adjacent normal tissue for the reason of hypoxia and overgrouth. This fact could be of use in the tumor diagnoses.     

A model for the stabilization of atomic hydrogen centers in borate glasses

A previously proposed model describing the trapping site of the interstitial atomic hydrogen in borate glasses is analyzed. In this model the atomic hydrogen is stabilized at the centers of oxygen polygons belonging to B–O ring structures in the glass network by van der Waals forces. The previously reported atomic hydrogen isothermal decay experimental data are discussed in the light of this microscopic model. A coupled differential equation system of the observed decay kinetics was solved numerically using the Runge Kutta method. The experimental untrapping activation energy of 0.7×10⁻¹⁹ J is in good agreement with the calculated results of dispersion interaction between the stabilized atomic hydrogen and the neighboring oxygen atoms at the vertices of hexagonal ring structures.     

Large time behavior to the system of incompressible non-Newtonian fluids in R

In this paper, the authors study the large time behavior for the weak solutions to a class system of the incompressible non-Newtonian fluids in R². It is proved that the weak solutions decay in L² norm at (1+t)^−1/2 and the estimate for the decay rate is sharp in the sense that it coincides with the decay rate of a solution to the heat equation.