The two-level atom laser: analytical results and the laser transition

The problem of the two-level atom laser is studied analytically. The steady-state solution is expressed as a continued fraction, and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected with the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$, such that $g^2/\kappa$ stays finite and $g^2/\kappa > 2 \gamma$, where $\gamma$ is the rate of atomic losses. The same scaling procedure is also shown to describe a similar change to Poisson distribution in the Scully-Lamb laser model too, suggesting that the low-$\kappa$, low-$g$ asymptotics is of a more general significance for the laser transition.Comment: 23 pages, 3 figures. Extended discussion of the paper aim (in the Introduction) and of the results (Conclusions and Discussion). Results unchange

Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if $K_{n=1}^{\infty}a_{n}/b_{n}$ is the even part); (ii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.Comment: 16 page

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

Quantifying Low Energy Proton Damage in Multijunction Solar Cells

An analysis of the effects of low energy proton irradiation on the electrical performance of triple junction (3J) InGaP2/GaAs/Ge solar cells is presented. The Monte Carlo ion transport code (SRIM) is used to simulate the damage profile induced in a 3J solar cell under the conditions of typical ground testing and that of the space environment. The results are used to present a quantitative analysis of the defect, and hence damage, distribution induced in the cell active region by the different radiation conditions. The modelling results show that, in the space environment, the solar cell will experience a uniform damage distribution through the active region of the cell. Through an application of the displacement damage dose analysis methodology, the implications of this result on mission performance predictions are investigated

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Lung exposure of titanium dioxide nanoparticles induces innate immune activation and long-lasting lymphocyte response in the Dark Agouti rat

Nanomaterial of titanium dioxide (TiO2) is manufactured in large-scale production plants, resulting in risks for accidental high exposures of humans. Inhalation of metal oxide nanoparticles in high doses may lead to both acute and long-standing adverse effects. By using the Dark Agouti (DA) rat, a strain disposed to develop chronic inflammation following exposure to immunoactivating adjuvants, we investigated local and systemic inflammatory responses after lung exposure of nanosized TiO2 particles up to 90 days after intratracheal instillation. TiO2 induced a transient response of proinflammatory and T-cell-activating cytokines (interleukin [IL]-1α, IL-1β, IL-6, cytokine-induced neutrophil chemoattractant [CINC]-1, granulocyte-macrophage colony-stimulating factor [GM-CSF], and IL-2) in airways 1-2 days after exposure, accompanied byaninfluxofeosinophilsand neutrophils. Neutrophil numbers remained elevated for 30 days, whereas the eosinophils declined to baseline levels at Day 8, simultaneously with an increase of dendritic cells and natural killer (NK) cells. The innate immune activation was followed by a lymphocyte expansion that persisted throughout the 90-day study. Lymphocytes recruited to the lungs were predominantly CD4+ helper T-cells, but we also demonstrated presence of CD8+T-cells, B-cells, and CD25+T-cells. In serum, we detected both an early cytokine expression at Days 1-2 (IL-2, IL-4, IL-6, CINC-1, IL-10, and interferon-gamma [IFN-γ] and a second response at Day 16 of tumor necrosis factor-alpha (TNF-α), indicating systemic late-phase effects in addition to the local response in airways. In summary, these data demonstrate a dynamic response to TiO2 nanoparticles in the lungs of DA rats, beginning with an innate immune activation of eosinophils, neutrophils, dendritic cells, and NK cells, followed by a long-lasting activation of lymphocytes involved in adaptive immunity. The results have implications for the assessment of risks for adverse and persistent immune stimulation following nanoparticle exposures in sensitive populations