Deaths Exceed Births in Most of Europe, But Not in the United States

In this brief, authors Kenneth Johnson, Layton Fields, and Dudley Poston, Jr. present important new findings about the diminishing number of births compared to deaths in Europe and the United States from their recent article in Population and Development Review. Their research focuses on the prevalence and dynamics of natural decrease in subareas of Europe and the United States in the first decade of the twenty-first century using counties (United States) or county-equivalents (Europe). The authors report that 58 percent of the 1,391 counties of Europe had more deaths than births during that period compared to just 28 percent of the 3,137 U.S. counties. Natural decrease is more widespread in Europe because its population is older, fertility rates are lower, and there are fewer women of child-bearing age. Natural decrease is a major policy concern because it drains the demographic resilience from a region, diminishing its economic viability and competitiveness. The implications of the recent European immigrant surge for natural decrease are uncertain, but the authors’ analysis suggests that natural decrease is likely to remain widespread in Europe for the foreseeable future

A Multi-Sims Investigation of Water Content and D/H Ratios in Roberts Massif 04262 with Insight to Sources of Hydrogen in Maskelynite

We want to define the H2O content ([H2O]) and hydrogen (H) isotope composition of meteoritic material from Mars [1-3] with motivation to understand Mars volatile history, constrain geochemical signatures of interior water reservoirs (i.e. the Martian mantle) and explore effects of planetary (e.g. planet formation, magma ocean degassing) and local (e.g. volcanic degassing, impact melting and degassing) processes on H incorporated in minerals. Secondary ion mass spectrometry (SIMS) allows multiple avenues to address these questions. However, application to (1) precious astromaterials and (2) low level H measurements, pose specific challenges that are further complicated when combined. We present preliminary data of a multi-approach (SIMS vs. NanoSIMS) study of H in Roberts Massif 04262 (RBT 04262), an enriched lherzolitic shergottite with nonpoikilitic (NP) and poikilitic (P) lithologies [4]. We analyze olivine, pyrox-ene, and melt inclusions to compare indigenous mantle water, with impact-generated maskelynite to investigate H signatures due to shock

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

Chalcogenide-glass polarization-maintaining photonic crystal fiber for mid-infrared supercontinuum generation

In this paper, we report the design and fabrication of a highly birefringent polarization-maintaining photonic crystal fiber (PM-PCF) made from chalcogenide glass, and its application to linearly-polarized supercontinuum (SC) generation in the mid-infrared region. The PM fiber was drawn using the casting method from As38Se62 glass which features a transmission window from 2 to 10 $\mu m$ and a high nonlinear index of 1.13.10$^{-17}$m$^{2}$W$^{-1}$. It has a zero-dispersion wavelength around 4.5 $\mu m$ and, at this wavelength, a large birefringence of 6.10$^{-4}$ and consequently strong polarization maintaining properties are expected. Using this fiber, we experimentally demonstrate supercontinuum generation spanning from 3.1-6.02 $\mu m$ and 3.33-5.78 $\mu m$ using femtosecond pumping at 4 $\mu m$ and 4.53 $\mu m$, respectively. We further investigate the supercontinuum bandwidth versus the input pump polarization angle and we show very good agreement with numerical simulations of the two-polarization model based on two coupled generalized nonlinear Schr\"odinger equations.Comment: 13 pages, 8 figure

Fundamental noise limitations to supercontinuum generation in microstructure fiber

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50 % for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schroedinger equation, finding good quantitative agreement over a range of input pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input pulse shot noise and the spontaneous Raman scattering down the fiber.Comment: 16 pages with 6 figure

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

We use caustic beam shaping on 100 fs pulses to experimentally generate non-paraxial accelerating beams along a 60 degree circular arc, moving laterally by 14 \mum over a 28 \mum propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of non-paraxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic

A Meinardus theorem with multiple singularities

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size $n$, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.Comment: 26 pages. This version incorporates the following two changes implied by referee's remarks: (i) We made changes in the proof of Proposition 1; (ii) We provided an explanation to the argument for the local limit theorem. The paper is tentatively accepted by "Communications in Mathematical Physics" journa

Influence of turbulence on the dynamo threshold

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite correlation time reinforces this effect

Understanding the dynamics of photoionization-induced solitons in gas-filled hollow-core photonic crystal fibers

We present in detail our developed model [Saleh et al., Phys. Rev. Lett. 107] that governs pulse propagation in hollow-core photonic crystal fibers filled by an ionizing gas. By using perturbative methods, we find that the photoionization process induces the opposite phenomenon of the well-known Raman self-frequency red-shift of solitons in solid-core glass fibers, as was recently experimentally demonstrated [Hoelzer et al., Phys. Rev. Lett. 107]. This process is only limited by ionization losses, and leads to a constant acceleration of solitons in the time domain with a continuous blue-shift in the frequency domain. By applying the Gagnon-B\'{e}langer gauge transformation, multi-peak `inverted gravity-like' solitary waves are predicted. We also demonstrate that the pulse dynamics shows the ejection of solitons during propagation in such fibers, analogous to what happens in conventional solid-core fibers. Moreover, unconventional long-range non-local interactions between temporally distant solitons, unique of gas plasma systems, are predicted and studied. Finally, the effects of higher-order dispersion coefficients and the shock operator on the pulse dynamics are investigated, showing that the resonant radiation in the UV [Joly et al., Phys. Rev. Lett. 106] can be improved via plasma formation.Comment: 9 pages, 10 figure

Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in Rd\R^d

We consider a class of second order linear nonautonomous parabolic equations in R^d with time periodic unbounded coefficients. We give sufficient conditions for the evolution operator G(t,s) be compact in C_b(R^d) for t>s, and describe the asymptotic behavior of G(t,s)f as t-s goes to infinity in terms of a family of measures mu_s, s in R, solution of the associated Fokker-Planck equation