Limit theorems for renewal shot noise processes with decreasing response functions

We consider shot noise processes $(X(t))_{t \geq 0}$ with deterministic response function $h$ and the shots occurring at the renewal epochs $0= S_0 < S_1 < S_2 ...$ of a zero-delayed renewal process. We prove convergence of the finite-dimensional distributions of $(X(ut))_{u \geq 0}$ as $t \to \infty$ in different regimes. If the response function $h$ is directly Riemann integrable, then the finite-dimensional distributions of $(X(ut))_{u \geq 0}$ converge weakly as $t \to \infty$. Neither scaling nor centering are needed in this case. If the response function is eventually decreasing, non-integrable with an integrable power, then, after suitable shifting, the finite-dimensional distributions of the process converge. Again, no scaling is needed. In both cases, the limit is identified. If the distribution of $S_1$ is in the domain of attraction of an $\alpha$-stable law and the response function is regularly varying at $\infty$ with index $\beta$ (with $\beta < 1/\alpha$ or $\beta \leq 1/\alpha$, depending on whether $\mathbb{E} S_1 < \infty$ or $\mathbb{E} S_1 = \infty$), then scaling is needed to obtain weak convergence of the finite-dimensional distributions of $(X(ut))_{u \geq 0}$. The limiting processes are fractionally integrated stable L\'{e}vy motions if $\mathbb{E} S_1 < \infty$ and fractionally integrated inverse stable subordinators if $\mathbb{E} S_1 = \infty$.Comment: 58 pages, submitted in a shortened form; the present version corrects a coupling defined in Section 3.1 and used in various parts of the pape

Quantum theory of light diffraction

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the approach of relativistic quantum theory. We find that the slit length, slit width, slit thickness and wave-length of light have affected to the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern can not be explained by wave-optical approach, and it can be explained in quantum theory. We compare the theoretical results with single and multiple slits experiment data, and find the theoretical results are accordance with the experiment data. Otherwise, we give some theory prediction. We think all the new prediction will be tested by the light diffraction experiment.Comment: 10 page

Characterising the sea ice environment using a newly developed sensor array mounted on an under-ice trawl

One of the most pronounced impacts of climate change is the changing sea ice cover, which has implications for sea ice-associated ecosystems that depend on carbon produced by ice-associated algae. In order to fully understand these ecosystems there is a need to understand both the physical and biological components. We present preliminary results from Polarstern cruises to the Eastern Central Arctic Ocean (summer 2012) and Weddell Sea (fall-winter 2013). Biological samples were acquired from the under-ice environment using the Surface and Under-Ice Trawl (SUIT) and from within the ice by extracting ice cores. Biophysical properties of sea ice and under-ice environments were characterized using a sensor array mounted on the SUIT that measured ice thickness, under-ice light spectra, water properties and chlorophyll a biomass (in- and under-ice). Modal ice thicknesses were between 0.45-1.38 m (Arctic) and 0.23-0.70 m (Weddell Sea). Sea ice properties were related to the distribution of some key under-ice species (e.g. Polar Cod and Antarctic Krill). Previous studies have used under-ice light spectra to derive ice-algal biomass but were limited to local-scale point measurements. We present a new method for calculating ice-algal biomass from under-ice spectra on local- to meso-scales and compare the results using both methods

Development of a chromium-thoria alloy

Low temperature ductility and high temperature strength of pure chromium and chromium-thoria alloy prepared from vapor deposited powder

Interference of Clocks: A Quantum Twin Paradox

The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational time dilation (redshift). Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that light-pulse interferometers without internal transitions are not sensitive to gravitational time dilation, whereas they can constitute a quantum version of the special-relativistic twin paradox. We propose an interferometer geometry isolating the effect that can be used for quantum-clock interferometry.Comment: 9 Pages, 2 Figure

Antarctic sympagic meiofauna in winter: Comparing diversity, abundance and biomass between perennially and seasonally ice-covered regions

This study of Antarctic sympagic meiofauna in pack ice during late winter compares communities between the perennially ice-covered western Weddell Sea and the seasonally ice-covered southern Indian Ocean. Sympagic meiofauna (proto- and metazoans >20 μm) and eggs >20 μm were studied in terms of diversity, abundance and carbon biomass, and with respect to vertical distribution. Metazoan meiofauna had significantly higher abundance and biomass in the western Weddell Sea (medians: 31.1×103 m−2 and 6.53mg m−2, respectively) than in the southern Indian Ocean (medians: 1.0×10 103 m−2and 0.06 mg m−2, respectively). Metazoan diversity was also significantly higher in the western Weddell Sea. Furthermore, the two regions differed significantly in terms of meiofauna community composition, as revealed through multivariate analyses. The overall diversity of sympagic meiofauna was high, and integrated abundance and biomass of total meiofauna were also high in both regions (0.6–178.6×103 m−2 and 0.02–89.70mg m−2, respectively), mostly exceeding values reported earlier from the western Weddell Sea in winter. We attribute the differences in meiofauna communities between the two regions to the older first-year ice and multi-year ice that is present in the western Weddell Sea, but not in the southern Indian Ocean. Our study indicates the significance of perennially ice-covered regions for the establishment of diverse and abundant meiofauna communities. Furthermore, it highlights the potential importance of sympagic meiofauna for the organic matter pool and trophic interactions in sea ice

Moderate deviations for random field Curie-Weiss models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.Comment: 21 page

Sea ice CO2 flux in the Southern Ocean during mid-winter and early spring

第4回極域科学シンポジウム個別セッション：[OB] 生物圏11月12日（火）13:00-14:00　国立国語研究所 ２階ラウン