Breather solutions for a quasi‐linear (1+1)‐dimensional wave equation

We consider the (1 + 1)-dimensional quasi-linear wave equation $()_{} − _{} + ℎ()(^{3}_{} )_{} = 0$ on ℝ×ℝ that arises in the study of localized electromagnetic waves modeled by Kerr-nonlinear Maxwell equations. We are interested in time-periodic, spatially localized solutions. Here $∈ ^{∞}(ℝ)$ is even with ≢ 0 and $ℎ() = _{0}()$ with ∈ ℝ∖{0} and $_{0}$ the delta-distribution supported in 0. We assume that 0 lies in a spectral gap of the operators _{} = − \frac {d^{2}}{d^{2}} − ^{2}^{2} on $^{2}(ℝ)$ for all ∈ 2ℤ+1 together with additional properties of the fundamental set of solutions of $_{}$. By expanding into a Fourier series in time, we transfer the problem of finding a suitably defined weak solution to finding a minimizer of a functional on a sequence space. The solutions that we have found are exponentially localized in space. Moreover, we show that they can be well approximated by truncating the Fourier series in time. The guiding examples, where all assumptions are fulfilled, are explicitly given step potentials and periodic step potentials . In these examples, we even find infinitely many distinct breathers

Breather solutions for a quasilinear (1+1)-dimensional wave equation

We consider the $(1 + 1)$-dimensional quasilinear wave equation $g(x)w_{tt} − w_{xx} + h(x)(w^3_t)_t = 0$ on $\mathbb{R}\times\mathbb{R}$ which arises in the study of localized electromagnetic waves modeled by Kerr-nonlinear Maxwell equations. We are interested in time-periodic, spatially localized solutions. Here $g\in L^{\infty}(\mathbb{R})$ is even with $g\not\equiv 0$ and $h(x) = \gamma\delta_0(x)$ with $\gamma\in\mathbb{R}\backslash\{0\}$ and $\delta_0$ the delta distribution supported in $0$. We assume that $0$ lies in a spectral gap of the operators $L_k = \frac{d^2}{dx^2}-k^2\omega^2g$ on $L^2(\mathbb{R})$ for all $k\in 2\mathbb{Z}+1$ together with additional properties of the fundamental set of solutions of $L_k$. By expanding $w$ into a Fourier series in time we transfer the problem of finding a suitably defined weak solution to finding a minimizer of a functional on a sequence space. The solutions that we have found are exponentially localized in space. Moreover, we show that they can be well approximated by truncating the Fourier series in time. The guiding examples, where all assumptions are fulfilled, are explicitely given step potentials and periodic step potentials $g$. In these examples we even find infinitely many distinct breathers

Paper Session I-C - Autonomous Microgravity Industrial Carrier (AMICA) Initiative

GE Astro-Space Division, Pnnceton, New Jersey, has joined with MBB-ERNO of Germany* Aerltalla, and MATRA, in proposing a program employing two spacecraft which would offer flight opportunities to the space science community in the 1990s. The first of these spacecraft would be obtained by transfer of the European Retrievable Carrier (EURECA) to this initiative. EURECA is a spacecraft currently under development, scheduled for launch in May 1991 and retrieval in January 1992. The second spacecraft, called the - Autonomous Microgravity Industrial Carrier (AMIGA), would also be built, as a\u27 duplicate of EURECA... The entire program is referred to as the AMIGA Initiative. AMICA Is a free-flyer spacecraft that features the highest degree of mlcrogravlty, extended flight duration, cleanliness, retrlevablllty and re-flight. \u27It. Is therefore a key element 1n the 1990s Industrialization of space. The program evolves from the EURECA. program which will in 11991 carry a variety of experiments In Solar Physics, Atmospheric Physics, Gamma-Ray Astronomy, Astrophysics* Materials Science, Life Science, and technology development. The EURECA spacecraft, in turn, employs techniques used in the Shuttle Pallet Satellite. AMIGA, therefore, represents a low-risk approach based on extensive space flight experience

Star formation environments and the distribution of binary separations

We have carried out K-band speckle observations of a sample of 114 X-ray selected weak-line T Tauri stars in the nearby Scorpius-Centaurus OB association. We find that for binary T Tauri stars closely associated to the early type stars in Upper Scorpius, the youngest subgroup of the OB association, the peak in the distribution of binary separations is at 90 A.U. For binary T Tauri stars located in the direction of an older subgroup, but not closely associated to early type stars, the peak in the distribution is at 215 A.U. A Kolmogorov-Smirnov test indicates that the two binary populations do not result from the same distibution at a significance level of 98%. Apparently, the same physical conditions which facilitate the formation of massive stars also facilitate the formation of closer binaries among low-mass stars, whereas physical conditions unfavorable for the formation of massive stars lead to the formation of wider binaries among low-mass stars. The outcome of the binary formation process might be related to the internal turbulence and the angular momentum of molecular cloud cores, magnetic field, the initial temperature within a cloud, or - most likely - a combination of all of these. We conclude that the distribution of binary separations is not a universal quantity, and that the broad distribution of binary separations observed among main-sequence stars can be explained by a superposition of more peaked binary distributions resulting from various star forming environments. The overall binary frequency among pre-main-sequence stars in individual star forming regions is not necessarily higher than among main-sequence stars.Comment: 7 pages, Latex, 4 Postscript figures; also available at http://spider.ipac.caltech.edu/staff/brandner/pubs/pubs.html ; accepted for publication in ApJ Letter

Nonlocal thermoelectricity in a Cooper-pair splitter

We investigate the nonlocal thermoelectric transport in a Cooper-pair splitter based on a double-quantum-dot-superconductor three-terminal hybrid structure. We find that the nonlocal coupling between the superconductor and the quantum dots gives rise to nonlocal thermoelectric effects which originate from the nonlocal particle-hole breaking of the system. We show that Cooper-pair splitting induces the generation of a thermo-current in the superconducting lead without any transfer of charge between the two normal metal leads. Conversely, we show that a nonlocal heat exchange between the normal leads is mediated by non-local Andreev reflection. We discuss the influence of finite Coulomb interaction and study under which conditions nonlocal power generation becomes possible, and when the Cooper-pair splitter can be employed as a cooling device.Comment: 12 pages, 7 figure

Lasing in Si₃N₄-organic hybrid (SiNOH) waveguides

Silicon nitride (Si$_{3}$N$_{4}$) waveguides offer low-loss wave propagation over a wide spectral range including visible wavelengths and lend themselves to photonic integrated circuits for bio-photonic applications. The Si$_{3}$N$_{4}$ device portfolio, however, is so far limited to passive devices that need to be fed by external light sources. This often requires delicate and costly fiber-chip coupling schemes that are subject to stringent alignment tolerances. In this paper, we present and investigate a class of lasers that combine Si$_{3}$N$_{4}$ waveguides with light-emitting organic cladding materials in a hybrid approach. These Si$_{3}$N$_{4}$-organic hybrid (SiNOH) lasers are operated by optical pumping from the top with low alignment precision. We theoretically and experimentally investigate different SiNOH laser concepts based on spiral-shaped ring resonators and distributed feedback (DFB) resonators. While our devices are designed for an emission wavelength of approximately 600 nm, the SiNOH laser concept can be transferred to a large range of wavelengths in the visible spectrum. The devices are amenable to cost-efficient mass production and have the potential to address a wide range of applications in bio-photonics and point-of-care diagnostics

Mitochondrial DNA content in paired normal and cancerous breast tissue samples from patients with breast cancer

Introduction: We develop a multiplex quantitative real-time PCR for synchronized analysis of mitochondrial DNA (mtDNA) and nuclear DNA (nDNA) to investigate relative mtDNA abundance in paired normal and cancerous breast tissues. Materials and methods: The amounts of nDNA and mtDNA in 102 tissue samples were quantified for both glyceraldehype-3-phosphodehydrogenase (GAPDH) gene and mtDNA encoded ATPase (MTATP) 8 gene. The average threshold cycle (Ct) number values of the nDNA and mtDNA were used to calculate relative mtDNA content in breast tissues. Results: The median delta Ct (ΔCt) and the median mtDNA content for normal and cancerous breast tissues were 6.73 and 2.54, as well as 106.50 and 5.80 (P=0.000, respectively). The mtDNA content was decreased in 82% of cancerous breast tissues compared with the normal ones. The changes were associated with hormone receptor status. Conclusion: Our finding suggests that decreased mtDNA content in breast cancer may have diagnostic and prognostic value for the diseas

Biophotonic sensors with integrated Si3_{3}N4_{4}-organic hybrid (SiNOH) lasers for point-of-care diagnostics

Early and efficient disease diagnosis with low-cost point-of-care devices is gaining importance for personalized medicine and public health protection. Within this context, waveguide-(WG)-based optical biosensors on the silicon-nitride (Si$_{3}$N$_{4}$) platform represent a particularly promising option, offering highly sensitive detection of indicative biomarkers in multiplexed sensor arrays operated by light in the visible-wavelength range. However, while passive Si3N4-based photonic circuits lend themselves to highly scalable mass production, the integration of low-cost light sources remains a challenge. In this paper, we demonstrate optical biosensors that combine Si3N4 sensor circuits with hybrid on-chip organic lasers. These Si3N4-organic hybrid (SiNOH) lasers rely on a dye-doped cladding material that are deposited on top of a passive WG and that are optically pumped by an external light source. Fabrication of the devices is simple: The underlying Si3N4 WGs are structured in a single lithography step, and the organic gain medium is subsequently applied by dispensing, spin-coating, or ink-jet printing processes. A highly parallel read-out of the optical sensor signals is accomplished with a simple camera. In our proof-of-concept experiment, we demonstrate the viability of the approach by detecting different concentrations of fibrinogen in phosphate-buffered saline solutions with a sensor-length (L-)-related sensitivity of S/L = 0.16 rad nM−1 mm−1. To our knowledge, this is the first demonstration of an integrated optical circuit driven by a co-integrated low-cost organic light source. We expect that the versatility of the device concept, the simple operation principle, and the compatibility with cost-efficient mass production will make the concept a highly attractive option for applications in biophotonics and point-of-care diagnostics