Coupled oscillators and Feynman's three papers

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

High Fluid‐Pressure Patches Beneath the Décollement: A Potential Source of Slow Earthquakes in the Nankai Trough off Cape Muroto

南海トラフのスロー地震震源域近傍に高圧の間隙水帯を確認 --スロー地震発生のメカニズム解明へ前進--. 京都大学プレスリリース. 2021-06-17.Pore pressure plays a key role in the generation of earthquakes in subduction zones. However, quantitative constraints for its determination are quite limited. Here, we estimate the subsurface pore pressure by analyzing the transient upwelling flow of drilling mud from borehole C0023A of the International Ocean Discovery Program (IODP) Expedition 370, in the Nankai Trough off Cape Muroto. This upward flow provided the first direct evidence of an overpressured aquifer in the underthrust sediments off Cape Muroto. To estimate the pre-drilling pore pressure in the overpressured aquifer around a depth of 950–1, 050 m below sea floor, we examined the measured porosities of core samples retrieved from nearby IODP wells; we then proceeded to explain the observed time evolution of the flow rate of the upwelling flow by modeling various sized aquifers through solving a radial diffusion equation. It was observed that for a permeability of 10⁻¹³ m², the aquifer possessed an initial excess pore pressure of ∼5–10 MPa above the hydrostatic pressure, with a lateral dimension of several hundred meters and thickness of several tens of meters. The overpressure estimates from the porosity-depth profile at Site C0023 differ from those at other drill sites in the region, suggesting the possible existence of multiple overpressured aquifers with a patchy distribution in the underthrust sediments of the Nankai Trough. As pore pressure is relevant in maintaining fault stability, the overpressured aquifers may be the source of slow earthquakes that have been observed around the drilling site

Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

Formation of air-gap structure at a GaN epilayer/substrate interface by using an InN interlayer

We propose a new technique for “air‐gap” formation at a GaN/sapphire interface by using an InN interlayer. This is aimed to grow epitaxial GaN films with reduced stress and cracks. First, an InN interlayer of about 0.2 μm thick is grown at 600 °C in atmospheric pressure. Then a 30 nm‐thick GaN buffer layer is grown on the InN layer at 550 °C. The substrate temperature is ramped up to 1000 °C in the NH3 flow, and finally a 1.5 μm‐thick GaN epilayer is grown on the annealed GaN buffer layer using nitrogen carrier gas. Consequently, an “air‐gap” structure is naturally formed close to the substrate surface. During the ramping period of substrate temperature, the InN layer decomposes due to its thermal instability and metallic In is formed. It is found that metallic In drops as a result of InN decomposition contribute to the air‐gap formation. No cracks are found on the GaN surface and a reduced stress in the layer is confirmed by PL and Raman shift measurements

Identification of DBC1 as a transcriptional repressor for BRCA1

BACKGROUND: DBC1/KIAA1967 (deleted in breast cancer 1) is a putative tumour-suppressor gene cloned from a heterozygously deleted region in breast cancer specimens. Caspase-dependent processing of DBC1 promotes apoptosis, and depletion of endogenous DBC1 negatively regulates p53-dependent apoptosis through its specific inhibition of SIRT1. Hereditary breast and ovarian cancer susceptibility gene product BRCA1, by binding to the promoter region of SIRT1, is a positive regulator of SIRT1 expression. METHODS: A physical interaction between DBC1 and BRCA1 was investigated both in vivo and in vitro. To determine the pathophysiological significance of DBC1, its role as a transcriptional factor was studied. RESULTS: We found a physical interaction between the amino terminus of DBC1 and the carboxyl terminus of BRCA1, also known as the BRCT domain. Endogenous DBC1 and BRCA1 form a complex in the nucleus of intact cells, which is exported to the cytoplasm during ultraviolet-induced apoptosis. We also showed that the expression of DBC1 represses the transcriptional activation function of BRCT by a transient expression assay. The expression of DBC1 also inhibits the transactivation of the SIRT1 promoter mediated by full-length BRCA1. CONCLUSION: These results revealed that DBC1 may modulate the cellular functions of BRCA1 and have important implications in th

Robust H-infinity filtering for 2-D systems with intermittent measurements

This paper is concerned with the problem of robust H∞ filtering for uncertain two-dimensional (2-D) systems with intermittent measurements. The parameter uncertainty is assumed to be of polytopic type, and the measurements transmission is assumed to be imperfect, which is modeled by a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of an H∞ filter such that the filtering error system is stochastically stable and preserves a guaranteed H∞ performance. This problem is solved in the parameter-dependent framework, which is much less conservative than the quadratic approach. By introducing some slack matrix variables, the coupling between the positive definite matrices and the system matrices is eliminated, which greatly facilitates the filter design procedure. The corresponding results are established in terms of linear matrix inequalities, which can be easily tested by using standard numerical software. An example is provided to show the effectiveness of the proposed approac