Inviscid incompressible limits of the full Navier-Stokes-Fourier system

We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on the three dimensional Euclidean space. The Euler-Boussinesq approximation is identified as the limit system

An improved short-term swash zone beach profile change model focusing on berm formation and erosion

A short-term swash zone beach profile change model focusing on berm formation and erosion proposed by Suzuki and Kuriyama (2010) was improved. The model was developed using a 2.5-year data set of beach profiles and offshore waves observed at the Hasaki coast, Ibaraki, Japan, facing the Pacific Ocean. The distributions of cross-shore sediment transport rate for berm formation and erosion were determined using the curve slopes at the inflection points. The curve slopes for berm formation and erosion were estimated by using the wave energy flux, and the product of the wave height of long-period wave and berm height, respectively. The investigation area was set from the maximum wave run-up position to the shoreline position at the mean tide level. The both models were applied to the calculation of the beach profile change for three months, which results were compared with observed data. It is found that the present model well predicts not only the shoreline change, but also the beach profile change, including the berm formation and erosion. The correlation coefficient (R) of shoreline position at the high tide level between the numerical results and observed data is 0.70, which is 0.37 higher than the previous model. Also, the averaged correlation coefficient of shoreline positions at five different ground elevations is R = 0.73

Climate simulation of the latest Permian: Implications for mass extinction

This report presents the results of climate modeling research which indicates that elevated levels of carbon dioxide in the atmosphere at the end of the Permian period led to climatic conditions inhospitable to both marine and terrestrial life. The Permian-Triassic boundary (about 251 million years ago) was the time of the largest known mass extinction in Earth's history, when greater than ninety percent of all marine species, and approximately seventy percent of all terrestrial species, died out. The model, which used paleogeography and paleotopography correct for the time period, indicated that warm high-latitude surface air temperatures and elevated carbon dioxide levels may have resulted in slowed circulation and stagnant, anoxic conditions in Earth's oceans. The report also suggests that the excess carbon dioxide (and sulfur dioxide) may have originated from volcanic activity associated with eruption of the Siberian Trap flood basalts, which took place at the same time. Educational levels: Undergraduate lower division, Undergraduate upper division, Graduate or professional

Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment

In this paper, we study inverse scattering of massless Dirac fields that propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a stationary approach we determine precisely the leading terms of the high-energy asymptotic expansion of the scattering matrix that, in turn, permit us to recover uniquely the mass of the black hole and its charge up to a sign

Simultaneous Two-Photon Absorption of the Thioguanosine Analogue 2′,3′,5′-Tri‑<i>O</i>‑acetyl-6,8-dithioguanosine with Its Potential Application to Photodynamic Therapy

2',3',5'-Tri-O-acetyl-6,8-dithioguanosine (taDTGuo) is an analogue of nucleosides and currently under investigation as a potential agent for photodynamic therapy (PDT). Excitation by simultaneous two-photon absorption of visible or near-infrared light would provide an efficient PDT for deep-seated tumors. The two-photon absorption spectrum of taDTGuo was obtained by optical-probing photoacoustic spectroscopy (OPPAS). A two-photon absorption band corresponding to the S5 ← S0 transition was observed at 556 nm, and the two-photon absorption cross-section σ(2) was determined to be 26 ± 3 GM, which was much larger than that of other nucleobases and nucleosides. Quantum chemical calculations suggested that the large σ(2) value of taDTGuo was responsible for large transition dipole moments and small detuning energy resulting from the thiocarbonyl group at 6- and 8-positions. This is the first report on two-photon absorption spectra and cross-sections of thionucleoside analogues, which could be used to develop a more specific PDT for cancers in deep regions

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case

On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

We study the inverse scattering problem for electric potentials and magnetic fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy.Comment: This is a slightly edited version of the previous pape