Radiative Transfer in a Discrete Random Medium Adjacent to a Half-Space with a Rough Interface

For a macroscopically plane-parallel discrete random medium, the boundary conditions for the specific coherency dyadic at a rough interface are derived. The derivation is based on a modification of the Twersky approximation for a scattering system consisting of a group of particles and the rough surface, and reduces to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave propagating in a discrete random medium with non-scattering boundaries. In a matrix-form setting, the boundary conditions for the specific coherency dyadic imply the boundary conditions for specific intensity column vectors which in turn, yield the expressions for the reflection and transmission matrices. The derived expressions are shown to be identical to those obtained by applying a phenomenological approach based on a facet model to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave

Poisson structure and Action-Angle variables for the Camassa-Holm equation

The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.Comment: 20 pages, LaTeX. The original publication is available at www.springerlink.co

A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calder\'on in dimension $2$, for conductivities \sigma>0 with $\log \sigma \in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on classical fractional integrals, as well as a new result on $L^2$-boundedness of pseudo-differential operators with non-smooth symbols, valid in all dimensions

Evolutionary constraints on the complexity of genetic regulatory networks allow predictions of the total number of genetic interactions

Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete. In this study, we analyzed the distribution of GRN structural properties across a large set of distinct prokaryotic organisms and found a set of constrained characteristics such as network density and number of regulators. Our results allowed us to estimate the number of interactions that complete networks would have, a valuable insight that could aid in the daunting task of network curation, prediction, and validation. Using state-of-the-art statistical approaches, we also provided new evidence to settle a previously stated controversy that raised the possibility of complete biological networks being random and therefore attributing the observed scale-free properties to an artifact emerging from the sampling process during network discovery. Furthermore, we identified a set of properties that enabled us to assess the consistency of the connectivity distribution for various GRNs against different alternative statistical distributions. Our results favor the hypothesis that highly connected nodes (hubs) are not a consequence of network incompleteness. Finally, an interaction coverage computed for the GRNs as a proxy for completeness revealed that high-throughput based reconstructions of GRNs could yield biased networks with a low average clustering coefficient, showing that classical targeted discovery of interactions is still needed.Comment: 28 pages, 5 figures, 12 pages supplementary informatio

Vacuum Polarization on the Schwarzschild Metric with a Cosmic String

We consider the problem of the renormalization of the vacuum polarization in a symmetry space-time with axial but not spherical symmetry, Schwarzschild space-time threaded by an infinite straight cosmic string. Unlike previous calculations, our framework to compute the renormalized vacuum polarization does not rely on special properties of Legendre functions, but rather has been developed in a way that we expect to be applicable to Kerr space-time

Hybrid k⋅p\mathbf{k\cdot p}-tight-binding model for intersubband optics in atomically thin InSe films

We propose atomic films of n-doped $\gamma$-InSe as a platform for intersubband optics in the infrared (IR) and far infrared (FIR) range, coupled to out-of-plane polarized light. Depending on the film thickness (number of layers) of the InSe film these transitions span from $\sim 0.7$ eV for bilayer to $\sim 0.05$ eV for 15-layer InSe. We use a hybrid $\mathbf{k} \cdot \mathbf{p}$ theory and tight-binding model, fully parametrized using density functional theory, to predict their oscillator strengths and thermal linewidths at room temperature

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk and it may be possible to access a turbulent regime in which many modes are unstable.Comment: 4 pages, 4 figures, to be published in Physical Review Letter

Peran Orang Tua sebagai Pendidik Anak dalam Keluarga

Artikel ini membahas tentang peran orang tua sebagai pendidik anak dalam rumah tangga. Para sarjana Muslim banyak menukil ayat-ayat qur\u27an dan hadis sebagai dasar petingnya pendidikan anak dalam keluarga. Keluarga sebagai instrumen terkecil  dalam masyarakat dan sebagai peletak dasar sekaligus tempat pendidikan awal bagi setiap anak. Peran orang tua sangatlah pentingdalam pendidikan anak. Orang tua yang mampu memposisikan diri sebagai pelindung, pengayom, dan pendidik anak tentunya akan koheren dengan harapan agar mendapat calon generasi penerus yang baik, karena sifat dasar anak adalah membutuhkan kasih sayang dan rhatian dari orang tuanya. Wasiat Lukman al-Hakim dalam Q.S. Luqman ayat 13-19 merupakan manifestasi dari pentingnya pendidikan anak oleh orang tua dalam keluarga. Pendidikan dalam keluarga bukan hanya dibatasi dalam pendidikan agama saja, namun juga memberikan pendidikan akhlaq, kepribadian, dan sosial. Orang tua sepantasnya mampu melaksanakan pendidikan holistik kepada anak dalam keluarga sehingga mampu mewujudkan tujuan pendidikan yaitu menjadikan insan paripurna yang seimbang antara emosi, intelektual, dan spiritual