Nanogroove array on thin metallic film as planar lens with tunable focusing

Numerical results for the distributions of light transmitted through metallic planar lenses composed of symmetric nanogroove arrays on the surfaces of a gold film are presented and explained. Both the near- and far-field distributions of the intensity of light transmitted are calculated by using a Green's function formalism. Results for an optimal transverse focus based on a quadratic variation of groove width are obtained. Meanwhile, a significant dependence of the focal length on the wavelength of light incident from the air side through the gold film into a dielectric substrate is found for this detector configuration.Comment: 14 pages, 6 figure

Gr\"obner-Shirshov bases for LL-algebras

In this paper, we firstly establish Composition-Diamond lemma for $\Omega$-algebras. We give a Gr\"{o}bner-Shirshov basis of the free $L$-algebra as a quotient algebra of a free $\Omega$-algebra, and then the normal form of the free $L$-algebra is obtained. We secondly establish Composition-Diamond lemma for $L$-algebras. As applications, we give Gr\"{o}bner-Shirshov bases of the free dialgebra and the free product of two $L$-algebras, and then we show four embedding theorems of $L$-algebras: 1) Every countably generated $L$-algebra can be embedded into a two-generated $L$-algebra. 2) Every $L$-algebra can be embedded into a simple $L$-algebra. 3) Every countably generated $L$-algebra over a countable field can be embedded into a simple two-generated $L$-algebra. 4) Three arbitrary $L$-algebras $A$, $B$, $C$ over a field $k$ can be embedded into a simple $L$-algebra generated by $B$ and $C$ if $|k|\leq \dim(B*C)$ and $|A|\leq|B*C|$, where $B*C$ is the free product of $B$ and $C$.Comment: 22 page

BCS-BEC Crossover in Symmetric Nuclear Matter at Finite Temperature: Pairing Fluctuation and Pseudogap

By adopting a $T$-matrix based method within $G_0G$ approximation for the pair susceptibility, we studied the effects of pairing fluctuation on the BCS-BEC crossover in symmetric nuclear matter. The pairing fluctuation induces a pseudogap in the excitation spectrum of nucleon in both superfluid and normal phases. The critical temperature of superfluid transition was calculated. It differs from the BCS result remarkably when density is low. We also computed the specific heat which shows a nearly ideal BEC type temperature dependence at low density but a BCS type behavior at high density. This qualitative change of the temperature dependence of specific heat may serve as a thermodynamic signal for BCS-BEC crossover.Comment: 11 pages,11 figures,1 table, published version in Phys. Rev. C

Remote sounding through semi-transparent cirrus cloud

A large portion of the earth is covered by thin semi-transparent cirrus cloud. The cirrus results from the natural injection of moisture into the upper troposphere by deep convection (i.e., anvils) and from man-made moisture injected into the upper troposphere by jet aircraft. Although most cirrus clouds are semi-transparent to infrared wavelengths, their heights, thicknesses, and spectral absorption properties must be known in order to retrieve atmospheric temperature and moisture profiles from the data. An algorithm is developed for accounting for the radiative properties of semi-transparent cloud in the retrieval of vertical temperature and moisture profiles. The algorithm is to be applied to the NASA ER2 HIS data collected during the FIRE cirrus field program

Thermal effects on nuclear symmetry energy with a momentum-dependent effective interaction

The knowledge of the nuclear symmetry energy of hot neutron-rich matter is important for understanding the dynamical evolution of massive stars and the supernova explosion mechanisms. In particular, the electron capture rate on nuclei and/or free protons in presupernova explosions is especially sensitive to the symmetry energy at finite temperature. In view of the above, in the present work we calculate the symmetry energy as a function of the temperature for various values of the baryon density, by applying a momentum-dependent effective interaction. In addition to a previous work, the thermal effects are studied separately both in the kinetic part and the interaction part of the symmetry energy. We focus also on the calculations of the mean field potential, employed extensively in heavy ion reaction research, both for nuclear and pure neutron matter. The proton fraction and the electron chemical potential, which are crucial quantities for representing the thermal evolution of supernova and neutron stars, are calculated for various values of the temperature. Finally, we construct a temperature dependent equation of state of $\beta$-stable nuclear matter, the basic ingredient for the evaluation of the neutron star properties.Comment: 18 pages, 10 figures, 1 table, accepted for publication in Physical Review

Spontaneous current generation in the gapless 2SC phase

It is found that, except chromomagnetic instability, the gapless 2SC phase also exhibits a paramagnetic response to the perturbation of an external color neutral baryon current. The spontaneously generated baryon current driven by the mismatch is equivalent to the one-plane wave LOFF state. We describe the 2SC phase in the nonlinear realization framework, and show that each instability indicates the spontaneous generation of the corresponding pseudo Nambu-Golstone current. We show this Nambu-Goldstone currents generation state covers the gluon phase as well as the one-plane wave LOFF state. We further point out that, when charge neutrality condition is required, there exists a narrow unstable LOFF (Us-LOFF) window, where not only off-diagonal gluons but the diagonal 8-th gluon cannot avoid the magnetic instability. We discuss that the diagonal magnetic instability in this Us-LOFF window cannot be cured by off-diagonal gluon condensate in color superconducting phase, and it will also show up in some constrained Abelian asymmetric superfluid/superconducting system.Comment: 8 pages, no figure, final version to appear in PR

Virial Expansion of the Nuclear Equation of State

We study the equation of state (EOS) of nuclear matter as function of density. We expand the energy per particle (E/A) of symmetric infinite nuclear matter in powers of the density to take into account 2,3,. . .,N-body forces. New EOS are proposed by fitting ground state properties of nuclear matter (binding energy, compressibility and pressure) and assuming that at high densities a second order phase transition to the Quark Gluon Plasma (QGP) occurs. The latter phase transition is due to symmetry breaking at high density from nuclear matter (locally color white) to the QGP (globally color white). In the simplest implementation of a second order phase transition we calculate the critical exponent ? by using Landau's theory of phase transition. We find ? = 3. Refining the properties of the EOS near the critical point gives ? = 5 in agreement with experimental results. We also discuss some scenarios for the EOS at finite temperatures

Ka-band MMIC beam steered transmitter array

A 32-GHz six-element linear transmitter array utilizing monolithic microwave integrated circuit (MMIC) phase shifters and power amplifiers was designed and tested as part of the development of a spacecraft array feed for NASA deep-space communications applications. Measurements of the performance of individual phase shifters, power amplifiers, and microstrip radiators were carried out, and electronic beam steering of the linear array was demonstrated. The switched-line phase shifters were accurate to within 7 percent on average and the power amplifier 1-dB compressed output power varied over 0.3 dB. The array had a beamwidth of 7.5 deg and demonstrated acceptable beam steering over + or - 8 deg. From the results, it can be concluded that this MMIC phased array has adequate beam-scanning capability for use in the two-dimensional array. The areas that need to be improved are the efficiency of the MMIC power amplifier and the insertion loss of the MMIC phase shifter

Competition between symmetry breaking and onset of collapse in weakly coupled atomic condensates

We analyze the symmetry breaking of matter-wave solitons in a pair of cigar-shaped traps coupled by tunneling of atoms. The model is based on a system of linearly coupled nonpolynomial Schr\"odinger equations (NPSEs). Unlike the well-known spontaneous-symmetry-breaking (SSB) bifurcation in coupled cubic equations, in the present model the SSB competes with the onset of collapse in this system. Stability regions of symmetric and asymmetric solitons, as well as the collapse region, are identified in the parameter space of the system.Comment: Physical Review A, in pres

Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure

We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and V\'azquez, where the pressure is obtained as a Riesz potential associated to the density. We take advantage of the displacement convexity of the Riesz potential in one dimension to show a functional inequality involving the entropy, entropy dissipation, and the Euclidean transport distance. An argument by approximation shows that this functional inequality is enough to deduce the exponential convergence of solutions in self-similar variables to the unique steady states