The radiation from slots in truncated dielectric-covered surfaces

A theoretical approach based on the geometrical theory of diffraction is used to study the electromagnetic radiation from a narrow slot in a dielectric-covered perfectly-conducting surface terminated at an edge. The total far-zone field is composed of a geometrical optics field and a diffracted field. The geometrical optics field is the direct radiation from the slot to the field point. The slot also generates surface waves which are incident at the termination of the dielectric cover, where singly-diffracted rays and reflected surface waves are excited. The diffraction and reflection coefficients are obtained from the canonical problem of the diffraction of a surface wave by a right-angle wedge where the dielectric-covered surface is approximated by an impedance surface. This approximation is satisfactory for a very thin cover; however, the radiation from its vertical and faces cannot be neglected in treating the thicker dielectric cover. This is taken into account by using a Kirchhoff-type approximation, which contributes a second term to the diffraction coefficient previously obtained. The contributions from the geometrical optics field, the singly-diffracted rays and all significant multiply-diffracted rays are summed to give the total radiation. Calculated and measured patterns are found to be in good agreement

Light bulb heat exchanger for magnetohydrodynamic generator applications - Preliminary evaluation

The light-bulb heat-exchanger concept is investigated as a possible means of using a combustion heat source to supply energy to an inert gas MHD power generator system. In this concept, combustion gases flow through a central passage which consists of a duct with transparent walls through which heat is transferred by radiation to a radiation receiver which in turn heats the inert gas by convection. The effects of combustion-gas emissivity, transparent-wall-transmissivity, radiation-receiver emissivity, and the use of fins in the inert gas coolant passage are studied. The results indicate that inert gas outlet temperatures of 2500 K are possible for combustion temperatures of 3200 K and that sufficient energy can be transferred from the combustion gas to reduce its temperature to approximately 2000 K. At this temperature more conventional heat exchangers can be used

Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings

We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.Comment: 5 pages, revtex, no figure

Third-order cosmological perturbations of zero-pressure multi-component fluids: Pure general relativistic nonlinear effects

Present expansion stage of the universe is believed to be mainly governed by the cosmological constant, collisionless dark matter and baryonic matter. The latter two components are often modeled as zero-pressure fluids. In our previous work we have shown that to the second-order cosmological perturbations, the relativistic equations of the zero-pressure, irrotational, multi-component fluids in a spatially near flat background effectively coincide with the Newtonian equations. As the Newtonian equations only have quadratic order nonlinearity, it is practically interesting to derive the potential third-order perturbation terms in general relativistic treatment which correspond to pure general relativistic corrections. Here, we present pure general relativistic correction terms appearing in the third-order perturbations of the multi-component zero-pressure fluids. We show that, as in a single component situation, the third-order correction terms are quite small (~ 5 x10^{-5} smaller compared with the relativistic/Newtonian second-order terms) due to the weak level anisotropy of the cosmic microwave background radiation. Still, there do exist pure general relativistic correction terms in third-order perturbations which could potentially become important in future development of precision cosmology. We include the cosmological constant in all our analyses.Comment: 20 pages, no figur

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. Considering the general curvature ($K$) and the cosmological constant ($\Lambda$) in the background medium, the perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in general scales. In the first part, we elaborate these Newtonian correspondences. In the second part, using the identified gauge-invariant variables with correct Newtonian correspondences, we present the relativistic results with general pressures in the background and perturbation. We present the general super-sound-horizon scale solutions of the above mentioned variables valid for general $K$, $\Lambda$, and generally evolving equation of state. We show that, for vanishing $K$, the super-sound-horizon scale evolution is characterised by a conserved variable which is the perturbed three-space curvature in the comoving gauge. We also present equations for the multi-component hydrodynamic situation and for the rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra

Conserved cosmological structures in the one-loop superstring effective action

A generic form of low-energy effective action of superstring theories with one-loop quantum correction is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in the cosmological spacetime. Using the solutions we identify conserved quantities characterizing the perturbations: the amplitude of gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular-momentum of rotational perturbation are conserved independently of changing gravity sector. Implications for calculating perturbation spectra generated in the inflation era based on the string action are presented.Comment: 5 pages, no figure, To appear in Phys. Rev.

Cosmological perturbations in a gravity with quadratic order curvature couplings

We present a set of equations describing the evolution of the scalar-type cosmological perturbation in a gravity with general quadratic order curvature coupling terms. Equations are presented in a gauge ready form, thus are ready to implement various temporal gauge conditions depending on the problems. The Ricci-curvature square term leads to a fourth-order differential equation for describing the spacetime fluctuations in a spatially homogeneous and isotropic cosmological background.Comment: 5 pages, no figure, To appear in Phys. Rev.

On a self-sustained process at large scale in the turbulent channel flow

Large-scale motions, important in turbulent shear flows, are frequently attributed to the interaction of structures at smaller scale. Here we show that, in a turbulent channel at Re_{\tau} \approx 550, large-scale motions can self-sustain even when smaller-scale structures populating the near-wall and logarithmic regions are artificially quenched. This large-scale self-sustained mechanism is not active in periodic boxes of width smaller than Lz ~ 1.5h or length shorter than Lx ~ 3h which correspond well to the most energetic large scales observed in the turbulent channel

Third order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third and higher order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations we take the comoving gauge. We discover that the third-order correction terms are of $\phi_v$-order higher than the second-order terms where $\phi_v$ is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential we have $\delta \Phi \sim {3 \over 5} \phi_v$ to the linear order. Therefore, the pure general relativistic effects are of $varphi_v$-order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear order gravitational potential perturbation strength. From the temperature anisotropy of cosmic microwave background we have ${\delta T \over T} \sim {1 \over 3} \delta \Phi \sim {1 \over 5} \phi_v \sim 10^{-5}$. Therefore, our present result reinforces our previous important practical implication that near current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near the horizon.Comment: 9 pages, no figur