The Spatiotemporal Variability of Nonorographic Gravity Wave Energy and Relation to Its Source Functions

The way the large-scale flow determines the energy of the nonorographic mesoscale inertia–gravity waves (IGWs) is theoretically significant and practically useful for source parameterization of IGWs. The relations previously developed on the f plane for tropospheric sources of IGWs including jets, fronts, and convection in terms of associated secondary circulations strength are generalized for application over the globe. A low-pass spatial filter with a cutoff zonal wavenumber of 22 is applied to separate the large-scale flow from the IGWs using the ERA5 data of ECMWF for the period 2016–19. A comparison with GRACILE data based on satellite observations of the middle stratosphere shows reasonable representation of IGWs in the ERA5 data despite underestimates by a factor of smaller than 3. The sum of the energies, which are mass-weighted integrals in the troposphere from the surface to 100 hPa, as given by the generalized relations is termed initial parameterized energy. The corresponding energy integral for the IGWs is termed the diagnosed energy. The connection between the parameterized and diagnosed IGW energies is explored with regression analysis for each season and six oceanic domains distributed over the globe covering the Northern and Southern Hemispheres and the tropics. While capturing the seasonal cycle, the domain area-average seasonal mean initial parameterized energy is weaker than the diagnosed energy by a factor of 3. The best performance in regression analysis is obtained by using a combination of power and exponential functions, which suggests evidence of exponential weakness.

ON THE WEIGHTED FRACTIONAL OPERATORS OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION

The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.

Two-Dimensional Supersonic Thrust Vectoring Using Staggered Ramps

The thrust vectoring performance of a novel nozzle mechanism was numerically investigated. The nozzle was designed for supersonic, air-breathing engines using published engine data, isentropic relationships, and piecewise quartic splines. The mechanism utilizes two staggered, adjustable ramps. A baseline inviscid numerical simulation without ramps verified the nozzle design by comparing the results to the analytical data. Nine ramp configurations were analyzed under steady-state turbulent viscous conditions, using two sets of inlet parameters corresponding to inlet conditions with and without an afterburner (AB). The realizable k – ε model was used to model the turbulence field. Area-weighted integrals of the exit flow showed superior flow deflection with the nonafterburning inlet flow parameters. Calculations of the mean flow deflection angles showed that the flow can be deflected as much as 30 deg in a given direction with the largest ramp length and angle values. The smallest ramp length (less than 5% of the nozzle length) demonstrated as much as 21 deg in flow deflection.

A high-speed algorithm for computation of fractional differentiation and fractional integration

A high-speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm, the stored data are not the function to be differentiated or integrated but the weighted integrals of the function. The intervals of integration for the memory can be increased without loss of accuracy as the computing time-step n increases. The computing cost varies as , as opposed to n 2 of standard algorithms.

Tensorial Minkowski functionals of triply periodic minimal surfaces

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.

Units and Geometry

This chapter explores units and geometry in light measurement. For biologists not working on humans, it comes down to a few simple rules: use photons not watts; use wavelength not frequency, but be extremely careful when comparing the peaks of light spectra to sensitivity curves; stick to measuring radiance and irradiance, but be a pioneer and add scalar irradiance measurements to your papers; irradiance sometimes obeys the inverse-square law; radiance rarely does; do not use photometric units, except possibly for lux. However, the underlying principle of weighted integrals is useful for modeling animal vision and other wavelength-dependent processes.

High Speed Algorithm for Computation of Fractional Differentiation and Integration

A high speed algorithm for computing fractional differentiations and fractional integrations in fractional differential equations is proposed. In this algorithm the stored data is not the history of the function to be differentiated or integrated but the history of the weighted integrals of the function. It is shown that, by the computational method based on the new algorithm, the integration time only increases in proportion to n log n, different from n2 by a standard method, for n steps of integrations of a differential integration.