We derive an implicit-explicit (IMEX) formalism for the three-dimensional (3D) Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud resolving and mesoscale (flow in a 3D Cartesian domain) as well as global regimes (flow in spherical geometries). This general IMEX formalism admits numerous types of methods including single-stage multistep methods (e.g., Adams methods and backward difference formulas) and multistage singlestep methods (e.g., additive Runge-Kutta methods). The significance of this result is that it allows a numerical model to reuse the same machinery for all classes of time-integration methods described in this work. We also derive two classes of IMEX methods, one-dimensional and 3D, and show that they achieve their expected theoretical rates of convergence regardless of the geometry (e.g., 3D box or sphere) and introduce a new second-order IMEX Runge-Kutta method that performs better than the other second-order methods considered. We then compare all the IMEX methods in terms of accuracy and efficiency for two types of geophysical fluid dynamics problems: buoyant convection and inertia-gravity waves. These results show that the high-order time-integration methods yield better efficiency particularly when high levels of accuracy are desired.
Introduction.In a previous article  we introduced the nonhydrostatic unified model of the atmosphere (NUMA) for use in limited-area modeling (i.e., mesoscale or regional flow), namely, applications in which the flows are in large, three-dimensional (3D) Cartesian domains (imagine flow in a 3D box where the grid resolutions are below 10 km); the emphasis of that paper was on the performance of the model on distributed-memory computers with a large number of processors. In that paper we showed that the explicit RK35 time integrator (also used in this paper) was able to achieve strong linear scaling for processor counts on the order of 10 5 . The emphasis of the present article is on the mathematical framework of the model dynamics (i.e., we are not considering the subgrid-scale parameterization at this point;
A device for in situ SEM examination of crack propagation during loading of compact tension specimens is described, with a specific demonstration on an alumina ceramic. The device facilitates direct qualitative observations of the inception and subsequent frictional pullout of grain-localized bridges at the crack interface. Quantitative data on the bridging mechanism are obtained from measurements of the crack-opening displacements behind the crack tip. The crack profile is found to be closer to linear than parabolic at the bridged interface. Deconvolution of these crack-opening data allow for an evaluation of the closure tractions operative at the crack walls within the bridging zone, and thence the R-curve. [
Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation ͓"Time domain wave-equations for lossy media obeying a frequency power-law," J. Acoust. Soc. Am. 96, 491-500 ͑1994͔͒ is an approximation to this equation. This paper derives analytical time-domain Green's functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1 / 3, 1 / 2, 2 / 3, 3 / 2, and 2, the Green's function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green's functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green's functions are expressed as Fox and Wright functions and are noncausal.However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green's function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green's function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement.
Microencapsulation of fish oil was achieved by spray-drying homogenized emulsions of fish oil using 3 different types of casein as emulsifier and lactose as filler. As the degree of aggregation of the casein emulsifier increased, the vacuole volume of the microencapsulated powders decreased. The shelf life of the powders increased as the degree of aggregation of the casein emulsifier increased at the high homogenization conditions. When micellar casein was used as emulsifier, the shelf life also increased as homogenization conditions increased. Free fat but not surface fat was inversely related to shelf life. Since the type of casein used was confounded with the powder vacuole volume, the increased shelf life may have been due to either factor.
Fourier transform infrared (FTIR) spectroscopy and attenuated total reflection (ATR) sampling have been used to detect adulteration of honey samples. The sample set comprised 320 spectra of authentic (n = 99) and adulterated (n = 221) honeys. Adulterants used were solutions containing both d-fructose and d-glucose prepared in the following respective weight ratios: 0.7:1.0, 1.2:1.0 (typical of honey composition), and 2.3:1.0. Each adulterant solution was added to individual honeys at levels of 7, 14, and 21% w/w. Spectral data were compressed and analyzed using k-nearest neighbors (kNN) and partial least squares (PLS) regression techniques. A number of data pretreatments were explored. Best classification models were achieved with PLS regression on first derivative spectra giving an overall correct classification rate of 93%, with 99% of samples adulterated at levels of 14% w/w or greater correctly identified. This method shows promise as a rapid screening technique for detection of this type of honey adulteration.
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