Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Petrographic/geochemical studies of primary and alteration–weathering minerals in garnetiferous ultramafic xenoliths–basanite, Tartous Province, NW Syria

Kimberlitic–pyropic peridotite–xenolites, probably of Jurassic–Cretaceous age, were found mixed with a younger Upper Tertiary basanitic diabase, as flow texture of plagioclase laths and ilmenite rods around those xenoliths indicated. Mafic–ultramafic rocks were crushed, sheared, and cropped along a creek about 15–18 km NE of the town of Dreikeesh, NW Syria. ⁴⁰K–⁴⁰Ar isotopic dating of a pure fresh black cpx sample, collected from the peridotite xenoliths, yielded an age of about 70 Ma. This age is concurrent to the time when Africa, Eurasia, and America were part of the super continent Pangaea. It also suggests that kimberlite–pyropic peridotitic rocks were located within a cratonic pipe prior to their 2000-km eastward journey (starting from the Mid-Atlantic Rift). Sampled outcrops were located within a ring of about 40 km diameter, considered to be a dome consisting of one or more clusters of kimberlitic pipes. The dome structure, mostly covered with Upper Jurassic–Cretaceous carbonate beds, was tilted westward, and rifted and sheared along its eastern edge. Tilting and crushing were accomplished after the opening of the Red Sea in the Miocene, and the counterclockwise movements of the Arabian plate, which folded the carbonate beds to form the N–S-trending Alawite mountain range along the Syrian coast. Olivine, cpx, and pyrope were the major phases in peridotite. Pyrope, including its Cr–Ni-contents, was found to be the best indicator to decipher the temperature–pressure (T–P) conditions for the system. The inferred temperature was found to be about 1460 °C, at a pressure of 62 kb (around 207 km-depth). Petrographic studies revealed many zoned, resorbed, octahedral and non-metasomatized tiny grains, associated with partly to wholly metasomatized and iddingsitized olivines.     

Improved estimation of a covariance matrix in an elliptically contoured matrix distribution

In this paper, the problem of estimating the covariance matrix of the elliptically contoured distribution (ECD) is considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean is proposed. It is shown that this new estimator dominates the unbiased estimator under the squared error loss function. Two special classes of ECD, namely, the multivariate-elliptical t distribution and the ε-contaminated normal distribution are considered. A simulation study is carried out and indicates that this new shrinkage estimator provides a substantial improvement in risk under most situations.     

Fast and Accurate Floating Point Summation with Application to Computational Geometry

We present several simple algorithms for accurately computing the sum of n floating point numbers using a wider accumulator. Let f and F be the number of significant bits in the summands and the accumulator, respectively. Then assuming gradual underflow, no overflow, and round-to-nearest arithmetic, up to ?2 ^F?f /(1?2^?f )?+1 numbers can be accurately added by just summing the terms in decreasing order of exponents, yielding a sum correct to within about 1.5 units in the last place. In particular, if the sum is zero, it is computed exactly. We apply this result to the floating point formats in the IEEE floating point standard, and investigate its performance. Our results show that in the absence of massive cancellation (the most common case) the cost of guaranteed accuracy is about 30–40% more than the straightforward summation. If massive cancellation does occur, the cost of computing the accurate sum is about a factor of ten. Finally, we apply our algorithm in computing a robust geometric predicate (used in computational geometry), where our accurate summation algorithm improves the existing algorithm by a factor of two on a nearly coplanar set of points.     

Tandem silylformylation-allyl(crotyl)silylation: a new approach to polyketide synthesis

Tandem intramolecular silylformylation-allyl(crotyl)silylation reactions have been developed that allow the highly efficient synthesis of polyketide fragments. The substrates are subjected to Rh(I)-catalyzed silylformylation to afford β-(diallyl)silyl aldehydes which undergo spontaneous uncatalyzed allylsilylation. This unusual spontaneous allylsilylation reaction is driven by strain release Lewis acidity, which arises from the ∼95° O-Si-C bond angle in the oxasilacyclopentane product of the silylformylation reaction. The methodology has been developed both for alkene and alkyne substrates, may be used to establish as many as three stereocenters, and has been shown to be amenable to use in an iterative fashion.     

Accurate Gain Flattening Filters Manufactured by Optical Compensation Monitoring Method

GFFs with less than 0.4 dB peak-to-peak error functions are routinely fabricated using commercially available coating machines by utilizing the natural error compensation mechanism of wavelength variable turning point optical monitoring method.     

Role of water vapor and CO2 in the paleoclimatic fluctuations along northwestern and southern Syria, and the adjacent Mediterranean Sea

Microscopic petrified grains were collected from a mafic–ultramafic pipe, NE of Dreikeesh, NW Syria. The grains were identified as anthers/gynoecia in herb/grass flowers. Three of the grains showed evidence of magnetism, two slowly dissolved in concentrated HCl, and three microprobed grains showed a montmorillonitic composition. Iron originating from pyroxene was oxidized to magnetite. Released silica formed the mineral suite agate–chalcedony–opal. Warm/cold paleoclimatic fluctuations, occurring during late Pliocene–Holocene, depended on water vapor, CO₂ production, and cinders in the atmosphere. Most of these were associated with changing volcanic/tectonic events. Fluctuations were controlled by heat reflected from the Earth's surface being absorbed by water vapor and CO₂, which both re-reflected the heat back to the surface, thus, raising the temperature. This cycle was repeated several times during late Pliocene–Holocene.     

Some New uniform frames with block size four and index one or three

In this paper, some new uniform frames with block size four and index one or three are obtained. The known existence results for (4,1)‐frames and (4,3)‐frames are both improved to the extent that only a finite number of possible exceptions remain. © 2003 Wiley Periodicals, Inc.