Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Substituent effects on the ring‐opening mechanism of gem‐dibromospiropentanes to related allenes: a theoretical study

Density functional theory computations at B3LYP and X3LYP levels were performed for ring openings of substituted gem‐dibromospiropentanes (R = ―H, ―Cl, ―Br, ―CH₃, ―SiH₃, ―OH, ―OCH₃, ―CF₃, ―BF₂, and ―SH) to related allenes. The conversion of spiropentanoids 5a , 5b , 5c , 5d , 5e , 5f , 5g , 5h , 5i , 5j to the corresponding allenes 7a , 7b , 7c , 7d , 7e , 7f , 7g , 7h , 7i , 7j can proceed in both concerted and stepwise mechanism except for R = ―H. Both ring‐opening mechanisms have similar activation energy barriers to open the spiropentanylidene ring and generate the structure of allene at all theoretical levels used herein. Generally the π electron‐donating group (―OH or ―SH) decreases the activation barrier for the follow‐up reaction of 1‐bromo‐1‐lithiospiropentanoid and free spiropentanylidene. Hence, both bearing electron‐donating substituents are more reactive than those with electron‐withdrawing group, and the first one to open the ring to the LiBr–allene complex does so more readily than the second. The sEDA index used to measure sigma‐electron excess/deficiency of the cyclopropylidene ring is mutually correlated for the studied systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Equilibrium Formation of Stable All‐Silicon Versions of 1,3‐Cyclobutanediyl

Main group analogues of cyclobutane‐1,3‐diyls are fascinating due to their unique reactivity and electronic properties. So far only heteronuclear examples have been isolated. Here we report the isolation and characterization of all‐silicon 1,3‐cyclobutanediyls as stable closed‐shell singlet species from the reversible reactions of cyclotrisilene c‐Si₃Tip₄ (Tip=2,4,6‐triisopropylphenyl) with the N‐heterocyclic silylenes c‐[(CR₂CH₂)(NtBu)₂]Si: (R=H or methyl) with saturated backbones. At elevated temperatures, tetrasilacyclobutenes are obtained from these equilibrium mixtures. The corresponding reaction with the unsaturated N‐heterocyclic silylene c‐(CH)₂(NtBu)₂Si: proceeds directly to the corresponding tetrasilacyclobutene without detection of the assumed 1,3‐cyclobutanediyl intermediate.     

Renal-related perinephric fluid collections: MRI findings

We retrospectively reviewed MR studies on 10 patients with renal-related perinephric fluid collections who underwent MRI in three institutions between January 2001 and August 2004. All patients underwent MRI of the abdomen and T1-weighted, T2-weighted and serial contrast-enhanced images, including delayed-phase contrast-enhanced images 10-12 min after contrast injection, were obtained. Perinephric fluid collections in 5 patients revealed MRI findings of simple fluid content (i.e., hypointense on T1-weighted images and hyperintense on T2-weighted images). In another 5 patients, a complex perinephric fluid content (i.e., mixed hyper/hypointense on T1-weighted images and mixed hypo/hyperintense on T2-weighted images compatible with blood breakdown products and pus) was observed. In 5 patients, contrast extravasation on late-phase images that was compatible with urine leak was demonstrated. Our results suggest that MRI may determine the content of perinephric fluid collections on noncontrast T1-weighted and T2-weighted images and that contrast extravasation on late-phase images is associated with urine extravasation from renal collecting systems.     

Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance

Multivariate adaptive regression splines (MARS) has become a popular data mining (DM) tool due to its flexible model building strategy for high dimensional data. Compared to well-known others, it performs better in many areas such as finance, informatics, technology and science. Many studies have been conducted on improving its performance. For this purpose, an alternative backward stepwise algorithm is proposed through Conic-MARS (CMARS) method which uses a penalized residual sum of squares for MARS as a Tikhonov regularization problem. Additionally, by modifying the forward step of MARS via mapping approach, a time efficient procedure has been introduced by S-FMARS. Inspiring from the advantages of MARS, CMARS and S-FMARS, two hybrid methods are proposed in this study, aiming to produce time efficient DM tools without degrading their performances especially for large datasets. The resulting methods, called SMARS and SCMARS, are tested in terms of several performance criteria such as accuracy, complexity, stability and robustness via simulated and real life datasets. As a DM application, the hybrid methods are also applied to an important field of finance for predicting interest rates offered by a Turkish bank to its customers. The results show that the proposed hybrid methods, being the most time efficient with competing performances, can be considered as powerful choices particularly for large datasets.     

A chalcone showing positional disorder,two related diarylcyclohexenones showing enantiomeric disorder and a related hydroxyterphenyl,all derived from simple carbonyl precursors

Four compounds are reported, all of which lie along a versatile reaction pathway which leads from simple carbonyl compounds to terphenyls. (2E)‐1‐(2,4‐Dichlorophenyl)‐3‐ [4‐(prop‐1‐en‐2‐yl)phenyl]prop‐2‐en‐1‐one, C₁₈H₁₄Cl₂O, (I), prepared from 4‐(prop‐1‐en‐2‐yl)benzaldehyde and 2,4‐dichloroacetophenone, exhibits disorder over two sets of atomic sites having occupancies of 0.664 (6) and 0.336 (6). The related chalcone (2E)‐3‐(4‐chlorophenyl)‐1‐(4‐fluorophenyl)prop‐2‐en‐1‐one reacts with acetone to produce (5RS)‐3‐(4‐chlorophenyl)‐5‐[4‐(propan‐2‐yl)phenyl]cyclohex‐2‐en‐1‐one, C₂₁H₂₁ClO, (II), which exhibits enantiomeric disorder with occupancies at the reference site of 0.662 (4) and 0.338 (4) for the (5R) and (5S) forms; the same chalcone reacts with methyl 3‐oxobutanoate to give methyl (1RS,6SR)‐4‐(4‐chlorophenyl)‐6‐[4‐(propan‐2‐yl)phenyl]‐2‐oxocyclohex‐3‐ene‐1‐carboxylate, C₂₃H₂₃ClO₃, (III), where the reference site contains both (1R,6S) and (1S,6R) forms with occupancies of 0.923 (3) and 0.077 (3), respectively. Oxidation, using 2,3‐dichloro‐5,6‐dicyano‐1,4‐benzoquinone, of ethyl (1RS,6SR)‐6‐(4‐bromophenyl)‐4‐(4‐fluorophenyl)‐2‐oxocyclohex‐3‐ene‐1‐carboxylate, prepared in a similar manner to (II) and (III), produces ethyl 4′′‐bromo‐4‐fluoro‐5′‐hydroxy‐1,1′:3′,1′′‐terphenyl‐4′‐carboxylate, C₂₁H₁₆BrFO₃, (IV), which crystallizes with Z′ = 2 in the space group P. There are no significant intermolecular interactions in the structures of compounds (I) and (II), but for the major disorder component of compound (III), the molecules are linked into sheets by a combination of C—H...O and C—H...π(arene) hydrogen bonds. The two independent molecules of compound (IV) form two different centrosymmetric dimers, one built from inversion‐related pairs of C—H...O hydrogen bonds and the other from inversion‐related pairs of C—H...π(arene) hydrogen bonds. Comparisons are made with related compounds.     

Solvent,substituent, and dimerization effects on the ring-opening mechanisms of monosilacyclopropylidenoids: a theoretical study

Density functional theory and ab initio computations elucidated the ring-opening of substituted (R = –CF₃, –CN, –CH₃, –H, –NH₂, –OCH₃, –OH, –SiH₃) 1-bromo–1-lithiosilirane 1 and 2-bromo–2-lithiosilirane 2 to LiBr complexes of 2-silaallene and 1-silaallene, respectively. Formally, two competitive pathways can be considered. The ring-opening reaction can take place through a concerted manner via TS3. Alternatively, the reaction may proceed in a stepwise fashion with the intermediacy of a free silacyclopropylidene–LiBr complex 7. In both cases, the position of the substituents determines the kinetic of the reactions. The structures with an electron-donating group are generally unstable, whereas the silacyclopropylidenoids bearing electron-withdrawing substituents are particularly stable species. Here, we propose the ring-opening of 5a–h to corresponding LiBr complexes of 2-silaallenes can proceed in both concerted and stepwise mechanism except for –H, –CH₃, and –SiH₃. The obtained activation energies for the ring-openings of 5a–h to related 2-silaallenes are too high for a reaction at room temperature with up to 61.4 kcal/mol. In contrast, the activation energy barriers for the isomerization of 6a–h to the LiBr complexes of 1-silaallenes was determined to be relatively low at the B3LYP/6-31+G(d,p), M06/6-31+G(d,p), and MP2/6-31+G(d,p) levels. Moreover, we have also investigated the solvent effect on the unsubstituted models using both implicit and explicit solvation models. The energy barriers of the solvated models are found to be slightly higher than the results of gas phase calculations. Additionally, the ring-opening of dimer 6 (6–Dim) is also calculated for the ring-opening mechanism with the energy barrier of 3.7 kcal/mol at B3LYP/6-31+G(d,p) level of theory.     

Pediatric abdominal masses: diagnostic accuracy of diffusion weighted MRI

Purpose

To retrospectively identify apparent diffusion coefficient (ADC) values of pediatric abdominal mass lesions, to determine whether measured ADC of the lesions and signal intensity on diffusion-weighted (DW) images allow discrimination between benign and malignant mass lesions.

Materials and Methods

Approval for this retrospective study was obtained from the institutional review board. Children with abdominal mass lesions, who were examined by DW magnetic resonance imaging (MRI) were included in this study. DW MR images were obtained in the axial plane by using a non breath-hold single-shot spin-echo sequence on a 1.5-T MR scanner. ADCs were calculated for each lesion. ADC values were compared with Mann–Whitney U test. Receiver operating characteristic curve analysis was performed to determine cut-off values for ADC. The results of visual assessment on b800 images and ADC map images were compared with chi-square test.

Results

Thirty-one abdominal mass lesions (16 benign, 15 malignant) in 26 patients (15 girls, 11 boys, ranging from 2 days to 17 years with 6.9 years mean) underwent MRI. Benign lesions had significantly higher ADC values than malignant ones (P<.001). The mean ADCs of malignant lesions were 0.84±1.7×10⁻³ mm²/s, while the mean ADCs of the benign ones were 2.28±1.00×10⁻³ mm²/s. With respect to cutoff values of ADC: 1.11×10⁻³ mm²/s, sensitivity and negative predictive values were 100%, specificity was 78.6% and positive predictive value was 83.3%. For b800 and ADC map images, there were statistically significant differences on visual assessment. All malignant lesions had variable degrees of high signal intensity whereas eight of the 16 benign ones had low signal intensities on b800 images (P<.001). On ADC map images, all malignant lesions were hypointense and most of the benign ones (n=11, 68.7%) were hyperintense (P<.001).

Conclusion

DW imaging can be used for reliable discrimination of benign and malignant pediatric abdominal mass lesions based on considerable differences in the ADC values and signal intensity changes.     

A generalized Weiszfeld method for the multi-facility location problem

An iterative method is proposed for the K facilities location problem. The problem is relaxed using probabilistic assignments, depending on the distances to the facilities. The probabilities, that decompose the problem into K single-facility location problems, are updated at each iteration together with the facility locations. The proposed method is a natural generalization of the Weiszfeld method to several facilities.