Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier--Stokes equations

To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes equations. The explicit particle method is based on a penalty problem, which converges theoretically to the incompressible Navier--Stokes equations, and is discretized in space by generalized approximate operators defined as a wider class of approximate operators than those of the smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods. By considering an analytical derivation of the explicit particle method and truncation error estimates of the generalized approximate operators, sufficient conditions of convergence are conjectured.Under these conditions, the convergence of the explicit particle method is confirmed by numerically comparing errors between exact and approximate solutions. Moreover, by focusing on the truncation errors of the generalized approximate operators, an optimal weight function is derived by reducing the truncation errors over general particle distributions. The effectiveness of the generalized approximate operators with the optimal weight functions is confirmed using numerical results of truncation errors and driven cavity flow. As an application for flow problems with free surface effects, the explicit particle method is applied to a dam break flow.Comment: 27 pages, 13 figure

Interspecific differences in the larval performance of Pieris butterflies (Lepidoptera: Pieridae) are associated with differences in the glucosinolate profiles of host plants

The tremendous diversity of plants and herbivores has arisen from a coevolutionary relationship characterized by plant defense and herbivore counter adaptation. Pierid butterfly species feed on Brassicales plants that produce glucosinolates as a chemical deterrent against herbivory. In turn, the larvae of pierids have nitrile specifier proteins (NSPs) that are expressed in their gut and disarm glucosinolates. Pierid butterflies are known to have diversified in response to glucosinolate diversification in Brassicales. Therefore, each pierid species is expected to have a spectrum of host plants characterized by specific glucosinolate profiles. In this study, we tested whether the larval performance of different Pieris species, a genus in Pieridae (Lepidoptera: Pieridae), was associated with plant defense traits of putative host plants. We conducted feeding assays using larvae of three Pieris species and 10 species of the Brassicaceae family possessing different leaf physical traits and glucosinolate profile measurements. The larvae of Pieris rapae responded differently in the feeding assays compared with the other two Pieris species. This difference was associated with differences in glucosinolate profiles but not with variations in physical traits of the host plants. This result suggests that individual Pieris species are adapted to a subset of glucosinolate profiles within the Brassicaceae. Our results support the idea that the host ranges of Pieris species depend on larval responses to glucosinolate diversification in the host species, supporting the hypothesis of coevolution between butterflies and host plants mediated by the chemical arms race

Arthrectomy for traumatic proximal interphalangeal arthritis in the lateral digit in a heifer

ΔΕΝ ΔΙΑΤΙΘΕΤΑΙ ΠΕΡΙΛΗΨΗInstructive information on the treatment for chronic deep infections of digital joints in a 9-month-old Holstein heifer is described in this report. Preoperative ultrasonographic and radiographic examinations revealed soft tissue swelling and subchondral bone lysis at the distal part of the proximal phalanx in the lateral digit. Arthrectomy was performed under xylazine sedation to remove infectious articular cartilage tissues. Immature callus formation was observed via radiography at the surgical site by the 28th postoperative day. On the 48th postoperative day, callus fellinto disrepair on the radiographs along with aggravation of the locomotion score. After the application of a half-limb cast, the immature callus formed again by the 62nd postoperative day (11 months), and bony callus formation was observed by the 74th postoperative day. Thereafter, the heifer could walk well with marked improvement in the locomotion score. The withers height of the heifer at 13 months (136 cm) was within the range of that in control heifers of the same age on this farm (133 ± 3 cm); however, the body weight (BW) of this heifer (322 kg) was lower than the BW of controls (384 ± 26 kg). The BW gain from 11 to 13 months of age seemed to be higher in the present heifer (+76 kg) than in controls (+55±20 kg), suggesting that BW of the present heifer was returning to the original BW. Based on these observations, we suggested that arthrectomy was an effective treatment option for the present case of digital joint arthritis