Growth and formation of the foreleg skeleton inbred mice and rats under conditions of hypo-, normo- and hyperdynamia

Inbred 1 month old males of C57B 1/6, CBA, CC57Br/Mw interlinear hybrid mice of the first generation and rats of the August and Wistar lines were subjected to conditions of hypo-, normo- and hyperdynamia for 2 months. The statistically reliable dependence is shown between mechanical underloadings and overloadings and macro microscopic changes in the hind limb skeleton of animals. Genetic determination of growth and formation of the forelimb skeleton is established. Hereditary susceptibility and the phenomenon of heterosis are preserved under all motor conditions

Scattering by a perforated sandwich membrane: method of Riemann surfaces

The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is exactly solved. The model is governed by two Helmholtz equations for the velocity potentials in the upper and lower half-planes coupled by the Leppington effective boundary condition and the equation of vibration of a membrane in a fluid. Two methods of solution are proposed and discussed. Both methods reduce the problem to an order-2 vector Riemann-Hilbert problem. The matrix coefficients have different entries, have the Chebotarev-Khrapkov structure and share the same order-4 characteristic polynomial. Exact Wiener-Hopf matrix factorization requires solving a scalar Riemann-Hilbert on an elliptic surface and the associated genus-1 Jacobi inversion problem solved in terms of the associated Riemann $\theta$-function. Numerical results for the absolute value of the total velocity potentials are reported and discussed.Comment: 28 pages. 9 figure

Supercavitating motion of a wedge in a jet

The problem of determining the free surface of a jet incident on a rigid wedge and the bound- ary of a cavity behind the wedge is considered. The single- and double-spiral-vortex models by Tulin are used to describe the flow at the rear part of the cavity. The location of the wedge in the jet and the sides lengths are arbitrary. This circumstance makes the flow domain doubly connected for the single-vortex model whilst it is simple connected for the double-vortex model. Both the models are solved in closed form by the method of conformal mappings. The maps are expressed through the solutions to certain Riemann-Hilbert problems. For the former model, this problem is formulated on a genus-1 Riemann surface. The double-vortex model requires the solution to a standard Riemann-Hilbert problem on a plane. It is found that the drag and lift are practically the same whilst the jet surface, the cavity boundary at the rear part and the deflection angle of the jet at infinity are different. Also, the problem of determining the parameters for the conformal mapping in the singlevortex model has two solutions. It is shown that one of the solutions leads to a non-physical shape of the cavity and needs to be discarded. The case of a wedge in a channel with a free surface is also analyzed.http://deepblue.lib.umich.edu/bitstream/2027.42/84229/1/CAV2009-final21.pd

Faddeev calculation of pentaquark Θ+\Theta^+ in the Nambu-Jona-Lasinio model-based diquark picture

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $\Theta^+$ in the diquark picture of Jaffe and Wilczek in which $\Theta^+$ is a diquark-diquark-${\bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of ${\bar s}D$ and $D D$. With the use of coupling constants determined from the meson sector, we find that ${\bar s}D$ interaction is attractive in s-wave while $DD$ interaction is repulsive in p-wave. With only the lowest three-body channel considered, we do not find a bound $\frac 12^+$ pentaquark state. Instead, a bound pentaquark $\Theta^+$ with $\frac 12^-$ is obtained with a unphysically strong vector mesonic coupling constants.Comment: 22 pages, 11 figures, accepted version in Phys. Rev. C. Summary of main changes/corrections: 1. "which only holds at tree level" below the eq. (23) is added. 2. In the last paragraph of p.23 we added a remark that the coupling constant obtained from Lambda mass is different from the estimate as obtained from the meson spectru