The Steady Boltzmann and Navier-Stokes Equations

The paper discusses the similarities and the differences in the mathematical theories of the steady Boltzmann and incompressible Navier-Stokes equations posed in a bounded domain. First we discuss two different scaling limits in which solutions of the steady Boltzmann equation have an asymptotic behavior described by the steady Navier-Stokes Fourier system. Whether this system includes the viscous heating term depends on the ratio of the Froude number to the Mach number of the gas flow. While the steady Navier-Stokes equations with smooth divergence-free external force always have at least one smooth solutions, the Boltzmann equation with the same external force set in the torus, or in a bounded domain with specular reflection of gas molecules at the boundary may fail to have any solution, unless the force field is identically zero. Viscous heating seems to be of key importance in this situation. The nonexistence of any steady solution of the Boltzmann equation in this context seems related to the increase of temperature for the evolution problem, a phenomenon that we have established with the help of numerical simulations on the Boltzmann equation and the BGK model.Comment: 55 pages, 4 multiple figure

Temperature, pressure, and concentration jumps for a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation

The half-space problem of the temperature, pressure, and concentration jumps for a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. First, the problem is shown to be reduced to three elemental ones: the problem of the jumps caused by the net evaporation or condensation, that caused by the gradient of temperature, and that caused by the gradient of concentration. Then, the latter two are investigated numerically in the present contribution because the first problem has already been studied [Yasuda, Takata, and Aoki, Phys. Fluids 17, 047105 (2005)]. The numerical method is a finite-difference one, in which the complicated collision integrals are computed by the extension of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] to the case of a gas mixture. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic quantities but also at the level of the velocity distribution function. In addition, accurate formulas of the temperature, pressure, and concentration jumps are constructed for arbitrary values of the concentration of the background reference state by the use of the Chebyshev polynomial approximation. The solution of the corresponding problem of a vapor-gas mixture and that of the temperature-jump problem on a simple solid wall are also obtained as special cases of the present problem

Stereotypical diel movement and dive pattern of male sperm whales in a submarine canyon revealed by land-based and bio-logging surveys

Male sperm whales are under pressure to grow larger in order to increase their mating opportunities, which could lead them to more efficiently forage in high latitude feeding grounds. Movement patterns of male sperm whales in Nemuro Strait, Japan, were investigated horizontally and vertically using land-based observation and bio-logging methods to determine how they facilitate foraging in the narrow submarine canyon. Eleven tagged whales showed the distinct diel pattern for dive depth, as it was deeper at night than during the day. Five-year data of land-based observation and GPS data from six tagged whales revealed the tendency of whales to change the north-south direction of their horizontal movement every 4–6 h, and this movement direction was not related to the direction of the current. Their periodic heading change is thought to be a consequence of the whales making two round trips each day within the foraging area, one during the day to shallow layers and one during the night to deep layers. These tactics may help the whales to search for prey in this narrow submarine canyon efficiently. Most whales changed their direction of movement in a similar manner, which is probably due to the whales’ tendency to stay close enough to each other to obtain information about the prey environment using the echolocation clicks of other whales. The results emphasize the ability of male sperm whales to adapt their foraging tactics according to the prey environment of their habitat and intense pressure to grow faster may be the drive for this ability. The importance of social cohesion among foraging male sperm whales was also suggested

25 学校ボランティア通信 No.13

発行日：2009年7月15

Revisiting symmetries of lattice fermions via spin-flavor representation

Employing the spin-flavor representation, we investigate the structures of the doubler-mixing symmetries and the mechanisms of their spontaneous breakdown in four types of lattice fermion formulation. We first revisit the U(4)\timesU(4)A symmetries of the naive fermion with the vanishing bare mass m, and re-express them in terms of the spin-flavor representation. We apply the same method to the Wilson fermion, which possesses only the U(1) vector symmetry for general values of m. For a special value of m, however, there emerges an additional U(1) symmetry to be broken by pion condensation. We also explore two types of minimally doubled fermion, and discover a similar kind of symmetry enhancement and its spontaneous breakdown.Comment: 25 pages, no figure;v2 typos corrected;v3 Sec.2 is shortened. To appear in JHE

A Shock-Induced Pair of Superbubbles in the High-Redshift Powerful Radio Galaxy MRC 0406-244

We present new optical spectroscopy of the high-redshift powerful radio galaxy MRC 0406$-$244 at redshift of 2.429. We find that the two extensions toward NW and SE probed in the rest-frame ultraviolet image are heated mainly by the nonthermal continuum of the active galactic nucleus. However, each extension shows a shell-like morphology, suggesting that they are a pair of superbubbles induced by the superwind activity rather than by the interaction between the radio jet and the ambient gas clouds. If this is the case, the intense starburst responsible for the formation of superbubbles could occur $\sim 1 \times 10^9$ yr ago. On the other hand, the age of the radio jets may be of the order of $\sim 10^6$ yr, being much shorter than the starburst age. Therefore, the two events, i.e., the starburst and the radio-jet activities, are independent phenomena. However, their directions of the expanding motions could be governed by the rotational motion of the gaseous component in the host galaxy. This idea appears to explain the alignment effect of MRC 0406$-$244.Comment: 4 pages (emulateapj.sty), Fig. 1 (jpeg) + Fig.2 (eps). Accepted for publications in ApJ (Letters

Knee joint preservation surgery in osteosarcoma using tumour-bearing bone treated with liquid nitrogen

Purpose: To preserve the joint structure in order to maintain good limb function in patients with osteosarcoma, we perform epiphyseal or metaphyseal osteotomy and reconstruction using frozen autografts that contain a tumour treated with liquid nitrogen. There are two methods of using liquid nitrogen-treated autografts: the free-freezing method and the pedicle-freezing method. The purpose of this study was to evaluate the results of intentional joint-preserving reconstruction using the free-freezing method and the pedicle-freezing method in patients with osteosarcoma. Methods: Between 2006 and 2014, we performed joint-preserving surgery (12 with the free-freezing method and six with the pedicle freezing method) to treat 18 cases of osteosarcoma (12 distal femurs and six proximal tibias) in patients who had achieved a good response to neoadjuvant chemotherapy. Results: Among the 18 patients (nine boys and nine girls) who had a mean age of 11.6 years, 13 remained continuously disease-free, three showed no evidence of disease, one was alive with the disease, and one died from the disease. Functional outcomes were assessed as excellent in 15 patients and poor in three, with a mean follow-up period of 46.1 months. The mean Musculoskeletal Tumour Society (MSTS) score was 90.2%. Except for one patient who underwent amputation, all patients could bend their knee through >90° flexion, and nine achieved full ROM. All but two patients could walk without aid, and 11 were able to run normally throughout the follow-up period. No intraoperative complications were observed, such as surrounding soft-tissue damage, neurovascular injury, or recurrence from frozen bone. Conclusions: Joint-preserving reconstruction using frozen autografts yielded excellent function in patients with osteosarcoma. © 2017 The Author(s)in Press / Embargo Period 12 month