A compressible near-wall turbulence model for boundary layer calculations

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects

On quantization of weakly nonlinear lattices. Envelope solitons

A way of quantizing weakly nonlinear lattices is proposed. It is based on introducing "pseudo-field" operators. In the new formalism quantum envelope solitons together with phonons are regarded as elementary quasi-particles making up boson gas. In the classical limit the excitations corresponding to frequencies above linear cut-off frequency are reduced to conventional envelope solitons. The approach allows one to identify the quantum soliton which is localized in space and understand existence of a narrow soliton frequency band.Comment: 5 pages. Phys. Rev. E (to appear

Spontaneous Magnetization of Solid Quark-cluster Stars

Pulsar-like compact stars usually have strong magnetic fields, with the strength from $\sim 10^8$ to $\sim 10^{12}$ Gauss on surface. How such strong magnetic fields can be generated and maintained is still an unsolved problem, which is, in principle, related to the interior structure of compact stars, i.e., the equation of state of cold matter at supra-nuclear density. In this paper we are trying to solve the problem in the regime of solid quark-cluster stars. Inside quark-cluster stars, the extremely low ratio of number density of electrons to that of baryons $n_e/n_b$ and the screening effect from quark-clusters could reduce the long-range Coulomb interaction between electrons to short-range interaction. In this case, the Stoner's model could apply, and we find that the condition for ferromagnetism is consistent with that for validity of Stoner's model. Under the screened Coulomb repulsion, the electrons inside the stars could spontaneously magnetized and become ferromagnetic, and hence would contribute non-zero net magnetic momentum to the whole star. We conclude that, for most cases in solid quark-cluster stars, the amount of net magnetic momentum, which is proportional to the amount of unbalanced spins $\xi=(n_+-n_-)/n_e$ and depends on the number density of electrons $n_e=n_++n_-$, could be significant with non-zero $\xi$. The net magnetic moments of electron system in solid quark-cluster stars could be large enough to induce the observed magnetic fields for pulsars with $B\sim 10^{11}$ to $\sim 10^{13}$ Gauss.Comment: 7 pages, 1 figure. Accepted by Chinese Physics

Dissipative chaotic scattering

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte

A Polytropic Model of Quark Stars

A polytropic quark star model is suggested in order to establish a general framework in which theoretical quark star models could be tested by observations. The key difference between polytropic quark stars and the polytropic model studied previously for normal (i.e., non-quarkian) stars is related to two issues: (i) a constant term representing the contribution of vacuum energy may be added in the energy density and the pressure for a quark star, but not for a normal star; (ii) the quark star models with non-vanishing density at the stellar surface are not avoidable due to the strong interaction between quarks. The first one implies that the vacuum inside a quark star is different from that outside, while the second one is relevant to the effect of color confinement. The polytropic equations of state are stiffer than that derived in conventional realistic models (e.g., the bag model) for quark matter, and pulsar-like stars calculated with a polytropic equation of state could then have high maximum masses (> 2 M_sun). Quark stars can also be very low massive, and be still gravitationally stable even if the polytropic index, n, is greater than 3. All these would result in different mass-radius relations, which could be tested by observations. In addition, substantial strain energy would develop in a solid quark star during its accretion/spindown phase, and could be high enough to take a star-quake. The energy released during star-quakes could be as high as ~ 10^{47} ergs if the tangential pressure is ~ 10^{-6} higher than the radial one.Comment: 17 pages, 4 figures, last version accepted for publication in Astroparticle Physic