ANALYSIS OF ENERGY SPECTRA BY THE VORTEX METHOD WITH ARTIFICIAL TURBULENCE

First, in order to use as an inlet condition for turbulent simulation, a method is presented which produces numerically an artificial turbulence, namely, a series of velocity fluctuations of which frequency is Gaussian, and energy spectrum and root mean square correspond to the given ones. Besides, the fluctuation data are determined by the characteristic parameters of turbulent flows such as the inlet mean velocity, the kinematic viscosity, the Kolmogorov scale and the integral time scale. Our examples show excellent accuracy and flexibility of the method. Secondly, the vortex method has been studied to see the ability of the method to deal with turbulent flows. It is found that the energy spectra produced by this agree well with the ones given as the inlet condition, and that the vortex method is able to produce turbulent flows with the given parameters described above

Efficiency of Turbulent Reacceleration by Solenoidal Turbulence and Its Application to the Origin of Radio Megahalos in Cluster Outskirts

Recent radio observations with the Low Frequency Array (LOFAR) discovered diffuse emission extending beyond the scale of classical radio halos. The presence of such megahalos indicates that the amplification of the magnetic field and acceleration of relativistic particles are working in the cluster outskirts, presumably due to the combination of shocks and turbulence that dissipate energy in these regions. Cosmological magnetohydrodynamical (MHD) simulations of galaxy clusters suggest that solenoidal turbulence has a significant energy budget in the outskirts of galaxy clusters. In this paper, we explore the possibility that this turbulence contributes to the emission observed in megahalos through second-order Fermi acceleration of relativistic particles and magnetic field amplification by the dynamo. We focus on the case of A2255 and find that this scenario can explain the basic properties of the diffuse emission component that is observed under assumptions that are used in previous literature. More specifically, we conduct a numerical follow-up, solving the Fokker-Planck equation by using a snapshot of an MHD simulation and deducing the synchrotron brightness integrated along the lines of sight. We find that a volume-filling emission, ranging between 30% and almost 100% of the projected area, depending on our assumptions on the particle diffusion and transport, can be detected at LOFAR sensitivities. Assuming a magnetic field B ∼ 0.2 μG, as derived from a dynamo model applied to the emitting region, we find that the observed brightness can be matched when ∼1% of the solenoidal turbulent energy flux is channeled into particle acceleration

A topology optimization method in rarefied gas flow problems using the Boltzmann equation

This paper presents a topology optimization method in rarefied gas flow problems to obtain the optimal structure of a flow channel as a configuration of gas and solid domains. In this paper, the kinetic equation, the governing equation of rarefied gas flows, is extended over the entire design domain including solid domains assuming the solid as an imaginary gas for implicitly handling the gas-solid interfaces in the optimization process. Based on the extended equation, a 2D flow channel design problem is formulated, and the design sensitivity is obtained based on the Lagrange multiplier method and adjoint variable method. Both the rarefied gas flow and the adjoint flow are computed by a deterministic method based on a finite discretization of the molecular velocity space, rather than the DSMC method. The validity and effectiveness of our proposed method are confirmed through several numerical examples

Robust circadian clocks from coupled protein modification and transcription-translation cycles

The cyanobacterium Synechococcus elongatus uses both a protein phosphorylation cycle and a transcription-translation cycle to generate circadian rhythms that are highly robust against biochemical noise. We use stochastic simulations to analyze how these cycles interact to generate stable rhythms in growing, dividing cells. We find that a protein phosphorylation cycle by itself is robust when protein turnover is low. For high decay or dilution rates (and co mpensating synthesis rate), however, the phosphorylation-based oscillator loses its integrity. Circadian rhythms thus cannot be generated with a phosphorylation cycle alone when the growth rate, and consequently the rate of protein dilution, is high enough; in practice, a purely post-translational clock ceases to function well when the cell doubling time drops below the 24 hour clock period. At higher growth rates, a transcription-translation cycle becomes essential for generating robust circadian rhythms. Interestingly, while a transcription-translation cycle is necessary to sustain a phosphorylation cycle at high growth rates, a phosphorylation cycle can dramatically enhance the robustness of a transcription-translation cycle at lower protein decay or dilution rates. Our analysis thus predicts that both cycles are required to generate robust circadian rhythms over the full range of growth conditions.Comment: main text: 7 pages including 5 figures, supplementary information: 13 pages including 9 figure