Mixing and Un-mixing by Incompressible Flows

We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\|\nabla u(\cdot,t)\|_p\leq 1$ we show that any function can be mixed to scale $\epsilon$ in time $O(|\log\epsilon|^{1+\nu_p})$, with $\nu_p=0$ for $p<\tfrac{3+\sqrt 5}2$ and $\nu_p\leq \tfrac 13$ for $p\geq \tfrac{3+\sqrt 5}2$. Known lower bounds show that this rate is optimal for $p\in(1,\tfrac{3+\sqrt 5}2)$. We also show that any set which is mixed to scale $\epsilon$ but not much more than that can be un-mixed to a rectangle of the same area (up to a small error) in time $O(|\log\epsilon|^{2-1/p})$. Both results hold with scale-independent finite times if the constraint on the flow is changed to $\|u(\cdot,t)\|_{\dot W^{s,p}}\leq 1$ with some $s<1$. The constants in all our results are independent of the mixed functions and sets.Comment: 37 pages, 5 figure

Turbulent mixing

The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics of such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach of direct simulation, especially in high Schmidt number fluids, such as water, in which species diffusion scales are one and a half orders of magnitude smaller than the smallest flow scales. The discussion below attempts to provide an overview of turbulent mixing; the attendant experimental, theoretical, and computational challenges; and suggests possible future directions for progress in this important field

Code Mixing Used by the Presenter on Visi Fm

This study deals with code-mixing used by presenters on VISI FM. The objectives of this study are to : (1) find out the forms ofcode-mixing, that are used by VISI FM's presenters. (2) find out the form of code- mixing that is dominantly used by VISI FM's presenter. This research applied descriptive quantitative method.The object of this study is presenter of VISI FM namely Deris and Lia. The tape recorder is used for collecting the data where the utterence of presenters were recorded while presenting that program.After collecting the data, the writer found that forms of code mixing occured in the presenters's utterances are code mixing in forms words, phrases, and sentences. Code mixing in form of word is dominantly used by male presenters namely Deris, where the percentage of the occurrence of code mixing in his utterances are 255 code mixing, where there are 29 code mixing in form of sentences, 92 code mixing in form of phrases, and 133 code mixing in form of words and code mixing in form of sentence is dominantly used by female presenter namely Lia where the percentage of the occurrence of code mixing in her utterances are 184 code mixing occured where there are 82 code mixing in form of sentences, 44 code mixing in form of phrases, and 58 code mixing in form of words. Keyword : Code Mixin

B Mixing

The neutral $B$ mesons, $B^0$ and $B_s$, can oscillate between their particle and antiparticle states owing to flavor-changing weak interactions. In recent years, techniques to detect these oscillations as a function of the meson's decay time have been developed. In this article the physics of flavor oscillations is reviewed and theoretical predictions are summarized. The many observations that demonstrate the time-dependence of B^0-\B0bar oscillations are presented along with a combined measurement of its frequency, $\delta m_d$. The attempts to measure the $B_s$ oscillation frequency, both directly and indirectly, are then summarized. Finally, values for the CKM elements $|V_{td}|$ and $|V_{ts}/V_{td}|$ are extracted

Vector meson ω\omega-ϕ\phi mixing and their form factors in light-cone quark model

The vector meson $\omega$-$\phi$ mixing is studied in two alternative scenarios with different numbers of mixing angles, i.e., the one-mixing-angle scenario and the two-mixing-angle scenario, in both the octect-singlet mixing scheme and the quark flavor mixing scheme. Concerning the reproduction of experimental data and the $Q^2$ behavior of transition form factors, one-mixing-angle scenario in the quark flavor scheme performs better than that in the octet-singlet scheme, while the two-mixing-angle scenario works well for both mixing schemes. The difference between the two mixing angles in the octet-singlet scheme is bigger than that in the quark flavor scheme.Comment: 16 pages, 7 figures, final version to appear in PR