Non-uniqueness for specifications in $\ell ^{2+\unicode[STIX]{x1D716}}$
Sign Up to like & getrecommendations! Published in 2017 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2016.101
Abstract: For every $p>2$ , we construct a regular and continuous specification ( $g$ -function), which has a variation sequence that is in $\ell ^{p}$ and which admits multiple Gibbs measures. Combined with a result of… read more here.
Keywords: non uniqueness; ell unicode; specifications ell; stix x1d716 ... See more keywords
On the normalized dissipation parameter $C_{\unicode[STIX]{x1D716}}$ in decaying turbulence
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Fluid Mechanics"
DOI: 10.1017/jfm.2017.110
Abstract: The Reynolds number dependence of the non-dimensional mean turbulent kinetic energy dissipation rate $C_{\unicode[STIX]{x1D716}}=\overline{\unicode[STIX]{x1D716}}L/u^{\prime 3}$ (where $\unicode[STIX]{x1D716}$ is the mean turbulent kinetic energy dissipation rate, $L$ is an integral length scale and $u^{\prime }$ is… read more here.
Keywords: stix x1d716; dissipation; unicode stix; turbulence ... See more keywords
A note on acoustic turbulence
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DOI: 10.1017/jfm.2019.523
Abstract: We consider a three-dimensional acoustic field of an ideal gas in which all entropy production is confined to weak shocks and show that similar scaling relations hold for such a field as for forced Burgers… read more here.
Keywords: stix; unicode stix; turbulence; stix x1d716 ... See more keywords
QUADRATIC NONRESIDUES AND NONPRIMITIVE ROOTS SATISFYING A COPRIMALITY CONDITION
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972718001065
Abstract: Let $q\geq 1$ be any integer and let $\unicode[STIX]{x1D716}\in [\frac{1}{11},\frac{1}{2})$ be a given real number. We prove that for all primes $p$ satisfying $$\begin{eqnarray}p\equiv 1\!\!\!\!\hspace{0.6em}({\rm mod}\hspace{0.2em}q),\quad \log \log p>\frac{2\log 6.83}{1-2\unicode[STIX]{x1D716}}\quad \text{and}\quad \frac{\unicode[STIX]{x1D719}(p-1)}{p-1}\leq \frac{1}{2}-\unicode[STIX]{x1D716},\end{eqnarray}$$ there exists… read more here.
Keywords: nonprimitive roots; stix x1d716; frac; nonresidues nonprimitive ... See more keywords