Robert Anderssen, A.R. Davies, F. R. de Hoog, R. J. Loy,
... of the storage and loss moduli, $G^{\prime }(\unicode[STIX]{x1D714})$ and $G^{\prime \prime }(\unicode[STIX]{x1D714})$ , respectively, are only measured and recorded for a number of values of the frequency $\unicode[STIX]{x1D714}$ in some well-defined finite range $[\unicode[STIX]{x1D714}_{\text{min}},\unicode[STIX]{x1D714}_{\text{max}}]$ . In many practical situations, when the range $[\unicode[STIX]{x1D714}_{\text{min}},\unicode[STIX]{x1D714}_{\text{max}}]$ is sufficiently large, information ... interrelationship between the frequency dependence of $G^{\prime }(\unicode[STIX]{x1D714})$ and $G^{\prime \prime }(\unicode[STIX]{ ...
Tópico(s): Material Dynamics and Properties
2016 - Cambridge University Press | The ANZIAM Journal
Michael Dodd, Antonino Ferrante,
... at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$ . In the droplet-laden cases, ... droplet- to carrier-fluid density ratio ( $1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$ ) or the droplet- to carrier-fluid viscosity ratio ( $1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$ ). In this work, ... DNS results show that increasing $\mathit{We}_{rms}$ , $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\ ...
Tópico(s): Fluid Dynamics and Turbulent Flows
2016 - Cambridge University Press | Journal of Fluid Mechanics
Let $\unicode[STIX]{x1D706}$ denote the Liouville function. The Chowla conjecture, in the two-point correlation case, asserts that $$\begin{eqnarray}\mathop{\sum }_{n\leqslant x}\unicode[STIX]{x1D706}(a_{1}n+b_{1})\unicode[STIX]{x1D706}(a_{2}n+b_{2})=o( ... logarithmically averaged version $$\begin{eqnarray}\mathop{\sum }_{x/\unicode[STIX]{x1D714}(x)<n\leqslant x}\frac{\unicode[STIX]{x1D706}(a_{1}n+b_{1})\unicode[STIX]{x1D706}(a_{2}n+b_{2})}{n}=o(\log \unicode[STIX]{x1D714}(x))\end{eqnarray}$$ of the Chowla conjecture as $x\rightarrow \infty$ , where $1\leqslant \unicode[STIX]{x1D714}(x)\leqslant x$ is an arbitrary ...
Tópico(s): Limits and Structures in Graph Theory
2016 - Cambridge University Press | Forum of Mathematics Pi
... of an exact area-preserving twist map $\bar{\unicode[STIX]{x1D711}}$ and consider the tilted Frenkel–Kontorova ( ... depinning force is the critical value $F_{d}(\unicode[STIX]{x1D714})$ depending on the mean spacing $\unicode[STIX]{x1D714}$ of particles, above which the tilted ... exists an invariant circle with irrational rotation number $\unicode[STIX]{x1D714}$ for $\bar{\unicode[STIX]{x1D711}}$ if and only if $F_{d}(\unicode[STIX]{x1D714})=0$ . For rational $\unicode[STIX]{x1D714}$ , $F_{d}(\unicode[STIX]{x1D714})=0$ ...
Tópico(s): Theoretical and Computational Physics
2016 - Cambridge University Press | Ergodic Theory and Dynamical Systems
Jinyul Hwang, Jin Lee, Hyung Jin Sung,
... turbulent pipe and channel flows at $\mathit{Re}_{\unicode[STIX]{x1D70F}}\approx 930$ are used to investigate ... arise from the dominant contributions of the LSMs ( $\unicode[STIX]{x1D706}_{x}>3\unicode[STIX]{x1D6FF}$ ) to the Reynolds shear stress in ... the spectra of velocity–vorticity correlations, $\langle v\unicode[STIX]{x1D714}_{z}\rangle$ and $\langle -w\unicode[STIX]{x1D714}_{y}\rangle$ , which are related to ... is due to the contribution of $\langle -w\unicode[STIX]{x1D714}_{y}\rangle$ at longer wavelengths ( $\unicode[ ...
Tópico(s): Plant Water Relations and Carbon Dynamics
2016 - Cambridge University Press | Journal of Fluid Mechanics
... to analytical expressions for the first and second ( $\unicode[STIX]{x1D615}_{1}$ and $\unicode[STIX]{x1D615}_{2}$ ) normal stress differences and other ... Burnett-order constitutive relations. Theoretical expressions for both $\unicode[STIX]{x1D615}_{1}$ and $\unicode[STIX]{x1D615}_{2}$ and those for pressure and ... 0.5$ ). While the first normal stress difference $\unicode[STIX]{x1D615}_{1}$ is found to be positive ... the dense limit, the second normal stress difference $\unicode[STIX]{x1D615}_{2}$ is negative and positive in ...
Tópico(s): Material Dynamics and Properties
2016 - Cambridge University Press | Journal of Fluid Mechanics
Let $\unicode[STIX]{x1D6E4}$ be a countable discrete group that acts on a unital $C^{\ast }$ -algebra $A$ through an action $\unicode[STIX]{x1D6FC}$ . If $A$ has a faithful $\unicode[STIX]{x1D6FC}$ -invariant tracial state $\unicode[STIX]{x1D70F}$ , then $\unicode[STIX]{x1D70F}^{\prime }=\unicode[STIX]{x1D70F}\circ {\mathcal{E}}$ is a faithful tracial state of $A\rtimes _{\unicode[STIX]{x1D6FC},r}\unicode[STIX]{x1D6E4}$ where ${\mathcal{E}}:A\rtimes _{\unicode[STIX]{x1D6FC},r}\unicode[STIX]{x1D6E4}\rightarrow A$ is the canonical faithful ...
Tópico(s): Algebraic structures and combinatorial models
2016 - Cambridge University Press | Bulletin of the Australian Mathematical Society
... action (or $(\mathbb{N}\cup \{0\})^{l}$ -action) $\unicode[STIX]{x1D70F}$ on a non-empty compact metrisable space $\unicode[STIX]{x1D6FA}$ , for some $l\in \mathbb{N}$ . ... of the restriction of the entropy map $h^{\unicode[STIX]{x1D70F}}$ to the set of ergodic states is dense in the graph of $h^{\unicode[STIX]{x1D70F}}$ . We assume that $h^{\unicode[STIX]{x1D70F}}$ is finite and upper semi-continuous. ... notion: Gateaux differentiability of the pressure map $P^{\unicode[STIX]{x1D70F}}$ on some sets dense in the space $C(\unicode[STIX]{x1D6FA})$ of real-valued continuous functions on $\ ...
Tópico(s): advanced mathematical theories
2016 - Cambridge University Press | Ergodic Theory and Dynamical Systems
Yantao Yang, Roberto Verzicco, Detlef Lohse,
... a very weak dependence on the density ratio $\unicode[STIX]{x1D6EC}$ , which is the ratio of the ... are dependent on both $\mathit{Ra}_{S}$ and $\unicode[STIX]{x1D6EC}$ . However, the rescaled Reynolds number $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ and the rescaled convective heat flux $(\mathit{Nu}_{T}-1)\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{T}^{eff}}$ depend only on $\mathit{ ... and are determined from the numerical results as $\unicode[STIX]{x1D6FC}_{u}^{eff}=0.25\pm 0.02$ and $\unicode[STIX]{x1D6FC}_{T}^{eff}=0.75\pm 0. ...
Tópico(s): Plant Water Relations and Carbon Dynamics
2016 - Cambridge University Press | Journal of Fluid Mechanics
Ashish Patel, Bendiks Jan Boersma, René Pecnik,
... Navier–Stokes equations. Different constitutive relations for density $\unicode[STIX]{x1D70C}$ and viscosity $\unicode[STIX]{x1D707}$ as a function of temperature are ... of the semilocal Reynolds number, defined as $Re_{\unicode[STIX]{x1D70F}}^{\star }\equiv Re_{\unicode[STIX]{x1D70F}}\sqrt{(\overline{\unicode[STIX]{x1D70C}}/\overline{\unicode[STIX]{x1D70C}}_{w})}/(\overline{\unicode[STIX]{x1D707}}/\overline{\unicode[STIX]{x1D707}}_{w})$ (the bar and subscript $w$ ... Reynolds averaging and wall value respectively, while $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number based ...
Tópico(s): Combustion and flame dynamics
2016 - Cambridge University Press | Journal of Fluid Mechanics
... 12.3$ in cylindrical samples with aspect ratios $\unicode[STIX]{x1D6E4}$ (diameter $D$ over height $L$ ) of ... The measurements were primarily for the radial positions $\unicode[STIX]{x1D709}=1-r/(D/2)=1.00$ and $\unicode[STIX]{x1D709}=0.063$ . In both cases, data ... by the power law $P(f)\sim f^{-\unicode[STIX]{x1D6FC}}$ . For all $\unicode[STIX]{x1D709}$ and $\unicode[STIX]{x1D6E4}$ , the $\unicode[STIX]{x1D6FC}$ value is less than one near ... Mech. , vol. 731, 2013, pp. 46–63), where $\unicode[STIX]{x1D6FC}=1$ is found or expected in ...
Tópico(s): Wind and Air Flow Studies
2016 - Cambridge University Press | Journal of Fluid Mechanics
Hesam Salehipour, C. P. Caulfield, W. R. Peltier,
... tanh (z/d)$ and initial density distribution $\overline{\unicode[STIX]{x1D70C}}(z,0)=\unicode[STIX]{x1D70C}_{0}[1-\tanh (z/\unicode[STIX]{x1D6FF})]$ away from a hydrostatic reference state $\unicode[STIX]{x1D70C}_{r}\gg \unicode[STIX]{x1D70C}_{0}$ . When the ratio $R=d/\unicode[STIX]{x1D6FF}$ of the characteristic length scales over ... Richardson number $Ri_{g}(0)=Ri_{b}=g\unicode[STIX]{x1D70C}_{0}d/\unicode[STIX]{x1D70C}_{r}U_{0}^{2}$ , where $Ri_{g}(z)=-([g/\unicode[STIX]{x1D70C}_{r}]\,\text{d}\overline{\unicode[STIX]{ ...
Tópico(s): Meteorological Phenomena and Simulations
2016 - Cambridge University Press | Journal of Fluid Mechanics
... E\sim t$ yield three length scales, $l_{\unicode[STIX]{x1D714}}$ , $l_{E}$ and $l_{\unicode[STIX]{x1D713}}$ , associated with the vorticity field, energy ... areas grow linearly in time, $A\sim l_{\unicode[STIX]{x1D714}}^{2}\sim t$ , while the spectral peak wavenumber $k_{E}\equiv 2\unicode[STIX]{x03C0}l_{E}^{-1}\sim t^{-1}$ . ... vortex number density distribution, $n(A)\sim t^{\unicode[STIX]{x1D6FC}_{i}}A^{-r_{i}},~i\in ... v}^{cm}=(2{\mathcal{D}})^{-1}\int \overline{\unicode[STIX]{x1D714}_{v}^{2}}A^{2}n(A)\,\ ... d}A$ is conserved in $A$ -space intervals $[\unicode[STIX]{x1D707}A_{0}(t),A_{0}(t)]$ ...
Tópico(s): Meteorological Phenomena and Simulations
2016 - Cambridge University Press | Journal of Fluid Mechanics
Produção Nacional
Revisado por pares
Amanda de Lima, Daniel Smania,
... classes of such maps. Given a Lipchitz observable $\unicode[STIX]{x1D719}$ consider the function $$\begin{eqnarray}{\mathcal{R}}_{\unicode[STIX]{x1D719}}(t)=\int \unicode[STIX]{x1D719}\,d\unicode[STIX]{x1D707}_{t},\end{eqnarray}$$ where $\unicode[STIX]{x1D707}_{t}$ is the unique absolutely continuous invariant probability of $f_{t}$ . Suppose that $\unicode[STIX]{x1D70E}_{t}>0$ for every $t\in [a,b]$ , where $$\begin{eqnarray}\unicode[STIX]{x1D70E}_{t}^{2}=\unicode[STIX]{x1D70E}_{t}^{2}(\unicode[STIX]{x1D719})=\lim _{ ...
Tópico(s): Stochastic processes and statistical mechanics
2016 - Cambridge University Press | Journal of the Institute of Mathematics of Jussieu
K.L. de Graaf, PA Brandner, BW Pearce,
... 1.5\times 10^{6}$ with cavitation numbers, $\unicode[STIX]{x1D70E}$ , ranging from inception to supercavitation. Three ... regimes are identified: a uni-modal regime for $\unicode[STIX]{x1D70E}>0.9$ and two bi-modal regimes for $0.9>\unicode[STIX]{x1D70E}>0.675$ and $0.675>\unicode[STIX]{x1D70E}>0.3$ . For small cavity lengths ( $\unicode[STIX]{x1D70E}>0.9$ ), Kelvin–Helmholtz instability and ... breakup and coherent vortex formation. At greater lengths ( $\unicode[STIX]{x1D70E}<0.9$ ), larger-scale shedding ensues, ...
Tópico(s): Cavitation Phenomena in Pumps
2016 - Cambridge University Press | Journal of Fluid Mechanics
... of bubbles in the small-solid-fraction limit $\unicode[STIX]{x1D716}\ll 1$ . Using scaling arguments and ... elucidate the singularity of the slip length as $\unicode[STIX]{x1D716}\rightarrow 0$ : relative to the periodicity it scales as $\log (1/\unicode[STIX]{x1D716})$ for protrusion angles $0\leqslant \unicode[STIX]{x1D6FC}<\unicode[STIX]{x03C0}/2$ and as $\unicode[STIX]{x1D716}^{-1/2}$ for $0<\unicode[STIX]{x03C0}/2-\unicode[STIX]{x1D6FC}=O(\unicode[STIX]{x1D716}^{1/2})$ . We continue with a ...
Tópico(s): Fluid Dynamics and Thin Films
2017 - Cambridge University Press | Journal of Fluid Mechanics
Xindong Li, Zongmin Hu, Zonglin Jiang,
... theoretical formula for the bulk viscosity coefficient (BVC) $\unicode[STIX]{x1D701}$ is derived by the continuum medium ... further understanding of the bulk viscosity, i.e. $\unicode[STIX]{x1D701}$ is equal to the product of the bulk modulus $K$ and the relaxation time $\unicode[STIX]{x1D70F}$ ( $\unicode[STIX]{x1D701}=K\unicode[STIX]{x1D70F}$ ). The continuum and kinetic theories present ... of temperature. In addition, the vibrational contributions to $\unicode[STIX]{x1D701}$ are controlled by a rapid exponential ... proceeds for the rotational cases. The relaxation time $\unicode[STIX]{x1D70F}$ , collision number $Z$ , BVC $\unicode[STIX]{ ...
Tópico(s): Atomic and Subatomic Physics Research
2017 - Cambridge University Press | Journal of Fluid Mechanics
Zhang Cao, Jin Wang, William K. Blake, Joseph Katz,
... map the deformation. The Reynolds number is $Re_{\unicode[STIX]{x1D70F}}=2300$ , and the Young’s modulus ... advected and non-advected modes are $0.04~\unicode[STIX]{x03BC}\text{m}$ $(0.004\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}})$ and $0.2~\unicode[STIX]{x03BC}\text{m}$ ( $0.02\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ ), respectively, much smaller than the wall unit ( $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ ), hence they do not affect the ...
Tópico(s): Aerodynamics and Acoustics in Jet Flows
2017 - Cambridge University Press | Journal of Fluid Mechanics
Wan Cheng, D. I. Pullin, Ravi Samtaney,
... the cylinder, each of sinusoidal shape with height $\unicode[STIX]{x1D716}$ , invariant in the spanwise direction. Based on the two parameters, $\unicode[STIX]{x1D716}/D$ and the Reynolds number $Re_{D}=U_{\infty }D/\unicode[STIX]{x1D708}$ where $U_{\infty }$ is the free- ... velocity, $D$ the diameter of the cylinder and $\unicode[STIX]{x1D708}$ the kinematic viscosity, two main sets of simulations are described. The first set varies $\unicode[STIX]{x1D716}/D$ from $0$ to $1/32$ ... C_{p}$ , the skin-friction coefficient $C_{f\unicode[STIX]{x1D703}}$ and the non-dimensional pressure gradient ...
Tópico(s): Wind and Air Flow Studies
2017 - Cambridge University Press | Journal of Fluid Mechanics
Julio Delgado, Michael Ruzhansky,
... for smooth symbols are formulated using $\mathscr{S}_{\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF}}^{m}(G)$ classes which are a suitable extension of the well-known $(\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF})$ ones on the Euclidean space. The ... results have immediate consequences on general manifolds for $\unicode[STIX]{x1D70C}>\max \{\unicode[STIX]{x1D6FF},1-\unicode[STIX]{x1D6FF}\}$ , our results do not require the condition $\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$ . Moreover, one of our results also ...
Tópico(s): Advanced Mathematical Physics Problems
2017 - Cambridge University Press | Journal of the Institute of Mathematics of Jussieu
Akshay Sridhar, D. I. Pullin, Wan Cheng,
... friction velocity $U_{\infty }^{+}\equiv U_{\infty }/u_{\unicode[STIX]{x1D70F}}$ , are streamwise constant. For $Re_{x}$ ... must be the linear form $k_{s}(x)=\unicode[STIX]{x1D6FC}x$ , where $x$ is the distance from the boundary layer of zero thickness and $\unicode[STIX]{x1D6FC}$ is a dimensionless constant. This is shown to give a two-parameter $(m,\unicode[STIX]{x1D6FC})$ family of solutions, for which $U_{\ ... in the streamwise direction with similarity variable $z/(\unicode[STIX]{x1D6FC}x)$ , where $z$ is the wall- ... Results from this model over a range of $\unicode[STIX]{x1D6FC}$ are discussed for several cases, including ...
Tópico(s): Wind and Air Flow Studies
2017 - Cambridge University Press | Journal of Fluid Mechanics
L. Djenidi, N. Lefeuvre, Md. Kamruzzaman, R. A. Antonia,
... 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 ... is investigated in decaying turbulence. Expressions for $C_{\unicode[STIX]{x1D716}}$ in homogeneous isotropic turbulent (HIT), as ... evolves in compliance with self-preservation (SP), $C_{\unicode[STIX]{x1D716}}$ remains constant for a given flow ... which does comply with SP, show that $C_{\unicode[STIX]{x1D716}}$ decreases in the former case and ...
Tópico(s): Combustion and flame dynamics
2017 - Cambridge University Press | Journal of Fluid Mechanics
Alexander Z. Zinchenko, Robert H. Davis,
... One base flow is planar extension (PE) ( $\dot{\unicode[STIX]{x1D6E4}}x_{1},-\dot{\unicode[STIX]{x1D6E4}}x_{2},0$ ), the other one is planar mixed flow (PM) ( $\dot{\unicode[STIX]{x1D6FE}}x_{2}$ , $\dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D712}x_{1}$ , 0) with $\unicode[STIX]{x1D712}=0.16$ . A small but finite $\unicode[STIX]{x1D712}$ (a precise choice in the range $\unicode[STIX]{x1D712}\sim 0.1$ is unimportant) provides ... Ca$ and small drop-to-medium viscosity ratios $\unicode[STIX]{x1D706}$ . The database rheological functions are obtained ...
Tópico(s): Surfactants and Colloidal Systems
2017 - Cambridge University Press | Journal of Fluid Mechanics
Dheeraj Varma, Manikandan Mathur,
... m}$ and $k_{n}$ ) at a fixed frequency $\unicode[STIX]{x1D714}$ results in two different terms in ... solution: (i) a superharmonic wave of frequency $2\unicode[STIX]{x1D714}$ , horizontal wavenumber $k_{m}+k_{n}$ ... is infinitely large along specific curves on the $(\unicode[STIX]{x1D714}/N_{0},f/\unicode[STIX]{x1D714})$ plane, where $N_{0}$ and $f$ ... stratifications, a unique divergence curve occurs on the $(\unicode[STIX]{x1D714}/N_{0},f/\unicode[STIX]{x1D714})$ plane for those $(m,n\neq ... can result in multiple divergence curves on the $(\unicode[STIX]{x1D714}/N_{0},f/\unicode[STIX]{x1D714})$ ...
Tópico(s): Tropical and Extratropical Cyclones Research
2017 - Cambridge University Press | Journal of Fluid Mechanics
Yang Zhang, Quan Zhou, Chao Sun,
We investigate the statistical properties of the kinetic $\unicode[STIX]{x1D700}_{u}$ and thermal $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}$ energy dissipation rates in two-dimensional ( ... Our results show that the ensemble averages $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ scale as $Ra^{- ... total dissipations, our results further reveal that $\langle \unicode[STIX]{x1D700}_{u}\rangle _{V,t}$ and $\langle \unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}\rangle _{V,t}$ ...
Tópico(s): Combustion and flame dynamics
2017 - Cambridge University Press | Journal of Fluid Mechanics
Sathish K. P. Sanjeevi, Johan T. Padding,
... We compute the mean drag coefficient $C_{D,\unicode[STIX]{x1D719}}$ at different incident angles $\unicode[STIX]{x1D719}$ for a wide range of Reynolds ... that the sine-squared drag law $C_{D,\unicode[STIX]{x1D719}}=C_{D,\unicode[STIX]{x1D719}=0^{\circ }}+(C_{D,\unicode[STIX]{x1D719}=90^{\circ }}-C_{D,\unicode[STIX]{x1D719}=0^{\circ }})\sin ^{2}\unicode[STIX]{x1D719}$ holds up to large Reynolds numbers, $\ ... is possible to perform just two simulations at $\unicode[STIX]{x1D719}=0^{\circ }$ and $\unicode[STIX]{x1D719}=90^{\circ }$ for a given $\mathit{ ...
Tópico(s): Aerosol Filtration and Electrostatic Precipitation
2017 - Cambridge University Press | Journal of Fluid Mechanics
... state gravity current of height $h$ and density $\unicode[STIX]{x1D70C}_{1}$ that propagates into an ambient motionless fluid of height $H$ and density $\unicode[STIX]{x1D70C}_{2}$ with an upper surface open ... with speed $U$ and causes a depth decrease $\unicode[STIX]{x1D712}$ of the top surface. This is ... 248) seminal solution for a fixed-top channel ( $\unicode[STIX]{x1D712}=0$ ). In the present case, the determination of $\unicode[STIX]{x1D712}$ is part of the problem. The ... the problem are $a=h/H$ and $r=\unicode[STIX]{x1D70C}_{2}/\unicode[STIX]{x1D70C}_{1}$ . We ...
Tópico(s): Hydrology and Sediment Transport Processes
2017 - Cambridge University Press | Journal of Fluid Mechanics
... the structure of the quotient $\text{A}_{{\sim}}(\unicode[STIX]{x1D6E4},X,\unicode[STIX]{x1D707})$ of the space of measure-preserving ... the convex combination operation on $\text{A}_{{\sim}}(\unicode[STIX]{x1D6E4},X,\unicode[STIX]{x1D707})$ . This formalism allows us to define ... also discuss a topology on $\text{A}_{{\sim}}(\unicode[STIX]{x1D6E4},X,\unicode[STIX]{x1D707})$ due to Abért and Elek in ... that the convex structure of $\text{A}_{{\sim}}(\unicode[STIX]{x1D6E4},X,\unicode[STIX]{x1D707})$ is compatible with the topology, and ...
Tópico(s): Mathematical Dynamics and Fractals
2017 - Cambridge University Press | Ergodic Theory and Dynamical Systems
Gerrit E. Elsinga, Takashi Ishihara, Manu Goudar, Carlos B. da Silva, J. C. R. Hunt,
... turbulence over a Reynolds number range from $Re_{\unicode[STIX]{x1D706}}=34.6$ up to 1131, and ... whose dimensions scale with the Kolmogorov length scale, $\unicode[STIX]{x1D702}$ . The vorticity stretching motions scale with the Taylor length scale, $\unicode[STIX]{x1D706}_{T}$ , while the flow outside the ... of this characteristic small-scale structure is $120\unicode[STIX]{x1D702}$ in all directions based on the ... vorticity stretching motions on the scale of $4\unicode[STIX]{x1D706}_{T}$ shows that transitions in flow ...
Tópico(s): Plant Water Relations and Carbon Dynamics
2017 - Cambridge University Press | Journal of Fluid Mechanics