共查询到20条相似文献,搜索用时 31 毫秒
1.
G. H. Keetels W. Kramer H. J. H. Clercx G. J. F. van Heijst 《Theoretical and Computational Fluid Dynamics》2011,25(5):293-300
Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z μ Re0.8{Z\propto{\rm Re}^{0.8}} and P μ Re2.25{P\propto {\rm Re}^{2.25}} for 5 × 102 ≤ Re ≤ 2 × 104 and Z μ Re0.5{Z\propto{\rm Re}^{0.5}} and P μ Re1.5{P\propto{\rm Re}^{1.5}} for Re ≥ 2 × 104 (with Re based on the velocity and size of the dipole). A critical Reynolds number Re
c
(here, Rec ? 2×104{{\rm Re}_c\approx 2\times 10^4}) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity
ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following
scaling relations are obtained: Z μ Re3/4, P μ Re9/4{Z\propto{\rm Re}^{3/4}, P\propto {\rm Re}^{9/4}} , and dP/dt μ Re11/4{\propto {\rm Re}^{11/4}} in agreement with the numerically obtained scaling laws. For Re ≥ Re
c
the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate
boundary-layer theory, this yields: Z μ Re1/2{Z\propto{\rm Re}^{1/2}} and P μ Re3/2{P\propto {\rm Re}^{3/2}}. 相似文献
2.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}We study the regularity of the extremal solution of the semilinear biharmonic equation
D2 u=\fracl(1-u)2{{\Delta^2} u=\frac{\lambda}{(1-u)^2}}, which models a simple micro-electromechanical system (MEMS) device on a ball
B ì \mathbbRN{B\subset{\mathbb{R}}^N}, under Dirichlet boundary conditions u=?n u=0{u=\partial_\nu u=0} on ?B{\partial B}. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” λ* > 0 such that a stable classical solution u
λ with 0 < u
λ < 1 exists for l ? (0,l*){\lambda\in (0,\lambda^*)}, while there is none of any kind when λ > λ*. Our main result asserts that the extremal solution ul*{u_{\lambda^*}} is regular (supB ul* < 1 ){({\rm sup}_B u_{\lambda^*} <1 )} provided
N \leqq 8{N \leqq 8} while ul*{u_{\lambda^*}} is singular (supB ul* = 1){({\rm sup}_B u_{\lambda^*} =1)} for
N \geqq 9{N \geqq 9}, in which case
1-C0|x|4/3 \leqq ul* (x) \leqq 1-|x|4/3{1-C_0|x|^{4/3} \leqq u_{\lambda^*} (x) \leqq 1-|x|^{4/3}} on the unit ball, where
C0:=(\fracl*[`(l)])\frac13{C_0:=\left(\frac{\lambda^*}{\overline{\lambda}}\right)^\frac{1}{3}} and
[`(l)]: = \frac89(N-\frac23)(N- \frac83){\bar{\lambda}:= \frac{8}{9}\left(N-\frac{2}{3}\right)\left(N- \frac{8}{3}\right)}. 相似文献
3.
Qinjun Kang Peter C. Lichtner Hari S. Viswanathan Amr I. Abdel-Fattah 《Transport in Porous Media》2010,82(1):197-213
We apply a multi-component reactive transport lattice Boltzmann model developed in previous studies for modeling the injection
of a CO2-saturated brine into various porous media structures at temperatures T = 25 and 80°C. In the various cases considered the porous medium consists initially of calcite with varying grain size and
shape. A chemical system consisting of Na+, Ca2+, Mg2+, H+, CO2°(aq){{\rm CO}_2^{\circ}{\rm (aq)}}, and Cl− is considered. Flow and transport by advection and diffusion of aqueous species, combined with homogeneous reactions occurring
in the bulk fluid, as well as the dissolution of calcite and precipitation of dolomite are simulated at the pore scale. The
effects of the structure of the porous media on reactive transport are investigated. The results are compared with a continuum-scale
model and the discrepancies between the pore- and continuum-scale models are discussed. This study sheds some light on the
fundamental physics occurring at the pore scale for reactive transport involved in geologic CO2 sequestration. 相似文献
4.
Yuji Aoki Kentaro Hirayama Koji Kikuchi Masataka Sugimoto Kiyohito Koyama 《Rheologica Acta》2010,49(10):1071-1076
A poly(vinyl chloride) (PVC, Mw = 102×103)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity
and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition
behavior with elevating temperature. The critical gel temperature (Tgel) characterized with a power–law relationship between the storage and loss moduli, G′ and G″, and frequency ω, G¢=G¢¢/tan ( np/2 ) μ wn{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the Tgel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This
finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations
were expressed by the neo-Hookean model at high temperature (135°C) near the Tgel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature.
These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated
from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions. 相似文献
5.
The detailed mean flow and turbulence measurements of a turbulent air slot jet impinging on two different semi-circular convex surfaces were investigated in both free jet and impingement wall jet regions at a jet Reynolds number Rew=12,000, using a hot-wire X-probe anemometer. The parametric effects of dimensionless circumferential distance, S/W=2.79-7.74, slot jet-to-impingement surface distance Y/W=1-13, and surface curvature D/W=10.7 and 16 on the impingement wall jet flow development along a semi-circular convex surface were examined. The results show that the effect of surface curvature D/W increases with increasing S/W. Compared with transverse Reynolds normal stress, [`(v2 )] /Um2 \overline {v^2 } /U_{\rm m}^2 , the streamwise Reynolds normal stress, [`(u2 )] /Um2 \overline {u^2 } /U_{\rm m}^2 , is strongly affected by the examined dimensionless parameters of D/W, Y/W and S/W in the near-wall region. It is also evidenced that the Reynolds shear stress, -[`(uv)] /Um2 - \overline {uv} /U_{\rm m}^2 is much more sensitive to surface curvature, D/W. 相似文献
6.
This article presents a nonlinear stability analysis of a rotating thermoconvective magnetized ferrofluid layer confined between
stress-free boundaries using a thermal non-equilibrium model by the energy method. The effect of interface heat transfer coefficient
( H¢){( {{\mathcal H}^{\prime}})}, magnetic parameter (M
3), Darcy–Brinkman number ( [^(D)]a){( {\hat{{\rm D}}{\rm a}})}, and porosity modified conductivity ratio (γ′) on the onset of convection in the presence of rotation (TA1){({T_{{\rm A}_1}})} have been analyzed. The critical Rayleigh numbers predicted by energy method are smaller than those calculated by linear
stability analysis and thus indicate the possibility of existence of subcritical instability region for ferrofluids. However,
for non-ferrofluids stability and instability boundaries coincide. Asymptotic analysis for both small and large values of
interface heat transfer coefficient (H¢){({{\mathcal H}^{\prime}})} is also presented. A good agreement is found between the exact solutions and asymptotic solutions. 相似文献
7.
A time-dependent collisional-radiative model for air plasma has been developed to study the effects of nonequilibrium atomic
and molecular processes on population densities in a weakly ionized high enthalpy flow. This model consists of 15 species:
e-,N, N+,N2+,O, O+,O2+,O-,N2,N2+,NO, NO+,O2,O2+{{\rm e}^{-},{\rm N, N}^{+},{\rm N}^{2+},{\rm O, O}^{+},{\rm O}^{2+},{\rm O}^{-},{\rm N}_{2},{{\rm N}_{2}}^{+},{\rm NO, NO}^{+},{\rm O}_{2},{{\rm O}_{2}}^{+}}, and O2-{{{\rm O}_{2}}^{-}} with their major electronic excited states. Many elementary processes are considered in the number density range of 1012/cm3 ≤ N ≤ 1019/cm3 and the temperature range of 300 K ≤ T ≤ 40,000 K. We then compare our results with an existing collisional-radiative code to validate our model. Additionally,
the unsteady nature of pulsively heated air plasma is investigated. When the ionization relaxation time is of the same order
as the time scale of a heating pulse, the effects of unsteady ionization are important for estimating air plasma states. From
parametric computations, we determine the appropriate conditions for the collisional-radiative steady state, local thermodynamic
equilibrium, and corona equilibrium models in that density and temperature range. 相似文献
8.
In this study, fully developed heat and fluid flow in a parallel plate channel partially filled with porous layer is analyzed
both analytically and numerically. The porous layer is located at the center of the channel and uniform heat flux is applied
at the walls. The heat and fluid flow equations for clear fluid and porous regions are separately solved. Continues shear
stress and heat flux conditions at the interface are used to determine the interface velocity and temperature. The velocity
and temperature profiles in the channel for different values of Darcy number, thermal conductivity ratio, and porous layer
thickness are plotted and discussed. The values of Nusselt number and friction factor of a fully clear fluid channel (Nu
cl = 4.12 and fRe
cl = 24) are used to define heat transfer increment ratio (eth = Nup/Nucl)({\varepsilon _{\rm th} =Nu_{\rm p}/Nu_{\rm cl})} and pressure drop increment ratio (ep = fRep/fRecl )({\varepsilon_{\rm p} =fRe_{\rm p}/fRe_{\rm cl} )} and observe the effects of an inserted porous layer on the increase of heat transfer and pressure drop. The heat transfer
and pressure drop increment ratios are used to define an overall performance (e = eth/ep)({\varepsilon = \varepsilon_{\rm th}/\varepsilon_{\rm p})} to evaluate overall benefits of an inserted porous layer in a parallel plate channel. The obtained results showed that for
a partially porous filled channel, the value of e{\varepsilon} is highly influenced from Darcy number, but it is not affected from thermal conductivity ratio (k
r) when k
r > 2. For a fully porous material filled channel, the value of e{\varepsilon} is considerably affected from thermal conductivity ratio as the porous medium is in contact with the channel walls. 相似文献
9.
Blade tip vortices are the dominant vortical structures of the helicopter flow field. The inherent complexity of the vortex
dynamics has led to an increasing interest in full-scale in situ experiments, where the near field, closely behind the blade,
is of particular interest, since measures of vortex control mostly target this initial stage of development. To examine the
near field, three-component particle image velocimetry (PIV) measurements of blade tip vortices of a full-scale helicopter
in simulated hover flight in ground effect were conducted. A feasible and robust evaluation procedure was developed to minimise
the shortcomings of full-scale PIV applications, such as a moderate spatial resolution and an elevated measurement noise level.
At vortex ages ranging from yv=1°\psi_{\rm v}=1^{\circ} to 30°, a pronounced aperiodicity and asymmetry of the vortex were observed in -sections perpendicular to the vortex axes.
At yv=1°\psi_{\rm v}=1^{\circ}, a preferential orientation of the vortex was observed. For increasing wake age, vortex wandering increased while the asymmetry
of the vortex cores decreased. The high level of aperiodicity and core asymmetry must be taken into account when considering
phase-averaged vortex characteristics in the near wake region. 相似文献
10.
In this paper we study the following coupled Schr?dinger system, which can be seen as a critically coupled perturbed Brezis–Nirenberg problem: {ll-Du +l1 u = m1 u3+buv2, x ? W,-Dv +l2 v = m2 v3+bvu2, x ? W,u\geqq 0, v\geqq 0 in W, u=v=0 on ?W.\left\{\begin{array}{ll}-\Delta u +\lambda_1 u = \mu_1 u^3+\beta uv^2, \quad x\in \Omega,\\-\Delta v +\lambda_2 v =\mu_2 v^3+\beta vu^2, \quad x\in \Omega,\\u\geqq 0, v\geqq 0\, {\rm in}\, \Omega,\quad u=v=0 \quad {\rm on}\, \partial\Omega.\end{array}\right. 相似文献
11.
We prove a regularity result for the anisotropic linear elasticity equation ${P u := {\rm div} \left( \boldmath\mathsf{C} \cdot \nabla u\right) = f}We prove a regularity result for the anisotropic linear elasticity equationP u : = div ( C ·?u) = f{P u := {\rm div} \left( \boldmath\mathsf{C} \cdot \nabla u\right) = f} , with mixed (displacement and traction) boundary conditions on a curved polyhedral domain
W ì \mathbbR3{\Omega \subset \mathbb{R}^3} in weighted Sobolev spaces Km+1a+1(W){\mathcal {K}^{m+1}_{a+1}(\Omega)} , for which the weight is given by the distance to the set of edges. In particular, we show that there is no loss of Kma{\mathcal {K}^{m}_{a}} -regularity. Our curved polyhedral domains are allowed to have cracks. We establish a well-posedness result when there are
no neighboring traction boundary conditions and |a| < η, for some small η > 0 that depends on P, on the boundary conditions, and on the domain Ω. Our results extend to other strongly elliptic systems and higher dimensions. 相似文献
12.
The one-dimensional, gravity-driven film flow of a linear (l) or exponential (e) Phan-Thien and Tanner (PTT) liquid, flowing
either on the outer or on the inner surface of a vertical cylinder or over a planar wall, is analyzed. Numerical solution
of the governing equations is generally possible. Analytical solutions are derived only for: (1) l-PTT model in cylindrical
and planar geometries in the absence of solvent, b o [(h)\tilde]s/([(h)\tilde]s +[(h)\tilde]p)=0\beta\equiv {\tilde{\eta}_s}/\left({\tilde{\eta}_s +\tilde{\eta}_p}\right)=0, where [(h)\tilde]p\widetilde{\eta}_p and [(h)\tilde]s\widetilde{\eta}_s are the zero-shear polymer and solvent viscosities, respectively, and the affinity parameter set at ξ = 0; (2) l-PTT or e-PTT model in a planar geometry when β = 0 and x 1 0\xi \ne 0; (3) e-PTT model in planar geometry when β = 0 and ξ = 0. The effect of fluid properties, cylinder radius, [(R)\tilde]\tilde{R}, and flow rate on the velocity profile, the stress components, and the film thickness, [(H)\tilde]\tilde{H}, is determined. On the other hand, the relevant dimensionless numbers, which are the Deborah, De=[(l)\tilde][(U)\tilde]/[(H)\tilde]De={\tilde{\lambda}\tilde{U}}/{\tilde{H}}, and Stokes, St=[(r)\tilde][(g)\tilde][(H)\tilde]2/([(h)\tilde]p +[(h)\tilde]s )[(U)\tilde]St=\tilde{\rho}\tilde{g}\tilde{\rm H}^{2}/\left({\tilde{\eta}_p +\tilde{\eta}_s} \right)\tilde{U}, numbers, depend on [(H)\tilde]\tilde{H} and the average film velocity, [(U)\tilde]\widetilde{U}. This makes necessary a trial and error procedure to obtain [(H)\tilde]\tilde{H}
a posteriori. We find that increasing De, ξ, or the extensibility parameter ε increases shear thinning resulting in a smaller St. The Stokes number decreases as [(R)\tilde]/[(H)\tilde]{\tilde{R}}/{\tilde{H}} decreases down to zero for a film on the outer cylindrical surface, while it asymptotes to very large values when [(R)\tilde]/[(H)\tilde]{\tilde{R}}/{\tilde{H}} decreases down to unity for a film on the inner surface. When x 1 0\xi \ne 0, an upper limit in De exists above which a solution cannot be computed. This critical value increases with ε and decreases with ξ. 相似文献
13.
A pore-scale analysis of nonaqueous phase liquid (NAPL) blob dissolution and mobilization in porous media was presented. Dissolution
kinetics of residual NAPLs in an otherwise water-saturated porous medium was investigated by conducting micromodel experiments.
Changes in residual NAPL volume were measured from recorded video images to calculate the mass transfer coefficient, K and the lumped mass transfer rate coefficient, k. The morphological characteristics of the blobs such as specific and intrinsic area were found to be independent of water
flow rate except at NAPL saturations below 2%. Dissolution process was also investigated by separating the mass transfer into
zones of mobile and immobile water. The fractions of total residual NAPL perimeters in contact with mobile water and immobile
water were measured and their relationship to the mass transfer coefficient was discussed. In general, residual NAPLs are
removed by dissolution and mobilization. Although these two mechanisms were studied individually by others, their simultaneous
occurrence was not considered. Therefore, in this study, mobilization of dissolving NAPL blobs was investigated by an analysis
of the forces acting on a trapped NAPL blob. A dimensional analysis was performed to quantify the residual blob mobilization
in terms of dimensionless Capillary number (Ca
I). If Ca
I is equal to or greater than the trapping number defined as , then blob mobilization is expected. 相似文献
14.
Dongho Chae 《Journal of Mathematical Fluid Mechanics》2010,12(2):171-180
Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier–Stokes equations in a space-time
domain containing z0=(x0, t0)z_{0}=(x_{0}, t_{0}), and let Qz0,r = Bx0,r ×(t0 -r2, t0)Q_{z_{0},r}= B_{x_{0},r} \times (t_{0} -r^{2}, t_{0}) be a parabolic cylinder in the domain. We show that if either $\nu
\times \frac{\omega}{|\omega|} \in
L^{\gamma,\alpha}_{x,t}(Q_{z_{0},r})$\nu
\times \frac{\omega}{|\omega|} \in
L^{\gamma,\alpha}_{x,t}(Q_{z_{0},r}) with $\frac{3}{\gamma} + \frac{2}{\alpha} \leq 1, {\rm or} \omega \times
\frac{\nu} {|\nu|} \in L^{\gamma,\alpha}_{x,t} (Q_{z_{0},r})$\frac{3}{\gamma} + \frac{2}{\alpha} \leq 1, {\rm or} \omega \times
\frac{\nu} {|\nu|} \in L^{\gamma,\alpha}_{x,t} (Q_{z_{0},r}) with
\frac3g + \frac2a £ 2\frac{3}{\gamma} + \frac{2}{\alpha} \leq 2, where Lγ, αx,t denotes the Serrin type of class, then z0 is a regular point for ν. This refines previous local regularity criteria for the suitable weak solutions. 相似文献
15.
Vieri Benci Marco Ghimenti Anna Maria Micheletti 《Archive for Rational Mechanics and Analysis》2012,205(2):467-492
We study the behavior of the soliton solutions of the equation i\frac?y?t = - \frac12m Dy+ \frac12We¢(y) + V(x)y,i\frac{\partial\psi}{{\partial}t} = - \frac{1}{2m} \Delta\psi + \frac{1}{2}W_{\varepsilon}^{\prime}(\psi) + V(x){\psi}, 相似文献
16.
We prove that, if ${u : \Omega \subset \mathbb{R}^n \to \mathbb{R}^N}We prove that, if
u : W ì \mathbbRn ? \mathbbRN{u : \Omega \subset \mathbb{R}^n \to \mathbb{R}^N} is a solution to the Dirichlet variational problem
minwòW F(x, w, Dw) dx subject to w o u0 on ?W,\mathop {\rm min}\limits_{w}\int_{\Omega} F(x, w, Dw)\,{\rm d}x \quad {\rm subject \, to} \quad w \equiv u_0\; {\rm on}\;\partial \Omega, 相似文献
17.
S. I. Maksymenko 《Nonlinear Oscillations》2009,12(4):522-542
Let
D2 ì \mathbbR2 {D^2} \subset {\mathbb{R}^2} be a closed unit 2-disk centered at the origin
O ì \mathbbR2 O \subset {\mathbb{R}^2} and let F be a smooth vector field such that O is the unique singular point of F, and all other orbits of F are simple closed curves wrapping once around O: Thus, topologically, O is a “center” singularity. Let D+ (F) {\mathcal{D}^{+} }(F) be the group of all diffeomorphisms of D
2 that preserve the orientation and orbits of F. Recently, the author described the homotopy type of D+ (F) {\mathcal{D}^{+} }(F) under the assumption that the 1-jet j
1
F(O) of F at O is nondegenerate. In this paper, the degenerate case j
1
F(O) is considered. Under additional “nondegeneracy assumptions” on F, the path components of D+ (F) {\mathcal{D}^{+} }(F) with respect to distinct weak topologies are described. These conditions imply that, for each h ? D+ (F) h \in {\mathcal{D}^{+} }(F) , its path component in D+ (F) {\mathcal{D}^{+} }(F) is uniquely determined by the 1-jet of h at O. 相似文献
18.
Mahesh Nerurkar 《Journal of Dynamics and Differential Equations》2011,23(3):451-473
Consider the class of C
r
-smooth
SL(2, \mathbb R){SL(2, \mathbb R)} valued cocycles, based on the rotation flow on the two torus with irrational rotation number α. We show that in this class,
(i) cocycles with positive Lyapunov exponents are dense and (ii) cocycles that are either uniformly hyperbolic or proximal
are generic, if α satisfies the following Liouville type condition:
|a-\fracpnqn| £ C exp (-qr+1+kn)\left|\alpha-\frac{p_n}{q_n}\right| \leq C {\rm exp} (-q^{r+1+\kappa}_{n}), where C > 0 and 0 < k < 1{0 < \kappa <1 } are some constants and
\fracPnqn{\frac{P_n}{q_n}} is some sequence of irreducible fractions. 相似文献
19.
A. V. Fursikov 《Journal of Mathematical Fluid Mechanics》2001,3(3):259-301
For 2D Navier--Stokes equations defined in a bounded domain W \Omega we study stabilization of solution near a given steady-state flow [^(v)](x) \hat v(x) by means of feedback control defined on a part G \Gamma of boundary ?W \partial\Omega . New mathematical formalization of feedback notion is proposed. With its help for a prescribed number s > 0 \sigma > 0 and for an initial condition v0(x) placed in a small neighbourhood of [^(v)](x) \hat v(x) a control u(t,x'), x¢ ? G x' \in \Gamma , is constructed such that solution v(t,x) of obtained boundary value problem for 2D Navier--Stokes equations satisfies the inequality: ||v(t,·)-[^(v)]||H1\leqslant ce-st for t \geqslant 0 \|v(t,\cdot)-\hat v\|_{H^1}\leqslant ce^{-\sigma t}\quad {\rm for}\; t \geqslant 0 . To prove this result we firstly obtain analogous result on stabilization for 2D Oseen equations. 相似文献
20.
Sherifull-Din Jamalud-Din D. Andrew S. Rees B. V. K. Reddy Arunn Narasimhan 《Heat and Mass Transfer》2010,46(3):333-343
Steady state natural convection of a fluid with Pr ≈ 1 within a square enclosure containing uniformly distributed, conducting square solid blocks is investigated. The side
walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The natural convection flow
is predicted employing the nondimensional volumetric flow rate (Qmax* Q_{\max }^{*} ) by using a network model and also using numerical simulations. For identical solid and fluid thermal conductivities (i.e.
k
s
= k
f
), a parametric study of the effect of number of blocks (N
2), gap size (δ) and enclosure Rayleigh number (Ra) on Qmax* Q_{\max }^{*} is performed using the two approaches. Network model predictions are observed to agree well with that from the simulations
until Raδ3 ~ 12. Considering the enclosure with blocks as a porous medium, for a fixed enclosure Ra number, increasing the number of blocks for a fixed volumetric porosity leads to a decrease in enclosure permeability, which
in turn reduces the flow rate. When the number of blocks is fixed, and for a given Ra number, the flow rate increases as the porosity increases by widening the gap between the blocks. 相似文献
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