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(3) Group of moving persons: Three persons walking towards or away from the radar at a normal velocity of 3 5 km/h and either synchronously or asynchronously.
A normal velocity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.2\,\hbox {ms}^{-1}$$\end{document} was set for the blood flow in each inlet vessel.
Embolic particles were injected in each site with a normal velocity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$20 ~\hbox {cm}/\hbox {s}$$\end{document}, the same as the blood flow.
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Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions.
The method is formed of four constitutive parts: a scheme for approximating a closed curve (the interface (partialvarOmega_(t))), a scheme to approximate the instantaneous normal velocity of the interface, a scheme to propagate the contour according to the normal velocity, and a strategy to remesh or postprocess the contour, if needed.
A Green function potential formulation expresses the normal velocity of the free surface in terms of the bathymetry and its motion.
Outputs include (but are not limited to): arc-length-parameterized contours for each frame in the sequence, the normal velocity of the cell edge as a function of space and time, the area of the cell as a function of time, and a cross-correlation plot for the normal velocity as a function of arc-length and time.
We then calculated the normal velocity of the cell edge as a function of arc-length and time (Fig. 1F, Movie S2) and performed correlation analyses on the velocity functions.
We demonstrate numerically that the error is closely correlated to the size of the normal velocity and that there is a stability limit of the form ΔT≤C/(|un|∞)γ, whereundenotes the normal velocity of the free surface and γ ≈ 2.6.
Rows B illustrate the evolution of the interface ( u = h, golden outline) due to the normal velocity of the boundary (green arrows, to scale but enlarged by a factor 50).
In each of the domains (Q^{pm}(t)) the liquid motion is described by its own Darcy system of filtration, and at the free boundary the normal velocities of the liquids coincide with the normal velocity of the free boundary.
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