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Marc Barthelemy - One of the best experts on this subject based on the ideXlab platform.
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Optimal Geometry of transportation networks
Physical Review E, 2019Co-Authors: David Aldous, Marc BarthelemyAbstract:Author(s): Aldous, David; Barthelemy, Marc | Abstract: Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network G of given length L that is Optimal in a certain sense. In the general model, the Optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the Optimal network changes as L increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the Optimal networks. As a second variant we consider the Optimal network that minimizes the average travel time to a central destination, and we discuss both analytically and numerically some simple shapes such as the star network, the ring, or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as L increases, resources go preferentially to radial branches and that there is a sharp transition at a value L_{c} where a loop appears.
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Optimal Geometry of transportation networks
Physical Review E, 2019Co-Authors: David Aldous, Marc BarthelemyAbstract:Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is Optimal in a certain sense. In the general model, the Optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the Optimal network changes as $L$ increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the Optimal networks. As a second variant we consider the Optimal network that minimizes the average travel time to a central destination, and discuss both analytically and numerically some simple shapes such as the star network, the ring or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as $L$ increases, resources go preferentially to radial branches and that there is a sharp transition at a value $L_c$ where a loop appears.
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Optimal Geometry of transportation networks.
Physical review. E, 2019Co-Authors: David Aldous, Marc BarthelemyAbstract:Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network G of given length L that is Optimal in a certain sense. In the general model, the Optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the Optimal network changes as L increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the Optimal networks. As a second variant we consider the Optimal network that minimizes the average travel time to a central destination, and we discuss both analytically and numerically some simple shapes such as the star network, the ring, or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as L increases, resources go preferentially to radial branches and that there is a sharp transition at a value L_{c} where a loop appears.
David Aldous - One of the best experts on this subject based on the ideXlab platform.
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Optimal Geometry of transportation networks
Physical Review E, 2019Co-Authors: David Aldous, Marc BarthelemyAbstract:Author(s): Aldous, David; Barthelemy, Marc | Abstract: Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network G of given length L that is Optimal in a certain sense. In the general model, the Optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the Optimal network changes as L increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the Optimal networks. As a second variant we consider the Optimal network that minimizes the average travel time to a central destination, and we discuss both analytically and numerically some simple shapes such as the star network, the ring, or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as L increases, resources go preferentially to radial branches and that there is a sharp transition at a value L_{c} where a loop appears.
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Optimal Geometry of transportation networks
Physical Review E, 2019Co-Authors: David Aldous, Marc BarthelemyAbstract:Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network $G$ of given length $L$ that is Optimal in a certain sense. In the general model, the Optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the Optimal network changes as $L$ increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the Optimal networks. As a second variant we consider the Optimal network that minimizes the average travel time to a central destination, and discuss both analytically and numerically some simple shapes such as the star network, the ring or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as $L$ increases, resources go preferentially to radial branches and that there is a sharp transition at a value $L_c$ where a loop appears.
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Optimal Geometry of transportation networks.
Physical review. E, 2019Co-Authors: David Aldous, Marc BarthelemyAbstract:Motivated by the shape of transportation networks such as subways, we consider a distribution of points in the plane and ask for the network G of given length L that is Optimal in a certain sense. In the general model, the Optimality criterion is to minimize the average (over pairs of points chosen independently from the distribution) time to travel between the points, where a travel path consists of any line segments in the plane traversed at slow speed and any route within the subway network traversed at a faster speed. Of major interest is how the shape of the Optimal network changes as L increases. We first study the simplest variant of this problem where the optimization criterion is to minimize the average distance from a point to the network, and we provide some general arguments about the Optimal networks. As a second variant we consider the Optimal network that minimizes the average travel time to a central destination, and we discuss both analytically and numerically some simple shapes such as the star network, the ring, or combinations of both these elements. Finally, we discuss numerically the general model where the network minimizes the average time between all pairs of points. For this case, we propose a scaling form for the average time that we verify numerically. We also show that in the medium-length regime, as L increases, resources go preferentially to radial branches and that there is a sharp transition at a value L_{c} where a loop appears.
Valerian Hongjie Chen - One of the best experts on this subject based on the ideXlab platform.
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Optimal Geometry of nonlinear silicon slot waveguides accounting for the effect of waveguide losses.
Optics express, 2015Co-Authors: Jun Rong Ong, Valerian Hongjie ChenAbstract:The Optimal Geometry of silicon-organic hybrid slot waveguides is investigated in the context of the efficiency of four-wave mixing (FWM), a χ(3) nonlinear optical process. We study the effect of slot and waveguide widths, as well as waveguide asymmetry on the two-photon absorption (TPA) figure of merit and the roughness scattering loss. The Optimal waveguide core width is shown to be 220nm (symmetric) with a slot width of 120nm, at a fixed waveguide height of 220nm. We also show that state-of-the-art slot waveguides can outperform rib waveguides, especially at high powers, due to the high TPA figure-of-merit.
Louis Gosselin - One of the best experts on this subject based on the ideXlab platform.
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Optimal Geometry and flow arrangement for minimizing the cost of shell and tube condensers
International Journal of Energy Research, 2008Co-Authors: Benoit Allen, Louis GosselinAbstract:This paper presents a model for estimating the total cost of shell-and-tube heat exchangers (HEs) with condensation in tubes or in the shell, as well as a designing strategy for minimizing this cost. The optimization process is based on a genetic algorithm. The global cost includes the energy cost (i.e. pumping power) and the initial purchase cost of the exchanger. The choice of the best exchanger is based on its annualized total cost. Eleven design variables are optimized. Ten are associated with the HE Geometry: tube pitch, tube layout patterns, baffle spacing at the center, baffle spacing at the inlet and outlet, baffle cut, tube-to-baffle diametrical clearance, shell-to-baffle diametrical clearance, tube bundle outer diameter, shell diameter, and tube outer diameter. The last design variable indicates whether the condensing fluid should flow in the tubes or in the shell. Two case studies are presented and the results obtained show that the procedure can rapidly identify the best design for a given heat transfer process between two fluids, one of which is condensing. Copyright © 2008 John Wiley & Sons, Ltd.
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Optimal Geometry of l and c shaped channels for maximum heat transfer rate in natural convection
International Journal of Heat and Mass Transfer, 2005Co-Authors: A K Da Silva, Louis GosselinAbstract:Abstract The present paper documents the geometric optimization of L and C-shaped channels in laminar natural convection subject to global constraints. The objective is to maximize the heat transfer rate from the hot wall to the coolant fluid. Three different configurations were considered: (i) an L-shaped asymmetric vertical heated channel with an adiabatic horizontal inlet, (ii) an asymmetric vertical heated channel with an adiabatic vertical outlet, and finally, (iii) a C-shaped vertical channel with horizontal inlet and outlet. The two first configurations are free to morph according to two degrees of freedom: the wall-to-wall spacing and inlet (or outlet) height. The third configuration is optimized with respect to the wall-to-wall spacing, and the heights of the inlet and outlet ports. The effect of the inlet or outlet horizontal adiabatic duct lengths is also investigated. The optimization is performed numerically by using the finite element technique, in the range 105
A. O. Rodriguez - One of the best experts on this subject based on the ideXlab platform.
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Numerical Study of the Optimal Geometry of MRI Surface Coils
2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2007Co-Authors: R. Rojas, A. O. RodriguezAbstract:An image based method to compute the signal to noise ratio and specific energy absorption rate of MRI surface resonator coil for different polygonal geometries is proposed. A commercial software tool based on the Finite Element Method was used to numerically solve the Maxwell's equations to form bidimensional images of the electric and magnetic fields. These images represent the point by point fields inside the surface coil. With this data, MATLAB specifically written programs were used to numerically compute the signal to noise ratio and the specific absorption rate for different surface coil geometries. Bidimensional images and contours of the signal to noise ratio and specific absorption rate were also computed and compared. Uniformity profiles of various geometries were calculated using the resulting data to determine the Optimal field uniformity. According to the signal to noise ratio images, the squared shaped coil shows the most suitable uniformity for magnetic resonance imaging applications. This can be a good candidate for phased array imaging and parallel imaging.