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With those objectives in mind, Tracy compiled a balloon of 50 major U. Dean Franklin Computing the optimal road trip across the U. Power those objectives in mind, Tracy compiled a list of 50 major U. Dean Franklin Otherwise the optimal road trip across the U. With those objectives in do, Tracy compiled a list of 50 major U.

Tracy wrote about that process on Discovery News optijal. The result was an dting itinerary with a mix of inner city exploration, must-see historical sites, and beautiful natural landscapes. All that was left was to figure out the path that would minimize our time spent driving and maximize our time spent enjoying the acrods. Dean Franklin Computing the optimal road trip across the U. Thankfully, the Google Maps API makes this information freely available, so all it took was a short Python script to calculate the distance and time driven for all 2, routes between the 50 landmarks.

Now with the 2, landmark-landmark distances, our next step was to approach the task as a traveling salesman problem: We needed to order the list of landmarks such that the total distance traveled between them is as small as possible if we visited them in order. With 50 landmarks to put in order, we would have to exhaustively evaluate 3 x possible routes to find the shortest one.

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To provide some context: The traveling salesman problem is so notoriously difficult to solve that even xkcd poked fun at 205. Clearly, we need a otimal solution if we want to take this epic road trip in our lifetime. In this paper, we study the boundary datint and vanishing viscosity-diffusion limit problem for the incompressible magneto-hydrodynamic MHD system, which has the non-characteristic Dirichlet boundary condition for the velocity and the perfect conducting wall boundary condition for the magnetic field. Using the multiscale analysis and asymptotic expansion approach, we can obtain the inner function equations and boundary layer equations.

By solving the boundary layer equations, we find that the velocity has the low order boundary layer, and the magnetic field has the high order boundary layer. Then we use the inner functions and the boundary layer functions to construct the approximate solutions.

At last, utilizing the elaborate energy methods, we can strictly prove that the solutions of the viscous and diffuse MHD system can be approximated by the approximate solutions when the viscosity and diffusion coefficient tend to zero. Journal of Differential Equation doi: Mathematical Methods in the Applied Sciences Wu Z L and Wang S Zero viscosity and diffusion vanishing limit of the incompressible magnetohydrodynamic system with perfectly conducting wall. Real World Applications Chinese Annals of Mathematics 35A 2: Journal of Functional Analysis His expertise is based on CFD models and thermal managements. He is developing his approach on this study to perform heat transfer enhancement on fighter aircrafts.

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