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Question: drosophila larvae have some mobility and it has been shown...

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Drosophila larvae have some mobility and it has been shown that their motion can be regulated by temperature changes. In order to characterize their mobility in an experiment the stage of a microscope is heated. The temperature field as a function of the spatial coordinates of the stage reads T(x,y) = 2-4 (arbitrary units) where x,y E (-2,2). Plot the isotherms that pass through (1,1) and (1,1). The velocity field of the larvae is a direct reading of the gradient of the temperature field: plot schematically the velocity field of the larvae in the microscope stage and the trajectory that will follow a particular larva that is initially placed at the point (1,1). In another experiment the temperature field satisfies T (x y-x2 + y2 + 4: plot the isotherm that satisfies in that case T (x,y) = 2.

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