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We study Logarithmically Spiral Trajectories and, in particular, we look for a solution to minimize the transit time of a Spacecraft propelled by a Solar Sail, while simultaneously minimizing the area of the Solar Sail, which would allow us to carry more payload on board. We start by analyzing the forces that act on the Spacecraft taking into account that its propellant is a Solar Sail; we use the studied forces to deduce the motion equations. We then solve this motion equation with a Runge-Kutta 4 method and transform the problem of minimizing time and area to a Non-linear Optimization problem. When solving the NLP we also try to minimize the relative final speed of th spacecraft with the destination planet in order to guarantee the possibility of a safe landing on its surface. The model improves when an angle parameter α (describing the angle formed by the Solar Sail with the colliding photons) is defined as a piecewise constant function and optimized whose values are optimized in every interval to minimize transit time and Area. Using the developed model to optimize the trajectory to be followed for sending from Earth to Mars a 2000kg-spacecraft propelled by a Solar Sail, subject to the condition that at trajectory start Mars and Earth were at their closest approach, and the Arrival Relative Velocity is less than 9km/s, give us a minimal transit time of 500days and a minimal area for the Solar Sail of 183158m2, meaning that the maximal payload would be 718kg. Compared with different number of partitions of α, the optimum stays stable. This gives a solid optimal trajectory and a great result for the numerical method used. Actually, waiting until the best moment to throw the Spacecraft, id est, Mars is at 1.14 radians respectively to Earth initial position, the minimal sail area 145950 m2 and, therefore, ables to transport until 978 kg of payload with the same transit time. In addition and to conclude we tried the model to optimize the inverse trajectory.

Mohit Sarvaiya's CV (Mechanical Engineer)

Taller álgebra lineal

These are the words that I manifest.

Naveen Kommuri's CV

Quantum Dots are semiconductor nanocrystals whose diameter is in the range of 2-10 nm, corre- sponding to 10 to 50 atoms in diameter and a total of 100 to 100,000 atoms within the quantum dot volume. Many types of quantum dot emit light of specific frequencies if electricity or light is applied to them, and these frequencies can be precisely tuned by changing the dots’ size, shape and material, giving rise to many applica- tions. Because of their high tunable properties, quantum dots are of wide interest. It finds its applications in nanotechnology, medical imaging, transistors, solar cells, LED’s, diode lasers, quantum computing, etc. With this project, we intend to further understand and study the properties of quantum dots by using atomic force microscopy.

Thermal wave phenomenon is observed is thin metallic rod by application of periodic heating. In this way, it is demonstrated that there is no wave nature in these improperly called thermal waves by showing that they do not transport energy and its propagation properties can be used to determine the thermal diffusivity of the material.