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The report on the molecular motors consists of answers to the following questions. The answers should be complete and written in such a way that the Chemist (who doesnât know anything about the project other than the structure of the molecules) can understand them. Keep it self-contained, short but clear. The structure of the report should follow the questions below. The report is due March 11. Send it by email to [email protected] I) (10) Describe the problem the chemist presented to us. In particular, describe the shape of the molecular motor and the main questions we were asked to answer. II) (10) Describe the model, a Markov process, for the flipper motion of a single molecule. III) (10) Explain how the model can be used to predict the concentrations of molecules in the different states. Explain how this can be used to validate the model. IV) (10) Explain the dynamical situation at equilibrium. V) (10) Describe a simulation of the flipper motion of a single molecule. Explain how the output of a simulation, given by the second program, of a single molecule relates to the actual motion of the flipper. Include several examples. VI) (10) What is the problem with the simulations and how can we solve it? Explain why we have to use statistical methods. Explain with data/examples: Present the results of the simulations. Explain what is the time scale to get reasonable results. (The results are tables with estimated rotational speed for different values of T). VII) (10) Give the final table of rotational speeds dependent on the light intensity. Use groups of molecules and simulations of long enough time. Explain that the size of the groups and the time you use are suffciently large. What is the influence of the simulation time? VIII) (10) Give a formula for the speed in terms of the probability matrix and the equilibrium concentrations. Compare with the results of the table of question VII). IX) (10) Discuss the qualitative behavior of the rotation speed in terms of the light intensity. When is the speed optimal? Hint: give two 1 2 differences between low light freuency (k=0) and high light freuency (k=15). Explain qualitatatively the observed velocity for k=0 and k=15. X) (10) Give a summary for the chemist of the results. Suppose the motor is build into a nanocar. Make a manual for the chemist describing how to drive the car. The numbers between parenthesis are the points you can get for the question. Grade=total number of points/ 10, something between 0 and 10. Often math majors use these reports to satisfy their writting requirements (MAT487). At the end of the semester let me know whether you want to use your reports for this purpose.
Sample Solution
Despite the feeling of positivity surrounding FDRs landslide win in the 1936 presidential election, he was wary of the Supreme Court. FDR was concerned that he conservative Supreme Court might look to strike down his New Deal era policies. His motive was the shaping of the ideological balance of the court. The way he would go about this was he solution was to propose the expansion of the number of Supreme Court justices.The proposed bill would have added one justice for each justice over the age of 70. The plan was widely and vehemently criticized, the elites viewed the proposed bill as an undemocratic power grab. However, for reasons historians still donât quite understand, shortly after FDR made the plan public, the Court upheld several government regulations it had formerly found unconstitutional. Many have attributed this and similar decisions to a politically motivated change of heart on the part of Justice Owen Roberts. Some legal scholars have rejected this narrative, however, asserting that Robertsâ 1937 decisions were not motivated by Rooseveltâs proposal and can instead be reconciled with his prior jurisprudence. This shifted the majority to favour federal welfare and regulatory enactments. Ultimately by 1942, all but two of the supreme court justices were Roosevelt appointees. Despite the legislative gridlock FDR found himself embroiled in, there was a lot of decisive legislation passed. The creation of the US housing authority provided homes for thousands of Americans. For FDR, more Americans owning more homes meant more consumption, more tax revenue. The Fair Labour Standards Act set employment standards for companies whoâs business transcended state boundaries. This meant that corporations had to respect a 40 hour work week, as well as pay a living minimum wage. Perhaps most crucially the act called for the end of child labour. Unfortunately, this only applied to those employed in interstate corporations; domestic servants, agricultural workers, and service employees were not protected. It is only when things start to unfold in Europe that FDR can reconstitute himself as the leader of the people in a time of need. On the cusp of World War Two FDR runs against and defeats Wendel>
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Despite the feeling of positivity surrounding FDRs landslide win in the 1936 presidential election, he was wary of the Supreme Court. FDR was concerned that he conservative Supreme Court might look to strike down his New Deal era policies. His motive was the shaping of the ideological balance of the court. The way he would go about this was he solution was to propose the expansion of the number of Supreme Court justices.The proposed bill would have added one justice for each justice over the age of 70. The plan was widely and vehemently criticized, the elites viewed the proposed bill as an undemocratic power grab. However, for reasons historians still donât quite understand, shortly after FDR made the plan public, the Court upheld several government regulations it had formerly found unconstitutional. Many have attributed this and similar decisions to a politically motivated change of heart on the part of Justice Owen Roberts. Some legal scholars have rejected this narrative, however, asserting that Robertsâ 1937 decisions were not motivated by Rooseveltâs proposal and can instead be reconciled with his prior jurisprudence. This shifted the majority to favour federal welfare and regulatory enactments. Ultimately by 1942, all but two of the supreme court justices were Roosevelt appointees. Despite the legislative gridlock FDR found himself embroiled in, there was a lot of decisive legislation passed. The creation of the US housing authority provided homes for thousands of Americans. For FDR, more Americans owning more homes meant more consumption, more tax revenue. The Fair Labour Standards Act set employment standards for companies whoâs business transcended state boundaries. This meant that corporations had to respect a 40 hour work week, as well as pay a living minimum wage. Perhaps most crucially the act called for the end of child labour. Unfortunately, this only applied to those employed in interstate corporations; domestic servants, agricultural workers, and service employees were not protected. It is only when things start to unfold in Europe that FDR can reconstitute himself as the leader of the people in a time of need. On the cusp of World War Two FDR runs against and defeats Wendel>
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