DOCK GATES. (INCLUDES PLATE AND APPENDICES).

Sequential Bayesian Search Appendices

Assume that at the beginning of game t, the system's belief in the user's preference is P t. Then, the certainty-equivalet user preference during game t is π * t (i) = E π∼Pt [π(i)] ∀i ∈ I. Recall we define π * min = min i∈I π * (i), Lemma A-1 formalizes the result that if π * t is " close " to π * , then for any decision tree T , E i∼π * t [N (T, i)] is " close " to E i∼π * [N (T, i)]: Lemma A...

Authority in the Dock

The dock problem revisited

The dock problem (cf. [2], [4, 5]), which is that of understanding the scattering of surface water waves by a thin semi-infinite rigid plate floating on the free surface of water of infinite depth, gives rise to the following mixed boundary value problem, involving Laplace’s equation in two dimensions, with (x, y) representing the rectangular Cartesian coordinates, assuming linearised theory of...

File S1: Appendices

We wish to reduce the number of parameters in the model and make it so that the model is more easily comparable to our previous work [1]. To do this we first look at the nonspatial single morph model which is given by: Ni(t+ 1) = (1 + b)Ni(t) exp(−mi −mi (1 + b)Nt) For the purpose of this model we want the carrying capacity K to be fixed by the equilibrium population density. We therefore calcu...

The finite dock problem

The scattering of water waves by a dock of finite width and infinite length in water of finite depth is solved using the modified residue calculus technique. The problem is formulated for obliquely incident waves and the case of normal incidence is recovered by taking an appropriate limit. Exciting forces and pitching moments are calculated as well as reflection and transmission coefficients. T...