Commissioned by MIT's in-house artist Jane Philbrick, we evolve an abstract 2D surface (resembling Marta Pan's 1961 "Sculpture Flottante I") under mean curvature, all the while calculating the eigenmodes and eigenvalues of the Laplace-Beltrami operat...

11 Article(s)

1, 2

Document(s)

Title

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly...

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compress...

We define the Euler number of a bipartite graph on $n$ vertices to be the number of labelings of the vertices with $1,2,...,n$ such that the vertices alternate in being local maxima and local minima. We reformulate the problem of computing the Euler ...

An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is as accura...

A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact conservation of...

We study the vibrations of a hanging thin flexible rod, in which the dominant restoring force in most of the domain is tension due to the weight of the rod, while bending elasticity plays a small but non-negligible role. We consider a linearized desc...

The problem of finding the optimal tapering of a free (non-supported) javelin is described and solved. For the optimal javelin, the lowest mode of vibration has the highest possible frequency. With this tapering inner damping will lead to the cessati...

We present a new model of homogeneous aggregation that contains the essential physical ideas of the classical predecessors, the Becker-Doring and Lifshitz-Slyovoz models. These classical models, which give different predictions, are asymptotic limits...

A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous sy...