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- Mark A. Duchaineau, Murray Wolinsky, David E. Sigeti, Mark C. Miller, Charles Aldrich, Mark B. Mineev-Weinstein
- IEEE Visualization
- 1997

Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good… (More)

- Leif Ristroph, Matthew Thrasher, Mark B Mineev-Weinstein, Harry L Swinney
- Physical review. E, Statistical, nonlinear, and…
- 2006

Our experiments on viscous fingering of air into oil contained between closely spaced plates reveal two selection rules for the fjords of oil that separate fingers of air. (Fjords are the building blocks of solutions of the zero-surface-tension Laplacian growth equation.) Experiments in rectangular and circular geometries yield fjords with base widths… (More)

We solve the Saffman-Taylor finger selection problem in the absence of surface tension by showing that an arbitrary interface in a Hele-Shaw cell evolves to a single uniformly advancing finger occupying one half of the channel width. This result contradicts all previous work in this field and the generally accepted belief that surface tension is… (More)

The Laplacian growth problem in the limit of zero surface tension is proved to be equivalent to finding a particular solution to the dispersionless Toda lattice hierarchy. The hierarchical times are harmonic moments of the growing domain. The Laplacian growth equation itself is the quasiclassical version of the string equation that selects the solution to… (More)

- U Frisch, M Mineev-Weinstein
- Physical review. E, Statistical, nonlinear, and…
- 2003

It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity nu and no force are of the form u=-2nu inverted Delta ln P, where the P's are explicitly known algebraic (or trigonometric) polynomials in the space variables with polynomial (or exponential) dependence on time. Such… (More)

- Alexander Leshchiner, Matthew Thrasher, Mark B Mineev-Weinstein, Harry L Swinney
- Physical review. E, Statistical, nonlinear, and…
- 2010

Harmonic moments are integrals of integer powers of z=x+iy over a domain. Here, the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension… (More)

- Oleg Alekseev, Mark Mineev-Weinstein
- Physical review. E
- 2016

A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The classical point for the action, defined as a minus logarithm of the growth probability, describes the most probable scenario… (More)

- Robert Yi, Yossi Cohen, +4 authors Daniel H Rothman
- Proceedings. Mathematical, physical, and…
- 2017

Valleys that form around a stream head often develop characteristic finger-like elevation contours. We study the processes involved in the formation of these valleys and introduce a theoretical model that indicates how shape may inform the underlying processes. We consider valley growth as the advance of a moving boundary travelling forward purely through… (More)

A new class of solutions to Laplacian growth (LG) with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls… (More)

Using exact time-dependent non-singular solutions 3], we solve the Saaman-Taylor nger selection problem in the absence of surface tension. We show that a generic interface in a Hele-Shaw cell evolves to a non-linearly stable single uniformly advancing nger occupying one half of the channel width. This result contradicts the generally accepted belief that… (More)