Whitham-Toda Hierarchy in the Laplacian Growth Problem

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 the hierarchy.Comment: 7 pages, no figures, Talk given at the Workshop NEEDS 99 (Crete, Greece, June 1999

Students Serve Refugees in Georgia

In a time in which travel is limited, Cedarville University students will be serving the nations who have come to the States this summer

New MBA Specialties will Prepare Graduates for High-demand Careers

Three new concentrations will be added to Cedarville University’s online Master of Business Administration (MBA) program, starting with the fall 2018 semester. The new concentrations include business analytics, cybersecurity, and innovation and entrepreneurship* (*pending approval of the Higher Learning Commission)

Velocity selection (without surface tension) in multi-connected Laplacian growth

We predict a novel selection phenomenon in nonlinear interface dynamics out of equilibrium. Using a recently developed formalism based on the Schottky-Klein prime functions, we extended the existing integrable theory from a single interface to multiple moving interfaces. After applying this extended theory to the two-dimensional Laplacian growth, we derive a new rich class of exact (non-singular) solutions for the unsteady dynamics of an arbitrary assembly of air bubbles within a layer of a viscous fluid in a Hele-Shaw cell. These solutions demonstrate that all bubbles reach an asymptotic velocity, $U$, which is {\it precisely twice} greater than the velocity, $V$, of the uniform background flow, i.e., $U=2V$. The result does not depend on the number of bubbles. It is worth to mention that contrary to common belief, the predicted velocity selection does not require surface tension.Comment: 5 pages, 1 figure. Updated versio

Planar elliptic growth

The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for area-preserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.Comment: 27 page

Emerging truth and the defeat of scientific racism

This paper looks at the attack on scientific racism in the 20th century by a group of social and biological scientists. I will utilize the apparatus of my model of emerging truth to show how even in complex socially conditioned argumentation the ultimate virtue is seeking the truth through increasingly powerful logical connections and deeply embedded warrants