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- Peter V Gordon, Christine Sample, Alexander M Berezhkovskii, Cyrill B Muratov, Stanislav Y Shvartsman
- Proceedings of the National Academy of Sciences…
- 2011

Some aspects of pattern formation in developing embryos can be described by nonlinear reaction-diffusion equations. An important class of these models accounts for diffusion and degradation of a locally produced single chemical species. At long times, solutions of such models approach a steady state in which the concentration decays with distance from the… (More)

- Cyrill B Muratov, Peter V Gordon, Stanislav Y Shvartsman
- Physical review. E, Statistical, nonlinear, and…
- 2011

Morphogen gradients are concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues and play a fundamental role in various aspects of embryonic development. We discovered a family of self-similar solutions in a canonical class of nonlinear reaction-diffusion models describing the formation of morphogen… (More)

- Peter V Gordon, Cyrill B Muratov, Stanislav Y Shvartsman
- The Journal of chemical physics
- 2013

We analyze the transient dynamics leading to the establishment of a steady state in reaction-diffusion problems that model several important processes in cell and developmental biology and account for the diffusion and degradation of locally produced chemical species. We derive expressions for the local accumulation time, a convenient characterization of… (More)

- Alexander Babchin, Irina Brailovsky, Peter Gordon, Gregory Sivashinsky
- Physical review. E, Statistical, nonlinear, and…
- 2008

Departing from the classical Buckley-Leverett theory for two-phase immiscible flows in porous media, a reduced evolution equation for the water-oil displacement front is formulated and studied numerically. The reduced model successfully reproduces the basic features of the finger-forming dynamics observed in recent direct numerical simulations.

- Peter V Gordon, Daniel J Gotti, Uday G Hegde, Michael C Hicks, Michael J Kulis, Gregory I Sivashinsky
- Proceedings. Mathematical, physical, and…
- 2015

In this paper, we formulate and analyse an elementary model for autoignition of cylindrical laminar jets of fuel injected into an oxidizing ambient at rest. This study is motivated by renewed interest in analysis of hydrothermal flames for which such configuration is common. As a result of our analysis, we obtain a sharp characterization of the autoignition… (More)

- Nicholas M. Bessonov, Peter V. Gordon, Gregory I. Sivashinsky, Ann Zinoviev
- Appl. Math. Lett.
- 2005

- Peter V. Gordon, Cyrill B. Muratov
- SIAM J. Math. Analysis
- 2015

- Peter V Gordon, Vitaly Moroz
- Proceedings. Mathematical, physical, and…
- 2014

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two-phase materials, where, in contrast to the classical Gelfand problem which uses a single temperature approach, the state of the system is described by two different… (More)

- Peter V. Gordon, Uday G. Hegde, Michael C. Hicks, Michael J. Kulis
- SIAM Journal of Applied Mathematics
- 2016

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess travel-ing wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show… (More)