Leonid Pechenik

Publications (4)0 Total impact

• Source

  Available from: David Kessler

  Article: Steady-state mode I cracks in a viscoelastic triangular lattice

  Leonid Pechenik, Herbert Levine, David A. Kessler
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  ABSTRACT: We construct exact solutions for Mode I steady-state cracks in an ideally brittle viscoelastic triangular lattice model. Our analytic solutions for the infinite lattice are compared to numerical results for finite width systems. The issues we address include the crack velocity versus driving curve as well as the onset of additional bond breaking, signaling the emergence of complex spatio-temporal behavior. Somewhat surprisingly, the critical velocity for this transition becomes a decreasing function of the dissipation for sufficiently large values thereof. Lastly, we briefly discuss the possible relevance of our findings for experiments on mode I crack instabilities.
  Journal of the Mechanics and Physics of Solids. 03/2000;
• Source

  Available from: David Kessler

  Article: Steady-state mode III cracks in a viscoelastic lattice model

  Leonid Pechenik, Herbert Levine, David A. Kessler
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  ABSTRACT: We extend the Slepyan solution of the problem of a steady-state crack in an infinite ideally brittle lattice model to include dissipation in the form of Kelvin viscosity. As a demonstration of this technique, based on the Wiener-Hopf method, we apply the method to mode III cracks in a square lattice. We use this solution to find the critical velocity at which the steady-state solution becomes inconsistent due to additional bond-breaking; this point signaling the onset of complex dynamical behavior.
  03/2000;
• Source

  Available from: arxiv.org

  Article: Interfacial Velocity Corrections due to Multiplicative Noise

  Leonid Pechenik, Herbert Levine
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  ABSTRACT: The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading edge which perforce has low density, it is interesting to study the role that finite particle number fluctuations have on this picture. Here, we use the well-known mapping of discrete Markov processes to stochastic differential equations and focus on the front velocity in the simple $A+A \stackrel{\leftarrow}{\to} A$ system. Our results are consistent with a recent (heuristic) proposal that $v_{MS} - v \sim {1\over \ln^2 {N}}$. Comment: 6 eps figures; submitted to Phys. Rev. E
  11/1998;
• Article: Refraction of waves in excitable media

  Leonid Pechenik, Herbert Levine
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  ABSTRACT: Waves in chemically excitable systems can refract when impinging on an interface between regions of different reaction kinetics and/or diffusion constants. Here we study this process using the thin reaction-zone limit wherein the dynamics of the system can be reduced to the tracking of the boundaries between quiescent and excited regions. We show how to derive an integrodifferential equation for the refraction of a single pulse and we subsequently solve this equation numerically. Our results predict that there can be an oscillatory recovery to the asymptotic (far from the interface) pulse; this could be checked by experiments on the Belousov-Zhabotinskii reaction.
  Phys. Rev. E. 58(3).