| Sergey A Dyachenko | |
|
|
|
Department of Mathematics University at Buffalo. |
|
|
|
|
| Research: | |
| Curriculum Vitae: | Sergey Dyachenko on ResearchGate Sergey Dyachenko on Google Scholar PDF (Sept 2023) |
| Research Interests: |
My interest lies in fluid dynamics, specifically in the singularity formation in flows with free surface. Dynamics of the ocean surface in the high steepness regime often demonstrates breaking waves, and whitecapping at the crests of the steep waves. These spectacular events are associated with singularity formation, and its evolution in the Euler (or Navier-Stokes) equations with the free boundary. In small steepness regime the envelope of a train of periodic travelling waves on the ocean surface is described by the nonlinear Schroedinger equation (NLSE), which is a spectacularly rich and interesting equation. The NLSE and other integrable systems are in the list of my most favoured models to work with. My toolbox consists of computational mathematics and methods of applied mathematics. I enjoy coding in C, Python, Matlab and Julia. |
| Research Interests (short version): |
Water waves (Link to Stokes wave website) Nonlinear waves in optical media Keller-Segel model Bose-Einstein condensaion Numerical simulations |
| Publications: |
14. S. A. Dyachenko and Vera Mikyoung Hur, Stokes Waves with Vorticity II: Folds and Gaps , in preparation (2018) 13. A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov, Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion, submitted to JFM (2018), arXiv link 12. S. A. Dyachenko, On the dynamics of a free surface of an ideal fluid in a bounded domain in the presence of surface tension, J. Fluid Mech (2019), vol. 860, pp. 408-418 PDF 11. S. A. Dyachenko and Vera Mikyoung Hur, Stokes Waves with Vorticity I: Numerical Computation., Accepted to SAPM(2018) arXiv link 10. P. M. Lushnikov, S. A. Dyachenko, D. A. Silantyev, New Conformal Maping for Adaptive Resolving of the Complex Singularities of Stokes Wave, Proc. Roy. Soc. A (2017), Link to paper 9. S. Dyachenko, A. Zlotnik, A., Korotkevich, M. Chertkov, Operator Splitting Method for Dynamic Simulations of Flows in Natural Gas Transport Networks , Physica D (2017) 8. S.A. Dyachenko, D.V. Zakharov, V.E. Zakharov, Primitive potentials and bounded solutions of the KdV equation , Physica D (2016) 7. D.V. Zakharov, S.A. Dyachenko, V.E. Zakharov, Bounded solutions of KdV and non-periodic one-gap potentials in quantum mechanics , Lett. Math. Phys. (2016) 6. D.V. Zakharov, V.E. Zakharov, S.A. Dyachenko, Non-periodic one-dimensional ideal conductors and integrable turbulence , Physics Letters A (2016) 5. S.A. Dyachenko, A.C. Newell, Whitecapping , Stud. in Appl. Math (2016) 4. S.A. Dyachenko, P.M. Lushnikov, A.O. Korotkevich, Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pade approximation,, Stud. in Appl. Math (2016) 3. S.A. Dyachenko, P.M. Lushnikov, A.O. Korotkevich, Complex Singularity of a Stokes wave,, JETP Letters (2013) 2. P.M. Lushnikov, S.A. Dyachenko and N. Vladimirova Beyond leading-order logarithmic scaling in the catastrophic self-focusing of a laser beam in Kerr media,, Phys Rev A (2013) 1. S.A. Dyachenko, P.M. Lushnikov and N. Vladimirova Logarithmic scaling of the collapse in the critical Keller-Segel equation, Nonlinearity (2013) |
|
|
|
| Teaching: | |
| Fall 2023: | Partial Differential Equations |
| Spring 2022: | Partial Differential Equations |
| Fall 2021: | Numerical Analysis I |
| Spring 2020: | Partial Differential Equations and Waves |
| Fall 2019: | Vector Calculus and Complex Variables |
| Spring 2019: | Intro to PDE |
| Fall 2018: | Intro to PDE |
| Spring 2018: | Applied Linear Algebra |
| Fall 2017: | Differential Equations |
| Spring 2016: | Intro to PDE |
| Fall 2015: | Intro to Differential Equations Plus |
| Spring 2015: | Linear Algebra (U of A) |
|
|
|
| Education | |
| Ph.D.: |
University of New Mexico Graduation: 18 August 2014 Academic Advisors: Prof. Pavel M. Lushnikov and Prof. Alexander O. Korotkevich Topic: Strongly nonlinear phenomena and singularities in optical, hydrodynamic and biological systems |
| Higher education: |
University of New Mexico, Albuquerque, USA, MA: December 2010 Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, BS: June 2007 |
|
|
|
| Contacts | |
| Office: | Math Bldg 312 |
| E-mail: | sergeydy@buffalo.edu |
| Address: |
Sergey A. Dyachenko Department of Mathematics, 312 Math Bldg, Buffalo, NY |