Professor of Mathematics
Fields of work: Pure and applied mathematics, physics and biology. Specific areas: Differential equations, integrable systems, acoustic and electromagnetic scattering (especially transmission anomalies and resonances), photonic crystals, exciton polaritons and recently micromagnetics.
Invited as one of the three Abel lecturers in the award of the Abel Prize to Peter Lax, The Norwegian Academy of Science and Letters, Oslo, Norway, May 2005
Appointments and Affiliations
- Professor of Mathematics
- Office Location: 104 Physics Bldg, Durham, NC 27708
- Office Phone: (919) 660-2815
- Email Address: firstname.lastname@example.org
- Ph.D. New York University, 1982
- M.S. Georgia Institute of Technology, 1979
- B.S. National Technical University of Athens (Greece), 1969
MICROMAGNETICS (NSF Supported)
This area of physics deals with the prediction of magnetic behaviors at sub-micrometer length scales. The area has great scientific and technological importance and involves challenging matehmatical questions. From wikipedia: “Apart from conventional magnetic domains and domain-walls, the theory also treats the statics and dynamics of topological line and point configurations, e.g. magnetic vortex and antivortex states or even 3d-Bloch points, where, for example, the magnetization leads radially into all directions from the origin, or into topologically equivalent configurations. Thus in space, and also in time, nano- (and even pico-)scales are used. The corresponding topological quantum numbers are thought to be used as information carriers, to apply the most recent, and already studied, propositions in information technology.”
I entered this area, working collaboratively in June 2017. Our paper on traveling domain walls (they separate two domains of different magnetization, submitted to "Nonlinearity" in June 2018) is currently in review. By analyzing the related Landau-Lifschits equation and using a topological argument, the paper proves the existence of traveling domain walls. We believe that this is the first such proof, in domain wall models that have fairly realistic assumptions. We are currently researching the profile of "skyrmions", that is, localized magnetic structures in a two dimensional magnetic medium that can be thought of as magnetization solitons.
ACOUSTIC AND ELECTROMAGNETIC SCATTERING: THEORETICAL AND COMPUTATIONAL (NSF supported) Collaborative work on the scattering from scatterers with spatially periodic geometry. Our paper has been accepted for publication by "Communications in Computational Physics". One of its strengths is that it can handle frequencies that exhibit the so-called Wood anomaly.
MATHEMATICAL BIOLOGY: I am a continuing member of the Kiehart dorsal closure group. My participation this year was mainly on a review paper from the group on the "Mathematical Modeling of Dorsal Closure", that appeared in Progress in Biophysics and Molecular Biology 137 (September 2018).
- MATH 353: Ordinary and Partial Differential Equations
- MATH 453: Introduction to Partial Differential Equations
- MATH 753: Ordinary and Partial Differential Equations
- MATH 754: Introduction to Partial Differential Equations
- MATH 790-90: Minicourse in Advanced Topics
- Komineas, S; Melcher, C; Venakides, S, The profile of chiral skyrmions of small radius, Nonlinearity, vol 33 no. 7 (2020), pp. 3395-3408 [10.1088/1361-6544/ab81eb] [abs].
- Komineas, S; Melcher, C; Venakides, S, Traveling domain walls in chiral ferromagnets, Nonlinearity, vol 32 no. 7 (2019), pp. 2392-2412 [10.1088/1361-6544/ab1430] [abs].
- Pérez-Arancibia, C; Shipman, SP; Turc, C; Venakides, S, Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies, Communications in Computational Physics, vol 26 no. 1 (2019), pp. 265-310 [10.4208/cicp.OA-2018-0021] [abs].
- Venakides, S; Komineas, S; Melcher, C, The profile of chiral skyrmions of large radius, Nonlinearity (2019) [abs].
- Aristotelous, AC; Crawford, JM; Edwards, GS; Kiehart, DP; Venakides, S, Mathematical models of dorsal closure., Progress in Biophysics and Molecular Biology, vol 137 (2018), pp. 111-131 [10.1016/j.pbiomolbio.2018.05.009] [abs].