Professor Demir’s research work concentrates on the mathematical modeling and numerical analysis of nonlinear, stochastic, statistical and noise phenomena that arise in physical, biological and engineered systems, a multi-disciplinary endeavor that lies at the intersection of electrical engineering, computer science, applied mathematics and the sciences.

Rigorous mathematical models based on first principles and analysis-based, efficient numerical simulation techniques are indispensable tools in forming a fundamental understanding of complex system behavior and in building computational prototypes for the design of various types of engineering systems, especially when nonlinear and stochastic phenomena co-exist and interfere with each other in determining the system behavior.

1. Computational prototyping of electronic & opto-electronic systems

2. Numerical modeling & analysis

3. Computational & quantitative biology

4. Computational neuroscience

1. Stochastic & nonlinear dynamical systems in electronics & biology

2. Noise & fluctuations in electronic, optical, communication & biological systems

3. Oscillators in electronic & biological systems

4. Phase models for oscillatory systems

5. Coarse-grained models for polymeric bio-molecules

6. Optimal real-time application deployment for multi-core systems

7. Statistical timing analysis for digital electronic circuits

8. Modeling & simulation of low-frequency noise in nano-devices & circuits

9. Modeling of auto-immune/inflammatory syndromes with a nonlinear dynamics perspective

10. Modeling & simulation of noise & correlations in neurons & neuronal networks

11. Numerical analysis of multi-domain and multi-physics systems

12. Spike timing precision in neuronal circuits