Dr Razvan Satnoianu 

Research Page

I do research in both Applied and Pure Mathematics. Subjects of interest are: mathematical biology, pattern formation in the natural environment, mathematical modelling and analysis with applications to biology, chemistry and economics, systems of reaction-diffusion-advection equations, nonlinear analysis and bifurcations, existence and stability of the solutions to the above, geometrical and analytical inequalities and their applications in Science, real analysis of functions.

Recently I have proposed in collaboration a new theoretical mechanism for pattern formation based on the combined action of both diffusion and advection (flow) termed FDS or flow and diffusion distributed structures (see references [5], [12], [13], [15], [16], [18] and [22] below). In its broadest sense FDS produces waves in both stationary and/or travelling form and encompasses as particular cases both the famous Turing as well as the DIFI mechanisms for pattern formation. More details on the FDS are found from the list of publications below (see papers 5, 12, 13, 15, 16, 18 and 22). I worked before (1995-1999) on the DIFI mechanism of instability proposed by Michael Menzinger and Arkady Rovinsky around 1993/4. All my results are collected in the papers 23, 24, 25, 26, 28, 29, 30, 31 below. 

Another topic of interest is the subject of geometric inequalities. I have recently been able to point to a general idea of approaching and refining many such classical results, see papers [4], [8], [9], [10] and [19] for more information. Other papers on geometric/analytic inequalities are [3], [7], [8], [15].   

Publications 

1. Razvan A. Satnoianu and Pauline van den Driessche, Some remarks on matrix stability with application to Turing instability, Journal of Linear Algebra and its Applications, 2004, (to appear)  

2. Razvan A. Satnoianu, Systems of reaction-diffusion equations, article in Encyclopedia of Nonlinear Science, edited by Alwyn Scott, Routledge Reference, Taylor and Francis, 2004 (to appear).  

3. Razvan A. Satnoianu, Geometric-arithmetic convexity inequalities, a conjecture of Walther Janous and an IMO 2001 problem, Gazeta Matematica A, 22, No. 1 (2004), 62-68

4. Razvan A. Satnoianu, The extension of the Erdos-Mordell inequality to polynomial functions, Gazeta Matematica B, 109, No. 1 (2004), 3-6  

5. Razvan A. Satnoianu, Coexistence of stationary and traveling waves in reaction-diffusion-advection systems, Physical Review E, 68 (2003), doi:10.1103/PhysRevE.68.032101. Published 12 September 2003 (4 pages)          (journal link)        (download local file)

6. Razvan Satnoianu, The Diffusion Equation, article in Encyclopedia of Nonlinear Science, edited by Alwyn Scott, Routledge Reference, Taylor and Francis, 2004 (to appear).

7. Razvan Satnoianu, A duality principle for obtaining geometric triangle inequalities,  Gazeta Matematica B 108 (2003).

8. Razvan Satnoianu, Refined geometric inequalities between two or more triangles obtained by dedublation, Mathematical Inequalities and Applications (to appear in 2004)

9. Razvan Satnoianu, The principle of the isosceles triangle, Elemente der Mathematik, (to appear in 2004)

10. Razvan Satnoianu, Inequalities of Erdos-Mordell type in triangles, American Mathematical Monthly,  110 (2003)        (cover page)   (journal link)  (download local file)

11. Razvan A. Satnoianu, Improved GA-convexity inequalities, Journal of Inequalities in Pure and Applied Mathematics (JIPAM), 3(5) (2002), Article 82 (electronic journal)

12. Razvan Satnoianu and M. Menzinger, A general mechanism for 'inexact' phase-differences in reaction-diffusion-advection systems, Physics Letters A 304 (2002) 149-156, DOI: 10.1016/S0375-9601(02)01387-7.       (download local file) 

13. Razvan Satnoianu, Flow-and-diffusion structures (FDS) or how Turing patterns come to life, UK Nonlinear News issue 28, May 2002,  front article with pdf figures        (click on the link in the title)         

14. Razvan Satnoianu, General power inequalities between the sides and circumscribed and inscribed radii related to the fundamental triangle inequality, Mathematical Inequalities and Applications 5 (2002), 745-751 

15. M. Kaern, Razvan Satnoianu, A.P. Munuzuri and M. Menzinger, Controlled pattern formation in the CDIMA reaction with a moving boundary of illumination, Nonlinear kinetics special issue, Physical Chemistry Chemical Physics (PCCP) 8 (2002), 1315-1319 DOI 10.139/b109387h                    (download local file)   

16. Razvan A. Satnoianu, P.K. Maini and M. Menzinger, Parameter space analysis, pattern sensitivity and model comparison for Turing and flow-distributed waves (FDS), Physica D 160 (2001), 79-102                             (download local file)

17. Razvan Satnoianu, The proof of the conjectured inequality from the 42nd IMO Washington DC 2001, Gazeta Matematica B 106 (2001), 390-393                                                                                                      

18. M. Kaern, Razvan A. Satnoianu, M. Menzinger and A. Hunding, Chemical waves in open flows of active media: Their relevance to axial segmentation in biology, Faraday Discussions 120 (2001), 295-312                (download local file)  

19. Razvan Satnoianu, A general method for establishing geometrical inequalities in a triangle, American Mathematical Monthly 108 (2001), 360-363      (cover page) (download local file)

20. Razvan A. Satnoianu, P.K. Maini, F.S. Garduno and J.P. Armitage, Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation, DCDS B 1 (2001), 339-362        (download local file)

21. Razvan A. Satnoianu, M. Menzinger and P.K. Maini, Turing instabilities in general systems, J. Maths. Biol. 41 (2000), 493-512        (download local file)

22. Razvan A. Satnoianu and Michael Menzinger, Flow-distributed structures: non-Turing stationary patterns with general diffusion and flow rates, Phys. Rev. E 62 (2000), 113-119             (download local file)

23. Razvan A. Satnoianu, John H. Merkin and Stephen K. Scott, The development of spatial structure in an ionic chemical system induced by applied electric fields, Dynamics and Stability of Systems 5 (2000), 209-230                 

24. Razvan A. Satnoianu, J.H. Merkin and S.K. Scott, Forced convective structures in a differential-flow reactor, Dynamics and Stability of Systems 4 (1999), 275-298              

25. Razvan A. Satnoianu, John H. Merkin and Stephen K. Scott, Pattern formation in a differential-flow reactor model, Chemical Engineering Science 55 (2000), 461-469 (special issue of Chemical Engineering Journal devoted to CHISA 98, Prague, 13th International Congress of Chemical and Process Engineering, 1998)              

26. Razvan A. Satnoianu, John H. Merkin and Stephen K. Scott, Spatio-temporal structures in a differential flow reactor with cubic autocatalator kinetics, Physica D 124 (1998), 345-367         (download local file)

27. Razvan A. Satnoianu, On the ordering of some important elements in a triangle (geometric inequalities), Timisoara Mathematical Journal (Timisoara, Romania), 2 (3rd year, 4th series), (1998), 4-5

28. Razvan A. Satnoianu, John H. Merkin and Stephen K. Scott, Interaction between Hopf and convective instabilities in a flow reactor with cubic autocatalator kinetics, Physical Review E, 57 (1998), 3246-3250              (download local file)

29. J. Merkin, Razvan Satnoianu and S. Scott, Spatiotemporal chaos in a differential flow reactor, J. Chem. Soc., Faraday Trans. 94 (1998), 1211-1216                (download local file)

30. Razvan A. Satnoianu, John H. Merkin and Stephen K. Scott, Differential flow-induced instability in a cubic autocatalator system, J. Enginering Mathematics 33 (1998), 77-102                  (download local file)

31. John H. Merkin, Razvan A. Satnoianu and Stephen K. Scott, Travelling waves in a differential flow reactor with simple autocatalytic kinetics, J. Enginering Mathematics 33 (1998), 157-174              (download local file)

32. Razvan A. Satnoianu, The neo-classical growth model with variable interest rate is chaotic, J. Cybernetics and Statistics   (Academy of Economic Studies Bucharest), XXXI, 4 (1997), 39-51           (download local file)

33. Razvan A. Satnoianu, On the representation of a field as a finite union of proper subfields, Computer Mathematica (Bucharest)  4, 1 (1994), 1-2

 

34. Razvan A. Satnoianu, On the Zaslavski and Marcus problem, Scientific Bulletin Technical University Bucharest 53, 1-2 (1991), 35-38

 

35. Razvan A. Satnoianu, Some remarks on the additive subgroups of the real line, Studies and Researches in Mathematics, Bucharest (Romanian Academy), 42, 3 (1990), 269-272

 

36. Radu Paltanea and Razvan Satnoianu, Functions whose level sets are all perfect, Real Analysis Exchange, Michigan (East Lansing), USA, 15 (1989-1990), 548-558

 

37. Razvan A. Satnoianu, Erdos-Mordell type inequalities in triangles and applications, Moisiliana Journal of Mathematics, 1, 2 (1986), 15-17

 

38. Razvan A. Satnoianu, On a Ramsey type problem for 2D and 3D convex geometry, in Romanian National Undergraduate Research Bulletin, Iasi, Romania, XIV (1986), 233-241

 

39. Razvan Satnoianu, Some refined inequalities for the number e, Moisiliana Journal of Mathematics 1, 1 (1986), 9-12

             

 

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