Oleg N. Kirillov

Standard and helical magnetorotational instability and MHD dynamo

1. O.N. Kirillov, F. Stefani, Standard and helical magnetorotational instability: How singularities create paradoxical phenomena in MHD. Acta Applicandae Mathematicae 2012 Vol. No. P. (PDF) 

2. O.N. Kirillov, D.E. Pelinovsky, G. Schneider, Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows.
Physical Review E (Rapid communication) 2011 Vol. 84 No. 6 P. 065301(R)

3. O.N. Kirillov, F. Stefani, Paradoxes of magnetorotational instability and their geometrical resolution. Physical Review E 2011. Vol. 84 No. 3 P. 036304

4. Kirillov O.N., Stefani F. On the relation of standard and helical magnetorotational instability. The Astrophysical Journal, 2010. Vol. 712 P. 52-68

5. Kirillov O.N., Guenther U., Stefani F. Determining role of Krein signature for three dimensional Arnold tongues of oscillatory dynamos. Physical Review E, 2009. Vol. 79. No. 1 016205

6. Guenther U., Kirillov O.N., Samsonov B.F., Stefani F. The spherically - symmetric alpha^2-dynamo and some of its spectral peculiarities. 
Acta Polytechnica. 2007. Vol. 47 No. 2–3. P. 75-81.

7. Guenther U., Kirillov O.N. A Krein space related perturbation theory for MHD alpha-2 dynamos and resonant unfolding of diabolical points. Journal of Physics A: Mathematical and General. 2006. Vol. 39. P. 10057-10076. 

Non-Hermitian physics, exceptional points and Berry phase

1. B. Dietz, H. L. Harney, O.N. Kirillov, M. Miski-Oglu, A. Richter, F. Schaefer, Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation. Physical Review Letters 2011. Vol. 106. No. 15. P. 150403

2. Mailybaev A.A., Kirillov O.N., Seyranian A.P. Berry phase around degeneracies. Doklady Mathematics. 2006. Vol. 73. No. 1. P. 129-133. 

3. Kirillov O.N., Mailybaev A.A., Seyranian A.P. Singularities of energy surfaces under non-Hermitian perturbations. Doklady Physics. 2005. Vol. 50. No. 11. P. 577-582. 

4. Mailybaev A.A., Kirillov O.N., Seyranian A.P. Geometric phase around exceptional points. Physical Review A. 2005. Vol. 72., 014104.

5. Kirillov O.N., Mailybaev A.A., Seyranian A.P. Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation. Journal of Physics A: Mathematical and General. 2005. Vol. 38. No. 24. P. 5531–5546.

6. Seyranian A.P., Kirillov O.N., Mailybaev A.A. Coupling of eigenvalues of complex matrices at diabolic and exceptional points. Journal of Physics A: Mathematical and General. 2005. Vol. 38. No. 8. P. 1723-1740.

Dissipation-induced instabilities and destabilization paradox

1. O.N. Kirillov, F. Verhulst, Dissipation-induced instabilities and symmetry. 
Acta Mechanica Sinica 2011. Vol. 27. No. 1. P. 2-6. 

2. Hoveijn I., Kirillov O.N. Singularities on the boundary of the stability domain near 1:1-resonance. Journal of Differential Equations, 2010. Vol. 248 No. 10 P. 2585–2607.

3. Kirillov O.N., Verhulst F. Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella? Z. angew. Math. Mech. 2010. Vol. 90, No. 6, P. 462 – 488. (Editor's choice)

4.  Verhulst F, Kirillov O.N., Bottema opende Whitney’s paraplu, Nieuw Archief voor Wiskunde, 2009. Vol. 5/10, No.4, P. 250-254. 

5. Kirillov O.N. Gyroscopic stabilization in the presence of nonconservative forces. Doklady Mathematics. 2007. Vol. 76. No. 2. P. 780-785.

6. Kirillov O.N. Bifurcation of the roots of the characteristic polynomial and destabilization paradox in friction induced oscillations. Theoretical and Applied Mechanics 2007 Volume 34, Issue 2, 87-109.

7. Kirillov O.N. On the stability of nonconservative systems with small dissipation. Journal of Mathematical Sciences. 2007. Vol. 145, No. 5. P. 5260-5270. 

8. Kirillov O.N. Destabilization paradox due to breaking the Hamiltonian and reversible symmetry. International Journal of Non-Linear Mechanics. 2007. Vol. 42. No. 1. P. 71-87.

9. Kirillov O.N. Gyroscopic stabilization of non-conservative systems. Physics Letters A. 2006. Vol. 359. No. 3. P. 204-210.

10. Kirillov O.N., Seyranian A.P. Instability of distributed nonconservative systems caused by weak dissipation. Doklady Mathematics. 2005. Vol. 71. No. 3. P. 470-475.

11. Kirillov O.N., Seyranian A.P. The effect of small internal and external damping on the stability of distributed non-conservative systems. J. Appl. Math. Mech. 2005. Vol. 69. No. 4. P. 529-552.

12. Kirillov O.N. A theory of the destabilization paradox in non-conservative systems. Acta Mechanica. 2005. Vol. 174. No. 3-4. P. 145-166. 

13. Kirillov O.N., Seyranian A.P. Stabilization and destabilization of a circulatory system by small velocity-dependent forces. Journal of Sound and Vibration. 2005. Vol. 283. No. 3-5. P. 781-800.

14. Kirillov O.N. Destabilization paradox. Doklady Physics. 2004. Vol. 49. No. 4. P. 239-245. 

15. Seyranian A.P., Kirillov O.N. Effect of small dissipative and gyroscopic forces on the stability of nonconservative systems. Doklady Physics. 2003. Vol. 48.  No. 12. P. 679-684.

16. Kirillov O.N. How do small velocity-dependent forces (de)stabilize a non-conservative system? DCAMM Report. No. 681. April 2003. 40 pages. 

Non-conservative rotor dynamics, friction-induced instabilities, acoustics of friction and brake squeal

1. O.N. Kirillov, Brouwer’s problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics. Physics Letters A 2011. Vol. 375 P. 1653–1660. 

2. O.N. Kirillov, Sensitivity of sub-critical mode-coupling instabilities in non-conservative rotating continua to stiffness and damping modifications. 
Int. J. Vehicle Struct. Syst. 2011. Vol. 3. No. 1. P. 1-13.

3. Kirillov O.N. Campbell diagrams of weakly anisotropic flexible rotors, 
Proc. of the Royal Society A 2009. Vol. 465, No. 2109, P. 2703-2723.

4. Kirillov O.N. Unfolding the conical zones of the dissipation-induced subcritical flutter for the rotationally symmetrical gyroscopic systems, 
Physics Letters A. 2009. Vol. 373, No.  10, P. 940–945. 

5. Kirillov O.N. Perspectives and obstacles for optimization of brake pads with respect to stability criteria. Int. J. of Vehicle Design, 2009. Vol. 51, Nos. 1/2, P. 143–167.

6. Kirillov O.N. How to play a disc brake: A dissipation-induced squeal. 
SAE Int. J. Passeng. Cars - Mech. Syst. 2009. Vol. 1 No. 1, P. 863-876.

7. Spelsberg-Korspeter G., Hochlenert D., Kirillov O.N., Hagedorn P. 
In- and out-of-plane vibrations of a rotating plate with frictional contact: Investigations on squeal phenomena. Trans. ASME, J. Appl. Mech. 2009. Vol. 76. No. 4, 041006, P. 1-15.

8. Kirillov O.N. Subcritical flutter in the acoustics of friction. Proceedings of the Royal Society A 2008. Vol. 464. No. 2097. P. 2321–2339.

9. Spelsberg-Korspeter G., Kirillov O.N., Hagedorn P. Modeling and stability analysis of an axially moving beam with frictional contact. Trans. ASME, J. Appl. Mech. 2008. Vol. 75. No. 3, 031001 P. 1-10. 

Perturbation of non-self-adjoint boundary eigenvalue problems

1. Kirillov O.N. Eigenvalue bifurcation in multiparameter families of non-self-adjoint operator matrices, Z. angew. Math. Phys. 2010. Vol. 61 No. 2 P. 221-234.

2.  Kirillov O.N., Seyranian A.P. Collapse of the Keldysh chains and stability of continuous non-conservative systems. SIAM Journal on Applied Mathematics. 2004. Vol. 64. No. 4. P. 1383-1407.

3. Kirillov O.N., Seyranian A.P. Collapse of Keldysh chains and the stability of non-conservative systems. Doklady Mathematics. 2002. Vol. 66. No. 1. P. 127-131. 

Stability and parametric optimization of circulatory systems

1. O. N. Kirillov, Singularities in Structural Optimization of the Ziegler Pendulum,
Acta Polytechnica 2011. Vol. 51 No. 4 P. 32-43.

2. Kirillov O.N., Seyranian A.P. Solution to the Herrmann-Smith problem. 
Doklady Physics. 2002. Vol. 47.  No. 10. P. 767-771. 

3. Kirillov O.N., Seyranian A.P. Metamorphoses of characteristic curves in circulatory systems. J. Appl. Math. Mech. 2002. Vol. 66. No. 3. P. 371-385. 

4. Kirillov O.N., Seyranian A.P. A non-smooth optimization problem.
Moscow University Mechanics Bulletin. 2002. Vol. 57. No. 3. P. 1-6. 

5. Seyranian A.P., Kirillov O.N. Bifurcation diagrams and stability boundaries of circulatory systems. Theoretical and Applied Mechanics. 2001. Vol. 26. P. 135-168. 

6. Kirillov O.N., Seyranian A.P. Overlapping of frequency curves in non-conservative systems. Doklady Physics. 2001. Vol. 46. No. 3. P. 184-189.

7. Kirillov O.N. Optimization of stability of the flying bar. Young Scientists Bulletin. Appl. Maths Mechs. 1999. Vol. 1 No.1 P. 64-78.