Department
of Mathematical Sciences
The
(Ph.D. 1987,
Moscow State University)
E-mail:
kalachev@mso.umt.edu
Phone: (406)
243-4373
FAX: (406)
243-2674
[Scientific Interests] [Ph.D. Thesis direction] [Publications] [Teaching]
Course web pages: MATH
150, Fall 2005
Remark: Papers [1*] - [11*] have appeared before 1995 (they are included in the list of all publications that can be found HERE ). Papers [43*], [44*] have appeared in the proceedings.
I am currently a member of the Bio-Nano Electronics Research Center in Japan (see http://www.toyo.ac.jp/bio/bio_sosiki.html),
and a member of Scientific Consortium Research Group in Finland (project
title:Development of Bayesian Methods with Applications in
Geophysical and Environmental Research;
see http://www.math.utu.fi/MaDaMe/projects/haario.html).
William Long (1997): Asymptotic analysis of the dissolution of a spherical bubble in the case of fast reaction.
Michael Kraemer (2001): Analysis of a class of integro-differential equations describing age structure dynamics of a natural forest.
Supawan Lertskrai (2002): Asymptotic analysis of a fast reaction outside a solid sphere in a creeping flow.
Greg Cripe
(2002): The effect of
information on a stochastic fishery model. [Joint with Professor Robert McKelvey.]
Eric Dolven
(1996): An analysis of a Hopf bifurcation in a host-parasite interaction.
Mary Sinamon
(1996): On principle of quasi-stationary concentrations in
the problems of chemical kinetics.
Lucas Casady (2004): Asymptotic reductions of a model describing facilitated diffusion in membrane transport.
Peter McCauley (2005): Dynamics of a single species natural forest in the presence
of a disease.
Nicholas McClure (2007): The effect of killer virus on competition in S. Cerevisiae (baker’s yeast).
2. R. M. Noyes, L.V. Kalachev
and R.J. Field, Mathematical
model of the Bray-Liebhafsky oscillations, J.
Phys. Chem. (1995), V. 99,
pp. 3514-3520.
3. L.V. Kalachev and R.E. O'Malley,Boundary value problems for differential-algebraic equations, Numer. Func. Anal. and Optimiz. (1995), V. 16, No. 3&4, pp. 363-378.
4. L.V. Kalachev and R.E. O'Malley, The regularization of linear differential-algebraic equations, SIAM J. Math. Anal. (1996), V. 27, No. 1, pp. 258 - 273.
5. T.I. Seidman
and L.V. Kalachev, The limit of a diffusion/reaction system with a fast
reaction, J. Math. Anal. Appl. (1997), V. 209,
pp. 392 - 414.
6. L.V. Kalachev and R.J. Field, Absence
of multiple steady states and a transition from steady state to monotonic
growth behavior of
[CO] and [O3] in a simple nonlinear
oscillatory model of tropospheric chemistry, Geoph. Research Letters
(1998), Vol. 25, No. 24,
pp. 4505-4508.
7. H. Haario,
L. Kalachev, T. Salmi and
J. Lehtonen,
Asymptotic analysis of chemical reactions, Chem. Eng. Sci. (1999), V.54,
pp.1131 - 1143.
8. H. Haario
and L. Kalachev, Model reductions for multi-phase phenomena, Math.
9. W. Derrick and L. Kalachev, Bray-Liebhafsky Oscillations, J. Nonlinear Science (2000), Vol. 10, No. 1, pp.131 - 144.
10. W. Long and L. Kalachev, On dissolution of a spherical gas bubble in the presence of fast reaction, Chem. Eng. Sci. (2000), Vol. 55,No. 12, pp. 2295-2301.
11. W. Long and L. Kalachev, Asymptotic analysis of dissolution of a spherical bubble (case of fast reaction outside the bubble), Rocky Mountain J. of Math. (2000), V. 30, No. 3, pp. 293 - 313.
12. L. V. Kalachev, Asymptotic methods: application to reduction of
models, Natural Resource Modeling (2000), V. 13, No. 3,
pp. 305 - 338.
13. L. Kalachev, H. Morimoto and T. Maekawa, Derivation of a scaling law in cluster - cluster aggregations from a modified Smoluchowski's coagulation equation, Intl. J. of Modern Physics B (2001), Vol. 15, No. 6 & 7, pp. 774-779.
14. R. Field, P. Hess, L. Kalachev, and S. Madronich, Characterization of oscillation and a period-doubling transition to chaos reflecting dynamic instability in a simplified model of tropospheric chemistry, J. Geoph. Res. (2001), Vol. 106, No. D7, pp. 7553 - 7565.
15. L. Kalachev and R. Field, Reduction of model describing ozone oscillations in the troposphere: example of an algorithmic approachto model reduction in atmospheric chemistry, J. Atm. Chem. (2001), Vol. 39, pp. 65 - 93.
16. M. Kraemer, L. Kalachev, and D. Coble, A class of models describing age structure dynamics in a natural forest, Natural Resource Modeling (2002), Vol. 15, No. 2, pp. 149 - 200.
17. S. Handrock-Meyer, L. Kalachev, and K. Schneider, A method to determine the dimension of long-time dynamics in multi-scale systems, J. Math. Chem. (2001), Vol. 30, No. 2, pp. 133 - 160.
18. M. Kraemer and L. Kalachev, Analysis of a class of nonlinear integro-differential equations arising in a forestry application, Quarterly of Applied Mathematics (2003), Vol. 61, No. 3, pp. 513 - 535.
19. D.V. Sakharov, L.V. Kalachev and D.C. Rijken, Numerical simulation of local pharmacokinetics of a drug after intravascular delivery with an eluting stent, Journal of Drug Targeting (2002), Vol. 10 (6), pp. 507 - 513.
20. L.V. Kalachev and T.I. Seidman, Singular perturbation analysis of a stationary diffusion/reaction system exhibiting a corner-type behavior in the interval interior, J. Math. Anal. Appl. (2003), Vol. 288, No. 2, pp. 722 - 743.
21. H. Haario
and L. Kalachev, Asymptotic analysis of a complex reaction scheme in
solid-liquid system, Chem. Eng. Sci.(2003), Vol. 58, pp. 2823 - 2834.
22. S. Lertskrai and L. Kalachev, Analysis of dissolution of a spherical gas bubble in a glass melt in the presence of a flow and a fast redox reaction, Glass Science and Technology (2003), Vol. 76, No. 5, pp.220 - 226.
23. W.R. Derrick, L.V. Kalachev and J.A. Cima, Characterizing the domains of attraction of stable stationary solutions of semilinear parabolic equations, International Journal of Pure and Applied Mathematics (2004), Vol. 11, No. 1, pp. 83-102.
24. L. Kalachev, and K. Schneider, Global behavior and asymptotic reduction of a chemical kinetics system with continua of equilibria, J. Math. Chem. (2005), Vol. 37, No. 1, pp. 57 - 74.
25. Junichi Aoyama, Toshiyuki Takani, Toru Toyabe and Leonid Kalachev, Threshold
Voltage Model of Single Gate SOI MOSFETs Derived from
Asymptotic Method, Proceedings of 2005 International Conference on
Simulation of Semiconductor Processes and Devices (SISPAD 2005), pp. 167
– 170
26. A.B. Vasil’eva
and L.V. Kalachev, Singularly perturbed periodic parabolic
equations with alternating boundary layer type solutions, Abstract and
Applied Analysis, Vol. 2006 (2006), Article ID 52856, 21 pages.
27. L.V. Kalachev,
Reduced model of neurotransmitter
transport in the presence of generic receptors and transporters, Journal of Physics: Conference
Series 55 (2006) 114–129.
28. A.B. Vasil’eva and
L.V. Kalachev, Alternating
boundary layer type solutions of some singularly perturbed periodic parabolic
equations with Dirichlet and Robin boundary
conditions, paper accepter for publication in the Journal of Computational
Mathematics and Mathematical Physics.
29. H. Haario, L. Kalachev and E. Tirronen, Optimal Experimental Protocol for
Identification of Dissolution Parameters in Presence of Fast Reaction, Chem.
Eng. Sci. 62 (2007), pp. 929 – 934.
30. William Derrick, Leonid Kalachev and Joseph Cima, Collapsing Heat Waves, Math. and Comp. Modelling 46 (2007), pp. 612 – 624.
31. L.V. Kalachev, H G. Kaper, T.J. Kaper, N. Popovic, A. Zagaris, Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion, 2006 International Conference in honor of Jacqueline Fleckinger. Electron. J. Diff. Eqns., Conference 16 (2007), pp. 155-184.
32. A.B.Vasil’eva,
L.V.Kalachev, and A.A.Plotnikov,
On certain control problems for a class of singularly perturbed
parabolic equations, Intl. J.
Modern Math., accepted for publication.
Book published:
A.B. Vasil'eva, A.B. Butuzov and L.V. Kalachev,The Boundary Function Method for Singular Perturbation
Problems,