Leonid V. Kalachev

Department of Mathematical Sciences
The University of Montana
Missoula, MT 59812

(Ph.D. 1987, Moscow State University)

E-mail: kalachev@mso.umt.edu
Phone: (406) 243-4373
FAX: (406) 243-2674

[Ph.D. Thesis direction]     [Publications]    [Teaching]

 Course web pages:  M512, Spring of 2013

Ph.D. Thesis direction (with the year of graduation):

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.]

Peter McCauley (2009):  Fatigue Risk Management: Modeling the Sleep/Wake-Based Dynamics of Performance.


Nick McClure (2012): Mathematical Modeling and Disease Related Applications: A New Method of Estimating Bacterial Mutation Rates, Dynamics of Killer Yeast in a Chemostat, and Other Problems.



MA Thesis direction (with the year of graduation):

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.

Shoeb Khan (2005): Mathematical Analysis of a Tropospheric Chemistry Model.

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).

Erica Miller (2009):  Optimizing Captive Rearing Management Strategy for an Endangered Butterfly Species Using an Extinction Probability Model. 


Publications (since 1995):


1. L.V. Kalachev and R.M.M.Mattheij, On optimally scaled systems for second order scalar singularly perturbed problems, Appl. Math. Math. Comp. (1995), V. 68, pp. 71-93;

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. Engrng Ind. (International  Journal of  Math. Engineering with Industrial Applications) (1999), V. 7, No. 4, pp. 457 - 478.

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 accepted 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. 2(2) (2007), pp. 177 – 190.


33.  P. McCauley, A.D. Smith, L. V. Kalachev, G.Belenky, D. F. Dinges, H. Van Dongen, A new mathematical model for the homeostatic effects of sleep loss on neurobehavioral performance, J. Theor. Biology 256 (2009), pp. 227 - 239. 


34.  H. Haario, L. Kalachev, and M. Laine, Reduced models of algae growth, Bull. Math. Biology (2009) Oct; 71(7), PP. 1626 - 48.


35. Kalachev L.V, Kelly T.C., O’Callaghan M.J., Pokrovskii A.V., and Pokrovskii A.A., Analysis of threshold type behavior in mathematical models of the intrusion of a novel macroparasite in a host colony, Math. Med. Biol. (2011) Dec; 28(4): 287 – 333.


36. Leary G.P., Holley D.C., Stone E.F., Lyda B.R., Kalachev L.V, and Kavanaugh M.P., The central cavity in trimeric glutamate transporters restricts ligand diffusion, Proc. Natl. Acad. Sci. USA. (2011) Sep 6; 108(36): 14980-5.


37. H. Haario, L. Kalachev, and M. Laine, Reduction and identification of dynamic models. Simple example: generic receptor model. Accepted for publication in the journal Discrete and Continuous Dynamical Systems. To appear in 2013.


 Book published:

A.B. Vasil'eva, A.B. Butuzov and L.V. Kalachev, The Boundary Function Method for Singular Perturbation Problems, Philadelphia: SIAM, 1995.

Publications before 1995 can be found HERE

Teaching at The University of Montana:

Graduate courses: Mathematical Biology and Asymptotic Methods (Math 511, Math 512); Asymptotic Methods (Math 511, Math 512), Nonlinear Systems and Bifurcations (Math 514), Mathematical Modeling: Solving Real World Problems (Math 514). 

Undergraduate courses: Introduction to Contemporary Mathematics (Math 107), Discrete Mathematics (Math 117), Applied Calculus (Math 150), Elementary Mathematical Modeling (Math 158), Multi-variable Calculus (Math 251), Ordinary Differential Equations (Math 311), Partial Differential Equations (Math 412), Computer Lab for ODEs and PDEs (Math 317, Math 418), Deterministic Models (Math 414), Statistical, Dynamical and Computational Modeling (M445).