**Department of Mathematical Sciences**

**The University of Montana**

**(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**

**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.

**
**

**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.* *

**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.

**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 ,**

**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 ,**

**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**

**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).