CURRICULUM VITAE 1. First name: Maksym 2. Last name ...

Dr. Maksym Berezhnyi – FB Mathematik-TU Darmstadt- 

Schlossgartenstraße 7 - 64289 Darmstadt - Tel. 06151-163495 

CURRICULUM VITAE 

1. First name: Maksym 

2. Last name: Berezhnyi 

3. Date of birth: 15.10.1981 

4. Sex: male 

5. Family situation: married 

6. e-mail: berezhnyi@mathematik.tu-darmstadt.de 

7. Permanent professional address: 

Fachbereich Mathematik, Technische Universität Darmstadt, 

Schlossgartenstraße 7, 64289 Darmstadt, Deutschland 

8. tel: (+49)-6151-16-3495 

9. Present Position: Wissenschaftlicher Mitarbeiter 

10. Education: 2003, Master’s Diploma in Applied Mathematics, 

Teaching of Mathematics and Compture Science, 

V.N. Karazin Kharkiv National University, Ukraine; 

2004-2007, Post-graduate student, 

B. Verkin Institute for Low Temperature Physics & Engineering, 

Ukraine 

PhD Thesis: 

- the date - 03.06.2009 

- scientific advisor – Member of the NASU, Professor E. Khruslov 

- the theme “Homogenized models of complex fluids” 

- obtained degree - “Candidate of physical-mathematical 

sciences” (equivalent to PhD in mathematics) 

- the speciality - mathematical physics 

11. Scientific interests: homogenization theory, asymptotic 

behavior of non-homogenized mediums, mathematical questions 

of elastic and fluid dynamics, PDEs, asymptotic analysis



12. Professional activity: 

2003-2004- Engineer, 2004-2007- PhD-student, 2007-2010- 

Researcher, B.Verkin Institute for Low Temperature Physics & 

Engineering, Kharkiv, Ukraine; 

2003-2007- Research assistant, Teacher, Kharkiv National 

Automobile & Highway University; 

since 2010- Wissenschaftlicher Mitarbeiter, TU Darmstadt, 

Germany 

13. Conferences: 

2005- Acad. Ya.S. Pidstrygach Conference of young scientists, 

Lviv, Ukraine; 

2006- Acad. M. Kravchuk International Scientific Conference, 

Kyiv, Ukraine; 

2007-2008 - Physics of Low Temperatures (conference of young 

scientists), Kharkiv, Ukraine; 

2007- Lyapunov Memorial Conference, Kharkiv, Ukraine 

(member of a local organizing committee); 

2008- International School-Conference «Tarapov’s Readings», 

Kharkiv, Ukraine; 

2008- CIMPA Summer School «Nonlinear Analysis and 

geometric PDE», Tsaghkadzor, Armenia; 

2009- «First Winter School on PDEs and inequalities», Madrid, 

Spain; 

2009- Ukrainian Mathematical Congress, Kyiv, Ukraine; 

2011- 10th GAMM-Seminar on Microstructures, Darmstadt, 

Germany;



2012- 83rd Annual Meeting of the International Association of 

Applied Mathematics and Mechanics, Darmstadt, Germany (Co- 

Chairman of the subsection «Generalized continua») 

14. Languages: Ukrainian , Russian, German, English 

15. IT-knowledge : LaTex, MS Office (Word, Excel), Maple, C++, 

Pascal 

List of publications of M. Berezhnyi. 

1. M.A. Berezhny and L.V. Berlyand “Continuum limit for threedimensional 

mass-spring networks and discrete Korn’s inequality”, 

Journal of the Mechanics and Physics of Solids, Volume 54, Issue 3, 

March 2006, p. 635-669. 

2. M.A. Berezhnyi. Small oscillations of a viscous incompressible fluid 

with small solid interacting particles of a large density.- 

Matematicheskaya fizika, analiz, geometriya (2005), vol. 12, No. 2, p. 

131-147 (in Russian). 

3. M.A. Berezhnyi. Small oscillations of a viscous incompressible fluid 

with small solid interacting particles of a large density.- Dopovidi 

Natsional’noyi Akademiyi Nauk Ukrayiny (2005), No. 7, p. 17-21 (in 

Russian). 

4. M.A. Berezhnyi. The asymptotic behavior of a viscous incompressible 

fluid small oscillations with solid interacting particles. Journal of 

Mathematical Physics, Analysis, Geometry (2007), vol. 3, No. 2, p. 

135-156. 

5. M. Berezhnyi, L. Berlyand and E. Khruslov. The homogenized model 

of complex fluids. NHM, Networks and heterogeneous media (2008), 

vol. 3, No. 4, p. 831-862. 

6. M. Berezhnyi. Homogenized models of complex fluids, PhD Thesis, 

B. Verkin Institute for Low Temperature Physics and Engineering 

(2009),159 p. (in ukrainian),URL: http://www.dlib.com.ua/userednenimodeli-strukturovanykh-ridyn.html. 

7. M. Berezhnyi. Small oscillations of a viscous incompressible fluid 

with a large number of small interacting particles in the case of their 

surface distribution, Ukrainian Mathematical Journal (2009), vol. 61, 

No. 3, p. 361-382. 

8. M. Berezhnyi and E. Khruslov. Non-standard dynamics of elastic 

composites. NHM, Networks and heterogeneous media (2011), vol. 6, 

No. 1, p. 89-109.



9. M. Berezhnyi. Discrete model of the non-symmetric theory of 

elasticity, Ukrainian Mathematical Journal (2011), vol. 63, No. 6, p. 

891-913. 

10. M. Berezhnyi and E. Khruslov. Asymmetric hydrodynamics of 

suspensions subjected to the influence of strong external magnetic 

fields. JMM, Journal of Multiscale Modeling (2012), vol. 4, No. 1, 

p.24-45. 

Grants. 

1. Leonhard-Euler project of DAAD (Germany, 2006). 

2. Research grant of the President of Ukraine for young 

scientists (2007-2009). 

3. Grant № 20-2007 of the National Academy of Sciences of 

Ukraine for young scientists (2007-2008). 

4. Grant of the Akhiezer fund (2009). 

5. PICS of CNRS, “Mathematical Physics- methods and 

applications” (France-Ukraine, 2009-2011). 

6. Medal "Talent, Inspiration, Work" by the National Academy 

of Sciences of Ukraine (2010).



TEACHING STATEMENT 

I assisted the following courses: 

1. Higher mathematics (in Ukrainian, 2003-2007, Kharkiv 

National Automobile & Highway University) 

2. Mathematical statistics (in Russian, the same) 

3. Probability theory (in Russian, the same) 

4. Econometric theory (in Russian, the same) 

5. Mathematical programming (in Russian, the same) 

6. Complex analysis (in English, 2010-2011, TU Darmstadt) 

7. Ordinary differential equations (in German, 2010-2011, TU 

Darmstadt) 

8. Calculus II for Computer Science (in German, 2011, TU 

Darmstadt) 

9. Mathematics III for Electronical Engineering (in German, 

2011-2012, TU Darmstadt) 

10.Proseminar “Introduction to the homogenization theory” (in 

English, 2010-2011, TU Darmstadt) 

11.Topology (in German, 2012, TU Darmstadt) 

12. Analsysis I (in German, 2012-2013, TU Darmstadt)



RESEARCH STATEMENT 

My scientific interests are homogenization theory, asymptotic behavior of 

non-homogenized mediums, mathematical questions of elastic and fluid 

dynamics, PDEs, calculus of variations, asymptotic analysis. 

Most of my papers deal with the modelling of complex fluids whose 

dispersed phase consists of a large number of small solid interacting particles, 

and the overall viscoelastic behavior is due to the interaction between particles 

and viscosity of the fluid phase. 

With the aid of variational methods we carry out an asymptotic analysis in 

a small parameter ε which characterizes the microstructure (defines the order of 

distances between the nearest particles) under different relations between the 

sizes of the particles and distances between the nearest of them. 

Depending on the size of particles and on the type of their motion, 

different asymptotic models are obtained. 

In my future work, it is intended to consider a non-linear problem 

describing the motion of a viscous incompressible fluid with a large number of 

small axially symmetric solid particles. It is assumed that the particles are 

identically oriented and under the influence of the fluid move translationally or 

rotate around a symmetry axis with the direction of their symmetry axes 

unchanged. The asymptotic behaviour of the oscillations of the system is 

planned to be studied, when the diameters of the particles and distances between 

the nearest particles are decreased. The equations, describing the homogenized 

model of the system, are planned to be derived under some general conditions 

on the motion of the particles. It is expected that the homogenized equations 

correspond to a non-standard hydrodynamics. Namely, it is expected that the 

homogenized stress tensor linearly depends not only on the strain tensor but also 

on the rotation tensor.

CURRICULUM VITAE 1. First name: Maksym 2. Last name ...

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