# Professor N. Brilliantov

##### Contact**: **nb144@leicester.ac.uk

+44 (0)116 252 3917

## Personal details

M.Sc, PhD, Doctor of Science

I studied at the Moscow State University, Faculty of Physics where I earned an M.Sc (1980), PhD (1984) and Doctor of Science (1999). I have a daughter, she is a biochemist and my hobbies include sport, travelling, art and literature.

### Websites

**Editorial work**

Editor: ** Member of the Editorial Board of The Physical Review ****Letters **

Editor: **of the book** (with T.Poeschel) "Granular Gas Dynamics",

Lecture Notes in Physics, v. 624.

Editor: **of the topical issue** "*Granular Hydrodynamics*" of the journal "Mothematical Modelling of Natural Phehomena", **v. 6** (4) 2011

### Appointments

**Department of Mathematics University of Leicester**, Leicester, UK

**Professor, Chair in Applied Mathematics**

**Nonlinear Dynamics Group**

**Department of Physics**

**University of Potsdam**, Potsdam, Germany.

**Visiting Scientist**, 2004-2007.

Statistical Physics and Theory of Chaos Group Department of Physics, University of Potsdam, Potsdam, Germany. **Visiting Scientist**, 2003.

Humboldt University / Charite Department of Biochemistry, Berlin, Germany. **Visiting Scientist**, 2002-2003.

University of Barcelona, Department of Physics, Barcelona, Spain. **Invited Professor**, 2001.

Max-Planck-Institute of Colloids and Interfaces, Potsdam, Germany. **Max-Planck Fellow**, 2000.

Humboldt University, Department of Physics, Berlin, Germany. **Visiting Scientist**, 1998-1999.

University of Toronto, Department of Chemistry

Toronto, Canada. Research Associate, Lecturer,1995-1997

Nonlinear Dynamics Group,

Department of Physics, University of Potsdam, Potsdam, Germany. **Max-Planck Fellow**, 1993.

Moscow State University, Faculty of Physics, Senior Researcher, Assistant Professor, 1989-1995.

**All-Union Research Institute of Current Sources, **Moscow, Russia, **Senior Researcher**, Group Leader, 1985-1989.

**Reviewing work**

Peer Review: Physical Review Letters, Physical Review E, European Physical Journal, Europhysics Letters, Journal of Physics A, Uspekhi Fizicheskikh Nauk.

**Honors, Fellowships and Service to the Scientific Community**

** **

**Organizer** of the International

Workshop "The Enigma of Enceladus: **Observation and Modeling", Leiester, June 19-20, 2009 **

** Organizer** of the International **CECAM Workshop "Granular Gases", Lyon, Sept. 2-5, 2002**

Member of the Scientific Committee of the International

The 14th International Conference on Discrete Simulation of Fluid Dynamics in

Complex Systems Kyoto University, Kyoto, Japan, August 22 - 26 (2005)

Member of the Scientific Committee of the International

DSFD 2004 13th International Conference on the Discrete Simulation of Fluid

Dynamics, Cambridge, Massachusetts, USA, 16-20 August 2004

Member of the Scientific Committee of the International

XII International Conference on the Discrete Simulation of Fluid Dynamics,

Augist 25-29 (2003), Beirut, Lebanon.

Co-organizer and member of the Scientific Committee of the International

"Statistical Mechanics of Complex Networks" XVIII Sitges Conference on Statistical Mechanics, Sitges, Barcelona, SPAIN, 10-14 June 2002

Member of the Scientific Committee of the International

XI international Conference of Discrete Simulation of Fluid Dynamics and

Soft Condensed Matter August 5-9 (2002), Shanghai, China

Fellowship in Max-Planck-Institute of Colloids and Interfaces,

Potsdam, Germany, 2000.

International Science Foundation Grant award, 1994.

Fellowship in Max-Planck-Institute, Nonlinear Dynamics Group,

University of Potsdam, Potsdam, Germany, 1993.

## Publications

**Books**

**Research**

** **Granular matter

**Granular Gases** are dilute systems of particles which collide inelastically.

Being rather simple by their nature, Granular Gases reveal very rich

behaviour: Cluster and vortex formation, characteristic shock waves

and non-Maxwellian velocity distribution may be mentioned as some

representative examples.

**Main publications on granular gases**

**Books**

**N.V.Brilliantov and T.Poeschel,** **Kinetic Theory of Granular Gases,** **Oxford University Press, (2004).**

**N.V.Brilliantov, T. Pöschel,** **Hydrodynamics and transport coefficients for Granular Gases,** **Phys. Rev. E, 67, (2003), 061304. pdf**

**T.Poeschel, and N.V.Brilliantov,** **Kinetic Integrals in the Kinetic Theory of dissipative gases,** **In: T. Poeschel, N.V. Brilliantov (Eds.) "Granular Gas Dynamics",** **Lecture Notes in Physics, vol. 624, Springer (Berlin, 2003), p. 131-162. pdf **

**N.V.Brilliantov and T.Poeschel,** **Hydrodynamics of granular gases of viscoelastic particles,** **Phil. Trans. R. Soc. Lond. A, 360, (2002) 415-429.**

**N.V.Brilliantov and T.Poeschel,** **Self-diffusion in granular gases,** **Phys.Rev. E, 61, (2000) 1716-1721. pdf file**

**N. V. Brilliantov, T. Poeschel,** **Granular Gases with Impact-velocity Dependent Restitution Coefficient,** **in "Granular Gases", ed. by S.Luding, and T.Poeschel,** **Lecture Notes in Physics Vol. 564, Springer (Berlin, 2000), p. 100.**

**Velocity distribution in granular gases**

**N. V. Brilliantov and T. Poeschel,** **Deviation from Maxwell Distribution in Granular Gases with Constant Restitution Coefficient.** ** Phys. Rev. E, 61, (2000) 2809-2812. pdf file**

**N. V. Brilliantov and T. Poeschel,** **Velocity distribution in granular gases of viscoelastic particles,** **Phys. Rev. E, 61, (2000) 5573-5587. pdf file**

**T.Poeschel, N.V. Brilliantov, and T. Schwager,** **Violation of Molecular Chaos in dissipative gases,** **Int. J. Mod. Phys. C, 13, (2002) 1263-1272.**

**N.V.Brilliantov and T.Poeschel,** **Granular Gases -- the early stage,** **in "Coherent Structures in Complex Systems", ed by D. Reguera, L.L. Bonilla, M. Rubi,****Lecture Notes in Physics, Vol.567, Springer (2001) p.408-419**

**Clustering and pattern formation in Granular Gases**

**T.Poeschel, N.V. Brilliantov, and T. Schwager,** **Long-time behavior of Granular Gases with impact-velocity dependent coefficient of restitution,** **Physica A, 325, (2003) 274-283. pdf file**

**Inelastic collisions**

The theory of a collision of *elastic *particles was developed by H. Hertz in 1885.

We generalized Hertz's theory for *dissipative* collisions, using the simplest model

of *viscoelastic *particles. The generalized collision law allows to derive the main

characteristics of dissipative collisions - the restitution coefficient. It occurs, that

this quantity is not a material parameter, as was assumed previously, but rather

complicated function of elastic and dissipative material constants and of the

impact velocity at a collision.

**Main publications on inelastic collisions**

**Generalization of Hertz's theory**

**N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, and T. Poeschel,** **Model for collisions in granular gases** **Phys. Rev. E, 53 (1996) 5382-5392. pdf file**

**N.V.Brilliantov, F. Spahn, J.-M. Hertzsch, and T. Poeschel,** **The collisions of particles in granular systems.** **Physica A, 231 (1996) 417-424.**

**J.-M.Hertzsch, F.Spahn, and N.V.Brilliantov,** **On low-velocity collisions of viscoelastic particles.** **J. de Phys. II France, 5 (1995) 1725 - 1738.**

**Coefficient of restitution**

**T. Poeschel and N. V. Brilliantov,** **Extremal collision sequences of particles on a line: optimal transmission of kinetic energy,** **Phys. Rev. E, 63, (2001) 021505. pdf file**

**R. Ramírez, T. Poeschel, N. V. Brilliantov, T. Schwager,** **Coefficient of restitution of colliding viscoelastic spheres.** **Phys. Rev. E, 60, (1999) 4465. pdf file**

### Rolling friction

Up to our knowledge there was no first-principle theory which relates the

coefficient of rolling friction to material properties and a size of a rolling body

without any model parameters. We have developed a simple theory

of a rolling of a soft sphere on a hard plane. We observe that rolling motion

may be treated as a "continuing collision". For a simple model of a soft plane

we developed a theory of a rolling of a hard cylinder on a soft plane.

**Main publications on rolling friction**

**N.V.Brilliantov and T.Poeschel,** **Rolling friction of a soft sphere on a hard plane.** **Europhys. Letters, 42 (1998) 511. pdf file**

**N. V. Brilliantov, T. Poeschel,** **Rolling as a "continuing collision,** **Europ. Phys. J. B, 12, (1999) 299. pdf file**

**T. Poeschel, T. Schwager, and N. V. Brilliantov,** **Rolling of a hard cylinder on a viscous plane,** **Europ. Phys. J. B, 10, (1999) 169-174. pdf file**

** Complex fluids**

**Polyelectrolytes and colloids**

Many important biological macromolecules, such as e.g. DNA, are Polyelectrolytes. Solutions of Polyelectrolytes and of Charged Colloidal paricles exhibit very interesting phase behavior: Phase transitions may be accompanied by a sudden change of a gyration radius of a polymer chain, of an average charge of a macromolecule, etc. We developed a theory of electrostatically driven chain collapse in dilute polyelectrolyte solutions, which occurs as a first-order phase transition (PRL 81, 1998). Later this phase transition has been detected in experiments (Mel'nikov et al, JACS, 121 (1999) 1130). We also developed a theory of phase transitions in colloidal solutions of particles with variable surface charges.

** Main publications**

** N.V.Brilliantov, D.V.Kuznetsov and R.Klein,** ** Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte Solutions,** ** Phys. Rev. Lett., 81, (1998) 1433. **

** N.V.Brilliantov,** ** Phase Transitions in Solutions of Variably Ionizable Particles,** ** Phys. Rev. E., 48, (1993) 4536. **

** N.V.Brilliantov, and V.V.Malinin,** ** Liquid-liquid type phase transitions and variation of the particle charge in colloidal ****solutions,** ** Colloidal Journal, 64, (2002) 261.**

**Hydrodynamics and brownian motion**

Particles in Complex Fluids, such as solutions of Polyelectrolyte or Colloids, often carry a considerable charge. Hence, the local properties of the solvent, such as e.g. viscosity, around the particles may be altered by the strong electric field. The other effect which is called the dielectric friction may also significantly influence the Brownian motion of particles in Complex Fluids. The molecular motion in these systems may be analyzed using the hydrodynamics of fluids with the internal degrees of freedom. For the case of polar solvents such hydrodynamic equations are called Hubbard-Onsager equations. Solving the these hydrodynamic

equations we obtain the generalization of Stokes-Einstein and Stokes-Einstein-Debye relations for translational and rotational Brownian motion.

**Main publications**

**N.V.Brilliantov, N.G.Vostrikova and O.P.Revokatov,** ** Role of electrical interactionss in rotational motion of** ** charged solute in polar solvents.** **J. Phys. Chem.B, 102, (1998) 6299.**

**N.V.Brilliantov, and N.G.Vostrikova** **Rotational motion of Brownian particles with surface charge,** **Molecular Physics, 77, (1992) 957**

**N.V.Brilliantov, and P.L.Krapivsky,** **Stokes laws for ions in solutions with ion-induced inhomogeneity,** **J. Phys. Chem., 95, (1991) 6055-6057.**

**N.V.Brilliantov, V.P.Denisov, and P.L.Krapivsky,** **Generalized Stokes-Einstein-Debye relation for charged** **Brownian particles in solution, Physica A, 175, (1991) 293-304.**

**Phase transitions and critical behavior**

The critical behavior of simple fluids as well as of other fluids with a short-range interaction

potential corresponds to that of the Ising universality class. This follows from experiments,

computer simulations and theoretical reasonings. For the Coulombic Fluids however, it is still not completely clear to which universality class do these fluids belong. The most direct analysis of the critical properties of the system may be performed using the Landau-Ginzburg-Wilson (LGW) form of the system Hamiltonian. We develop a method which allows a rigorous mapping of the fluid Hamiltonian onto the effective field-theoretical LGW Hamiltonian, which coefficients may be calculated analytically. Using this approach we derive some relations between critical parameters, which have been confirmed in numerical experiments (Camp P.J., Patey G.N., J. Chem.Phys. 114 (2001) 399) and analyze the coulombic criticality.

**Main publications**

**N.V.Brilliantov,** **Effective magnetic Hamiltonian and Ginzburg criterion for fluids,** **Phys.Rev.E, 58, (1998) 2628.**

**N.Brilliantov, and J.Valleau,** **Thermodynamic Scaling Monte Carlo Study of the Liquid--Gas Transition in the Square--Well Fluid,** **J.Chem.Phys., 108, (1998) 1115.**

**N.Brilliantov, and J.Valleau,** **Effective Hamiltonian Analysis of Fluid Criticality and Application to the Square--Well Fluid,** **J.Chem.Phys., 108, (1998) 1123.**

**N.V.Brilliantov, A.Yu.Loskutov and V.V.Malinin** **Field-Theoretic analysis of critical behavior of a symmetric binary fluid,** **Theor. Math. Phys., 130, (2002) p.123-135 (in russian).**

**Coulombic fluids**

Fluids with long-range coulombic interactions, such as ionic solutions, plasma, etc.

are called coulombic fluids. The problem of critical behavior of such fluids, i.e. of the **coulombic criticality**, is still under discussion, since some the ionic fluids demonstrate

Ising criticality, while other - the classical one. Using the effective LGW Hamiltonian

and nonperturbative RG approach, we show that very long crossover from the classical

to Ising critical behavior may be observed. For the simplest model of the coulombic fluid,

for the model of One Component Plasma we derived the equation of state (EOS) which is

very accurate for all values of plasma parameter, from the Debye-Huckel limit up to the

Wigner crystallization point. To derive this EOS we propose the Restricted Random Phase

Approximation.

**Main publications**

**N.V. Brilliantov, C. Bagnuls and C.Bervillier,** **Peculiarity of the Coulombic Criticality?,** **Phys. Lett. A, 245, (1998) 274. **

**N.V. Brilliantov,** **Accurate First-Principle Equation of State for the One-Component Plasma,** **Contrib. to Plasma Physics, 38, (1998) 489.**

**N.V.Brilliantov, V.V.Malinin and R.R.Netz,** **Systematic Field-Theory for the Hard-Core One-Component Plasma,** **Eur. Phys. J. D, 18, (2002) 339.**

**Molecular Biophysics**

**Molecular Models of Diseases Kinetics**

It is generally acknowledged that transmittable spongiform encephaloathies diseases (TSE), such as scrapie, kuru and kind of Creutzfeld-Jacob disease are related to formation of misfolded fibril-like prion proteins. Using a molecular model of the **aggregation kinetics** we describe the kinetics of the prion growth and derived the size distribution of the fibril aggregates.

** ****Main publications**

** T.Poeschel, N.V. Brilliantov, and C. Frommel,** ** Kinetics of Prion Growth,** ** Biophysical Journal, 85, (2003) 3460-3474.**

**Brownian motion of biomolecules**

Biological functions of biomolecules in nature are intrinsically related to their mobility, i.e. to

the properties of the Brownian motion of these particles. Usually they are strongly charged or have a large electrical dipolar moment. The intensive electrostatic interactions between the charged and/or dipolar biomolecules or between the macromolecules and the polar solvent influence significantly their Brownian Motion .

**Main publications**

**N.V.Brilliantov, N.G.Vostrikova, V.P.Denisov, Yu.M.Petrusievich and O.P.Revokatov** **Influence of dielectric friction and near-surface increase of viscosity on rotational** **Brownian motion of charged biopolymers in solution,** **Biophysical Chemistry, 46 (1993) 227-236.**

**Yu. M. Petrusevitch and N. V. Brilliantov,** **Dielectric properties of protein solutions and interactionof electromagnetic fields with biosystems.** **Bull. Mosc. State Univ., Ser.3, N4 (1994) 63-67 (in russian).**

**N.V.Brilliantov, A.I.Kviatkievich, Yu.M.Petrusievich and O.P. Revokatov,** **Influence of macromolecules dipolar moment on the frequency dependence of** **the NMR-relaxation coefficients of biopolymers in solution.** **Radiospektroskopiya, Perm, 1988,150-154 (in russian).**

**N.V.Brilliantov, A.I.Kviatkievich, Yu.M.Petrusievich and O.P.Revokatov,** **Rotational Brownian motion of polar macromolecules in solutions,** **Dokl. Akad. Sci. USSR, 304, N2 (1989) 340-345 (in russian).**