## Research

Areas: Polymer Physics, Computer Modelling, Quantum Mechanics, Statistical Mechanics, Gauge Field Theory, Confinement in Quantum Chromodynamics, General Relativity, Quantum Measurements Problem, Theories of Grand Unification

Dr Timoshenko’s undergraduate and postgraduate University education has been in the area of Theoretical Physics with emphasis on the Statistical Mechanics, Quantum Mechanics and Computer Simulations, and their applications to a broad range of interdisciplinary problems in Physics, Chemistry and Biology.

His early research was on caustics type of gravitational singularities and waves in General Relativity and a new gauge field model of the fifth interaction. Further doctoral studies were on the Hamiltonian and Path Integrals Fock-Schwinger gauge formulation of Quantum Chromodynamics, its boundary effects and variables at infinity, and especially the Confinement-Deconfinement phase transition in non-abelian Quantum Gauge Theory. A novel mechanism of colour confinement has been proposed for SU(N) gauge fields. The quarks string tension has been calculated via path integrals. A PhD degree in theoretical physics has been awarded in 1995 from the Nuclear Physics Institute of Moscow Lomonosov State University.

Further, Dr Timoshenko headed Theory and Computation Group at University College Dublin, Ireland. The main area of his research was on kinetics and dynamics of macromolecular and biomolecular conformational changes in dilute solutions. Gaussian Self-Consistent (GSC) approach for the equilibrium and kinetics was proposed for a single homopolymer chain in solution. This has led to elucidation of the kinetic laws at the collapse coil-to-globule transition of a homopolymer – an elusive problem of fundamental importance – and to the discovery of the `necklace of pearls’ polymer collapse process.

These theoretical studies by Monte Carlo simulations, were first performed on a lattice and then in continuous space, based on the Metropolis algorithm. Other methods, such as Molecular Dynamics and Stochastic Dynamics simulations, have been also utilised to understand the behaviour of macromolecular systems in solution and to make a reliable connection between the theory, simulations and experiment. In the consequent years, these techniques have been further generalised and extended to increasingly complex polymeric systems.

For a semi-flexible, or persistent, homopolymer a novel phase diagram with a number of distinct toroidal globules distinguished by the winding number and with complex kinetics of transitions between them has been discovered. This was experimentally found to apply to the conformational structure of a DNA condensed in the presence of counter-ions.

For amphiphilic heteropolymers, involving hydrophobic and hydrophilic units synthesised in a given primary sequence (e.g. di-block, tri-blocks or random), an emergence of non-trivial conformational structures, such as micro-phase separated globules and frustrated glassy states, with a corresponding multi-stage complex kinetics of folding on a rugged free energy landscape, have been discovered. The latter findings permitted one to make a connection to the problem of protein folding at a coarse-grained level.

Later on, study of amphiphilic copolymers at higher concentrations has lead the Group to the explanation of the mechanism of mesoglobules formations, earlier observed for PNIPAM polymers experimentally. These are hydrophobically self-assembled nano-sized spherical particles with a rather size monodispersed distribution and thermodynamically controlled mean size, resulting from equilibrium collapse and phase-separation arising in certain areas of the phase diagram, as opposed to kinetically controlled aggregation, within the two-phase separation region.

Further works involved theoretical and simulation studies of polymers with non-trivial macromolecular architectures such as stars, combs and dendrimers, as as well attempts to include iono-mers and, more generally, to account for Coulomb and more specific bonded interactions in macromolecular solutions at a higher level of detail.

One particularly successful collaborative project with the University of Leeds, UK involved the modelling of the nano self-assembly of short rigid oligo-peptides into a hierarchy of ribons, tapes and fibrils structures.

Dr Timoshenko’s recent interests involve functional integrals and symbols of operators in a more systematic approach to the Quantum Measurements theory, self-perpetuating networks and artificial intelligence. Insights from the string and membranes theories, as well as other attempts at Theories of Grand Unification beyond the Standard Model. These are being developed based on the proto-geometry and Theory of Categories ideas.