Collaboration

Ph.D. studies

During 2012 - 2018 I have worked on modelling of several types of materials and biochemical systems with utilized statistical mechanical and physiochemical kinetics approaches and techniques. The topics of interest include multi-input biomolecular signals processes used for actuation, drug delivery and release and other applications, percolation-type modeling of autonomous self-damaging in “smart” composite materials, Monte Carlo and mean-field simulation of certain polymerization processes, reaction-diffusion equations modelling of surface erosion of highly crosslinked polymers, analytical modeling of diffusion of oligonucleotides and other large molecules from hydrogel beads, modeling of progression of viral infection in cell culture resulting in cell apoptosis and necrosis, and cell culture dynamics under stress, etc.

My Thesis included:

• Multi-input biomolecular signals processes used for actuation, drug delivery and release and other applications

• Percolation-type modeling of autonomous self-damaging in “smart” composite materials

• Monte Carlo and mean-field simulation of certain polymerization processes

• Reaction-diffusion equations modelling of surface erosion of highly crosslinked polyanhydrides

• Analytical modeling of diffusion of oligonucleotides and other large molecules from hydrogel

• Modeling of progression of viral infection in cell culture resulting in cell apoptosis and necrosis

• Cell cultures dynamics under stress

Also worked on:

Quantum Chemistry methods. Computational techniques in non-adiabatic Molecular Dynamics

Visiting graduate student researcher at Los Alamos National Laboratory, Los Alamos, NM. Center for Nonlinear Studies. Fall semester of 2015. Supervisor: Dr. Dmitry Mozyrsky.

Research Topic: Non-Adiabatic Molecular Dynamics in Multi-Crossing Systems

Non-adiabatic molecular dynamics is important in the study of many photophysical and photochemical reactions. Various approximations are used to calculate transitions between electronic states in large systems such as real molecules. Many of the approaches either have the desired accuracy only in certain scenarios or lead to high computational costs. The novel accelerated Semi-classical Monte Carlo technique based on recently developed algorithm, has features of Surface hopping methods but accounts for quantum coherence effects, while neglecting some nuclear quantum effects such as tunneling, etc. We apply it to the test problems which demonstrate breakdown of common approximations, comparing the solution to that of existing approaches such as Ehrenfest method, Fewest Switches Surface Hopping method and exact quantum solution.

Visiting graduate student researcher at Los Alamos National Laboratory, Los Alamos, NM. Center for Nonlinear Studies. Summer of 2016. Supervisor: Dr. Dmitry Mozyrsky.

Research Topic: Thawed Gaussian Propagation with Recurrent Basis Expansions and Matching-Pursuit Basis Reduction for Simulations of Quantum Dynamics

Thawed Gaussian Approximation that is typically used in non-adiabatic quantum/semi-classical dynamics in multidimensional systems fails after relatively short propagation. Recurrent basis expansions into proper basis functions would lead to a rapid growth of the basis making computation unfeasible. Over the last decade, the Batista group has developed Matching-Pursuit method, along with Split-operator Fourier-transform (MP/SOFT) for basis reduction. Utilizing this method we show how an arbitrary wavefunction is presented as a superposition of Thawed Gaussian Wavepackets (TGWP) and propagated along an arbitrary adiabatic potential energy surfaces, e.g. Morse potential, double-well potential and Tully’s test problems, for desired time duration. With a proper description of a wavefunction on a single adiabatic surface we aim to study non-adiabatic semi-classical dynamics, specifically, a scattering problem.