My background covers a broad spectrum of theoretical and computational condensed and soft matter physics particularly processes of pattern formation, nonequilibrium thermodynamic and dynamics of material interfaces. In my research I employ different theoretical methods and computer simulations. A better understanding of the physical mechanisms by which structures are generated in materials, especially at the nanoscale, is important for practical purposes. Recently my background of a condensed matter physicist found application in another branch of physics—bio/medical physics.


Thermal Effects of Phase Transitions:

Dendritic Growth: Pattern Formation during Crystallization [Ref. 2-4, 7]

The well-known phenomenon of dendritic growth is important for crystallization of metals and organic materials from a supercooled melt. The purpose of my dissertation work was to create a physical model and numerically simulate different regimes of this phenomenon in conjunction with the large-scale modeling of solidification. For the first time the model was able to reproduce the snowflake-like patterns seen experimentally. The result of this research was twofold. On the one hand, this model allowed us to predict properties of a material obtained in real processing and by choosing the appropriate thermal regime increase the homogeneity of the latter.

On the other hand the model revealed many of the physical features pertaining to the growth of a dendrite. For example, for the first time the model was able to predict the mechanism of coarsening of the side-branch structure by period doubling which was confirmed later by experimental results and provides an important connection with the transition to chaotic structures. Also the model predicts the restoration of morphological stability under conditions of rapid solidification, i.e. far from equilibrium. Because of potential importance for applications this effect was analyzed later in the framework of a "string" or geometric model where the interface is viewed as a line of heat sources moving according to the evolution of the diffusion field and in compliance with the natural (geometric) properties of a string. In a strongly supercooled melt, the diffusion field in front of a moving interface is confined to small vicinity and a thermal boundary layer approximation can be introduced. Being applied together with a string model, this approximation allowed us to study stability properties of the interface and its dynamics close to the point of absolute morphological stability.

Dynamics of Interfaces [Ref. 1, 5, 6, 8, 9, 11, 13, 15, 17, 19, 24, 25]

Interfaces are crucial elements of modern sophisticated materials. Dynamics of their motion is accompanied by the process of heat redistribution, which affects the rate and morphology of the evolution in thermodynamic systems. In my early work, using a theoretical approach of a free-boundary problem, a previously unknown regime of interface motion was revealed and verified in numerical simulations. In my later studies, to analyze material's structure on different length scales, I adopted the continuum (phase-field) approach because it allowed me to study time evolution and equilibrium properties on the same basis. In the framework of this method the state of a system undergoing phase transition is characterized by the coarse-grained Hamiltonian (nonequilibrium Ginzburg-Landau free-energy) which, in addition to pressure, temperature and composition, depends on one more variable, order parameter, that changes continuously from one phase to another. Such parameter has relevance to many different transitions, e.g. crystallization, order-disorder, structural, ferromagnetic, ferroelectric, having different physical interpretations therein. Parameters of the phenomenological Hamiltonian can be obtained from the ab initio calculations or interatomistic computer modeling.

Previous attempts to describe heat release along with phase transitions had been based on heuristic ideas; my objective was to develop a thermodynamically consistent approach. The free-boundary problem is just a limiting case of this theory when the thermal length and the radius of curvature of an interface are much greater than its thickness. The analysis of systems with slow heat conduction shows that an adiabatic transition is possible such that the temperature of the final phase is higher than the equilibrium temperature (metastable or superheated phase production). This effect was called "heat-trapping" by analogy with the solute-trapping or partitionless solidification of alloys.

Close to the critical point the first-order transitions exhibit intriguing examples of periodic pattern formation when the transformation takes the path analogous to the spinodal decomposition characterized by the conserved order parameter (composition) although the original parameter is non-conserved (e.g. magnetization). This means that a weakly first-order transition can proceed by a continuous modulation mechanism controlled by heat-transfer. For the case of a structural transition where the order parameter is strain, we demonstrated that estimated properties of Fe-Pd alloys make this system a possible candidate for such behavior. In simulation of the dynamic behavior of such systems, coarsening of the internal domain structure has been observed to occur on late stages of evolution. In contrast to the well known Lifshitz-Slyozov-Wagner type of coarsening kinetics, valid for a small volume fraction of precipitate, this system, which had the volume fraction of the product phase about 50%, demonstrated absolutely different type of the second-phase coarsening behavior, whose distinguished feature was period doubling.

Another type of thermal effects has been predicted in materials that underwent a second-order (continuous) transition, e.g. ferromagnetic, or order-disorder, despite the lack of the latent heat in transitions. For instance, in materials with small thermal conductivity motion of the domain walls will proceed much slower than according to the predictions of the Landau-Lifshitz or Cahn-Allen theories that do not take the energy effect into account. This effect may be important for the theory of the hysteresis loop and magnetization dynamics and the continuous transition itself, changing time exponents of the latter.

Equilibrium Phase Diagrams [Ref. 9, 12, 27]

My calculations showed that the phase diagram of a small adiabatically insulated particle is more complicated than that of a large one: phase separation does not occur when it is supposed to. Instead, there is a considerable extension of the single-phase regions of ordered and disordered phases into the two-phase zone of the phase diagram. Moreover, in a particular energy band, equilibrium is achieved on the homogeneous transition state that corresponds to the saddle point of the free energy. Mechanical, electromagnetic and optical properties of such state are different from those of the bulk phases. Such particles provide opportunity to study the intrinsically unstable segments of the free energy of materials. This work has also very important ramifications on the theory of amorphization of pure metals.

Homogeneous/Heterogeneous Nucleation (ppt)

Nucleation is one of the core problems of the Condensed Matter Theory overall. The main idea of my approach is to use the concept of escape time to study thermal effects of nucleation in extended systems. Although relation between the escape time and nucleation rate is well documented, this approach has not been used to study the thermal effects. This project is going on in collaboration with Dr. H. Emmerich’s research group at the University of Bayreuth in Germany.

Alloy Dynamics and Thermodynamics:

Intermetallic Compound Growth [Ref. 20, 22]

My experience with dendritic solidification recently found an application in a technologically important problem of soldering. When a drop of melt (Sn-based alloy, solder) is brought into contact with a solid Cu-substrate, a layer of intermetallic compound Cu6Sn5 starts to grow between the two. Experimental observations demonstrate formation of an intricate microstructure on the surface of the layer, which is interplay of the metal’s crystalline properties and dissolution kinetics. My previous theoretical analysis of the intermetallic phase growth highlighted the early stage of soldering as the critical step for the microstructure formation. On the basis of those theoretical ideas I introduced a novel experimental technique, which allowed us to study entire early-stage evolution process on one micrograph. Later on I introduced a computer model that reproduced many of the experimentally observed features of the intermetallic phase structure.At present I am working on a computer model that will reproduce experimentally observed behavior of the intermetallic phase [Pub.22] (liquid-state soldering). However, when the solder is used at the temperature above its melting point (solid-state soldering) the structure of the growing intermetallic layer is significantly different.

Coarsening [Ref. 10, 13]

The widespread use of multicomponent alloys for the first-principals designing of new smart materials has stimulated my interest in coarsening process in multicomponent systems whose thermodynamics is different from that of binaries due to presence of many different components. It was necessary to analyze this process without simplifying assumptions on the solution thermodynamics of alloys that are usually not confirmed in practice. The derived coarsening behavior showed marked departure from a binary case and turned out to be a fundamental contribution to an interdisciplinary program of applying physics, mechanics and materials science to alloy design. This work was tested with the experimental results on the small angle neutron scattering in model alloys and at present is used in the conceptual designing of practical alloys.

Elastic Strain Effect [Ref. 16]

Change of the crystalline symmetry is usually accompanied by the development of the misfit strain in materials as a result of different lattice spacing in different phases. Small precipitates grow usually without loss of coherency on their interfaces. In my next project I have developed a consistent continuum approach to the problem of segregation at coherent interfaces and incorporated the coherency strain into the continuum model of microstructural evolution of multicomponent alloys.

Developing New Computational Tools for Material Design [Ref. 23, 28]

As the materials science modeling community is moving into a new era of quantitative modeling and design of real materials (e.g. multicomponent alloys), it is important to assess the challenges that we will be facing. One of those is obtaining reliable material parameters for the model. The problem is that now we are dealing with parameters which cannot be easily identified in experiments and obtained through direct measurements. For example, continuum modeling methodology uses the free energy of the system expanded in powers of the order parameter and its gradients. But the coefficients of expansion are not measurable parameters. The first attempts to find these coefficients consisted in guessing their (T, P)-dependence and comparing the theoretical values of the specific heat and compressibility with the experimental values. That strategy did not always work. Then researchers tried another strategy: extract the bulk free-energy and surface quantities (e.g. tension) from the model and compare them with the experimental or computable counterparts. This strategy meets certain challenges which, together with other approaches, are discussed in my publications.


Self-Organized Nanostructures:

Equilibria and Dynamics at Nanoscale [Ref. 12, 27]

Nanotechnology is defined as the creation of functional materials, devices and systems with at least one characteristic dimension at the scale of one to one hundred nanometers. It requires fundamental understanding of self-organization at the nanoscale. My interest in nanotechnology and organization at the nanoscale arose from the thermodynamic analysis of small adiabatically insulated systems. Later I extended the theory on the closed system of fixed volume capable of undergoing a phase transition and showed that in a small system below the critical size the transition state can be thermodynamically stable against the bulk phases if a certain material parameters criterion is fulfilled. This effect is analogous to stabilization of icosahedral structures in clusters of certain sizes and energies. I am planning to study nucleation in nanostructures using the escape-time approach.

Carbon Nanostructures for Carbon Nanoelectronics Applications [Ref. 26, 28]

This project was initiated by Dr. A. Zaitsev from the College of Staten Island (CUNY) who is working on the study of carbon nanowires that are produced by the process of Focused Ion Beam (FIB) irradiation of diamond substrates. In his experiments he detected many different carbon phases produced by FIB, which did not have theoretical explanation. We constructed a continuum theory of carbon phases based on the Landau theory of phase transitions. Our theory tied up many seemingly unrelated data on the carbon system. We analyzed stability of nanostructured amorphous carbon and interpreted it as the transition state of the free-energy function. This conjecture helped us to explain results of the experiments on the FIB irradiation of CVD-diamond nanofilms. The present theory may be used for the large-scale modeling of graphite and diamond crystallization; it can also be extended to include other structural modifications of carbon or an entirely different element such as silicon.

Phase Separation in Nanostructures

Many microelectronics devices rely on nanometer-scale films of solid solutions grown on substrates by different deposition techniques. Such films have properties very different from their bulk counterparts. For instance, silicon based semiconductors possess wider than normal band gaps, SnGeTe thin films become superconducting and gain anomalous Hall effect when alloyed with In. Semiconductor films may be grown in such a regime that the band-gap can be tuned by simply changing the dimensions of the material. Fe-Cu and Fe-Ag binary systems are virtually immiscible in the bulk. However, 70 nm nanoparticles of these materials were found to form supersaturated solid solutions. This inspired me to use the mean-field method in order to study the phase transitions in nanofilms of solid solutions.

Theory of Nanosystems: From Atomic Clusters to Nanoparticles

There are strong connections between behaviors of what we call atomic or molecular clusters and what we term nanomaterials, especially small nanoparticles. The only possible distinction might be that clusters are perhaps no larger than about a few thousand particles, while small nanoparticles can be no smaller than that. I would like to bridge the gap between the scientific approaches to clusters and nanomaterials and develop a working theoretical approach that will bring together the methods of condensed matter physics, materials science, and physical chemistry. The new theory will focus on open, challenging problems in the field of assemblages of order 100 to 10,000 atoms or molecules. This approach will include the following topics: the insulator-metal transition as it depends on the size and structure of the system; the origin of the anomalously high melting points of some metal clusters; the nature of the frequency dependence of conductivity in small particles; the size and temperature dependence of the structures taken on by such small particles; their behavior on cooling from liquid to solid and the kinds of structures they find; and the striking changes in the nature of bonding that occurs in some small systems.


Synergetic Approach in Medicine:

Role of Chaos in Physiology [Ref. 21]

Conventional wisdom in physiology and medicine (theory of homeostasis) holds that a healthy organism regulates itself to maintain constant rhythm, while erratic behavior of the organism is symptomatic of unfolding disease because it suppresses natural rhythms. However, interdisciplinary discoveries of the past decade in mathematics and human physiology convinced many practitioners that chaos in bodily functioning is not necessarily a bad thing. Dr. A. Golbin of Sleep and Behavior Medicine Institute in Chicago, IL and I have qualitatively analyzed many different cases of pathological symptoms in biological systems that may be explained as manifestation of the chaotic behavior and revealed the adaptive nature of chaos in them. The benefit of chaos in physiological systems is stability of the organism, structural or functional, as opposed to instability or death. A new, seemingly universal feature of the dynamical systems controlled by a chaotic subsystem was revealed. To delineate this feature we proposed the principle of compensation, according to which the loss of controlling function of one subsystem of a defective system may be compensated by chaotic behavior of another subsystem, less important for "survival" of the whole system. Briefly speaking, we are wired such that if a central organ fails, a peripheral one comes to rescue. Application of this principle to medicine may bring new treatment strategies.

Sleep Medicine [Ref. 29]

There are three commonly identified types of sleep apneas: obstructive, central, and mixed. Recently a new type of apnea, the strictly periodic sleep apnea (SPA), has been identified. In SPA periods of breathing and apneas oscillate with a strong periodicity and the time of breathing becomes comparable to the length of apnea. Although medical conditions that follow the appearance of SPA are associated with the high risk of sudden death or life threatening events, the nature of this type of apnea is not clear at this time. The typical characteristics of SPA are identifiable on air flow, chest, and abdomen movement channels of polysomnagraphical records (PR). There is a possibility that they may also be detected from the analysis of EEG channels of the same records. This fact presents a significant advantage for diagnostic practices of sleep studies. The objectives of this project were to analyze power spectra of all channels of PR records of SPA patients and to find mathematical correlations between the channels. The results of this project may help reveal the biophysical and physiological intercorrelations between the brain and breathing activities of a patient during episodes of SPA.

Origin of Life Research

Origin of Biological Functions [Ref. 18, 30] (ppt)

The experimental findings of the last couple of years inspired my interest in biophysical problems of the origin of life. Almost all tenable hypotheses of the origin of life on Earth describe transformation from geochemistry to biochemistry, which brought about the material of life, DNA-protein combination, and cellular organization of that material. Living organisms, however, are distinguished from a mixture of organic molecules by their high level of complexity, which allows them to carry out certain functions. I analyzed the hypothesis that the earliest forms of life (protocells) were formed through the process of phase transitions, e.g. crystallization. According to this hypothesis, inorganic materials helped build living systems by lending those functions so that organic chemical evolution is just one natural consequence of the evolution of matter in the universe. A self-replicating biological system with adaptation emerged from single molecules using completely abiotic mechanism of formation. This mechanism acted simultaneously at different places on the early Earth and created similar materials everywhere. Hence, the similarities in the living systems did not appear by chance, but as a necessity.

Abiogenic Evolution of Amino Acids

Together with Dr. M. B.Simakov from the Institute of Cytology of Russian Academy of Sciences, Sankt-Petersburg, Russia we proposed to study the effects of different astrophysical conditions on the process of abiogenic synthesis of complex organic molecules (oligopeptides) in/on dust grains of the interstellar medium or on the early Earth. The main objectives of the project are to investigate the roles of: (1) cosmic radiation—solar/stellar UV and solar wind; (2) thermal cycling—periodic crystallization and melting; (3) mineral surfaces, in the abiogenic synthesis of amino acids. Specifically, we will be working with simple amino acids—aliphatic (Glycine and Alanine) and aromatic (Phenylalanine and Tyrosine).

Crystallization of Biological Materials

Stochastic Model of Nucleation of Biological Crystals

While it had long been assumed that crystalline biominerals typically form by the classical mechanisms of ion-by-ion growth, it is now recognized that they often precipitate via amorphous precursor phases. Recent re-examination of the structure of many biominerals is also suggesting that "non-classical" crystallization pathways, where crystals grow from the assembly of precursor particles, may also be widespread. I am developing a theoretical model of nucleation where the critical nuclei have large degree of ramification. The model allows us to study the structure and entire pre-nucleation path of the ‘cluster’ that leads to the critical precipitate of the new phase. Computer-simulation analysis of the model shows that, contrary to the traditional view, the nucleation rate is inversely proportional to the square root of the volume instead of the volume itself.

Decision-Making across Biological Scales

Field Theory of Protein Folding

Statistical theory of protein folding has made significant progress in the past few years. However, the theory remains rather complicated with only a handful of concrete results. My approach is to capitalize on the numerous successes of the Landau theory of phase transitions and develop a continuum, field model of protein folding. In the framework of this model the probability of different protein conformations will be described by the free energy, which depends on a few order parameters—low-dimensional characteristics of the polypeptide chain and its topology.

Morphogenesis, Developmental Biology, and Biophysics of Neurons

Acetylcholinesterase (AChE) is an enzyme, which is classically known for its role in hydrolyzing neurotransmitters that diffuse across the synaptic cleft in the process of neuron-muscle cell communication. Recent studies, however, suggest that AChE may have a broader role, particularly in the development of nervous system. Deviations in normal levels of AChE at the initial moments of nervous system development appear to contribute to observed neuro-anatomic abnormalities such as altered neurite (axons and dendrites) outgrowth. Sequence similarities of AChE to some cell adhesion molecules appear to indicate its structural role of neurite adhesive in neuron development process. In this study, Dr. S. Chao, a Professor of Biology at FSU, and I used physical methods to explore the influence of different AChE inhibitors on the normal outgrowth of neurites of the specific neuroblastoma cells. Our results support the hypothesis that AChE promotes neurite outgrowth through adhesive function. In another project I am developing a computer simulation model of motility, chemo-, and thermo-taxes of DICTYOSTELIUM DISCOIDEUM amoebae.