Despite advances in computing, many common physical/chemical/biological process remain out of reach of computing power in forseeable future due to the requirement of simulating ever-larger systems and for ever-longer times. One way of advancing the field is to develop new methods and algorithms which “reduce the size” of the system and/or “reduce the time” of simulation, with out significant loss of accuracy.

Students with a good back ground in physics and mathematics will be a natural fit. However a good understanding of the "domain" of the project (for example biology, material science) can be a good starting point to apply the mathematical techniques in performing systematic studies to understand various properties of the system.
After working successfully on the project, the graduted students can be expected to be sufficiently trained in high performance computing, and all standard simulation methods and some advanced simulation methods.

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Development of new algorithms for automatic determination of reaction coordinates

Usually, the trajectories generated from the simulation of system is subsequently analyzed to understand the major players in process under study; in technial terms, analysis of the process yeilds the reaction coordinate appropriate for/controlling the process. So we need to have many such long trajectories for such an analysis, each of which is computationaly expensive to generate. We are currently investigating new methods whereby (1) generation of whole trajectories is not required and (2) identification of reaction coordinate is done in an automated fashion, so as to reduce the time and effort required for analysis and determination of reaction coordinate.

Force-field development

Classical mechanics based simulations have been shown to be helpful in understanding the nonbonded interactions between CNTs and other systems such as water, ions, other nanoparticles and DNA. However, most of the simulations that have been reported were performed based on ad hoc force field parameters. One of the most popular exercises that has been adopted is to model the carbon atoms of the CNTs as uncharged sp2 type carbons. It should be noted that the carbon atoms in the CNTs are nonplanar, and the parameters used were designed for planar carbon atoms. We plan to employ high level quantum mechanical calculations, and calculate vibrational frequencies of few CNTs, relative stabilities, and geometric parameters. Using these as target data, force field parameters related to bonds, angles, dihedral angles, and out-of-plane distortivities will be developed. In the second step, the most important parameter that is expected to capture all non bonded interactions, namely the Lennard-Jones parameters will be developed. The target data that will be used are the interaction energies, and distances between CNTs and rare gas atoms calculated using quantum mechanical calculations. An iterative procedure of the above steps would be carried out until a consensus is obtained between all the target, and data obtained from empirical parameters. Similar parameterization will be carried out on common functional groups that are covalently bound to CNTs. The second part involves the application of these force field parameters to understand the nonbond interactions between CNTs and other systems. One of the systems of study will involve the hybridization between CNTs and nucleic acid strands. The sequence dependence on the binding, the effect of spiraling and peeling will be studied in detail.

Shape Control of Nanoparticles

Nanoparticles are interesting, in that their properties are a strong fucntion of their shape and size; this is markedly in contrast to atoms and molecules, for which the properties are strong functions of their chemical composition. Due to this, nanoparicles offer an fundamentally new way of generating interesting properties. Experimentally, the control of shape (and to some extent the size) of the nanoparticle has remain an art; with the techniques used to generate different shapes (and phases) are found basically by serendipity. This lack of general principles of shape control is a huge obstacle to this field. We are currently using recent advances in Density Functional Methods, like Orbital Free Density Functional Theory, to study “periodic” systems of very large size; for example the nanoparticles themselves. Combining the results of the studies on adsorption on the nanoparticles with Classical Mechanical models for crystal growth, we plan to develop some general rules for shape control of nanoparticles.

Theoretical studies in chemical, biological and material science for simulating equilibrium and non-equlibrium processes

Computational Natural Sciences and Bioinformatics

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