Suresh Govindarajan

Bio: Suresh Govindarajan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Superpotential & Siegel modular form. The author has an hindex of 21, co-authored 130 publications receiving 1500 citations. Previous affiliations of Suresh Govindarajan include University of Pennsylvania & Indian Institutes of Technology.

Numerical modeling on flow of groundwater energies in transient well capture zones

Abstract: Capture zone delineation is indispensable in all wellhead protection programs for the safeguarding of groundwater supplies. Transients in the flow model tend to influence the capture zone geometry over time. Thus, transient analyses of well capture zones are superior to the steady-state analogs for all practical cases with time-varying flow parameters. Energy gradients drive groundwater flow like any other natural phenomena. Along with the evolving capture zone, energy transformations within the model domain were also, therefore, assessed to portray the state of the system with time. The energy components, in the form of frictional dissipation and change in internal energy, were estimated at all time steps beside delineating the capture zones. This paper numerically models a two-dimensional homogeneous isotropic confined aquifer and thereby delineating the capture zones by subsequent examination of the energies within. The energy approach facilitated the identification of areas having pronounced transient behavior compared to the entire region within the capture zone and model domain. The current study reveals that there was an unusual increase in the internal energy term for two time periods of the entire cycle investigated and highlighted the compressibility effects of the system. This has been correlated to the change in the distribution of capture fraction values within the capture zones of those specific time periods.

Modeling the sensitivity of hydrogeological parameters associated with leaching of uranium transport in an unsaturated porous medium

Abstract: The uranium ore residues from the legacies of past uranium mining and milling activities that resulted from the less stringent environmental standards along with the uranium residues from the existing nuclear power plants continue to be a cause of concern as the final uranium residues are not made safe from radiological and general safety point of view. The deposition of uranium in ponds increases the risk of groundwater getting contaminated as these residues essentially leach through the upper unsaturated geological formation. In this context, a numerical model has been developed in order to forecast the U and its progenies concentration in an unsaturated soil. The developed numerical model is implemented in a hypothetical uranium tailing pond consisting of sandy soil and silty soil types. The numerical results show that the U and its progenies are migrating up to the depth of 90 m and 800 m after 10 y in silty and sandy soil respectively. Essentially, silt may reduce the risk of contamination in the groundwater for longer time span and at the deeper depths. In general, a coupled effect of sorption and hydrogeological parameters (soil type, moisture context and hydraulic conductivity) decides the resultant uranium transport in subsurface environment.

Mathieu Moonshine and Siegel Modular Forms

Abstract: A second-quantized version of Mathieu moonshine leads to product formulae for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. For some conjugacy classes, but not all, they match known modular forms. In this paper, we express the product formulae for all conjugacy classes of $M_{24}$ in terms of products of standard modular forms. This provides a new proof of their modularity.

Crosscaps in Gepner Models and Type IIA Orientifolds

Abstract: As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with $G_2$ holonomy. Using the spacetime picture as well as the M-theory dual, we discuss aspects of the orientifold that should be obtained in the Gepner model. This is illustrated for the case of the quintic.

The Topological Vertex

Abstract: We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

Moduli spaces of local systems and higher Teichmüller theory

Abstract: Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely related to the moduli spaces of G-local systems on S. We show that they carry a lot of interesting structures. In particular we define a distinguished collection of coordinate systems, equivariant under the action of the mapping class group of S. We prove that their transition functions are subtraction free. Thus we have positive structures on these moduli spaces. Therefore we can take their points with values in any positive semifield. Their positive real points provide the two higher Teichmuller spaces related to G and S, while the points with values in the tropical semifields provide the lamination spaces. We define the motivic avatar of the Weil–Petersson form for one of these spaces. It is related to the motivic dilogarithm.

The statistics of string/M theory vacua

Abstract: We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective Lagrangians, which can be used to precisely study the predictive power of string theory, and in simple examples can lead to universality results. Using these ideas, we outline an approach to estimating the number of vacua of string/M theory which can realize the Standard Model.