Home               Research                  CV                Publications                  Personal    

Catastrophic regime shifts

Empirical studies on ecosystems, such as lakes and vegetation, indicate that drastic responses in an ecological state can occur even for smallest changes in external conditions. Such unexpected and dramatic changes occur in systems showing alternative stable states and they are often referred to as catastrophic regime shift. In this context, I studied a simple lake model exhibiting alternative stable states (oligotrophic and eutrophic states). An
analysis of the resulting stochastic difference equations (using analytical and numerical solutions) showed that frequent regime shifts between oligotrophic and eutrophic states can occur even when the average nutrient input is far from the bifurcation.

Vegetation in semi-arid regions provide critical ecosystem resources and can undergo catastrophic desertification. We studied a spatially
extended model of self-organizing vegetation patterns which explicitly incorporated the seasonal characteristics of plant
growth. The resulting coupled nonlinear partial differential equations were solved numerically. Contrary to the assumption of previous studies that the average rainfall drives the pattern formation, my work showed that seasonal redistribution and variance in rainfall can substantially alter (i.e. either enhance or reduce the productivity and related measures) the self-organization in ecosystem. These results are in qualitative agreement with recently
published data from Savanna grasslands.

From an applied perspective, it is critical that we identify the ecosystems which are prone to catastrophic regime shifts so that
appropriate policy or management strategies can be initiated. Working in this direction, I showed by studies on spatially implicit
ecological models that the system will develop asymmetries near an impending regime shift. This asymmetry can be quantified by the
skewness of the probability distribution of the time series data. This research work showed that an easily measurable quantity from
available data can potentially be used as an early warning signal of an imminent catastrophic regime shift.

Seed dispersal by animals.

Folding and Aggregation in Biomolecules

During Fall 2004 and Winter 2004, I worked on an RNA folding problem with Dr. Bundschuh. These are heteropolymer systems wherein the competition between the inter molecular base attraction and the intra molecular base pair attraction drives the structure formation. For instance, in the field of riboswitches where such competition is used to regulate the expression for genes in dependence on the concentrations of the RNAs involved. Another example being the repeated sequence structure in the double stranded DNA in the repeat regions of the genes (ex - Huntington's disease gene). Here we consider a toy model to study the phase transition from a molten phase to an aggregated phase. This work is published as:

Nonsaturating Magnetoresistance in Silver Chalconides

During Spring 2004 to Winter 2005, I worked with Prof. David Stroud on the transport properties of Inhomogeneous Semiconductors. The materials such as on Ag2+δTe and Ag2+δSe show exact linear behavior in the transverse magnetoresistance for large range of the magnetic fields. Using duality argument, a 2-dimensional disordered model was proposed which is analytically shown to have an exact linear high field magnetoresistance. For 3-dimensional case, effective medium approximation was used which also has some interesting and relevant features.  This work was published as: