Browsing by Advisor "Venkatapathi, Murugesan"
Now showing items 1-7 of 7
-
Algorithms for Estimating Integrals in High Dimensional Spaces
Sampling, estimation and integration in high dimensional continuous spaces is required in diverse areas ranging from modeling multi-particle physical systems and optimization to inference from data. When the number of ... -
An importance sampling in N Sphere Monte Carlo and its performance analysis for high dimensional integration
Statistical methods for estimating integrals are indispensable when the number of dimensions (parameters) become greater than ~ 10, where numerical methods are unviable in general. Well-known statistical methods like ... -
Multiplexing Nanoplasmonic Sensors
Complex biological samples such as serum contain thousands of proteins and other molecules spanning up to 13 orders of magnitude in concentration. Present measurement techniques such as protein microarrays and quantum dot ... -
Numerical Analysis of Some Preconditioners and Associated Error Estimators for Solving Linear Systems
Convergence of iterative algorithms in solving large linear systems is largely affected by the condition number of the matrix. Preconditioners reduce the condition number of the system matrix, thereby letting the linear ... -
A Numerical Method for Modeling Light Scattering from Spherical Particles with a Probability Density in the Parametric Space
With modern computational tools, modeling light scattering from a particle with known physical parameters has become relatively trivial. Evaluation using analytical solutions is highly eficient compared to a full ... -
Semi-analytical solution for eigenvalue problems of lattice models with boundary conditions
Closed-form relations for limiting eigenvalues of an infinite k-periodic spatial lattice in any number of dimensions d, and its semi-analytical extensions for any given size n of the lattice with free-free boundary ... -
Understanding spontaneous emission in the strong coupling regime of an emitter and absorbing matter
This thesis proposes a partition of optical states into radiative and non-radiative parts when an emitter is proximal to resonant absorbing nanostructures. The conventional partition is valid only for the weak coupling ...