Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Physics at MIT, Fall 2005 STATEMENT OF OBJECTIVES I currently pursue a dual degree at BITS Pilani, India, an M.Sc. (Hons) Physics being the first degree and a B.E.(Hons) Electrical and Electronics the second. My exemplary performance in the school final examinations ensured that I secured an admission at BITS, one of India's premier institutions for science and engineering. The latitude and depth of my undergraduate education combined with my love for physics urges me to pursue graduate studies in physics. Within physics I have identified Astrophysics and Condensed Matter Theory as my major areas of interest. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation, and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof.B.S.Sathyaprakash(Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been

uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9) All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. Two courses, one in statistical mechanics and another in solid-state physics (Jan-May 2003), sparked my interest in condensed matter physics. In both, I topped my class of 35 students. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. I believe that the Department of Physics at MIT will provide me an ideal setting in which to carry out research, since some of the work in relativistic astrophysics and condensed matter theory, currently being pursued there closely matches my own interests. I am particularly interested in working on gravitational collapse and gravitational waves emitted by inspiralling compact binaries. I believe the background I have gained will enable me to contribute to the theoretical, numerical or data analysis aspects of the work carried out by the LIGO group. I will be able to apply concepts learnt in signal processing as a part of my course work in Electrical Engineering, to the detection of gravitational wave signals. I also believe that my exposure to Condensed Matter Physics combined with my flair for programming makes me ideal for work in areas such as Solid State Physics, Non-Equilibrium Statistical Mechanics and Theoretical Biophysics. Hence, I believe that the distinguished faculty and the world-class facilities at your university will provide me with both, insight into research in these areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that MIT will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Astronomy and Astrophysics at Caltech, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree at BITS Pilani, India, an M.Sc. (Hons) Physics being the first degree and a B.E.(Hons) Electrical and Electronics the second. My exemplary performance in the school final examinations ensured that I secured an admission at BITS, one of India's premier institutions for science and engineering. The latitude and depth of my undergraduate education combined with my love for Astronomy and Astrophysics urges me to pursue graduate studies in Astronomy and Astrophysics. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof.B.S.Sathyaprakash(Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be

presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates I believe that the Department of Astronomy at California Institute of Technology will provide me an ideal setting in which to carry out research, since some of the work in Astronomy and Astrophysics, currently pursued there closely matches my own interests. My interests are broad and I would like to explore different areas before specializing in one of them. I believe that my courses and projects in General Relativity combined with my unique background as an Electrical and Electronics engineer makes me ideal for working on the LIGO project. My study of General Relativity has given me an exposure to the theoretical aspects of gravitational waves. I will be able to apply concepts learnt in signal processing to the detection of gravitational wave signals. My flair for programming will be useful for numerical and data analysis work. My overall education in electronics will enhance understanding the construction and working of the detector. Thus, the background I have gained will enable me to contribute to the theoretical, numerical or data analysis aspects of the work carried out by the LIGO group. I believe that the distinguished faculty and the excellent facilities at CIT will provide me with both, insight into research in diverse areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that California Institute of Technology will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application ID No: 352448 Application for Graduate Studies in Physics at The University of Texas at Austin, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree at Birla Institute of Technology and Science, Pilani, India, an M.Sc. (Hons) Physics being the first degree and a B.E.(Hons) Electrical and Electronics the second. My exemplary performance in the school final examinations ensured that I secured an admission at BITS, one of India's premier institutions for science and engineering. The latitude and depth of my undergraduate education combined with my love for physics urges me to pursue graduate studies in physics. Within physics, I have identified Astrophysics and Condensed Matter Theory as my major areas of interest. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof.B.S.Sathyaprakash (Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the

paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. Two courses, one in statistical mechanics and another in solid-state physics (Jan-May 2003), sparked my interest in condensed matter physics. In both, I topped my class of 35 students. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. I believe that the Department of Physics at The University of Texas at Austin will provide me an ideal setting in which to carry out research, since some of the work currently pursued there, closely matches my own interests. My interests are broad and I would like to explore different areas before specializing in one of them. I believe the background I have gained will enable me to contribute to the work carried out in Relativistic Astrophysics by the Relativity group. My study of General Relativity has given me an exposure to the theoretical aspects of gravitational waves. My flair for programming will be useful for computational and numerical work. I also believe that my exposure to Condensed Matter Physics and Statistical Mechanics makes me ideal for the theoretical work being carried out in this area. Hence, I believe that the distinguished faculty and the excellent facilities at your university will provide me with both, insight into research in these areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that The University of Texas at Austin will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Physics at UCSB, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree at BITS Pilani, India, an M.Sc. (Hons) Physics being the first degree and a B.E.(Hons) Electrical and Electronics the second. My exemplary performance in the school final examinations ensured that I secured an admission at BITS, one of India's premier institutions for science and engineering. The latitude and depth of my undergraduate education combined with my love for physics urges me to pursue graduate studies in physics. Within physics I have identified Astrophysics and Condensed Matter Theory as my major areas of interest. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof.B.S.Sathyaprakash(Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been

uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. Two courses, one in statistical mechanics and another in solid-state physics (Jan-May 2003), sparked my interest in condensed matter physics. In both, I topped my class of 35 students. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. I believe that the Department of Physics at The University of California, Santa Barbara will provide me an ideal setting in which to carry out research, since some of the work currently pursued there, closely matches my own interests. My interests are broad and I would like to explore different areas before specializing in one of them. I believe the background I have gained will enable me to contribute to the work carried out in Relativistic Astrophysics. My study of General Relativity has given me an exposure to the theoretical aspects of gravitational waves. My flair for programming will be useful for computational and numerical work. I also believe that my exposure to Condensed Matter Physics and Statistical Mechanics makes me ideal for the theoretical work being carried out in this area. Hence, I believe that the distinguished faculty and the excellent facilities at your university will provide me with both, insight into research in these areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that The University of California, Santa Barbara will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Physics at UW-Milwaukee, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree at Birla Institute of Technology and Science, Pilani, India, an M.Sc. (Hons) Physics being the first degree and a B.E.(Hons) Electrical and Electronics the second. My exemplary performance in the school final examinations ensured that I secured an admission at BITS, one of India's premier institutions for science and engineering. The latitude and depth of my undergraduate education combined with my love for physics urges me to pursue graduate studies in physics. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation, and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof. B.S.Sathyaprakash (Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be

presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates I believe that the Department of Physics at University of Wisconsin, Milwaukee will provide me an ideal setting in which to carry out research, since some of the work in Gravitation and Cosmology, currently pursued there closely matches my own interests. My interests are broad and I would like to explore different areas before specializing in one of them. I believe that my courses and projects in General Relativity combined with my unique background as an Electrical and Electronics engineer makes me ideal for working in the Gravitation and Cosmology group. My study of General Relativity has given me an exposure to the theoretical aspects of gravitational waves. I will be able to apply concepts learnt in signal processing to the detection of gravitational wave signals. My flair for programming will be useful for numerical and data analysis work. My overall education in electronics will enhance understanding the construction and working of the detector. Thus, the background I have gained will enable me to contribute to the theoretical, numerical or data analysis aspects of the work carried out by the group. I believe that the distinguished faculty and the excellent facilities at your university will provide me with both, insight into research in diverse areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that University of Wisconsin, Milwaukee will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Physics at Cornell University, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree (M.Sc. (Hons) Physics and B.E.(Hons) Electrical and Electronics) at the Birla Institute of Technology & Science, one of the premier educational institutes in India. I would like to pursue further education in Physics; either in Astrophysics or Condensed Matter Physics. Various projects I have been involved with (as outlined in the paragraphs below) have stoked my interest in these two subjects. Astrophysics and the Theory of Relativity: An elective course in my second year and a reading project on the Kerr Solution and Rotating Black Holes on relativity theory introduced me to the subject. That summer, I worked on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”. This was with Prof. T. P. Singh, at the Tata Institute of Fundamental Research. We examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper (www.arxiv.org; gr-qc/0212089) to the journal General Relativity and Gravitation, and the document is currently with the referees. Summer 2004 was spent working with Prof. Bala R Iyer at the Raman Research Institute, Bangalore (www.rri.res.in). We collaborated with Prof.B.S.Sathyaprakash (Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses comprising the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. This project, which involved considerable numerical and analytical work, has left me with an insight into gravitational wave-astrophysics. Condensed Matter Physics: Two courses, one in statistical mechanics and another in solid-state physics, introduced me to condensed matter physics. In both, I topped my class of 35 students and secured A’s. I undertook a semester-long project on advanced topics in statistical mechanics, where concepts such as the Ising model, critical phenomena, renormalization group and superfluidity were learnt. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I

am doing a thesis is on the application of field theory to the theory of Bose- Einstein condensates. Other experience:

In addition, I presented a term paper on 'controlling the chaotic pendulum' as a part of a course 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory.

Some achievements: I was among 9 students offered admission to TIFR's Ph.D. program starting in fall 2005: this was based on my project and the results of a test and interview which were conducted during the course of VSRP 2003. I won the first prize for presenting a paper on “Spherical Gravitational Collapse” in a competition during APOGEE (2004), the all-India academic festival at BITS.

I strongly believe that with my impeccable academic credentials and my potential for independent research, I am fully equipped to meet the high levels of standard set by your university. Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Physics at UIUC, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree (M.Sc. (Hons) Physics and B.E.(Hons) Electrical and Electronics) at the Birla Institute of Technology & Science, one of the premier educational institutes in India. I would like to pursue further education in Physics; either in Astrophysics or Condensed Matter Physics. Various projects I have been involved with (as outlined in the paragraphs below) have stoked my interest in these two subjects. Astrophysics and the Theory of Relativity: An elective course in my second year and a reading project on the Kerr Solution and Rotating Black Holes on relativity theory introduced me to the subject. That summer, I worked on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”. This was with Prof. T. P. Singh, at the Tata Institute of Fundamental Research. We examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper (www.arxiv.org; gr-qc/0212089) to the journal General Relativity and Gravitation, and the document is currently with the referees. Summer 2004 was spent working with Prof. Bala R Iyer at the Raman Research Institute, Bangalore (www.rri.res.in). We collaborated with Prof.B.S.Sathyaprakash (Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses comprising the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. This project, which involved considerable numerical and analytical work, has left me with an insight into gravitational wave-astrophysics. Condensed Matter Physics: Two courses, one in statistical mechanics and another in solid-state physics, introduced me to condensed matter physics. In both, I topped my class of 35 students and secured A’s. I undertook a semester-long project on advanced topics in statistical mechanics, where concepts such as the Ising model, critical phenomena, renormalization group and superfluidity were learnt. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I

am doing a thesis is on the application of field theory to the theory of Bose- Einstein condensates. Other experience:

In addition, I presented a term paper on 'controlling the chaotic pendulum' as a part of a course 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory.

Some achievements: I was among 9 students offered admission to TIFR's Ph.D. program starting in fall 2005: this was based on my project and the results of a test and interview which were conducted during the course of VSRP 2003. I won the first prize for presenting a paper on “Spherical Gravitational Collapse” in a competition during APOGEE (2004), the all-India academic festival at BITS.

I strongly believe that with my impeccable academic credentials and my potential for independent research, I am fully equipped to meet the high levels of standard set by your university. Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application for Graduate Studies in Physics at The Pennsylvania State University, Fall 2005 STATEMENT OF PURPOSE I currently pursue a dual degree at BITS Pilani, India, an M.Sc. (Hons) Physics being the first degree and a B.E.(Hons) Electrical and Electronics the second. My exemplary performance in the school final examinations ensured that I secured an admission at BITS, one of India's premier institutions for science and engineering. The latitude and depth of my undergraduate education combined with my love for physics urges me to pursue graduate studies in physics. Within physics I have identified Astrophysics and Condensed Matter Theory as my major areas of interest. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof.B.S.Sathyaprakash(Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the

journal Physical Review D and the document is currently being refereed. The manuscript has been uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. Two courses, one in statistical mechanics and another in solid-state physics (Jan-May 2003), sparked my interest in condensed matter physics. In both, I topped my class of 35 students. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. I believe that the Department of Physics at PSU will provide me an ideal setting in which to carry out research, since some of the work currently pursued there, closely matches my own interests. My interests are broad and I would like to explore different areas before specializing in one of them. I believe the background I have gained will enable me to contribute to the work carried out in Relativistic Astrophysics by the Gravity group. My study of General Relativity has given me an exposure to the theoretical aspects of gravitational waves. My flair for programming will be useful for computational and numerical work. I also believe that my exposure to Condensed Matter Physics and Statistical Mechanics makes me ideal for the theoretical work being carried out in this area. Hence, I believe that the distinguished faculty and the excellent facilities at your university will provide me with both, insight into research in these areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that PSU will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.

Name: Pranesh Adhyam Sundararajan Date of Birth: 10 June 1983 Email: pranesh106@yahoo.com Application PIN: 052567101 Application for Graduate Studies in Physics at Yale University, Fall 2005 PERSONAL STATEMENT I currently pursue a dual degree (M.Sc. (Hons) Physics and B.E.(Hons) Electrical and Electronics) at Birla Institute of Technology & Science, one of the premier educational institutes in India. The latitude and depth of my undergraduate education combined with my love for physics urges me to pursue graduate studies in physics. Within physics I have identified Astrophysics and Condensed Matter Theory as my major areas of interest. The underlying basis of my interest is the fact that the theory developed in these areas can be put to experimental or observational tests. An elective course on relativity theory (Jan-May 2002), which I took in my second year, introduced me to Einstein's relativity and its close connection with astrophysics. A reading project on The Kerr Solution and Rotating Black Holes was assigned to me as a part of the course. This course and further reading made me realize that I took to these concepts naturally, and I decided to explore research in relativistic astrophysics. I got this opportunity when the Tata Institute of Fundamental Research (TIFR, Mumbai), one of India’s finest research centers, selected me for their Visiting Students Research Program (VSRP) in 2003. As part of this program, about 50 students of science, across India are given the opportunity to do research during the summer. There I worked with Prof. T. P. Singh (Department of Astronomy and Astrophysics) on a paper titled “Gravitational Collapse of an Infinite Dust Cylinder”, where we examined the collapse of an infinite cylindrical distribution of time-like dust. Starting from a general form of the metric, we solved the Einstein field equations to obtain the exact form of the metric for homogeneous collapse. We showed that it could be matched to a time dependent exterior. The paper also discussed the nature of the resulting singularity. We have submitted the paper to the journal General Relativity and Gravitation and the document is currently with the referees. It can be found on the preprint archive, www.arxiv.org, (gr-qc/0212089). This project enhanced my interest in relativistic astrophysics and left me with enormous exposure to the theoretical work being done in the area. I was offered admission to TIFR's Ph.D. program starting in fall 2005, based on this project and the results of a test and interview that were conducted during the course of VSRP 2003. I was among the 9 students who were given this offer. Summer 2004 was spent working with Prof. Bala R. Iyer at the Raman Research Institute (RRI, Bangalore). We collaborated with Prof.B.S.Sathyaprakash(Cardiff University) and K.G.Arun(RRI) and worked on a project on gravitational waves emitted by inspiralling compact binaries, currently being observed in detectors such as LIGO and VIRGO. It involved a systematic study of the errors induced in estimation of parameters such as the masses composing the binary. We studied the effect of higher post-Newtonian terms in the phasing formula on parameter estimation, by incorporating higher order terms up to 3.5PN, in steps of 0.5PN. The performance of detectors such as LIGO and VIRGO in regard to parameter estimation was also discussed. Finally, we computed the amplitude corrections due to frequency sweep in the stationary phase approximation and investigated its implication for parameter estimation. We have submitted the paper to the journal Physical Review D and the document is currently being refereed. The manuscript has been

uploaded on the preprint archive, www.arxiv.org (gr-qc/0411146). Prof.B.S.Sathyaprakash will be presenting the paper during the Ninth Gravitational Wave Data Analysis Workshop (GWDAW9) to be held at LAPP (Laboratoire d'Annecy-le-Vieux de Physique des Particules, France) from 15-18 Dec, 2004 (http://lappc-in39.in2p3.fr/GWDAW9). All calculations were done on 'Mathematica'. The project involved detailed calculations and has provided me with considerable insight into the embryonic area of gravitational wave-astrophysics. Two courses, one in statistical mechanics and another in solid-state physics (Jan-May 2003), sparked my interest in condensed matter physics. In both, I topped my class of 35 students. A semester long project on advanced topics in statistical mechanics helped in understanding advanced concepts such as the Ising model, critical phenomena, renormalization group and superfluidity. Courses such as 'Electronic Devices and Integrated Circuits' and 'Microelectronic Circuits’ have exposed me to the direct application of concepts in solid-state physics to electronics. Presently, I am doing a thesis on the application of field theory to the theory of Bose- Einstein condensates. It consists of using the path integral approach to calculate the partition function and hence determine other properties such as critical temperature, entropy and free energy of the condensate. Apart from the ideal Bose gas, it discusses the properties of interacting and relativistic condensates. I have developed my overall skills as a physicist through a number of courses and projects in different areas. I presented a term paper on 'controlling the chaotic pendulum' as a part of a course in 'Non-linear Dynamics and Chaos.' A course in Optics required me to write a computer program in ‘C’, which used the Monte Carlo method to analyze diffraction from a circular aperture. I have done a reading course on Quantum field theory where I studied the Dirac equation, Klein Gordan equation, Feynman diagrams and the interactions between fundamental particles. I believe that the Department of Physics at Yale University will provide me an ideal setting in which to carry out research, since some of the work currently pursued there, closely matches my own interests. My interests are broad and I would like to explore different areas before specializing in one of them. I believe the background I have gained will enable me to contribute to the work carried out in Astrophysics. I also believe that my exposure to Condensed Matter Physics and Statistical Mechanics makes me ideal for the theoretical work being carried out in this area. Hence, I believe that the distinguished faculty and the excellent facilities at your university will provide me with both, insight into research in these areas and the opportunity to specialize in one of them. A Ph.D. will be in keeping with my long-term objective of carrying out research in an academic position in my own country. It will equip me with the maturity and technical knowledge that I will need through the length of my academic career as a physicist. I think that Yale University will provide me the appropriate environment to begin my research career. Aware of the excellent record and high standards established there, I am confident I will pursue my studies with commitment and purpose. I eagerly seek an opportunity to do my graduate studies and further the research in your university with my own contributions Pranesh Adhyam Sundararajan.