Teaching
2023
Mathematical Physics - PHY-C-503
Plasma Physics - PHY-E-714
Indian Contribution to Physics - PHY-V-504
This is a 4 credit elective course for MSc second semester in Physics.
Course Outcome:
The students are expected to become skilled, both theoretically and practically, in computer programming and are expected to be able to solve numerical problems that are frequently used in physics using computer programs.
Course Content:
Unit I:
Solution of Equations in One Variable
Bisection, Fixed-Point Iteration, Newton-Raphson, Secant, Regula Falsi, Aitken's and Steffensen's Method for Accelerating Convergence, Horner's Method for Polynomial Derivatives, Muller's Method for Complex Zeros.
Interpolation & Polynomial Approximation
Interpolation and Lagrange Polynomial: Neville's Method, Divided Differences, Hermite Interpolation, Natural and Clamped Cubic Spline Interpolation, Bezier Method for Parametric Curves.
Differentiation and Integration
Richardson's Extrapolaton, Composite Numerical Integration, Romberg Integration, Adaptive Quadrature Method, Gaussian Quadrature, Multiple Integrals: Simpson and Gaussian Double Integral, Gaussian Triple Integral, Improper Integrals.
Unit II:
Initial-Value Problems for ODE
Euler's Method, Higher-Order Taylor Methods, Runge-Kutta Methods, Error Control and Runge-Kutta-Fehlberg Method, Multistep Methods: Adams Predictor-Corrector Method, Variable Step-Size Multistep Methods, Extrapolation Methods, Higher-Order Equations and Systems of Differential Equations, Stability, Stiff Differential Equations: Trapezoidal with Newton's Iteration.
Direct Methods for Solving Linear Systems
Linear Systems of Equations: Gaussian Elimination with Backward Substitution, Gaussian Elimination with Partial Pivoting and Scaled Partial Pivoting, Determinant, Matrix Inversion and Factorization (LU, LDL^t, Cholesky and Crout for tridiagonal linear systems), Special Matrices.
Iterative Techniques in Matrix Algebra
Jacobi and Gauss-Siedel Iterative Technique, Relaxation Techniques for Solving Linear Systems: Successive Over Relaxation (SOR), Error Bounds and Iterative Refinement, Preconditioned Conjugate Gradient Method.
Unit III:
Approximation Theory
Discrete Least Square Approximation, Orthogonal Polynomials and Lease Square Approximation, Chebyshev Polynomials and Economization of Power Series, Rational Function Approximation: Pade, Chebyshev Rational Approximation, Trigonometric Polynomial Approximation, Fast Fourier Transforms.
Approximating Eigenvalues
Orthogonal Matrices and Similarity Transformations, Power Method, Symmetric and Inverse Power Method, Wielandt Deflation, Householder's Method, QR Algorithm, Singular Value Decomposition.
Nonlinear Systems of Equations
Newton's Method for Systems, Quasi-Newton Method: Broyden Method, Steepest Descent Techniques, Homotopy and Continuation Methods.
Unit IV:
Boundary-Value Problems for ODE
Linear Shooting Method, Shooting Method for Nonlinear Problems, Finite-Difference Method for Linear and Nonlinear Problems, Rayleigh-Ritz Method (Piecewise Linear and Cubic Spline).
Partial Differential Equations
Elliptic (Poisson Equation), Parabolic (Heat Equation with Backward Difference and Crank Nicolson), Hyperbolic (Wave Equation) PDEs, Finite Element Method, Finite Volume Method, Shock Capturing Schemes: (TVD, MUSCL), WENO and Galerkin Algorithms, Implementation of Flux Limiters.
Course Evaluation:
Internal Test 1 (25 Marks): Hands-on implementation of algorithms in class and submission of assignments in time.
Internal Test 2 (25 Marks): Presentation on a specific assigned topic to individual students .
Internal Test 3 (25 Marks): Surprise Test
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Text Books:
Numerical Analysis, by R L Burden and J D Faires (Brooks/Cole, Cengage Learning)
Reference Books:
Fundamentals of Engineering Numerical Analysis, by P Moin (Cambridge Univ Press)
This is a 4 credit elective course for MSc fourth semester in Physics.
Course Outcome:
The students would be able to get adequate idea on the Astronomy & Astrophysics specialization - about the astronomical observation, stellar structure, stellar evolution, the solar system, galaxies and also about the statistical tools to be used for astrophysical analysis.
Course Content:
Unit I:
Optical Telescopes, Radio Telescopes, Hubble Space Telescope, Astronomical Spectrographs, Photographic, Photoelectric and Spectro-Photometry, Detectors and Image Processing.
Magnitudes, Motions and Distances of Stars:
Stellar Magnitude Sequence, Absolute Magnitude and the Distance Modulus, Bolometric Magnitude, Different Magnitude Standards: The UBV System and Six-colour Photometry, Radiometric Magnitudes, The Colour-index of a Star, Luminosities of Stars, Stellar Parallax (Trigonometric) and Units of Stellar Distances, Stellar Positions: The Celestial Coordinates, Stellar Motions, Solar Motion and Peculiar Velocities of Stars, Velocity Dispersion, Statistical and Moving Cluster Parallax.
Spectral Classification of Stars:
Boltzman's Formula, Saha Ionisation Equation, Harvard System of Spectral Classification: Henry-Draper Catalogue, Luminosity Effect on Stellar Spectra, Spectroscopic Parallax, Hertzsprung-Russell Diagram.
The Photosphere: Limb-darkening, Solar Granulation, Faculae, Chromosphere, Corona, Prominences, The 11-year Solar Cycle and Sunspots, Solar Magnetic Fields, Theory of Sunspots, Solar Flares, Radio Emission, Solar Wind, Solr Neutrino Puzzle.
Equation of Transfer and it's solution, Absorption Processes in Stellar Atmosphere, Continuous Absorption by Negative Hydrogen Ions in Cooler Stars, Analysis of Spectral Line Broadening, Curve of Growth, Stellar Temperatures, Chemical Composition.
Unit II:
Visual Binary, Spectroscopic Binary, Eclipsing Binary, Multiple Stars, Origin of Binary Stars, Stellar Masses and Mass-Luminosity Relation, Mass Transfer in Close Binary Systems.
Classification of Variable Stars, Cepheid Group of Variables, Period-luminosity Relations of Cepheid Group of Variables, RV Tauri Variables, Mira-type Variables, Red Irregular and Semi-regular Variables, Beta Canis Majoris Variables, U Geminorum Stars, SS Cygni or Dwarf Novae, Flare Stars, Pulsation Theory of Variable Stars.
Distribution of Novae in Our Galaxy, Determination of Distance and Luminosity of Novae, Light Variation of Novae, Spectra of Novae, Cause of Nova Outburst, Supernovae, SN 1987 A.
Stars with Extended Atmosphere:
The Wolf-Rayet Stars, P Cygni and a Cygni Stars, Be Stars: Shell Stars, Of Stars.
Some Cooler Stars of Interest:
Peculiar A Stars and Metallic-line A Stars, T Tauri Stars, Emission-line Red Dwarf, R Coronae Borealis, Carbon and Heavy-metal Oxide Stars, Subdwarfs, Brown Dwarfs.
Unit III:
Clusters and Associations of Stars:
Galactic and Globular Clusters, Stellar Associations, Stellar Population Characteristics, Star Formation.
Classification and Galactic Distribution of Nebulae, Observational Techniques, Dark Nebulae, Reflection Nebulae, Diffuse Emission Nebulae: Theory of Emission Lines, Planetary Nebulae, The Crab Nebula: Supernova Remnants.
Large-scale Distribution of Interstellar Matter, Interstellar Lines, Interstellar Clouds, H I and H II Regions: Stromgren's Spheres, Interstellar Shock Waves, Interstellar Cloud Collisions, Energy Balance in Interstellar Gas, Intercloud Medium, Interstellar Grains.
Structure and Evolution of Stars:
Observational Basis, Equation of State for Stellar Interior, Mechanical and Thermal Equilibrium in Stars, Energy Transport in Stellar Interior, Energy Generation in Stars, Stellar Evolution, White Dwarfs.
Neutron Stars and Black Holes:
Discovery of Pulsars, Rotating Neutron Star Model of Pulsars, Period Distribution and Loss of Rotational Energy, Test of Rotating Neutron Star Model of Pulsars, Gold's Model of Pulsars, Distance and Distribution of Pulsars, Binary Pulsars, Black Holes.
Unit IV:
Differential Rotation of Galaxy, Determination of Rotation Parameters in Solar Neighbourhood, Radio Observation of Galaxy at 21-cm Wave-Length, Rotation Curve of Galaxy, Density Distribution of Gas and Spiral Structure of Galaxy: Radio and Optical Data, General Structure, Mass, Magnetic Field of Galaxy, Cosmic Rays, Continuous Radio Emission in the Galaxy.
Classification, Distribution, Luminosity Distribution and Spectra of Galaxies, Local Group, Distances and Nuclei of Galaxies, Theories of Spiral Structures of Disk Galaxies, Dwarf Galaxies, Ultra Compact Dwarf Galaxies, Compact Groups of Galaxies.
Clustering Nature of Galaxies, Morphological Classification of Clusters, cD Galaxies, Interacting Galaxies and Galaxy Mergers, X-Ray Emission from Galaxies and from Clusters of Galaxies: The Cooling Flow, Masses and Evolution of Galaxies, Dark Matter in Galaxies, Superclusters and Voids.
Techniques of Identification of Radio Objects, Structures of Radio Galaxies, Classification of Radio Galaxies and Their Typical Characteristics, Energy Processes in Radio Galaxies, Radio Galaxies in Evolutionary Sequence, Some Important Radio Galaxies, Seyfert Galaxies.
Discovery of Quasars, Radio and Optical Properties, Redshift of Quasars, Active Galactic Nuclei.
Redshift and Expansion of Universe, Matter Density in the Universe and the Deceleration Parameter, Cosmological Principle, Fundamental Equations of Cosmology, Current Theories, Observational Tests of Cosmological Models, Cosmic Microwave Background Radiation.
Course Evaluation:
Internal Test 1 (25 Marks)
Internal Test 2 (25 Marks)
Internal Test 3 (25 Marks)
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Text Books:
William K. Rose: Atrophysic, Dover Publications, (2010).
Padmanabhan, T., Theoretical Astrophysics, Vols.1-3, Cambridge University Press, 2005.
Badyanath Basu: An introduction to Astrophysics, Prentice Hall of India, (2003).
D. D. Clayton: Principle of Stellar evolution and nucleosynthesis, University Chicago Press, (1984).
R. Kippenhahn and A.Weigert: Stellar structure and evolution(Astronomy and Astrophysics Library), Springer, (1994).
K. D. Abhayankar: The Physics of Stars and Galaxies
H. L. Duorah and KalpanaDuorah.: Introduction to Astrophysics
Frank H. Shu: The Physical Universe: An Introduction to Astronomy, University Science Books, California, (1982).
Bradley W. Ostlie and Dale A. Carrol: An introduction to Modern Astrophysics, Addision-Wesley, (1996).
References
1. Harwit, M., Astrophysical Concepts, 3rd ed, Springer-verlag, 2006.
2. Erika Bohm-Vitense, Introduction to Stellar Astrophysics, Vol. 3 : Stellar structure and evolution --
3. Shapiro &Teukolsky,Black Holes, White Dwarfs & Neutron stars --.
2022
This is a 4 credit course for MSc first semester in Physics.
Advanced understanding of mathematical methods used in physics, including but not limited to calculus, differential equations, linear algebra, and probability theory.
Knowledge of mathematical techniques used in modern theoretical physics, such as functional analysis, group theory, and topology, as well as their applications to fundamental questions in physics.
Ability to apply mathematical methods to problems in physics, including the formulation and analysis of physical models, and the interpretation of experimental data.
Understanding of the mathematical foundations of quantum mechanics, classical mechanics, statistical mechanics, and other areas of physics, including the relationship between mathematics and physical concepts such as symmetry and conservation laws.
Syllabus:
Complex Analysis (Brown & Churchill)
Linear Algebra (Gilbert Strang)
Integral Transform (D C Champeney)
Special Functions (Charlie Harper)
Group Theory (Sattinger & Weaver)
Texts:
J W Brown and R V Churchill: Complex Variables and Applications [Book]
Gilbert Strang: Linear Algebra and its Applications [Book]
D C Champeney: Fourier Transforms and their Physical Applications [Book]
Charlie Harper: Introduction to Mathematical Physics [Book]
Sattinger & Weaver: Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics [Book]
References:
Mathews & Walker: Mathematical Methods of Physics [Book]
Dennery & Krzywicki: Mathematics for Physicists [Book]
Riley, Hobson, Bence: Mathematical Methods for Physics and Engineering [Book]
Paul R Halmos: Finite-Dimensional Vector Spaces [Book]
Michael Tinkham: Group Theory and Quantum Mechanics [Book]
Morton Hamermesh: Group Theory and its Applications to Physical Problems [Book]
Arfken, Weber & Harris: Mathematical Methods for Physicists [Book]
M R Spiegel: Schaum's Outline of Complex Variables [Book]
M L Boas: Mathematical Methods in the Physical Sciences [Book]
T L Chow: Mathematical Methods for Physicists [Book]
C M Bender & S A Orszag: Advanced Mathematical Methods for Scientists and Engineers [Book]
V I Arnold: Mathematical Methods of Classical Mechanics [Book]
This is a 4 credit course for PhD course work in Physics.
Syllabus:
Plasma Orbit Theory (F F Chen + A R Choudhuri)
Fluid dynamics and Magneto-Fluids (A R Choudhuri + R Kulsrud)
Waves in Plasmas (R O Dendy)
Nonlinear Theory of Plasmas (Strogatz + Krall & Travelpiece)
Theory of Instability and Turbulence (Goldston & Rutherford)
Collisional Processes in Plasmas (M W Kunz)
Plasma Kinetic Theory (D R Nicholson)
Plasma Applications (Hutchinson)
Nuclear Reactor Design (Goldston (notes) + Wesson + Helander (notes))
Texts:
Francis F Chen: Introduction to Plasma Physics and Controlled Fusion [Book]
Arnab Rai Choudhuri: The Physics of Fluids and Plasmas [Book]
Russell M Kulsrud: Plasma Physics for Astrophysics [Book]
Richard O Dendy: Plasma Dynamics [Book]
Steven H Strogatz: Nonlinear Dynamics and Chaos [Book]
N A Krall & A W Travelpiece: Principles of Plasma Physics [Book]
R J Goldston & P H Rutherford: Introduction to Plasma Physics [Book]
Matthew W Kunz: Lecture Notes on Introduction to Plasma Astrophysics [Webpage]
Dwight Roy Nicholson: Introduction to Plasma Theory [Book]
I H Hutchinson: Principles of Plasma Diagnostics [Book]
John Wesson: Tokamaks [Book]
Per Helander: Theory of plasma confinement in non-axisymmetric magnetic fields [Review Article]
Reference:
Uriel Frisch: Turbulence - The Legacy of A N Kolmogorov [Book]
Gurnett & Bhattacharjee: Introduction to Plasma Physics [Book]
Paul M Bellan: Fundamentals of Plasma Physics [Book]
Thomas H Stix: Waves in Plasmas [Book]
Stephen Jardin: Computational Methods in Plasma Physics [Book]
Roscoe B White: The Theory of Toroidally Confined Plasmas [Book]
John Krommes: (Lecture notes at Princeton)
Greg Hammett: (Lecture notes at Princeton)
Rob Goldston: (Lecture notes at Princeton)
This is a non-credit course for early PhD students.
Text:
Code samples provided in class.
Reference Book:
D C Rapaport: The Art of Molecular Dynamics Simulation [Book]
New Courses prepared under NEP 2020:
This is a 4 credit elective course for MSc fourth semester in Physics.
Course Objective:
The objective of this course is to make the students aware of the technological advancement on nuclear fission and fusion in India and world-wide. It will introduce the physics as well as the technological designs of different nuclear reactors, its safety strategies, international proliferation risks and lastly the path ahead in terms of improvement of fission and fusion physics.
Learning Outcome:
LO-1: The student will be able to understand the basic working principle of different fission reactors, distinguish the underlying physics of different fusion reactors world-wide.
LO-2: They will be able to estimate the capacity of different nuclear weapons and its direct and long-term effects.
LO-3: Stress will be given on the coherent world venture to harness the nuclear fusion energy for production of electricity from terrestrial reactors.
LO-4: Students will also be exposed to cutting edge research problems on industrialisation of nuclear fusion reactors.
Course Content:
Unit I: Nuclear Fission: Theory
Neutron interactions with matter: Cross section, Beam attenuation, Radiative absorption.
Neutron energy distribution: Logarithmic energy decrement, Four-factor formula, Neutron flux spectrum, Fast reactors.
Neutron spatial distribution: spatial diffusion equation, Critical mass of uranium sphere and enrichment.
Time-dependent phenomena and reactor safety: Reactor stability.
The nuclear fuel cycle: Enrichment, Burnup, Interim storage.
Unit II: Nuclear Fission: Applications
Nuclear weapons.
Direct effect of nuclear war.
Long term effect of nuclear war.
Estimation of capacity of nuclear weapons.
Nuclear proliferation: History of nuclear proliferation, Proliferation risks.
Advanced reactor design: Generation III and III+ and IV reactors, Thorium cycle, Breed and burn in place.
Unit III: Nuclear Fusion: Theory
Power and particle balance.
Particle motion: Passing and trapped orbits, Bootstrap current.
Plasmas as fluids: Plasma control.
Macroscopic stability: Ideal MHD modes, Ballooning and kink modes.
Collisions and their effects.
Turbulent transport: Bohm and GyroBohm diffusion, Transport barriers, Global scaling.
Unit IV: Nuclear Fusion: Applications
Nuclear fusion via magnetic confinement.
Mirrors, Helimacs, Q-machines, Stellarators, Tokamaks.
Divertors and scrape-off-layers, Edge localised modes.
Neutron interactive materials.
Blankets, safety, waste and proliferation.
Inertial fusion energy.
Power plant concepts, development path and deployment.
Course Evaluation:
Internal Test 1 (25 Marks)
Internal Test 2 (25 Marks)
Internal Test 3 (25 Marks)
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Textbooks:
Theory of Nuclear Fission, by H J Krappe; K Pomorski; Springer (2012)
Nuclear Reactor Engineering: Reactor Design Basics, by S. Glasstone, A. Sesonske; Springer (2014)
Nuclear Energy: Principles, Practices and Prospects, by D. Bodansky; Springer (2005)
Plasma Physics and Fusion Energy, by Jeffrey P. Freidberg; Cambridge University Press (2010)
Methods in Nonlinear Plasma Theory, by Ronald C Davidson, Elsevier (1972)
This is a 4 credit elective course for MSc second semester in Physics.
Course Objective:
The objective of this course is to familiarise the students with analytical solution techniques of nonlinear system of equations and thereby introduce chaos. Different types of turbulence will be taught including fluid, magneto-hydrodynamic and turbulence where physics of kinetic scales are involved. Stress will be given on numerical algorithms to solve such physics problems.
Learning Outcome:
LO-1: The students will learn stability analysis and bifurcation diagram of different nonlinear maps in both one and two dimensions.
LO-2: The student will be able to demonstrate different types of nonlinear attractors using basic computational schemes.
LO-3: Theory of turbulence phenomena will be taught to understand the turbulence at different length and time scales occurring in nature.
LO-4: Numerical schemes for simulating turbulence phenomena at fluid as well as kinetic scales will be demonstrated.
Course Content:
Unit I: Nonlinear Dynamics
Unit I: Nonlinear Dynamics
Flows on the line
Bifurcations
Flows on the circle
Linear systems
Phase plane
Limit cycles
Bifurcation in two dimensional flows
Lorenz equations
One-dimensional maps
Fractals
Strange attractors
Unit II: Hydrodynamic Turbulence
Symmetries and conservation laws
Probabilistic description of turbulence
Survey of probabilistic tools
Experimental laws of fully developed turbulence
Kolmogorov's theory of 1941
Turbulence phenomenology
Intermittency
Unit III: Hydromagnetic Turbulence
Basic equations
Flux freezing
Applications of flux freezing
Motions of lines of forces in a vacuum
Validity of hydromagnetic equations
An exact solution
Goldreich - Sridhar theory
Cowling's theorem
Mean-field dynamo models
Biermann battery
Fluctuation dynamo
Unit IV: Algorithms for turbulence simulations
Particle-in-Cell Method
Revision of numerical integration
Working knowledge of numerical interpolation
Cloud-in-Cell algorithm
Electromagnetic PIC algorithms
Algorithms for Continuum Vlasov simulation
Piecewise Parabolic Method
Galerkin Methods
Vlasov Maxwell systems
Course Evaluation:
Internal Test 1 (25 Marks)
Internal Test 2 (25 Marks)
Internal Test 3 (25 Marks)
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Textbooks:
Nonlinear Dynamics and Chaos by Steven H Strogatz
Turbulence: The Legacy of A N Kolmogorov by Uriel Frisch
Plasma Physics for Astrophysics by Russel Kulsrud
Plasma Physics via Computer Simulation by C K Birdsall
A Critical Comparison of Eulerian-Grid-Based Vlasov Solvers, by Arber and Vann; Journal of Computational Physics 180, 339–357 (2002)
Course Objective:
The student will get familiarised with Linux operating system, basic data-visualisation softwares, and will learn how to simulate some simple statistical ensembles in computer, for example, Ising models, spatio-temporal dynamics of molecules and fluid systems.
Learning Outcome:
LO-1: The student will learn how to use command-line interface to write codes in open-source platforms.
LO-2: The students will develop their own scripts for verifying statistics of different ensembles using Monte-Carlo method.
LO-3: They will benchmark phase-transition phenomena using Molecular dynamics algorithms for structureless particles.
LO-4: They will be able to compare growth rates of fluid instabilities using different spatiotemporal discretisation techniques.
Course Content:
Unit I: Introduction to computer simulation
Setting up Linux environment, compilers, editors etc
Basic Linux commands
Working knowledge of shell-scripting
Revision of numerical methods
Simple user-graphics interface example of simulation
Unit II: Simulation of Statistical Ensembles
Basic idea of random sampling
Importance sampling
Principle of detailed-balance
Metropolis algorithm
Algorithms for grid generation
Solving 2D Ising model
Monte-Carlo algorithm for statistical physics
Unit III: Algorithms for Ordinary Differential Equations
Introduction to ODE solvers
Error analysis
Comparison between ODE solvers
Symplectic algorithms
Boundary conditions
Minimum image convension and Ewald sum
Thermostats and Barostats
Integrated quantities for statistical analysis
Unit IV: Numerical Solution of Partial Differential Equations
Equations of Fluid Dynamics
Finite Difference algorithm
Finite Element algorithm
Finite Volume algorithm
Spectral algorithms
Flux limiters
Pseudo-Spectral method
Boundary effects
Comparison of accuracy
Course Evaluation:
Internal Test 1 (25 Marks)
Internal Test 2 (25 Marks)
Internal Test 3 (25 Marks)
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Textbooks:
A Guide to Monte Carlo Simulations in Statistical Physics, by David P Landau and Kurt Binder; Cambridge (2009)
The Art of Molecular Dynamics Simulation, by D C Rapaport; Cambridge University Press (2011)
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers, by David A Kopriva; Springer (2009)
Course Objective:
The objective of this course is to teach the students, how to launch jobs in any HPC system, how to write simple codes on single and multi-threaded environments.
Learning Outcome:
LO-1: The student will learn the different memory architectures, thread structures of shared as well as distributed memory computation.
LO-2: Basic debugging and profiling tools and computation in shared and distributed memory platforms will also be taught.
Course Content:
Unit I: Computation on Shared Memory Architecture
Basic concepts of parallel computing
The OpenMP execution model
Compiler directives, clauses, “sentinels” and pragmas
Data sharing of variables (shared, private, default)
Race conditions
Constructs and Regions
Parallel loops, Parallel sections, Load balancing, Scheduling of parallel operations
Collapsing loops, Orphan directives, Environment variables
Hands-on and Optimization
Unit II: Parallel Computing on Distributed Memory
Memory classification, Message passing (MPI) vs shared memory (OpenMP) parallel computing
Rank and size; error checking
MPI datatypes, Blocking communication, deadlocks and Non-blocking communication
Barriers, Broadcasts, Gathering and Scattering data
Constructing MPI datatypes for Fortran types and C structures.
Generating shell-scripts for HPC
Basic HPC commands
Hands-on, Performance optimization tools and techniques
Unit III: Computer Simulation using a single GPU device
Evolution of GPU architectures
Understanding Parallelism with GPU
CUDA Hardware Overview
Accelerators, Kernels Launch parameters
Thread hierarchy, Blocks, Grids, Warps
1D/2D/3D thread mapping
Memory hierarchy, DRAM / global, local / shared, private / local, textures, Constant Memory, Pointers, Parameter Passing, Arrays and dynamic Memory, Multi-dimensional Arrays, Memory Allocation, Memory copying across devices
Unit IV: Parallel Computation with multiple GPUs and FPGA
Programming on Heterogeneous Cluster
Common Problems: CUDA Error Handling, Parallel Programming Issues, Synchronization, Algorithmic Issues, Finding and Avoiding Errors.
Optimizing CUDA Applications: Problem Decomposition, Memory Considerations, Transfers, Thread Usage, Resource Contentions
Debugging GPU Programs: Profiling, Profile tools, Performance aspects
Introduction to FPGA: OpenCL Standard
Kernels
Host Device Interaction
Execution Environment
Memory Model
Basic OpenCL Examples
Course Evaluation:
Internal Test 1 (25 Marks)
Internal Test 2 (25 Marks)
Internal Test 3 (25 Marks)
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Textbooks:
Parallel Programming Patterns: Working with Concurrency in OpenMP, MPI, Java, and OpenCL – by Timothy G. Mattson, Berna Massingill and Beverly Sanders; Pearson Press
An Introduction to Parallel Programming with OpenMP, PThreads and MPI – by Robert Cook; Cook's Books (2011)
The OpenMP Common Core: Making OpenMP Simple Again (Scientific and Engineering Computation), by Timothy G. Mattson, Yun He, Alice E. Koniges; The MIT Press (2019)
Using MPI: Portable Parallel Programming with the Message-Passing Interface, by William Gropp, Ewing Lusk, Anthony Skjellum; The MIT Press (2014)
MPI: The Complete Reference, by Marc Snir, Jack Dongarra, Janusz S. Kowalik, The MIT Press
CUDA Programming: A Developer's Guide to Parallel Computing with GPUs, by Shane Cook; Elsevier Science (2012)
CUDA by Example: An Introduction to General-Purpose GPU Programming, by Edward Kandrot; Pearson (2010)
The CUDA Handbook: A Comprehensive Guide to GPU Programming, by Nicholas Wilt; Pearson (2013)
Reconfigurable Computing: The Theory and Practice of FPGA-Based Computation, by Andre DeHon, Scott Hauck; Morgan Kaufmann Publishers (2007)
Introduction to Reconfigurable Computing: Architectures, Algorithms, and Applications, by Christophe Bobda; Springer (2007)
Course Objective:
The objective of this course is to familiarise the students with basic philosophy of artificial intelligence and machine learning, teach the mathematical tools used for machine learning algorithms, and teach how-to-use open-source machine learning softwares.
Learning Outcome:
LO-1: The students will be able to learn the basic mathematical and computational tools of machine learning.
LO-2: The student will become familiarised with using public data-set, loading them in open-source ML tools categorise the data and test efficiency of their models.
Course Content:
Unit I: Basic concepts of Machine Learning
Philosophy of Artificial Intelligence
Machine Learning and its applications
Familiarization with the numerical tools
Various training models
Linear regression theory
Gradient descent
Polynomial regression
Logistic regression
Image classification
Image processing
Text processing
Introduction to Genetic Programming
Unit II: Hands-on implementation on open-source platforms.
Introduction to Computer Vision
Detecting Features in Images
Convolutions
Pooling
Implementing Convolutional Neural Networks.
Using Public Datasets with TensorFlow Datasets
Recurrent Neural Networks
Course Evaluation:
Internal Test 1 (25 Marks)
Internal Test 2 (25 Marks)
Internal Test 3 (25 Marks)
Final Exam (50 Marks)
Final evaluation sheet will be prepared using the best TWO out of the three Internal Tests (25+25 = 50 Marks) + Final Exam (50 Marks).
Textbooks:
Deep Learning with Python, François Chollet
AI and Machine Learning for Coders by Laurence Moroney
Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow, by Aurélien Géron
Genetic Programming, J R Koza
Fundamentals of Data Science - Theory & Practice, Kalita, Bhattacharyya, Roy; Academic Press, Elsevier, USA
Syllabus for a certificate course on Basic Computer Simulation:
There will be nine papers in this course.
Introduction to computer simulation
Setting up Linux environment, compilers, editors etc
Basic Linux commands
Working knowledge of shell-scripting
Revision of numerical methods
Simple user-graphics interface example of simulation
Monte-Carlo Simulation (Ref: K Binder)
Basic idea of random sampling
Importance sampling
Principle of detailed-balance
Metropolis algorithm
Algorithms for grid generation
Solving 2D Ising model
Monte-Carlo algorithm for statistical physics
Molecular-Dynamics Simulation (Ref: D C Rapaport)
Revision of ODE solvers
Error analysis
Symplectic algorithms
Boundary conditions
Minimum image convension and Ewald sum
Thermostats and Barostats
Integrated quantities for statistical analysis
Particle-in-Cell simulation (Ref: C Birdsall)
Revision of numerical integration
Working knowledge of numerical interpolation
Cloud-in-Cell algorithm
Electromagnetic PIC algorithms
Computational Fluid Dynamics (Ref: D Kopriva)
Equations of Fluid Dynamics
Finite Difference algorithm
Finite Element algorithm
Finite Volume algorithm
Spectral algorithms
Flux limiters
Pseudo-Spectral method
Boundary effects
Comparison of accuracy
Parallel Computing Algorithms (Ref: IBM Redbooks)
Basic concepts of parallel computing
Parallel computing on shared memory architecture
Parallel computing on distributed memory architecture
Heterogeneous parallel computing
Computation on single GPU
Computation on multiple GPUs
Introduction to FPGA
Implementation in HPC systems
Basic idea of High-Performance computing environment
Generating shell-scripts for HPC
Basic HPC commands
Hands-on and trouble-shooting
Performance optimization tools and techniques
Introduction to Machine Learning (Ref: L Moroney)
Philosophy of Artificial Intelligence
Machine Learning and its applications
Familiarization with the numerical tools
Open-source softwares for Machine Learning
Hands-on session
Introduction to Genetic Programming
Introduction to Quantum Computing (Ref: Nielsen and Chuang)
Brief recap of Linear Algebra
Pauli Matrices and Quantum Operators
Quantum Gates
Quantum Circuits
Hands on implementation of Quantum Gates
Basic Quantum Algorithms
Open-source quantum softwares
Quantum Teleportation
Course Outcome:
Course Syllabus:
Unit I:
Review of Lorentz transformations and special theory of relativity.
Tensors and their transformation laws; Christoffel symbol and Riemann tensor; geodesics; parallel transport along open lines and closed curves; general properties of the Riemann tensor.
Unit II:
Equivalence principle and its applications: gravity as a curvature of space-time; geodesics as trajectories under the influence of gravitational field; generalisation to massless particles; gravitational red-shift; motion of a charged particle in curved space-time in the presence of an electric field; Maxwells equation in curved space-time.
Einsteins equation, Lagrangian formulation, Einstein-Hilbert action.
Unit III:
Schwarzschild solution: construction of the metric and its symmetries; motion of a particle in the Schwarzschild metric; Schwarzschild black hole; white holes and Kruskal extension of the Schwarzschild solution: construction of the metric and its symmetries; Motion of a particle in the Schwarzschild metric; precession of the perihelion; bending of light; horizon, its properties and significance.
Unit IV:
Precession of the perihelion; bending of light; radar echo delay.
Linearised theory, gravitational waves, field far from a source, energy in gravitational waves, quadrupole formula
Elementary cosmology: principles of homogeneity and isotropy; Friedman- Robertson-Walker metric; open, closed and flat universes; Friedman equation and stress tensor conservation, equation of state, big bang hypothesis and its implications.
Text book:
1. A Relativist’s toolkit, by Eric Poisson, Cambridge University Press
2. Gravitation and Cosmology, by Steven Weinberg, Wiley
Introduction to General Relativity, by Lewis Ryder, Cambridge University Press
A first course in general relativity, by Bernard F Schutz, Cambridge University Press
General Relativity: An Introduction for Physicists, by M P Hobson, G P Efstathiou, A N Lasenby, Cambridge University Press
Gravitation: Foundations and Frontiers, by T Padmanabhan, Cambridge University Press
Reference book:
1. General Relativity, by Robert Wald, The University of Chicago Press
2. Gravitation, by C W Misner, K S Thorne, J A Wheeler, Princeton University Press
3.Gravity: An introduction to Einstein’s General Relativity, by James B Hartle, Pearson Education
4.Relativity, by Wolfgang Rindler, OUP Oxford
5.Semi-Riemannian Geometry, by Barrett O’Neill, Elsevier
6.Spacetime and Geometry: An introduction to General Relativity, by Sean M Carroll, Cambridge University Press
7.Exploring Black Holes, by Edwin F Taylor, John Archibald Wheeler, Addison Wesley Longman
8.General Relativity, by Norbert Straumann, Springer Berlin Heidelberg
9.The Mathematical Theory of Black Holes, by S Chandrasekhar, Clarendon Press
ICT in Physics
Course Objective:
This course aims to teach Arduino microcontroller and Raspberry Pis through hands on work in the lab. In this course students will learn the basic understanding of the use, terminology and potential of Arduino and Raspberry -pi. The examples taught in this course will be presented from an interdisciplinary approach which merges practices in science and technology.
Learning Outcome:
LO-1: The students will learn the essential skills for creating a simple sensor-driven physical computing system in microcontrollers and microprocessors.
LO-2: The students will reinforce their skills by making a simple interactive project.
Course Content:
Unit I: Arduino
Basic idea of microcontrollers, Basic terminology, Operating Arduino, Loading simple programs, Writing programs to blink the onboard LED, Creating simple temporal patterns, Program notation: variables, functions, control flow and Arduino conventions, delay functions, Analogue and Digital conversions, Data sampling, Using I/O pins.
Unit II: Raspberry - Pi
Microprocessors and its different variations, Introduction to Raspberry Pi, Understanding of SoC architecture and SoCs used in Raspberry Pi, Pin description, On board components, Introduction to Raspbian Operating system, Sensor interfaces, Interfacing using C, IoT applications based on Raspberry, GPIO Control, Data communication using on-board module.
References:
1. Basics of Arduino: https://www.arduino.cc/
2. Raspberry Pi Cookbook by Simon Monk.
3. The official raspberry Pi Projects Book, https://www.raspberrypi.org/magpi-issues/Projects_Book_v1.pdf
Indian Contributions in Physics
Course Objective:
Students will learn about the contribution and contributors from India to Physics and allied disciplines.
Course Outcome:
CO-1: To understand the the contributions to physics from India in ancient times.
CO-2: Traditional methods that are still in practice for different purposes.
CO-3: Contribution of several eminent Indian scientists in the last century.
CO-4: Ongoing research works and international collaborations in different fields of Physics from India.
Course Content:
Unit-I: Ancient India:
Mathematics: Discovery of Zero, Pi, Roots of quadratic equation etc.
Astronomy: Works of Aryabhatta, Barahmihir, Brahmagupta, Bhaskaracharya.
Medicine: Understanding the human body to develop instruments for surgery.
Chemistry: Metallurgy, medicine preparation, herbal medicine, Ayurveda.
Musical instruments in ancient India.
Architectures and town-planning of Indus-valley civilisation.
Unit-II: Traditional Knowledge:
Traditional Indian metal casting: Lost-Wax method (e.g. Dhokra Casting),
Iron smelting by Agariyas, Ashta-dhatu work, Brass-mirror work.
Natya-shastra’s classification of musical instruments, Jewellery making (Jaipur gold plating, diamond cutting).
Running water supply in Vijaynagar and Golconda (Hyderabad) townships.
Astronomical observatories: Works of Sawai Jai Singh
Unit-III: Modern Contribution:
Works of Jagadish Chandra Bose, Prafulla Chandra Roy, Meghnad Saha, Satyendra Nath Bose, C V Raman, S Chandrasekhar, Homi Jehangir Bhabha, Vikram Sarabhai, APJ Abdul Kalam, Amal Kumar Raychaudhuri.
Unit-IV: Ongoing Contribution:
Gravitational Wave Astronomy (LIGO), International Thermonuclear Experimental Reactor (ITER), Liquid Crystals and other soft matter, Quantum Computation.
References:
Indian Contribution to Science, Compiled by Vijnana Bharati
A History of Hindu Chemistry, by Prafulla Chandra Roy
The Scientific Edge - The Indian Scientist from Vedic to Modern Times, by Jayant Vishnu Narlikar, Penguin Books
Syllabus
References:
https://thebulletin.org/2018/09/how-to-make-progress-with-north-korea-now/
https://thebulletin.org/2018/04/iran-after-sunset/
https://www.nj.com/opinion/2017/04/princeton_scholar_interim_nuclear_deal_in_n_korea.html
https://www.nature.com/articles/ncomms12890
https://thebulletin.org/2015/02/negotiating-with-iran-breakout-and-sneakout/
https://www.nature.com/articles/nature13457
https://thebulletin.org/2018/04/why-fusion-2/
https://ideas.repec.org/a/gam/jsusta/v8y2016i5p421-d69153.html
https://www.sciencedirect.com/science/article/abs/pii/S0140988315002224
Physics of Defense Studies
Unit 1: Physics of Navigation and Communication Systems
Role of Physics in defense technology, Introduction on navigation and guidance systems, Understanding the Global Positioning System (GPS), GNSS (Global Navigation Satellite System), terrain based navigation, Mathematical modelling, Advanced capabilities of MATLAB & Simulink.
Elements of a communications system and their relationship to system performance, Free space optical communication, Fiber optics communication, Wireless/cellular communications. Analog and digital communications systems. Introduction to RADAR, Radar parameters/definitions, radar equations. Radar cross section (RCS) & Theory of detection.
Unit 2: Laser in Defense Applications
Laser beam characteristics, Effect of laser on metals & composite materials, Tools to analyze and predict Laser System performance under different conditions like
land, sea air, etc. Laser Communication: navigation, control, guidance. Types of military Lasers, Chemical Lasers, Solid State Lasers, Gas Lasers, Advantages of Laser weapons, Future trends.
Unit 3: Physics of Aerospace and marine technology
Classification & mode of operation of various propulsion systems, Computational fluid dynamics (flow modelling strategies, physical modelling, finite difference equations, etc.)
Basics of Missile Physics, Classification of Missiles, Missile Aerodynamic Configurations, Effect of Curvature of Earth, Rotation of Earth, Variation of Gravity on Missile Trajectory.
Sea Water as Physical medium, thermodynamics of seawater, interaction of light and other em-waves with seawater, SONAR Technology, Physics of Submarine Technology
Unit 4: Plasma Physics in national security
Fission and Fusion reactors, Reactor safety, Chernobyl disaster, Fukushima disaster, Nuclear weapons, Effect of nuclear weapons: Blast, Direct nuclear radiation, Thermal radiation, Fires, Electromagnetic pulse, Radioactive fallout, Demo numerical studies of such weapons, The dynamics of nuclear arms race, International coalition for nuclear threat reduction, Fusion reactors for future space propulsion, Plasma antenna, Plasma thrusters for satellite controls.
.
References / Suggested Books:
1. “Satellite communication”, by T. Pratt, C. W. Bostian, J. E.Allnut. Publisher: John Willey and sons
2. “Satellite Communications Systems: systems, techniques and technology”, by G. Maral, M.
Bousquet, Z. Sun. Publisher:John Willy and sons
3. “Digital Communications: Fundamentals and Applications”, B. Sklar . Prentice-Hall, Inc.
4. “Introduction to Radar Systems”,by M.I. Skolnik. Publisher: Tata Mcgraw hill edition, 2001.
5. “Radar Systems Analysis and Design using MATLAB”,by B.R.Mahafza. Publisher CRC Press, 2013.
5. “High Power Laser-Matter Interaction”, by Mulser, Peter, Bauer, Dieter. Publisher : Springer.
6. “An Introduction to Computational Fluid Dynamics: The Finite Volume Method” by H. Versteeg. Publisher : Pearson; 2nd edition.
7. “Modeling and Simulation of Systems Using MATLAB and Simulink” by Deven-dra K. Chaturvedi, Publisher: CRC Press, 2010
8. “Deadly Arsenals: Nuclear, Biological, and Chemical Threats”, J. Cir- incione, J. B. Wolfsthal, and M. Rajkumar, 2nd ed.
9. “Atomic Audit: The Costs and Consequences of U.S. Nuclear Weapons since 1940”, edited by S. I. Schwartz Brookings Institution, Washington, DC, 1998.
10. “Arms Control: The New Guide to Negotiations and Agreements”, J. Goldblat Sage, London, 2002.
11. “Nuclear Energy”, D. Bodansky, 2nd ed. Springer/AIP, New York, 2004.
12. “Managing Nuclear Operations”, edited by A. B. Carter, J. D. Stein- bruner, and C. A. Zraket Brookings Institution, Washington, DC, 1987.
13. “Plasma Antennas”, Theodore Anderson, Artech House Antennas and Propagation Library, 2011
14. “An Introduction to Plasma Physics and its Space Applications”, IOP Publishing, 2020