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Algebraic Topology 01

Posted on January 10, 2024

Introduction Distinguish between 2-sphere \(S^2\) and 2-torus \(S^1 \times S^1\). Homotopy rubber band on \(S^2\) contracts to a point. For continuous maps \(f, g\), they are homotpic \(f \simeq g\) if there exists a homotopy between them. Check equivalnce relation. Identify homeomorphically \(S^n\) without North Pole with \(\mathbb{R}^n\), via Stereographic... [Read More]
Tags: Convex Quotient Space Invariant Singular Category Theory Boundary Cycle Chain Complex Prism Simplex Latex Commutative Diagrams Homology Homotopy Algebra Topology MATH 592 Igor Kriz

Tomita-Takesaki Theory 02

Posted on June 2, 2021

TOMITA-TAKESAKI THEORY [Read More]
Tags: Minoru Tomita Osaka University Japan Masamichi Takesaki Tohoku University UCLA Theory 2016 Lin Zhang Hangzhou Dianzi University Junde We Zhejiang University Quantum Information Theory 2020 Thomas Faulkner UIUC Recovery 2018 Edward Witten IAS Princeton Entanglement Bisognano Wichman Unruuh Toshihiko Masuda Information Quantum Field Klein Gordon Hawking Penrose von Neumann Algebra Hilbert Epstein Glaser Jaffe Reeh Schleider Haag Hugenoltz Winnik Jones Kawahigashi Introduction

$$\circ$$ Classification of Physics Languages

Posted on June 9, 2020

Classifying Physics Languages [Read More]
Tags: Classification Conservative Cycle Conserved Nature Natural Intensive Extensive Language Structure Complementary Pairs Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

$$\circ$$ Classification of Languages

Posted on June 9, 2020

Abstract [Read More]
Tags: Classification Conservative Cycle Conserved Nature Natural Intensive Extensive Language Structure Complementary Pairs Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

$$\circ$$ Recycle

Posted on June 7, 2020

Recycle [Read More]
Tags: Recycle Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation A Law Fundamental Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

$$\circ$$ Let Thermodynamics Identify Energy Cycles to be Conserved

Posted on June 4, 2020

Identity [Read More]
Tags: Thermodynamics Conservative Cycle Conserved Nature Natural Intensive Extensive Language Structure Complementary Pairs Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cyclone Nisarga

Posted on June 3, 2020

\(\circ\) Nisarga [Read More]
Tags: Cyclone Nisarga Nature Rain Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cycle $$\circ$$ Communication

Posted on June 3, 2020

Communication [Read More]
Tags: Nature Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Identify that India Identifies

Posted on June 3, 2020

Identify that India Identifies [Read More]
Tags: Nature Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Nature Rain I Rain

Posted on June 2, 2020

Raining Naturally is part of Water Cycle [Read More]
Tags: Nature Rain Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cycle (Languages)

Posted on June 1, 2020

Base 0 Translation [Read More]
Tags: Nature Bengali Rabindranath Tagore Kannada Girish Karnad Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cycle (Karma)

Posted on June 1, 2020

Karma is Cycle [Read More]
Tags: Karma Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cycle (Chakraview)

Posted on June 1, 2020

Ball (Chakraview) [Read More]
Tags: Chakraview Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cycle (Reciprocity)

Posted on June 1, 2020

Periodicity in Cycles [Read More]
Tags: Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cycle (Symmetry Space-Time)

Posted on June 1, 2020

Space [Read More]
Tags: Light Identity Renaming Basis Change Cleaning Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Light is Identity

Posted on May 31, 2020

Let there be Light [Read More]
Tags: Light Identity Translation Renaming Basis Change Cleaning Farming Trees Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cyclic Translation (Change of Basis is Renaming Identity)

Posted on May 30, 2020

Identities: Basis in Language [Read More]
Tags: Identity Renaming Basis Change Cleaning Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Symmetry (Nodal Geometry)

Posted on May 29, 2020

Symmetry [Read More]
Tags: Node Geometry Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Cleaning is Cyclic Balance

Posted on May 28, 2020

Cleaning [Read More]
Tags: Cleaning Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Art is Mathematics is Art

Posted on May 25, 2020

Identifying Art and Mathematics [Read More]
Tags: Art Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Identification Compactifies

Posted on May 23, 2020

Identification Compresses [Read More]
Tags: Identity Compact Identification Compression Reflection Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Nature Algorithm

Posted on May 23, 2020

Algorithms and Nature Language [Read More]
Tags: Nature Algorithm Identity Reflection Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Reflections to Symmetry as Identity

Posted on May 23, 2020

Identity [Read More]
Tags: Identity Reflection Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Calculus Group Language

Posted on May 22, 2020

Abstract [Read More]
Tags: Group Cyclic Simple Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Communication Language Program

Posted on May 21, 2020

Terminology: Communication needs meeting of Languages. Communication is a base for Languages. Communication as a base itself forms a Language. Thus, Communication is Language. Thus the program may be renamed as LangLang Program. I am interested in a broader category of Languages than those currently seen as Language. I would... [Read More]
Tags: Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

$$ E = m c^2$$

Posted on May 21, 2020

Composing Energy-mass and Space-time gives Einstein’s Identity [Read More]
Tags: Einstein Identity Energy-mass Space-time Compose Conservation Law Fundamental Mass Balance Degree Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Equilibrium Thermodynamics Identifies Intensive-Extensive Duality

Posted on May 10, 2020

Abstract [Read More]
Tags: Intensive Extensive Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Duality is the Fundamental Law

Posted on May 10, 2020

(This is incomplete and currently being updated regularly, please be patient for the final version) [Read More]
Tags: Duality Composition Fundamental Laws Mass Balance Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Language Observes Empirically the Empirical Observations on Language

Posted on May 5, 2020

Language Observes Empirically the Empirical Observations on Language [Read More]
Tags: Language Structure Duality Knowledge Representation Rigid Entropy Fluid Temperature Differentiation Condensation Integration Evaporation Phase Degrees of Freedom Constraints Symmetry Reflection Approximate Exact Analysis Time Language of Languages Thermodynamics Calculus Abstract Record Theory Practice Communication Misrepresentation Compression Interpretation

Equipment and Process Design Lecture 15 and Quiz 3

Posted on February 20, 2020

\(6^{th}\) Lecture on Superheated Steam Gasification Find the lecture notes linked: Lecture notes 15 Compressor for instrument air. Very accurate instrument to sense values. Sense the signal and shut down some process. If the instrument malfunctions, there is a mess in maintenance. Build safety systems, instrumentation, valve controls, processing, all... [Read More]
Tags: Supreheated Steam Gasification Waste Energy Environment Equipment and Process Design MM 426 Prof Gaurishanker

Student Seminar in Mathematics

Posted on February 10, 2020

Rest With tests, assignments, checking duties for TAs and a heavy workshop: Global Homotopy Theory going on in the Math Deprartment, we shall not burden the students with more. Hence student seminars will take place only after the midterm exams end.
Tags: Rest Student Seminar Mathematics

Corrosion Quiz 1

Posted on February 10, 2020

Quiz 1 Find the Corrosion Quiz 1 linked: Quiz 1. Following four questions were asked: all based on the \(\textbf{Nernst Equation}\). Find the Cell Potential of a concentration cell: Metal in lower concentration of ions will be more readily oxidized hence acts as anode. Overall Spontaneous reaction is just metal... [Read More]
Tags: Quiz Nernst Equation Cell Pourbaix Diagram Thermodynamics Electrochemistry Reaction Corrosion MM 454 Vijayshankar Dandapani Quiz 1

Geometry and Physics

Posted on February 8, 2020

Books on Geometry and Physics Interplay of Geometry and Physics has always been a fascinating area of study, right from optics to classical mechanics and general relativity. Partial Differential Equations that form the language in which Laws of Physics are written are hence naturally intertwined with geometry. Here are listed... [Read More]
Tags: Geometry Physics

Analytical and Geometric Dynamics Week 3 Review

Posted on January 31, 2020

Tangent Spaces Differentiable Manifolds can be highly nonlinear, unlike the usual Euclidean Spaces. To handle such objects, we import notions of calculus from the euclidean spaces that we are used to. Just like in multivariable calculus, we approximate nonlinear functions by its linearization: its derivative at each point, this naturally... [Read More]
Tags: Tangent Space Differential Geometry Calculus Manifolds Analytical and Geomertic Dynamics SC 618 Sukumar Srikant

Intro to Machine Learning Lecture 5

Posted on January 29, 2020

\(L_2\) Rigression/ Ridge Regression Find the \(5^{th}\) lecture notes linked: CS 419 Lecture Notes 5 Continuing on Linear Regression, we examine the problem of Model Training. Using regularization helps to counter overfitting. [Read More]
Tags: Machine Learning Model Training Generalization $$L_1$$ Gradient Descent CS 419 Error Regularization Ridge Rigression Probability Linear Regression Complexity Overfitting Underfitting Bias Variance Optimization Preethi Jyothi Introduction

Heat Treatment 1

Posted on January 29, 2020

Find the report linked: Report 1. (Thanks to Shreyans Bhansali). Note that the Professors and experiments for the lab are slightly different so use this as a guideline and make sure you don’t blindly copy. Viva What is a TTT diagram? Draw and give examples. What is the phase on... [Read More]
Tags: Heat Treatment

Introduction to Algebraic Geometry by Prof. Dipendra Prasad Lecture 4

Guest Post by Kirtan Vora

Posted on January 27, 2020

Course Overview Prof. Dipendra Prasad is taking this course at an advanced graduate level. He taught Differential Topology last sem which followed Victor Guilleman and Pollack’s book. That background may help but is not necessary for this course. References are standard- David Mumford’s The Red Book of Varieties and Schemes... [Read More]
Tags: Algebraic Geometry Introduction MA 510 Algebra Dipendra Prasad

Intro to Machine Learning Lecture 4

Posted on January 24, 2020

Prediction Errors Find the \(4^{th}\) lecture notes linked: CS 419 M IITB lecture notes 1-4 (Google Drive link), CS 419 M IITB lecture notes 1-4 (Github Link) Recall of Probabilistic interpretation of Linear Regression. Complexity of model and \(\textbf{bias/variance}\) tradeoff. Overfitting and underfitting. [Read More]
Tags: Machine Learning CS 419 Error Prediction Introduction Probability Linear Regression Complexity Overfitting Underfitting Bias Variance Optimization

Fight Club Lecture 6

Posted on January 23, 2020

Functors Find the \(6^{th}\) lecture notes linked: Functors Lecture Notes 6 Functors are morphisms from one category to another that obey nice composition properties. Forgetful functor destroys structure associated with a category. There’s difference between imposing structure and imposing conditions. Structure is specified (constructive). Properties are answers to yes/no questions.... [Read More]
Tags: Category Theory Functors Fight Club Categories 2-Categories Higher Categories Kan Adjoint Limits Products objects morphisms MacLane Linear Algebra Algebra

Algebraic Topology Lecture 4

Posted on January 23, 2020

Find the \(4^{th}\) lecture notes linked: Algebraic Topology MA 842 Lecture 2 Using Snake Lemma or otherwise, prove theorem on long exact sequences based on short exact sequences, apply it to the specific case to get the Mayer-Vietoris Sequence. \(\textbf{Mayer-Vietoris Sequence}\) provides a very useful tool to practically compute homology... [Read More]

Optimization Lecture 4

Posted on January 21, 2020

Optimization on Open Sets Till now, we had only talked about optimization on closed sets (remember, Bolzano-Weierstrass assumes the feasible region to be closed and bounded). Now, we address optimization problem on open sets. Find the \(4^{th}\) lecture notes linked: SC 607 Lecture Notes 4 Taylor’s Theorem was stated and... [Read More]

Optimization Lecture 3

Posted on January 17, 2020

Optimization with Constraints Find the \(3^{3d}\) lecture notes linked: SC 607 IITB Lecture Notes 3 (Google Drive link), Lecture Notes 3 (Github link). Find the entire lecture notes linked: SC 607 IITB Lecture Notes 1-3 (Google Drive link), Lecture Notes 1-3 (Github link) Interior: \(C\) is any set then, \(\dot{C}... [Read More]
Tags: Weierstrass theorem Open Closed Unbounded Discontinuous Compact Interior Closure Boundary Optimization with constraints constraints inf sup Minimum Convergence Set Heine-Borel theorem Continuous Function equality constraints Inequality constraints Real Analysis Sequence Subsequence Calculus MA 105 Optimization SC 607 Ankur Kulkarni

Functional Analysis Lecture 2

Posted on January 17, 2020

Hilbert Spaces, Riesz Representation and Radon-Nikodym Theorem In the second Lecture of Functional Analysis MA 824, IITB, Prof. Mukherjee continued with definition of Hilbert Spaces, some properties, Riesz Representation Theorem and its application to prove Radon-Nikodym Theorem for finite measures. It was left as an exercise to extend the proof... [Read More]
Tags: Hilbert Space Riesz Representation Radon Nikodym Functional Analysis 2 Mayukh Mukherjee

Fight Club lecture 3

Posted on January 16, 2020

Tits Monoid [Read More]
Tags: Number theory Zeta function Mobius function Riemann Zeta function Incidence Algebras Posets Dirichlet Series exponential logarithm Monoid Tits Monoid Birkhoff Monoid Faces Cones Flats Product Tits product Support Map Arrangements Essentialization gisomorphism cisomorphism classification Isomorphism Category Theory Fight Club Categories objects morphisms MacLane structure Hopf Algebras quantum groups Linear Algebra Algebra 3

Corrosion by Vijayshankar Dandapani

Posted on January 13, 2020

Repositories Regular updates maybe found compiled on the linked page: Som Phene Log Tag: MM 454 and its relevant material on Som Phene Log Tag: Corrosion. The corresponding Github Repository for all the documents may be found linked in: Corrosion Github Repository [Read More]
Tags: References Introduction Faraday Objectives Course Complexity Interdisciplinary Thermodynamics Cycles Electrochemistry Reaction Corrosion MM 454 Vijayshankar Dandapani

Optimization by Ankur Kulkarni

Posted on January 10, 2020

Optimization by Prof. Ankur Kulkarni, SC 607 IITB (2020) Regular updates for this course can be found on the linked page: Som Phene Log Tag: SC 607 and relevant material on Som Phene Log Tag: Optimization. This log documents my work for the above course and is not checked to... [Read More]
Tags: Introduction Limit Convex Symmetry Geometry Metric space Convergence Existence Uniqueness Isoperimetric Real Analysis Sequence Optimization SC 607 Ankur Kulkarni

Complex Analysis

Posted on January 10, 2020

Complex Analysis (MA 412) by Prof. Gopal Krishna Srinivasan -1st class Prerequisites: Real Analysis, Fields. Set of Complex Numbers as a field. Field operations are compatible with metric space properties to make them continuous. Complex numbers as a field cannot be ordered. \(\mathbb{C}\) is a field which fails to be... [Read More]
Tags: Complex Analysis MA 412 Gopal Krishna Srinivasan

On Aesthetics and Science

Posted on October 19, 2018

Discussion with a friend in response to the latter’s piece “On Intellect and Emotion in Art”, engendered the corresponding dual in science. Here’s a few papers, articles closely related to how aesthetics matter in Science as well. [Read More]
Tags: Aesthetics Science

Computational Materials Science Departments Review

Posted on June 7, 2018

Some Departments and groups with respect to the field of Computational Materials Science are reviewed. These are purely based on my limited personal experiences and are not at all representative. I’d suggest treating these as just pointers which may be used for further exploration. All of these places are excellent... [Read More]
Tags: Computation Materials Science Physics Natural Density Functional Theory Ab-initio DFT Groups Departments Schools People Review List

Actors and directors List

Posted on March 15, 2018

Actors: Marlon Brando, Saoirse Ronan, Michael Fasbender, Joaquin Phoenix, Kate Winslet, Danielle day Lewis, Christian Bale, Leonardo di Caprio, Casey Affleck, Sean Penn, Jake Gyllenhaal, Phillip Seymour Hoffman, Jim Carey, Johnny Depp Directors: Andrei Tarkovsky, Ingmar Bergman, Robert Bresson, Alejandro G Innaritu, Denis Villeneuve, Darren Aronofsky, David Fincher, Terrence Mallick... [Read More]
Tags: Actors Directors List Movies Films

External as mirror to see Internal

Posted on December 2, 2017

I spent all the years of my life searching for meaning and I don’t find it anywhere. I never met a person that had an answer. How foolish all of them seemed to me- Ignorant, full of vanity, fooling themselves to being purposeful, but beneath their superficial faces I knew... [Read More]
Tags: External Mirror Internal

End

Posted on December 1, 2017

Why are we afraid of death? Why do we have to rationalize it? Why do we have this bias? All we do in this life trying to collect things, gain things, accumulate. The Self keeps growing and we call that achievement. It’s a really simple game. Starting with nature, everything... [Read More]
Tags: The End

Quantum espresso PWscf

Posted on June 30, 2017

Anshuman Kumar (then an EP alumnus, PhD student, now Professor at IITB) coming to the rescue for me again: “I am providing two approaches, which have generally been mentioned in the other answers. The only place where my answer differs is that it is specific to PWscf. Two methods: [Read More]
Tags: Quantum Espresso Resources Input

Plasmonics theory and computation

Posted on May 4, 2017

Stefan Maier’s book on Plasmonics. Learn Lumerical FDTD. Simulate transmission for one dimensional array of microholes, keeping finer mesh near the metal. Study Condensed Matter Physics from Ashcroft and Mermin. Study Electromagnetism from Griffiths and Optics from Born and Wolf- Covered History, chap1, overview. Propagation, Diffraction, interference theories. Calculus of... [Read More]
Tags: Plasmonics FDTD Lumerical Simulate Diffraction Electromagnetism Euler Calculus Variation Integral Path Optics

Mud

Posted on June 15, 2016

Mud Watched Mud. It was good to see Tye Sheridan in another important role, who formerly played as one of the kids in Terrence Malick’s Tree of Life. Matthew McConaughey and Reese Witherspoon gave amazing performances. This performance of McConaughey is what landed him the role in Nolan’s Interstellar. The... [Read More]
Tags: Films Movies Terrence Malick Christopher Nolan