Principles of Continuum Mechanics (2024)

Convener(s)
Name: Prof. Neetu Gupta Dr. Suraj Goyal
Mailing Address: Chairperson & Dean Sciences Department of Mathematics
J.C. Bose University of Science & Technology, YMCA Faridabad-1210 06, Haryana		 Assistant Professor
Department of Mathematics
J.C. Bose University of Science & Technology, YMCA Faridabad-1210 06, Haryana
Email:  neetuymca [at] yahoo [dot] co [dot] in  surajgoyal87 [at] jcboseust [dot] ac [dot] in

In this school, we will learn the basic principles of continuum mechanics and their use to study propagation of time harmonic waves in simple media. In particular, we will learn about Eulerian and Lagrangian coordinate systems, stress-strain tensors and their properties, governing differential equations of continuum mechanics, conservation laws for the mass, linear momentum, angular momentum, energy; Basic concepts of theory of elasticity: Hooke’s law and its generalization, symmetry of stress tensor; Waves in uniform elastic medium, Helmholtz decomposition of vector, body waves, reflections/ refraction phenomena; Surface waves - Rayleigh, Love and stoneley; Non-Local Elasticity.
Computational Fluid Dynamics: Need and Applications; concept of finite difference, finite difference discretization, convergence, consistency, and stability; second order wave equation using explicit method and its von-Neumann stability; vorticity – stream function formulation; flow over a backward-facing step problem. Convection problems in fluid Dynamics, Hydrodynamics of Rayleigh-Benard convection and Couette-Taylor problem, Numerical methods for hydrodynamic and the flow problems.

After learning these topics one can pursue research in solid and fluid mechanics. Through these topics we will discuss some current problems to have an idea of ongoing research in these areas. We will also learn how to use software like MATLAB for computations and graphical interpretation of results.
Our motivation is to promote applied mathematics in our region and improve the quality of teaching which is essential for motivating participants for research in mathematics. We hope that after attending this school, our participants will be able to motivate and encourage their students to study mathematics at a higher level.

Dates: 

Monday, June 3, 2024 - 19:00 to Saturday, June 15, 2024 - 19:00

Venue: 

Venue Address: 

 

 

Department of Mathematics,J.C.Bose University of Science & Technology, YMCA, Faridabad-121006, Haryana.

 

 

Venue State: 

Venue City: 

PIN: 

121006

Syllabus: 

  Detailed Syllabus:

Name of the Speaker

Number

of Lectures

Syllabus

Prof. S. K. Tomar

6

Elasticity and Wave Propagation

Basic concepts of theory of elasticity: stress, strain and their properties, Hooke’s law and its generalization, symmetry of stress tensor, equation of equilibrium and motion, compatibility conditions, Finite deformation; Waves in uniform elastic medium, Helmholtz decomposition of vector, body waves,boundary conditions, reflections/ refraction phenomena; Surface waves - Rayleigh, Love and stoneley.

Prof. Peeyush Chandra

6

Fundamental Principles
Eulerian and Lagrangian coordinate systems, stress-strain tensors and their properties, Polar Decomposition theorem, governing differential equations of continuum mechanics, conservation laws for the mass, linear momentum, angular momentum, energy, first and second laws of thermodynamics for a continuum, equations of state, boundary conditions, fundamental restrictions on constitutive laws.

Prof. Gopal Chandra Shit

6

Computational Fluid Dynamics (CFD)

 Need of CFD as tool, role in R&D, CFD Applications.

 Concept of Finite Difference, Finite difference discretization, Convergence, Consistency, and Stability, Boundary conditions, CFD model formulation, Tridiagonal linear system of equations solver (TDMA/ Thomas Algorithm).

Two time-level explicit scheme (Schmidt formula), Crank- Nicolson Implicit scheme and their von-Neumann stability analysis. Solution of one-dimensional wave equation using the Lax scheme, Lax-Wendroff Scheme and their von-Neumann stability analysis, CFL number.
Second order wave equation using explicit method and its von- Neumann stability. Five point formula, Point-Gauss-Seidel and Line Gauss-Seidel method, Point and line Successive over/under relaxation method for Laplace and Poisson equations. Vorticity – Stream function formulation.
MATALB program for Direct Numerical Solution of lid-driven cavity problem, Flow over a Backward-facing step problem. Graphical representation and validation of computational results. Basic concepts of the finite element methods for the solution of fluid dynamics problems.

Dr S. C.
Martha

  6

Problems of Water Wave Mechanics
Sturm-Liouville problem, Boundary value problem for two- dimensional periodic water wave, eigenfunction solutions of linearized water wave boundary value problem, approximate solution of dispersion equation by Newton-Raphson method with MATLAB program.
Least square method and its applications to water wave problems, energy balance equation using Green’s identity. Boundary element method (BEM), numerical implementation through MATLAB code, BEM applications to water wave problems.
Fredholm integral equations of second kind and its numerical solution and MATLAB applications, integral equation method for solving a problem on wave mechanics.
Dr Jitender Singh  6 Some Hydrodynamical Problems
Hydrodynamics of Rayleigh-Benard convection and Couette- Taylor problem, the mathematics of Boundary layer flows such as the stretching sheet problem.
Numerical methods for hydrodynamic and the flow problems: Shooting method, the method of matrix exponentials, homotopy perturbation technique
Dr Santanu Manna  6 Some Non-Elasticity Problems
Mohr’s circle diagram: principal stress & strain, Equations of deformation and equilibrium, combability etc.
Concept of nonlocal elasticity: dynamic equation of motion, waves of dilatation and distortion, body wave & surface wave, concept of damping and meta-surface.

Asymptotic analysis for elasticity problem, explicit models for surface waves, Bleustein-Gulyaev surface waves, comparison of asymptotic approach and analytical approach, hyperbolic- elliptic model of surface wave field.

Speakers:

  1. Prof. S. K. Tomar, Professor, Department of Mathematics, Panjab University, Chandigarh (Presently: Vice Chancellor, J. C. Bose University of Science and Technology, YMCA, Faridabad, Haryana).
  2. Prof. Peeyush Chandra (Rtd), Department of Mathematics, IIT Kanpur.
  3. Prof. Gopal Chandra Shit, Professor, Department of Mathematics, Jadavpur University, Kolkata.
  4. Dr. S. C. Martha, Associate Professor, Department of Mathematics, IIT Ropar.
  5. Dr. Jitender Singh, Associate Professor, Department of Mathematics, Guru Nanak Dev University, Amritsar.
  6. Dr. Santanu Manna, Associate Professor, Department of Mathematics, IIT Indore

Tutors:

  1. Dr. Dilbag Singh, Assistant Professor, Department of Mathematics, Panjab University, Chandigarh.
  2. Dr. Jai Bhagwan, Assistant Professor, Department of Mathematics, Government College, Panipat, Haryana.
  3. Dr. Manjeet Kumar, Assistant Professor, Department of Mathematics, Dr B R Ambedkar Government College, Dabwali, Haryana.
  4. Dr. Suraj Kumar, Assistant Professor, Department of Mathematics, Punjab Engineering College (Deemed to be University), Chandigarh.

 

 

Time Table: 

 

Day

Date

(June 2024)

L-1
(9:00-10:30)

10:30-11:00

L-2
(11:00-12:30)

12:30-2:00

L-3
(2:00-3:30)

3:30-4:00

Discussion/

Tutorial
(4:00-5:00)

Mon

3rd

SKT

 

 

 

 

 

Tea/ Snacks

PC

 

 

 

 

 

Lunch

PC

 

 

 

 

 

Tea/ Snacks

SKT,DS, SK

Tue

4th

SKT

PC

PC

PC, DS, SK

Wed

5th

SKT

PC

PC

PC, DS, SK

Thu

6th

SKT

SCM

SCM

SKT,DS, SK

Fri

7th

SKT

SCM

SCM

SCM,DS, SK

Sat

8th

SKT

SCM

SCM

SCM,DS,SK

Mon

10th

JS

GCS

GCS

JS, JB, MK

Tue

11th

JS

GCS

GCS

GCS,JB, MK

Wed

12th

JS

GCS

GCS

GCS,JB, MK

Thu

13th

JS

SM

SM

JS, JB, MK

Fri

14th

JS

SM

SM

SM, JB, MK

Sat

15th

JS

SM

SM

JS, JB, MK

  *Holiday on Sunday (June 09, 2024)

  • SKT-Prof. S. K. Tomar
  • PC-Prof. Peeyush Chandra
  • GCS-Prof. Gopal Chandra Shit
  • SCM-Dr S. C. Martha
  • JS-Dr Jitender Singh
  • SM-Dr Santanu Manna
  • DS- Dr Dilbag Singh
  • SK- Dr Suraj Kumar
  • JB- Dr Jai Bhagwan
  • MK- Dr Manjeet Kumar

 

Selected Applicants: 

 

  1. Selected candidates must confirm their participation by reverting to the email sent by the organisers (surajgoyal87@jcboseust.ac.in) on or before 13th May 2024, failing which the wait listed candidates will be given the opportunity.
  2. No accommodation will be provided to the local participants.
Sr.n SID Full Name Gender Affiliation Position in College/ University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
  Selected candidates(Faculty Applicants)    
1 55164 Ms. Nisha Singh Female JC Bose University of Science and technology,YMCA Assistant professor Panjab University 2010  
2 55283 Dr. Sangeeta Kumari Female Department of Mathematics, Chandigarh University, Gharuan Associate Professor Maharshi Dayanad University, Rohtak 2004 15/09/2014
3 55317 Dr. Bhimanand Pandurang Gajbhare Male Jawahar Education Society's Vaidyanath College, Parli-Vaijnath, Dist. Beed (M.S.) PIN 431515 Asso. Prof. Swami Ramanand Teerth Marathwada University, Nanded 2005 11/01/2022
4 55320 Ms. Manisha . Female Panjab University, Chandigarh Assistant professor M.Sc. (Honors) in Mathematics 2018  
5 55407 Mrs Umadevi Periyasamy Female Dr. NGP Arts and Science College Professor MSc Mathematics 2007 18/09/2017
6 55434 Mr. Priteshkumar Chensing Pavar Male Navjivan Science College Dahod Assistant Professor The M.S. University, Baroda 2010  
7 55563 Dr. Sandeep Singh Male Guru Jambheshwar University of Science & Technology Assistant Professor Guru Jambheshwar University of Science & Technology, Hisar 2005 22/11/2017
8 55623 Dr. Dr. Meenu Chawla Chawla Female J.C. Bose University of Science and Technology, YMCA Assistant Prof. M.Sc. 2007 30/09/2016
9 56082 Dr. Davinder Kumar Male Chandigarh University Assistant Professor Panjab University, Chandigarh 2016 16/09/2022
10 56596 Dr Kumari Shalini Female PGDAV COLLEGE,University of Delhi Assistant Professor TMBU BHAGALPUR,BIHAR 2002 30/08/2013
11 56674 Ms. Jyoti Rathee Female J.C. Bose University of Science and Technology, YMCA Faridabad Assistant Professor MAHARSHI DAYANAND UNIVERSITY, ROHTAK 2020  
12 56701 Dr Vanita Garg Female Amity University Noida Assistant Professor Punjabi University Patiala 2011 24/09/2017
13 56728 Dr. Shruti Tiwari Female J.C. Bose University of Science and Technology, YMCA Faridabad Guest Faculty M.Sc 2011 28/10/2020
14 56777 Dr Monika Solkhe Female PGDAV Assistant Professor Gju 2007 11/10/2000
15 56888 Dr. Shashi Sharma Female J.C. Bose University of Science and Technology, YMCA Assistant Professor Jamia Millia Islamia, New Delhi 2005 02/11/2015
16 56938 Mr. Smit Yadav Male Rao Birender Singh State Institute of Engineering and Technology, Assistant Professor Maharishi Dayanand University Rohtak Haryana 2012  
17 56940 Dr. Ramandeep Kaur Female Guru Nanak Dev University Assistant Professor M.Sc. 2006 10/07/2017
18 56942 Ms. Sakina Bano Female Govt. Degree College Womens Sopore Guest Faculty Jamia Millia Islamia /M.Sc. 2014 21/06/2023
19 56944 Dr. Muneer Nabi Male Chandigarh University Assistant Professor Jamia Millia Islamia /M.Sc. 2015 21/06/2023
20 56957 Dr. Shipra Bansal Female Yadavindra Department of Sciences,Punjabi University Guru Kashi Campus,Talwandi Sabo Assistant Professor Punjab University Chandigarh 2003 11/01/2021
21 56972 Mrs. Priyanka Lather Female Guru Jambeshwar university of science and technology Assistant Professor Maharshi Dayanand University , Rohtak 2015  
22 57003 Ms. Heena Rani Female Guru Jambheshwar University of Science and Technology Assistant Professor Kurukshetra University kurukshetra 2017  
  List of Selected candidates (Student Applicants)
1 55319 Ms. Madhvi Raj Female NIT DELHI PhD Patna University 2019  
2 55346 Ms. Sonali . Female National Institute of Technology PhD Department of mathematics Kurukshetra University, Kurukshetra 2019  
3 55482 Mr. Vishal Gautam Male National institute of technology Delhi PhD student Central University of Himachal Pradesh    
4 55535 Ms. Dhanisha Rani Female J. C. Bose University of Science and Technology, Faridabad, Haryana PhD Panjab University, Chandigarh 2019  
5 55537 Mr. Aakash Das Male J. C. Bose University of Science and Technology, YMCA, Faridabad Ph.D Indian Institute of Technology, Patna 2020  
6 56212 Mrs. Ritu Rani Female Vellore Institute of Technology PhD Guru Jambheshwar University of Science and Technology 2014  
7 56270 Mr. Srijit Goswami Male University Of Calcutta PhD University Of Calcutta 2019  
8 56763 Mr. Manik Sareen Male Guru Nanak Dev University PhD D.A.V. COLLEGE,AMRITSAR 2021  
9 57053 Ms. Payal . Female Jaypee Institute of Information Technology PhD M.Sc. 2020  
10 57099 Mr Binaya Kumar Baral Male Jaypee Institute of Information Technology PhD South Asian University 2016  
  Waiting List
1 57000 Dr. Rupali Srivastava Female Jaypee Institute of Information Technology JRF LUCKNOW UNIVERSITY 2016 26/02/2024
2 55886 Mr. Manish . Male National Institute Of Technology Hamirpur Research Scholar IIT Jodhpur 2020  
3 55912 Mr Manoj Mahawar Male Indian Institute of Technology, Roorkee PhD National Institute of Technology Warangal 2021  
4 57052 Ms Kirti . Female Indian Institute of Technology(ISM), Dhanbad PhD Jawaharlal Nehru University 2022  
5 57061 Ms. Sharmistha Kar Female Indian Institute of Technology (ISM) Dhanbad PhD Visva-Bharati 2022  
6 55777 Ms. Mansi Singh Female Indian Institute of Technology Kharagpur Prime Minister's Research Fellow (PMRF) Indian Institute of Technology Kharagpur 2019  
7 55859 Ms. Rozy Sharma Female National Institute of Technology Hamirpur PhD Himachal Pradesh University, Summerhill, Shimla, HP 171005 2019  
8 55989 Ms. Diksha Female National Institute of Technology Hamirpur PhD Himachal Pradesh University, Summerhill, Shimla, HP 171005 2022  
9 56080 Ms. Yashika Female National Institute of Technology Hamirpur Ph.D University of Delhi , M.Sc Maths 2020  
10 56949 Mrs Kanika Sardana Female CBLU Research Scholar   2018  

 

 

How to Reach: 

How to Reach
J. C. Bose University of Science & Technology, YMCA is situated in NCR on NH-2, Mathura-Delhi Highway, Sector-6, Faridabad, Haryana. (https://maps.app.goo.gl/6Q2k7EAWgnpKUNLi8?g_st=iw)

The campus is about 30km away from New Delhi. The University is very well connected with New Delhi via metro/ road and railways. The nearest metro situation is Escort Mujesar (on Violet line) which is at a walking distance (only about 100m) from the main Gate of the University.

One can reach the University by one of the following ways:

  1. Via Air
    • The nearest Airport is Indira Gandhi International Airport, which is about 45km from the University. One may come via metro: IGI Airport Metro Station (on Airport Express Line) to Escort Mujesar Metro Station (on Violet Line); or via Taxi or Local Bus.
  2. Via Train
    • Railway station, Faridabad, which is about 6km from the University (make an exit from platform number 6). From, there one can take Taxi/auto-rickshaw to reach the campus.
    • Railway station, New Delhi, which is about 36km from the University. One may come via metro: New Delhi Metro Station (on Yellow Line) to Escort Mujesar Metro Station (on Violet Line); or via Taxi or Local Bus.
    • Railway station, Old Delhi/ Delhi, which is about 38km from the University. One may come via metro: Chandni Chowk Metro Station (on Yellow Line) to Escort Mujesar Metro Station (on Violet Line); or via Taxi or Local Bus.
  3. Via Bus
    • Bus stand, Ballabh Garh, which is about 3km from the University. From there one can take Taxi/auto rickshaw to reach the campus.
    • Inter State Bus Terminal, Kashmere Gate, Delhi, which is about 40Km from the University. One may come via metro: from Kashmere Gate Metro Station (on Violet Line) to Escort Mujesar Metro Station (on Violet Line); or via Taxi or Local Bus.

 

School Short Name: 

pcm

Last Date Application: 

Sunday, May 28, 2023

School Type: 

IST

File Attachments: 

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