Probability Distribution
Prof. (Dr.) Rajib Kumar Bhattacharjya
Indian Institute of Technology Guwahati
Guwahati, Assam
Email: [email protected]
Web: www.iitg.ernet.in/rkbc
Visiting Faculty NIT Meghalaya
Probabilistic Approach:
A random variable X is a va
Module 2: MOVEMENT OF GROUNDWATER
1
Lecture 3: Darcys law
Key words: Darcys law, Darcys experiments, validity of Darcys law, piezometric head,
permeability
Darcys Experiment
In the year 1856, Henry Darcy, a French hydraulic engineer investigated the flow
Module 3: WELL HYDRAULICS
Lecture 15: Governing equation for radial flow in an aquifer
Key words: Radial flow, confined aquifer, unconfined aquifer, polar coordinate system, well
hydraulics
The flow towards a well situated in homogeneous and isotropic con
CE 311: Hydrology & Water Resources Engineering
Prof. (Dr.) Rajib Kumar Bhattacharjya
Indian Institute of Technology Guwahati
Guwahati, Assam
Email: [email protected]
Web: www.iitg.ernet.in/rkbc
CE 311: Hydrology & Water Resources Engineering (3-0-0)
Cou
CE 501: Surface Water Hydrology
Prof. (Dr.) Rajib Kumar Bhattacharjya
Indian Institute of Technology Guwahati
Guwahati, Assam
Email: [email protected] Web: www.iitg.ernet.in/rkbc
Introduction
Hydrologic Cycle
Evaporation from ocean
Evaporation from water
CE 501: Surface Water Hydrology
Prof. (Dr.) Rajib Kumar Bhattacharjya
Indian Institute of Technology Guwahati
Guwahati, Assam
Email: [email protected] Web: www.iitg.ernet.in/rkbc
Adequacy of Raingauge stations
The optimal number is calculated
=
2
is the
CE 501: Surface Water Hydrology
Prof. (Dr.) Rajib Kumar Bhattacharjya
Indian Institute of Technology Guwahati
Guwahati, Assam
Email: [email protected] Web: www.iitg.ernet.in/rkbc
Example 3:
The annual runoff of a stream is assumed to follow normal distri
CE 501: Surface Water Hydrology
Prof. (Dr.) Rajib Kumar Bhattacharjya
Indian Institute of Technology Guwahati
Guwahati, Assam
Email: [email protected]
Web: www.iitg.ernet.in/rkbc
Stream gauging station
= 0.2
is time in days
is the drainage area in km2
Class Notes on MapReduce
Lecture 7
3rd April 2017
By Paritosh Mittal
140101048
MapReduce
pg. 1
CS-344 Databases
What is MapReduce?
It is a framework or a programming model that is used for processing large data sets
over clusters of computers using parall
Google File
System
20th , 21st March , 2017
by Aneesh Barthakur
Roll No. 140101009
CSE
Introduction
Similar to Relational Databases, Googles proprietary data storage system Bigtable ( which is
manipulated using a programming model called MapReduce ) also
Notations: Note that for all the problems aTk denotes the k-th row of A and
ak denotes
the k-th column of A. The uik s have their usual meaning.
ei denotes the i th column of the identity matrix I.
Convention: For the system, Ax = b, x 0, always we have
Practise problems 5
1. For a balanced transportation problem of the form given below,
Minimize
cij xij
i
subject to
j
xij = bj ,
j = 1, 2, ., n,
xij = ai ,
i = 1, 2, ., m,
i
subject to
j
with
i ai =
justication.
x 0,
j bj ,
check the correctness of the fo
Convention: Throughout this discussion a feasible direction d at a point is by definition taken
to be a nonzero vector, although there is no significant harm even if assumed otherwise. Sometimes
I may have forgotten to explicitly write it.
Notation: 2 f (
R.K. Bhattacharjya/CE/IITG
1
Introduction To Genetic Algorithms
Dr. Rajib Kumar Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Email: [email protected]
7 November 2013
References
R.K. Bhattacharjya/CE/IITG
2
D. E. Goldberg, Genetic Algorithm
Engineering Optimization
Rajib Kumar Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Email: [email protected]
19 August 2013
R.K. Bhattacharjya/CE/IITG
1
Course content
Basics of engineering analysis and design, need for optimal
design, formul
Transformation method
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
15
Minimize
10
Infeasible
region
f(x)
5
0
10 2
10
Feasible
region
Subject to
3
Or, 3 0
-5
-10
-15
0
1
2
3
4
5
The problem can be written as
x
F ,
The bracket o
Linear Problem (LP)
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Linear programming
It is an optimization method applicable for the solution of optimization problem
where objective function and the constraints are linear
It was first a
Introduction to Particle
Swarm Optimization
Rajib Kumar Bhattacharjya
Department of Civil Engineering
Indian Institute of Technology Guwahati
Particle Swarm Algorithm
Inspired by social behavior of bird flocking and fish schooling
Suppose a group of birds
Convex Function
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
CONVEX FUNCTION
CONVEX FUNCTION
CONVEX
CONVEX
CONVEX FUNCTION
A function is said to be convex if for any pair of points = , , , ,
and = , , , , and all where 0 1
+ 1 +
Region Elimination Method
Rajib Kumar Bhattacharjya
Department of Civil Engineering
Indian Institute of Technology Guwahati
a
x1
x2
b
a
x1
x2
b
a
X1
X2
b
Interval halving method
a
X1
Xm
X2
b
Interval halving method
a
x1
Xm
X2
b
Interval halving method
a
x
Optimization Formulation
An Example
Objectives
Topology: Optimal
connectivity of the
structure
Minimum cost of material:
optimal cross section of all
the members
We will consider the
second objective only
The design variables are the cross
sectional area
Introduction to Differential Evolution
Rajib Kumar Bhattacharjya
Department of Civil Engineering
Indian Institute of Technology Guwahtai
Differential Evolution
It is a stochastic, population-based optimization algorithm for solving nonlinear
optimization
Multivariable problem with
equality and inequality
constraints
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Email: [email protected]
General formulation
Min/Max
Where = , , , ,
Subject to
= 0
= 1,2,3, ,
This is the minimum point