Laplace Transform
content:
PIERRE-SIMON LAPLACE
Existence of Laplace Transform
Laplace Transform of some basic functions
Piece Wise continuous function
Image Processing by using Laplace Transform
Real Life Application of Laplace Transform
Limitations of Laplace Transform
Conclusion
Laplace Transform
content:
PIERRE-SIMON LAPLACE
Existence of Laplace Transform
Laplace Transform of some basic functions
Piece Wise continuous function
Image Processing by using Laplace Transform
Real Life Application of Laplace Transform
Limitations of Laplace Transform
Conclusion
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
CLASSICAL AND QUASI-CLASSICAL CONSIDERATION OF CHARGED PARTICLES IN COULOMB F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the
Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity
theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb
centres is carried out. It is shown that the proton and electron can to create a stable connection with the
dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the
proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of
the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with
the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy
for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom
coincide with the Born orbits.
As we have realized in the class of Graph Algorithms, many problems can be represented as a graph. For example, we could be a electrical machine company with different possible sources of parts to the production of a particular engine.
Therefore, we want to minimize the transit between node in the graph.... we can use the Minimum Spanning Tree to obtain a really efficient distribution tree.
(If visualization is slow, please try downloading the file.)
Part 2 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
Comparative study of results obtained by analysis of structures using ANSYS, ...IOSR Journals
The analysis of complex structures like frames, trusses and beams is carried out using the Finite
Element Method (FEM) in software products like ANSYS and STAAD. The aim of this paper is to compare the
deformation results of simple and complex structures obtained using these products. The same structures are
also analyzed by a MATLAB program to provide a common reference for comparison. STAAD is used by civil
engineers to analyze structures like beams and columns while ANSYS is generally used by mechanical engineers
for structural analysis of machines, automobile roll cage, etc. Since both products employ the same fundamental
principle of FEM, there should be no difference in their results. Results however, prove contradictory to this for
complex structures. Since FEM is an approximate method, accuracy of the solutions cannot be a basis for their
comparison and hence, none of the varying results can be termed as better or worse. Their comparison may,
however, point to conservative results, significant digits and magnitude of difference so as to enable the analyst
to select the software best suited for the particular application of his or her structure.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
CLASSICAL AND QUASI-CLASSICAL CONSIDERATION OF CHARGED PARTICLES IN COULOMB F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the
Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity
theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb
centres is carried out. It is shown that the proton and electron can to create a stable connection with the
dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the
proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of
the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with
the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy
for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom
coincide with the Born orbits.
As we have realized in the class of Graph Algorithms, many problems can be represented as a graph. For example, we could be a electrical machine company with different possible sources of parts to the production of a particular engine.
Therefore, we want to minimize the transit between node in the graph.... we can use the Minimum Spanning Tree to obtain a really efficient distribution tree.
(If visualization is slow, please try downloading the file.)
Part 2 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
Comparative study of results obtained by analysis of structures using ANSYS, ...IOSR Journals
The analysis of complex structures like frames, trusses and beams is carried out using the Finite
Element Method (FEM) in software products like ANSYS and STAAD. The aim of this paper is to compare the
deformation results of simple and complex structures obtained using these products. The same structures are
also analyzed by a MATLAB program to provide a common reference for comparison. STAAD is used by civil
engineers to analyze structures like beams and columns while ANSYS is generally used by mechanical engineers
for structural analysis of machines, automobile roll cage, etc. Since both products employ the same fundamental
principle of FEM, there should be no difference in their results. Results however, prove contradictory to this for
complex structures. Since FEM is an approximate method, accuracy of the solutions cannot be a basis for their
comparison and hence, none of the varying results can be termed as better or worse. Their comparison may,
however, point to conservative results, significant digits and magnitude of difference so as to enable the analyst
to select the software best suited for the particular application of his or her structure.
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
Bound State Solution of the Klein–Gordon Equation for the Modified Screened C...BRNSS Publication Hub
We present solution of the Klein–Gordon equation for the modified screened Coulomb potential (Yukawa) plus inversely quadratic Yukawa potential through formula method. The conventional formula method which constitutes a simple formula for finding bound state solution of any quantum mechanical wave equation, which is simplified to the form; 2122233()()''()'()()0(1)(1)kksAsBscsssskssks−++ψ+ψ+ψ=−−. The bound state energy eigenvalues and its corresponding wave function obtained with its efficiency in spectroscopy.
Key words: Bound state, inversely quadratic Yukawa, Klein–Gordon, modified screened coulomb (Yukawa), quantum wave equation
Classical and Quasi-Classical Consideration of Charged Particles in Coulomb F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb centres is carried out. It is shown that the proton and electron can to create a stable connection with the dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom coincide with the Born orbits.
CLASSICAL AND QUASI-CLASSICAL CONSIDERATION OF CHARGED PARTICLES IN COULOMB F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the
Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity
theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb
centres is carried out. It is shown that the proton and electron can to create a stable connection with the
dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the
proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of
the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with
the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy
for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom
coincide with the Born orbits.
The paper examines the problem of systems redesign within the context of passive electrical networks and through analogies provides also the means of addressing issues of re-design of mechanical networks. The problem addressed here are special cases of the more general network redesign problem. Redesigning autonomous passive electric networks involves changing the network natural dynamics by modification of the types of elements, possibly their values, interconnection topology and possibly addition, or elimination of parts of the network. We investigate the modelling of systems, whose structure is not fixed but evolves during the system lifecycle. As such, this is a problem that differs considerably from a standard control problem, since it involves changing the system itself without control and aims to achieve the desirable system properties, as these may be expressed by the natural frequencies by system re-engineering. In fact, this problem involves the selection of alternative values for dynamic elements and non-dynamic elements within a fixed interconnection topology and/or alteration of the network interconnection topology and possible evolution of the cardinality of physical elements (increase of elements, branches). The aim of the paper is to define an appropriate representation framework that allows the deployment of control theoretic tools for the re-engineering of properties of a given network. We use impedance and admittance modelling for passive electrical networks and develop a systems framework that is capable of addressing “life-cycle design issues” of networks where the problems of alteration of existing topology and values of the elements, as well as issues of growth, or death of parts of the network are addressed.
We use the Natural Impedance/ Admittance (NI-A) models and we establish a representation of the different types of transformations on such models. This representation provides the means for an appropriate formulation of natural frequencies assignment using the Determinantal Assignment Problem framework defined on appropriate structured transformations. The developed natural representation of transformations are expressed as additive structured transformations. For the simpler case of RL or RC networks it is shown that the single parameter variation problem (dynamic or non-dynamic) is equivalent to Root Locus problems.
follow IEEE NTUA SB on facebook:
https://www.facebook.com/IeeeNtuaSB
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
1. Frame Element Stiffness Matrices
CEE 421L. Matrix Structural Analysis
Department of Civil and Environmental Engineering
Duke University
Henri P. Gavin
Fall, 2012
Truss elements carry axial forces only. Beam elements carry shear forces
and bending moments. Frame elements carry shear forces, bending moments,
and axial forces. This document picks up with the previously-derived truss
and beam element stiffness matrices in local element coordinates and proceeds
through frame element stiffness matrices in global coordinates.
1 Frame Element Stiffness Matrix in Local Coordinates, k
A frame element is a combination of a truss element and a beam element.
The forces and displacements in the local axial direction are independent of the
shear forces and bending moments.
N1
V1
M1
N2
V2
M2
=
q1
q2
q3
q4
q5
q6
=
EA
L
0 12EI
L3
sym
0 6EI
L2
4EI
L
−EA
L 0 0 EA
L
0 −12EI
L3 −6EI
L2 0 12EI
L3
0 6EI
L2
2EI
L 0 −6EI
L2
4EI
L
u1
u2
u3
u4
u5
u6
2. 2 CEE 421L. Matrix Structural Analysis – Duke University – Fall 2012 – H.P. Gavin
2 Relationships between Local Coordinates and Global Coordinates: T
The geometric relationship between local displacements, u, and global dis-
placements, v, is
u1 = v1 cos θ + v2 sin θ u2 = −v1 sin θ + v2 cos θ u3 = v3
or, u = T v.
The equilibrium relationship between local forces, q, and global forces, f,
is
q1 = f1 cos θ + f2 sin θ q2 = −f1 sin θ + f2 cos θ q3 = f3
or, q = T f, where, in both cases,
T =
c s 0
−s c 0 0
0 0 1
c s 0
0 −s c 0
0 0 1
c = cos θ =
x2 − x1
L
s = sin θ =
y2 − y1
L
The coordinate transformation matrix, T, is orthogonal, T−1
= TT
.
CC BY-NC-ND H.P. Gavin
3. Frame Element Stiffness Matrices 3
3 Frame Element Stiffness Matrix in Global Coordinates: K
Combining the coordinate transformation relationships,
q = k u
T f = k T v
f = TT
k T v
f = K v
which provides the force-deflection relationships in global coordinates. The
stiffness matrix in global coordinates is K = TT
k T
K =
EA
L c2 EA
L cs −EA
L c2
−EA
L cs
+12EI
L3 s2
−12EI
L3 cs −6EI
L2 s −12EI
L3 s2
+12EI
L3 cs −6EI
L2 s
EA
L s2
−EA
L cs −EA
L s2
+12EI
L3 c2 6EI
L2 c +12EI
L3 cs −12EI
L3 c2 6EI
L2 c
4EI
L
6EI
L2 s −6EI
L2 c 2EI
L
EA
L c2 EA
L cs
+12EI
L3 s2
−12EI
L3 cs 6EI
L2 s
sym
EA
L s2
+12EI
L3 c2
−6EI
L2 c
4EI
L
CC BY-NC-ND H.P. Gavin
4. 4 CEE 421L. Matrix Structural Analysis – Duke University – Fall 2012 – H.P. Gavin
4 Frame Element Stiffness Matrices for Elements with End-Releases
Some elements in a frame may not be fixed at both ends. For example,
an element may be fixed at one end and pinned at the other. Or, the element
may be guided on one end so that the element shear forces at that end are zero.
Or, the frame element may be pinned at both ends, so that it acts like a truss
element. Such modifications to the frame element naturally affect the elements
stiffness matrix.
Consider a frame element in which a set of end-coordinates r are released,
and the goal is to find a stiffness matrix relation for the primary p retained
coordinates. The element end forces at the released coordinates, qr are all zero.
One can partition the element stiffness matrix equation as follows
qp
qr
kpp kpr
krp krr
up
ur
The element displacement coordinates at the released coordinates do not equal
the structural displacements at the collocated structural coordinates, since the
coordinates r are released. Since the element end forces at the released coor-
dinates are all zero (qr = 0), the element end displacements at the released
coordinates must be related to the displacements at the primary (retained)
coordinates as:
ur = −k−1
rr krpup
The element stiffness matrix equation relating qp and up is
qp = kpp − kprk−1
rr krp up
The rows and columns of the released element stiffness matrix corresponding
to the released coordinates, r, are set to zero. The rows and columns of the
released element stiffness matrix corresponding to the retained coordinates, p,
are [kpp − kprk−1
rr krp]. This is the element stiffness matrix that should assemble
into the structural coordinates collocated with the primary (retained) coordi-
nates p. The following sections give examples for pinned-fixed and fixed-pinned
frame elements. Element stiffness matrices for many other end-release cases
can be easily computed.
CC BY-NC-ND H.P. Gavin
5. Frame Element Stiffness Matrices 5
4.1 Pinned-Fixed Frame Element in Local Coordinates, k . . . (r = 3)
k =
EA
L 0 0 −EA
L 0 0
3EI
L3 0 0 −3EI
L3
3EI
L2
0 0 0 0
EA
L 0 0
sym
3EI
L3 −3EI
L2
3EI
L
4.2 Pinned-Fixed Frame Element in Global Coordinates, K = TT
kT
K =
EA
L c2 EA
L cs 0 −EA
L c2
−EA
L cs −3EI
L2 s
+3EI
L3 s2
−3EI
L3 cs −3EI
L3 s2
+3EI
L3 cs
EA
L s2
0 −EA
L cs −EA
L s2 3EI
L2 c
+3EI
L3 c2
+3EI
L3 cs −3EI
L3 c2
0 0 0 0
EA
L c2 EA
L cs EI
L2 s
+3EI
L3 s2
−3EI
L3 cs
sym
EA
L s2
−3EI
L2 c
3EI
L3 c2
3EI
L
CC BY-NC-ND H.P. Gavin
6. 6 CEE 421L. Matrix Structural Analysis – Duke University – Fall 2012 – H.P. Gavin
4.3 Fixed-Pinned Frame Element in Local Coordinates, k . . . (r = 6)
k =
EA
L 0 0 −EA
L 0 0
3EI
L3
3EI
L2 0 −3EI
L3 0
3EI
L 0 −3EI
L2 0
EA
L 0 0
sym
3EI
L3 0
0
4.4 Fixed-Pinned Frame Element in Global Coordinates, K = TT
kT
K =
EA
L c2 EA
L cs −3EI
L2 s −EA
L c2
−EA
L cs 0
+3EI
L3 s2
−3EI
L3 cs −3EI
L3 s2
+3EI
L3 cs
EA
L s2 3EI
L2 c −EA
L cs −EA
L s2
0
+3EI
L3 c2
+3EI
L3 cs −3EI
L3 c2
3EI
L
3EI
L2 s −3EI
L2 c 0
EA
L c2 EA
L cs 0
+3EI
L3 s2
−3EI
L3 cs
sym
EA
L s2
0
+3EI
L3 c2
0
CC BY-NC-ND H.P. Gavin
7. Frame Element Stiffness Matrices 7
5 Notation
u = Element deflection vector in the Local coordinate system
q = Element force vector in the Local coordinate system
k = Element stiffness matrix in the Local coordinate system
... q = k u
T = Coordinate Transformation Matrix
... T−1
= TT
v = Element deflection vector in the Global coordinate system
... u = T v
f = Element force vector in the Global coordinate system
... q = T f
K = Element stiffness matrix in the Global coordinate system
... K = TT
k T
d = Structural deflection vector in the Global coordinate system
p = Structural load vector in the Global coordinate system
Ks = Structural stiffness matrix in the Global coordinate system
... p = Ks d
Local Global
Element Deflection u v
Element Force q f
Element Stiffness k K
Structural Deflection - d
Structural Loads - p
Structural Stiffness - Ks
For frame element stiffness matrices including shear deformations, see:
J.S. Przemieniecki, Theory of Matrix Structural Analysis, Dover Press, 1985.
(... a steal at $12.95)
CC BY-NC-ND H.P. Gavin
