text stringlengths 30 4k | source stringlengths 60 201 |
|---|---|
the car separations do not vary very rapid ly, except for a few isolated
places where \jumps" occur. This process is il lustrated by the MatLab script randCFSM in the
Athena 18311-Toolkit, which solves the equations in this model with random initial separations
between the cars. We wil l come back to these issues in re... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
since (cid:15) =
=
. In fact, note that (cid:15) = O(N
) | since
= O(1).
L
L
L(cid:26)
(cid:26)
N
J
J
L
(cid:26)
J
1
(cid:26)
(cid:3)
!
(cid:0)
1
(cid:3)
(cid:26)
Because of the way the equations were nondimensionalized, we see that:
The separation between cars satis(cid:12)es
(cid:15)
(cid:15)
h
= x
x
= O((cid:15)) :
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
0)
n
+1
n
!
(cid:0)
where the densities, velocities and positions are related, in the usual way, by u
= U ((cid:26)
) and
n
n
(cid:26)
= (cid:15)=(x
x
). Again, in addition to initial conditions a boundary condition is needed. For
n
n
n
+1
(cid:0)
example, if there are N cars, then velocity (or the density) u
of the le... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
:26)u = (cid:26)U ((cid:26)) = Q((cid:26)) and c = c((cid:26)) =
. Thus we obtain the same
dq
!
d(cid:26)
continuous tra(cid:14)c (cid:13)ow model that was developed in the lectures (see the lecture notes or the book
by Haberman) using a phenomenological approach and conservation of cars.
An interesting point arises no... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
in the equations. However,
as long as 0 < (cid:26)
1, neither of these two things can happen.
n
(cid:20)
Note 2.1 Notice that the argument in (ii) above shows that a density of one can be maintained
only if the density is identical ly one from some car on forward. Else a decrease in density wil l
propagate backward thr... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
also shows progressive steepening of the density
pro(cid:12)le. However, rather than \topple over" and develop multiple values
9
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
(as happens with the solution by characteristics of (2.5)), the solution of
(2.6)
(1.4) develops a very sharp tra... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
of the characteristic curves for equation (2.5), this means that the curves converge
into the shock | and terminate there. Thus the shock path acts as a \cut" in space{
time, where the characteristic curves end. This prevents their crossing and the formation
of multiply valued regions in the solution.
Simple Tra(cid:1... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
h
+
u
h
+ : : :,
n
+1
n
n
n
n
+1
n
n
n
(1)
(2)
2
1
where h
= x
x
and we use the notation u
=
(x
; t). Thus
n
n
n
n
+1
n
j
(cid:0)
@x
j
(
)
j
@
u
2
u
u
@u
1
1
@u
1
1
n
n
+1
(2)
(3)
2
(2)
2
(3)
(cid:0)
n
n
n
=
(x
; t) +
u
h
+
u
h
+ : : : =
(x
; t) +
(cid:15)u
+
(cid:15)
u
+ : : : ;
n
n
n
n
n
x
x
@x
2
6
@x
2(cid:26)
6(cid... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
:26), this yields the equation
@(cid:26)
@(cid:26)
1
@
@
+ c
=
(cid:15)
(cid:23) ((cid:26))
(cid:26)
;
(2.9)
@ t
@x
2
@x
@x
!
where (cid:23) =
(notice that (cid:23) is a POSITIVE function of (cid:26)). Thus a (small) amount of
dU
(cid:0)
d(cid:26)
di(cid:11)usion is added to equation (2.5). As long as the derivatives a... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
of a few cars, which agrees well with the numerical results in (2.6).
3 Numerical Issues. Sti(cid:11)ness of the equations.
We now go back to the discrete equations and perform an analysis to see what sort of time scales
are involved in their behavior. This is important for many reasons, some of which we will explain
l... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
7) t)
(cid:0)
(cid:0)
1
2
1
2
ik
(cid:14)
= e
; with (cid:27) = (cid:15)
(cid:23)
(cid:26)
e
1
= (cid:15)
(cid:23)
(cid:26)
(cos(k)
1) + i sin(k)
;
(3.3)
(cid:3)
(cid:3)
n
(cid:3)
(cid:3)
6
Notice that this is the same type of solution used in the von Neumann stability analysis of numerical schemes.
(cid:0)
f
(cid:0)
g... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
3.1 We note that (cid:28)
is a very short time. As pointed out in remark 1.2, O(1) times
m
in the nondimensional equations typical ly correspond to a few minutes in dimensional units. Since
(cid:15) = O(10
), we see that (cid:28)
corresponds to a dimensional time scale that must be measured
m
(cid:0)
2
in seconds! Now ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
a new car added (or one gone) to the line. Note that it is important that a mathematical model
be \stable" to such perturbations, else it is worthless (as the neglected e(cid:11)ects would be able to
completely change the nature of the solution). On this last account (at least), the model (1.4)
behaves the right way.
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
equations given by (1.4) this would mean a time
step as short as (cid:28)
, which is disastrous! That is, we would be forced to resolve time scales
m
in the order of seconds (or fractions), while in fact the phenomena we are real ly interested in
fol lowing take place over minutes or even hours. In fact, nothing happen... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
on being re-introduced by external perturbations). But the large scales have
decay times much longer than (cid:28)
| since the real part of (cid:27) behaves like k
for k smal l. Thus,
m
2
while short scale variations wil l be quickly dampened (and wil l become irrelevant), longer scales wil l
remain for \reasonable" ti... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
other e(cid:11)ects destabilize. The interesting fact is that the time scales associated with them are about
the same as those given by (cid:28)
. But perhaps this is not too surprising, if one postulates a tendency
m
to \push the envelope" in terms of safety. That is: drivers wil l drive as fast and as close to the
ne... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
15)
(cid:0)
Since u
= U ((cid:26)
+ (cid:14)
) = u
(cid:23)
(cid:14)
, we then have (using (3.4)
n
n
n
(cid:3)
(cid:3)
(cid:3)
(cid:0)
dy
1
n
=
(y
y
) ;
(3.5)
n
n
+1
dt
2 (cid:28)
m
(cid:0)
which (of course) is the same equation the (cid:14)
’s satisfy!
n
4 Examples.
In this section we consider examples of choices for ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
40 mph was reasonable). In general these numbers are meant only as bal lpark (cid:12)gures. After
nondimensionalization, we have the forms
Q = 4(cid:26)(1
(cid:26)) ; U = 4(1
(cid:26))
and c = 4(1
2(cid:26)) :
(4.1)
(cid:0)
(cid:0)
(cid:0)
In this case the shock speed in (2.7) is the average of the characteristic speed... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
26)
u
=
:
m
max
m
m
m
m
v
(cid:26)
r
J
v
(cid:26)
u
r
J
max
v
+ u
v
+ u
r
max
r
max
With u
= 50 mph, v
= 10 mph and (cid:26)
= 160 cpm this yields (cid:26)
27 cpm and q
1330 cph
max
r
J
m
m
(cid:25)
(cid:25)
| not altogether unreasonable numbers. One point though is that (cid:26)
= 160 cpm corresponds to
J
‘ = 33 f t, ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
:11) (1
(cid:11))
!
(cid:18)
(cid:19)
(cid:0)
(cid:0)
(cid:0)
where 0 < (cid:11) =
< 1. Note the strange feature of a piece-wise constant wave speed
(cid:26)
m
(cid:26)
J
c. Thus, in the continuum limit, the parts of the density pro(cid:12)le with (cid:26) > (cid:11) move (backwards) at
constant
speed ((cid:11)
1)
. Si... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
26, 1999 | Rosales.
5 Notes on the MatLab script quadCFSM.
The MatLab script quadCFSM in the Athena 18311-Toolkit solves the equations in (1.4) us-
ing the quadratic (cid:13)ow function (4.1) in example 4.1. A (cid:12)nite number of cars N is used, with
x
< x
< : : : < x
and the density 0 < (cid:26)
< 1 at the leading ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
have
h
(cid:0)
N
1
(cid:15)
(cid:25) = x
(0)
x
(0) =
:
N
p
(cid:0)
(cid:26)
n
n
p
=
X
9
The leading car velocity is then also constant
= 4(1
).
u
(cid:26)
N
N
(cid:0)
Simple Tra(cid:14)c Flow Model.
16
MIT, Friday March 26, 1999 | Rosales.
This equation determines the value of (cid:15) in terms of the number of cars i... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
(2.5) to deal with the well behaved
parts of the solution | where we can use the characteristic method | and equations (2.7) and
(2.8) to deal with the discontinuities (shocks).
Notice that in this case the wave speed satis(cid:12)es c = 4
8(cid:26) and is a linear function of the density
(cid:0)
(cid:26). It then foll... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
the value of x on the
(cid:0)
Simple Tra(cid:14)c Flow Model.
17
MIT, Friday March 26, 1999 | Rosales.
characteristic at time t = 0 and S (x; 0) =
(x). This follows from the general solution of the
dC
equation above for S along characteristics:
(cid:0)
dx
S ((cid:16) ; 0)
S =
:
1 + S ((cid:16) ; 0)t
An analysis of thi... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
hump "die" at the shock. More precisely, the density disturbance will be made up
only from characteristics that start near the leading edge (x = 0) of the initial hump, i.e.
x = ct + (cid:16) ; with c = c
C ((cid:16) ) and (cid:16) small and negative.
(5.4)
N
(cid:0)
Simple Tra(cid:14)c Flow Model.
18
MIT, Friday Marc... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
0)
x
2. For x
< x
c
t
: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : c =
.
S
N
(cid:20)
t
3. Elsewhere : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : c = c
.
N
4. The car density follows from : : : : : : : : : : ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
That is, so that
S
the equation 2A = (c
c
)(c
t
x
) holds. Note that here we have used the fact that c
N
S
N
S
itself is conserved, as stated earlier in (5.3).
(cid:0)
(cid:0)
A more detailed justi(cid:12)cation of the arguments above can be found in the book by G. B. Whitham:
Linear and Nonlinear Waves. Hopefully, it ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
initial data close to the origin, with the rest meaningful only
as far as determining the area parameter A. Thus, instead of reducing the information about this
10
Given any solution
=
(
),
=
(
) is also a solution (for any constants
and
). The problem
c
c
x; t
c
c
x
x
; t
t
x
t
(cid:0)
(cid:0)
(cid:3)
(cid:3)
(cid:3)
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
(cid:3)
>
>
>
2. For x
< x
c
t
: : : : : : : : : : : : : : : : : : : c = c
+
(x
c
t) =
,
>
S
N
N
N
(cid:0)
(cid:20)
(cid:0)
1 + B t
t
t
(cid:3)
(cid:0)
where x
= c
t
and t
=
1=B .
N
(cid:3)
(cid:3)
(cid:3)
(cid:0)
3. Elsewhere : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
(cid:20)
(cid:20)
until after the target time. It is then over this range x
x
0 that we need the approximation
‘
(cid:20)
(cid:20)
(5.6) to hold. Of course, the target time cannot be too small, for the range x
x
0 has to be
‘
(cid:20)
(cid:20)
small enough that an approximation of the form (5.6) makes sense. Once x
is ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
26, 1999 | Rosales.
Thus, we obtain
(cid:15)(N
‘) + x
(cid:26)
‘
N
B = 16
:
(5.8)
(cid:0)
2
x
‘
Exact and approximate solutions.
Shock
r
r
N
Dashed line = approximation.
x
Figure 5.4: This (cid:12)gure shows an example comparing an exact so-
lution of the continuum limit and the approximation given by (5.7).
Rema... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
Strategic Architectural Approaches at
NASA
Gary Martin
November 14, 2004
MIT
Overview
• Decadal Planning Team (DPT) /NASA Exploration Team (NEXT)
• Space Architect Team/New Vision for Space Exploration
• Advanced Planning and Integration Office
• A Few Points to Remember
2
Decadal Planning Team (DPT) /NASA
Explorat... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
order to support future missions
the NEXT team has identified the criteria that must be satisfied (the list runs in a
logical order from top to bottom).
• Transition to next chart: The technology needed to overcome these hurdles and
enable new missions is determined in a systematic way. The NEXT is structured to
co... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
food
•• Materials, factor of 20
Materials, factor of 20
avionics
/Nano-- avionics
•• MicroMicro--/Nano
••
••
ETO $/kg (under review)
•• ETO $/kg (under review)
Payload: 100+mt mt
Payload: 100+
space propulsion,
InIn--space propulsion,
Isp>3000 sec, high thrust
Isp>3000 sec, high thrust
Sustainable power
•• Sustai... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
and
Research and
Technology
Technology
3.03.0
Technology Flight
Technology Flight
Demonstrations
Demonstrations
2.12.1
Space
Space
Resources
Resources
Development
Development
2.22.2
Space Utilities
Space Utilities
and Power
and Power
2.32.3
Habitation and
Habitation and
BioBio--
astronautics
astronautics
2.... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
)
• Intelligent Systems
• ISTP
• SLI
• SBIR supporting (THREADS)
• New Millennium Program
• Data from Robotic Mars
Missions/Experiments
• In-Space Transportation
Technology Program (ISTP)
• Space Launch Initiative
(SLI--coordination)
• Instrument Incubator Program
• Advanced Technology Initiative
• Advanced Informat... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
w
o
L
n
I
s
s
a
M
l
a
i
t
i
n
I
4000
~~
2000
)
t
m
(
1500
1000
500
ISS
Mass
(~470 mt)
All Solar
Electric
Propulsion
7
3
Opp-class
Tether / Chemical
3 - Tether / Chemical
4 - High powered electric
propulsion/nuclear electric propulsion
(HPEP / NEP)
5 - Variable Specific Impulse Rocket
(VaSImR)
6 - Solar Electric (S... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
90
2000
1990
2000
25
35
45
55
1.0
1.8
2.5
3.0
0.4
0.6
0.9
1.7
1.5
2.5
3.2
4.0
0.7
1.0
1.5
3.0
Age at First Mission No. of 180-day LEO missions**
25
35
45
55
Female
0
1
1
2
Male
1
1
2
3
Considerations
• Costs of training
• Costs of crew
replacement
• Career corps vs one-
mission astronauts
* 1 SV = 100 REM. 1 REM = mea... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
• Experience and
Lessons Learned
• Mission Performance
Assessments
16
Example Science
Activities
Creating science
instruments and
observing platforms to
search for life sustaining
planets
Search for evidence of
life on planetary surfaces
Large Space Telescope Construction and Maintenance
Complexity/
Capabilit... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
and development plans
– Define and prioritize requirements
– Define and prioritize flight experiments
• Comparing architectures specific measures of merit;
– Safety
– Cost
– Performance
– Mission return
– Schedule
20
Space Architecture Planning Process
Strategic
Plan
Enterprise
Strategies
Architectural
Studies
Goals ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
3
Architecture Study #2 Focus
• Multi-Enterprise Lunar Surface Exploration
– Lunar surface biological research
– Ops preparation for human Mars exploration
– South Pole-Aitken Basin sample return
– ISRU identification and assessment
– South Pole observation station
– Opportunistic lunar science
Structure &
Evol... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
solar system and
beyond
Extend human presence across the solar system,
starting with a human return to the Moon by the
year 2020, in preparation for human exploration of
Mars and other destinations;
Develop the innovative technologies, knowledge,
and infrastructures both to explore and to support
decisions about ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Orbital Tech Demos
Lunar Exploration Systems
Life
Finder
Planet
Imager
Extrasolar
Planets
Deep Space Telescope
Deployment/Upgrades
Mars and Beyond
Exploration Systems
Building
Blocks
CEV Test Flights
CEV Operational
Station Assembly Complete
Human Research Complete
Station Transition
Space Shuttle Retirement
Soyuz and... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
purposes and to support human exploration.
(1.7) NASA shall conduct advanced telescope searches for Earth-like planets and
habitable environments around other stars.
28
Level 0 Exploration Requirements (cont)
(2) NASA shall acquire an exploration transportation system to support delivery of crew and cargo
from the s... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
30
Notional Architecture
Level 0 Architecture Trade Tree
Science Investigation
Surface Duration
SFL ancient Life
(See Chart ? for science
content)
SFL Modern Life
(See Chart ? for science content)
SFL extant life (Hydrothermal deposits)
SFL Global Evolution
1 - 29 Days
30-90 days (Short)
91-500 Days (Long)
(See C... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
deploy assets
conjunction (See chart ? for details)
deploy together
opposition
Aeroassisted Orbit Insertion
Direct Entry from Earth
Propulsive Orbit Insertion
Mars Arrival, Descent/Ascent & Departure
Separate Lander & Habitat
Lander as Habitat
Mars Orbit Rendezvous
Direct Return to Earth
Return in same vehicle
Orbit th... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
ELV
Different LV
New LV
HEO
HEO
Existing LV
GEO
GEO
Update existing infrastructure
Build new NASA Infrastructure
Use new Industry infrastructure
Nuclear
Nuclear
predeploy assets
crew & cargo together as
required for specific mission in
campaign
Advanced Chemical
Advanced Chemical
deploy together
Crew Separate/ Split ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Current Structure and
Management Methods
Keep current NASA
Infrastructure
Keep current NASA workforce
levels and competences
Yes, in critical path (i.e. ISS)
Government as System
Integrator
Design to cost
Capability/Technology Development
Develop Capabilities through infusion
of new technologies as they become
av... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
g
e
e
t
t
a
a
r
r
t
t
S
S
Crew to Orbit approach
Orbit Location for Assembly**
Orbit Location for final Crew
Rendezvous
Launch Infrastructure
Crew propulsive transit
Cargo Propulsive Transit
Cargo Predeployment
Earth to Moon Transit
Lunar Arrival
Lunar Ascent/Descent
Lunar Departure
Earth Arrival
Earth Surface Landing... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
30
2032
> 2032
Operations Infrastructure for Mars
Combined DRAs
IDs Overlaps
Mars Surface Systems & Operations
Science Investigation
Surface Duration
SFL ancient Life
(See Chart ? for science
content)
1 - 29 Days
SFL Modern Life
(See Chart ? for science content
30-90 days (Short)
(See Chart ? for infered capabilit... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
/Communication
Space Weather
Use existing US assets, no
additional investment
Use existing US assets, no
additional investment
Emplace additional evolved
infrastructure
Emplace additional evolved
infrastructure
Cargo to Earth Orbit & Assembly
Approach
System Level Assy. &
Docking - Infers AR&D an
HLLV (See Chart ? ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Mission
Duration on Moon
All Systems
Short (1-90days)
Must Systems
Long (>90da)
Location
Global Access
Equatorial
Must/Ought
(See charts ? For test approach)
Polar
(See Chart ? for location/orbit metrics)
Lunar Surface Systems and Operations
Use an appropriate mix o
military, NASA and indust
assets
Surface Approach
C... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Infrastructure
Use new Industry infrastructure
Nuclear
Nuclear
Advanced Chemical
Advanced Chemical
predeploy assets
deploy together
Transfer to Moon
Chem/electric
Chem/electric
crew & cargo together as
required for specific mission
campaign
Crew Separate/ Split Mission
Lunar Arrival, Descent/Ascent, and Return
Orbit... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Current Structure & new managem
methods
New Structure & management methods
Keep current NASA
Infrastructure
Keep current NASA workforc
levels and competences
Smaller NASA Infrastructure
optimized with industry,
universities, other agencies
Smaller NASA workforce optimiz
for critical NASA functions
New NASA Infrastru... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Mars Surface Landing
Separate Lander & Habitat
Lander as Habitat
Mars Departure
Mars Orbit Rendezvous
Direct Return
Heliocentric Transfer to Earth
Return in same vehicle
Return in different vehicle
Earth Return
Earth Arrival
Earth Surface Landing
Orbit then go get crew from
Earth
water
Orbit, then Enter
Direct Entry
r... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Orbit Operations
System Level assy. & docking
AR&D and Evolved ELV
Different LV
New LV
HEO
HEO
Existing LV
GEO
GEO
Update existing infrastructure Build new NASA Infrastructure
Use new Industry infrastructure
Nuclear
Nuclear
Advanced Chemical
Advanced Chemical
predeploy assets
deploy together
Transfer to Moon
Chem/elect... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
e
with flight hardware schedule
Develop Capabilities through infusion o
breakthrough technologies when they
become available
Agency Programmatic Approach
Management Structure
Current Structure and
Management Methods
Current Structure & new managem
methods
New Structure & management methods
Agency Infrastructure
Same ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
argo* separately
predeploy assets
deploy together
conjunction
opposition (See chart 8 for details)
conjunction (See chart 10 for details)
opposition
Aeroassisted Orbit Insertion
Direct Entry
Propulsive Orbit Insertion
Mars Arrival, Descent/Ascent & Departure
Separate Lander & Habitat
Lander as Habitat
Mars Orbit Rendez... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
evolved
infrastructure
Earth Orbit Approach
Crew to Orbit approach
Orbit Location for Assembly**
Orbit Location for final Crew
Rendezvous
Launch Infrastructure
Crew propulsive transit
Cargo Propulsive Transit
Cargo Predeployment
Earth to Moon Transit
Earth-to-Orbit and Orbit Operations
System Level assy. & docking
Au... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
onl
(See Chart ? for lunar robotic optio
Precursors
Start in 2011 - multiple missions (S
Chart ? for Mars robotic options)
Start in 2016 or later
Multiple orbiters, landers & sample returnsMultiple orbiters and landers
Bioastronautics
Use ground research only to
certify crews for deep space
Use ISS and ground research ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
ARTH
EARTH
33
Notional Architecture
Example Short-Stay Missions
•
Typically referred to as opposition class
missions
• Characterized by
– Only 1 Hohman transfer (short leg)
– High-propulsive requirements for
other leg (long leg)
• Venus swing-by or deep-space
Maneuvers
• Close perihelion passage
– Large variation i... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
requirements across mission
opportunities
Total Mission DV vs Earth Departure Date
Depart
Earth
2/18/31
Depart Mars
2/12/33
)
s
/
m
k
(
V
D
n
o
i
s
s
i
M
24
20
16
12
8
4
0
Sun
Arrive Earth
9/18/33
γ
Arrive Mars
9/16/31
01-Jan-15
31-Dec-18
30-Dec-22
29-Dec-26
28-Dec-30
Earth Departure Date
36
Notional Architect... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
vous and Docking
– On-orbit assembly
In-Space Transportation
– Aeroassist
– Electric propulsion
– Nuclear Propulsion
– High-efficiency chemical propulsion
– Long-Term Propellant storage and handling
• Planetary Operations
– Entry / Descent / Landing
• Aero Entry
• Precision landing
• Planetary Operations continued
– Su... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
A
Nuclear Transfer Propulsion DDT&E
Subscale Test
Off-Ramp
Non-Nuclear Transfer Propulsion DDT&E
Mars
President's Vision
President's Vision
Milestone
Milestone
ATP
ATP
Key Decision
Key Decision
Pre-Phase A
Transfer Vehicle DDT&E
Pre-Phase A
Lander
Pre-Phase A
Habitat
Demo
Pre-Phase A
Nuclear Surface Power
Pr... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Portfolio Integration/
Portfolio Management
Input to Strategic
Process
Academic &
Industrial
Community/
Directorates/
Centers
Planning and
Execution
Directorates
Advanced Planning and Integration Office
Directorates
43
•
Roadmapping
Strategic Roadmap – A coordinated and comprehensive longitudinal strategy,
with k... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Lab 3 Revisited
• Zener diodes
R
C
6.091 IAP 2008 Lecture 4
1
Lab 3 Revisited
ready
• Voltage regulators
• 555 timers
Vs = 5 V
Vin
Vc
V
c
=
V
s
−
t
RC
1
−
e
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
+15
270
1N758
0.1uf
5K
pot
VCC
8
Threshold
Control Voltage
Trigger
6
5
2
5k
5k
5k
V+
V-
.
+
Comp
A
_
+
Comp
B
_
2N2222
Vo
0.1uf
R
S
Flip
Flop
Q
I... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
AP 2008 Lecture 4
4
Digital Circuits
HCMOS 1 (high)
– Output high: >3.98v
– Input voltage high: >2.0V
HCMOS 0 (low)
– Output low: <0.4v
– Input voltage
low: 0.0 – 0.7v
+5V
+3.98V
input high
range
+2.0V
0.7V
Forbidden Zone
0.4V
input low
rage
output high
range
noise
margin
noise
margin
output low
range
6.091 IAP 2008... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
.091 IAP 2008 Lecture 4
10
74LS00 NAND Gate
Dual-In-Line Package
VCC
B4
A4
Y4
B3
A3
Y3
14
13
12
11
10
9
8
1
2
3
4
5
6
7
A1
B1
Y1
A2
B2
Y2
GND
This device contains four independent gates each
of which performs the logic NAND function.
Figure by MIT OpenCourseWare, adapted from the National Semiconductor 54LS00 datashee... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
51
8-1 Multiplexer
Dual-in-line Package
Data Inputs
Data Select
Inputs
ready
VCC
D4 D5 D6 D7
A
B
C
16
15
14
13
12
11
10
9
1
2
3
4
5
6
7
8
D3 D2 D1 D0
Y
W Strobe GND
Data Inputs
Outputs
Select
B
X
L
L
H
H
L
L
H
H
C
X
L
L
L
L
H
H
H
H
A
X
L
H
L
H
L
H
L
H
Strobe
S
H
L
L
L
L
L
L
L
L
Outputs
Y
L
D0
D1
D2
D3
D4
D5
D6
D7
W
H
... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
H
L
H
Z
L
H
H
L
6.091 IAP 2008 Lecture 4
Figure by MIT OpenCourseWare, based on Motorola datasheet.
16
74LS74 D Flip Flop
Note both Q and Qbar
SET-PRESET
CLK
SET
D
Q
Q
CLR
CLR
circle indicates
inversion
(active low)
CLK
D
Q
Reprinted with permission of National Semiconductor Corporation.
6.091 IAP 2008 Lecture 4
17
... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
parallel data to serial
data.
6.091 IAP 2008 Lecture 4
20
74LS175 4 Bit Shift Register
74LS175
13
15
12
10
5
7
4
2
SET
D
Q
SET
D
Q
SET
D
Q
SET
D
Q
CLR Q
CLR Q
CLR Q
CLR Q
9
1
14
clock clear
11
6
3
Clock and Clear are
common for all FF. The D
FF will store the state of
their individual D inputs on
the LOW to HIGH ... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
Cin A
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
B
0
1
0
1
0
1
0
1
Sum Cout
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
A
B
Cin
ADDER
Cout
Sum
Sum =
Cout =
6.091 IAP 2008 Lecture 4
23
Signed Numbers – Twos Complement
• Positive Number:
MSB=0
• Negative Number:
MSB=1
• 4 Bit example
• Simple addition &
subtraction
• Most common
notation
... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
008 Lecture 4
26
Lab Exercise
4 Bit Counter – Logic Analyzer
+5
Power connections not
shown for 74LS163
7
10
9
1
P
T
LD
CLR
14
13
12
11
QA
QB
QC
QD
74LS163
counter
+5
1.8432
Mhz
crystal
osc.
Attach LA probe
A2 to QA-QD
6.091 IAP 2008 Lecture 4
triangle is symbol
for clock input
27
Lab Exercise
Ramp Generator
R
R
... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
30
DA Summary
• Output from digital to analog conversion
are discrete levels.
• More bits means better resolution.
• An example of DA conversion
– Current audio CD’s have 16 bit resolution or
65,536 possible output levels
– New DVD audio samples at 192 khz with 24
bit resolution or 224 = 16,777,216
6.091 IAP 2008 ... | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
at the
end of the lab
6.091 IAP 2008 Lecture 4
37
Lab 5
• Design, build and keep
the electronics for a
digital lock.
• Unlock key based on
sequence of 0, 1.
6.091 IAP 2008 Lecture 4
38 | https://ocw.mit.edu/courses/6-091-hands-on-introduction-to-electrical-engineering-lab-skills-january-iap-2008/1ebc7a3c1f59bab488ae4a8b41c31296_lec4a.pdf |
6.867 Machine learning, lecture 6 (Jaakkola)
1
Lecture topics:
• Active learning
• Non-linear predictions, kernels
Active learning
We can use the expressions for the mean squared error to actively select input points
x1, . . . , xn, when possible, so as to reduce the resulting estimation error. This is an active... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
and therefore won’t affect how we should choose the inputs. When
the choice of inputs is indeed up to us (e.g., which experiments to carry out) we can select
them so as to minimize T r (XT X)−1 . One caveat of this approach is that it relies on the
underlying relationship between the inputs and the responses to be li... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
v = [xT , 1]T . We would like to find a valid v that minimizes
�
T r (A−1 + vv T )−1
�
The matrix inverse can actually be carried out in closed form (easy enough to check)
(A−1 + vv T )−1 = A −
1
(1 + vT Av)
AvvT A
so that the trace becomes
�
T r (A−1 + vv T )−1 = T r [A] −
�
= T r [A] −
= T r [A] −
�
T r... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
of A are positive as it is an inverse
of a positive definite matrix XT X). It is indeed advantageous in linear regression to have
the input points as far from each other as possible (see Figure 1). If we constrain �v� ≤ c,
then the maximizing v is the normalized eigenvector of A with the largest eigenvalue,
Cite as:... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
constrained to lie within [−1, 1]. Assume we
have already observed responses for x1 = 1 and x2 = −1. Thus
�
X =
1
1
−1 1
�
, XT X =
�
2 0
0 2
�
, A = (XT X)−1 =
�
�
1 1 0
0 1
2
(9)
v = [x, 1]T and therefore vT Av = (x2 + 1)/2 and vT AAv = (x2 + 1)/4. The criterion to
be maximized becomes
vT AAv
(1 +... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
on [DD Month YYYY].(cid:13)(cid:10)
6.867 Machine learning, lecture 6 (Jaakkola)
4
we are the most uncertain about. We again write v = [xT , 1]T so that
V ar{y|x, X} =
E
ˆθT x + ˆθ0 − θ∗T x − θ∗
��
��
=
E
x
1
�T ��
�
�
−
ˆθ
ˆθ0
�
�T
=
x
1
= σ∗2 · v T Av
�
σ∗2(XT X)−1 x
1
θ∗
θ∗
0
�
�
�2 ... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
∼ N (0, σ2). We can obtain a
quadratic model by simply mapping the input x to a longer feature vector that includes a
term quadratic in x. A third order model can be constructed by including all terms up to
degree three, and so on. Explicitly, we would make linear predictions using feature vectors
√
√
φ x → [1,
φ ... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
were generated from a linear
model). Note that all these models are linear in the parameters but non-linear in x, save
the standard linear regression model in Figure 2a.
The polynomial expansion of input vectors works the same in higher dimensions, e.g.,
x = [x1, x2]T → [1, x1, x2,
φ
√
2x1x2, x 1, x 2]T = φ(x)
2... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
of the power of this
approach, let’s evaluate the inner product between two feature vectors corresponding to
the specific cubic expansions of 1-dimensional inputs shown before:
φ(x) =
φ(x�) =
√
√
[1,
[1,
√
√
3x,
3x�,
,
3]T
2
3x , x
3x�2 , x�3]T ,
φ(x)T φ(x�) = 1 + 3xx� + 3(xx�)2 + (xx�)3 = (1 + xx�)3
(20)
... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
in conjunction with mapping
examples to higher dimensional feature vectors. The regularized least squares objective to
be minimized, with parameter λ, is given by
J(θ) =
n
� �
yt − θT φ(xt) �2 + λ�θ�2
(23)
t=1
Cite as: Tommi Jaakkola, course materials for 6.867 Machine Learning, Fall 2006. MIT OpenCourseWare
(h... | https://ocw.mit.edu/courses/6-867-machine-learning-fall-2006/1eedc5b3427ca3eef198d707f016f295_lec6.pdf |
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 8-1
Lecture 8 - Carrier Drift and Diffusion (cont.),
Carrier Flow
February 21, 2007
Contents:
1. Quasi-Fermi levels
2. Continuity equations
3. Surface continuity equations
Reading assignment:
del Alamo, Ch. 4, §4.6; Ch. 5, §§5.1, 5.2
Cite as... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
EF relates no with Nc and po with Nv:
no = NcF1/2(
EF − Ec
)
kT
po = NvF1/2(
Ev − EF
kT
)
Outside TE, EF cannot be used.
Define two ”quasi-Fermi levels” such that:
n = NcF1/2(
Efe − Ec
)
kT
p = NvF1/2(
Ev − Efh
)
kT
Under Maxwell-Boltzmann statistics (n (cid:3) Nc, p (cid:3) Nv):
n = Nc exp
Efe − Ec
kT
... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
Integrated Microelectronic Devices, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 8-5
� Physical meaning of ∇Ef
For electrons,
Then:
Je = μen
dEfe
dx
= −qnve
dE... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
(http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 8-7
2. Visualize currents
dEfe
Je = μen dx
= 0
• ∇Efe = 0 ⇒ Je = 0
⇒ Je = 0
• ∇Efe (cid:5)
• if n high, ∇Efe small to maintain a certain current lev... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007
Lecture 8-9
2. Continuity Equations
Semiconductor physics so far:
Gau... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
electrons in ΔV =
rate of electron generation in ΔV
- rate of electron recombination in ΔV
- net flow of electrons leaving ΔV per unit time
∂(nΔV )
∂t
= GΔV − RΔV − Fe.dS
� (cid:2) (cid:2)
Dividing by ΔV and taking the limit of small ΔV :
∂n
∂t
= G − R − (cid:2) F(cid:2)
e∇.
Cite as: Jesús del Alamo, course m... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
Gs-Rs=Fs
Fs>0
Fs<0
Fs<0
Fs>0
x
x
x
x
Rewrite in terms of current densities normal to surface:
|Us| =
1
q
|Jes| =
1
|Jhs|
q
Always, no net current into surface:
Js = Jes + Jhs = 0 =⇒ Jes = −Jhs
Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007.
MIT Open... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
- Spring 2007
Lecture 8-14
� If there is net generation or recombination at surface right below
ohmic contact ⇒ minority carrier current in addition to majority
carrier current
Three possible cases (examples for n-type):
I
Fes
I
Fes
I
Fhs
n
Fhs
Fes
n
ohmic contact
with net recombination
ohmic contact
w... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
Continuity equations: ”book-keeping” relations for carriers.
• Surfaces cannot store carriers: at all times must have current
balance at surface.
• At ”free” surface: electron and hole currents result from carrier
generation or recombination at surface (but net current is zero).
• At ohmic contact:
– additional m... | https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/1f1fc5af273b0f02a04022ef0899c178_lecture8.pdf |
3.37 (Class8)
Review
C4 (Area Array) 1000-2000 I/O
Cold welding
• Aluminum is the second easiest metal to cold weld
• Make near perfect welds in aluminum wire
Adhesive Bonding
• Unique in that it does not remove surface contamination
• Type I Adhesive Bonding results from attractive force of wetted liquid at th... | https://ocw.mit.edu/courses/3-37-welding-and-joining-processes-fall-2002/1f455cedc7837bb4390f13e61e2c94b0_33708.pdf |
Joints, Acad Press, 1961
o None of the modern books on adhesives go through this
• Force*time product = see equation on board
o Viscosity
o Initial and final separations
o Radius for a circular disc
• Looking at different forces, viscosities, radii, and separations
o Water at given parameters 7.5ms
o As the joi... | https://ocw.mit.edu/courses/3-37-welding-and-joining-processes-fall-2002/1f455cedc7837bb4390f13e61e2c94b0_33708.pdf |
MIT OpenCourseWare
http://ocw.mit.edu
18.727 Topics in Algebraic Geometry: Algebraic Surfaces
Spring 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
ALGEBRAIC SURFACES, LECTURE 4
LECTURES: ABHINAV KUMAR
We recall the theorem we stated and lemma we proved f... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
1)
S1
q
� �
S
q�
��������
� �
� S�
φ
The projections q, q� are birational morphisms and the diagonal morphism com
mutes. Since φ−1(q) is not defined, (q�)−1(p) is not defined either, so ∃C1 ⊂ S an
irreducible curve s.t. q�(C1) = {p}. Moreover, q(C1) = C is a curve in S: if not,
since S1 ⊂ S × S�, q(C1) a point ... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
p. Let Ox,q be the local ring of X at q,
and let mq be its maximal ideal. We claim that there is a local coordinate y on
S at p s.t. f ∗y ∈ m2
q . To see this, let (x, t) be a local system of coordinates at
p. If f ∗t ∈ m2
q , then f ∗t vanishes on
f −1(p) with multiplicity 1, so it defines a local equation for f ... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
morphism of surfaces. Then ∃ a
(k = 1, . . . , n) and an isomorphism S ∼ Sn
Proposition 1. Every morphism from S˜ to a variety X that contracts E to a
point must factor through S.
Proof. We can reduce to X affine, then to X = An, then to X = A1 . Then f
defines a function on ˜
�
Theorem 2. Let f : S
→
sequence of blowu... | https://ocw.mit.edu/courses/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/1f4f36355341a0e235b980608b418882_lect4.pdf |
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