text stringlengths 16 3.88k | source stringlengths 60 201 |
|---|---|
V. Else, choose a
random permutation p on [1..k] and send (G, C(p(G)), C(p)) to V.
• V: If received (G,”reject”) then output (G,0). Else, send a random
bit b to P.
• P:
If b=0 then decommit to all commitments of message 1.
If b=1 then open only the commitments of the edges in H.
• V:
Accept (output (G,1)) if all th... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/1d52d1e1de07e4fd8cf3ea9e3f689583_lecture3_4.pdf |
c=“no cheat” output (,(,x,0),(x,0)).
If c=“cheat” output (,(,x,b),(x,b)) for bÅ R {0,1}.
H
Claim: The basic Blum protocol securely realizes Fwzk
.
Proof sketch: Let A be an adversary that interacts with the
protocol. Need to construct an ideal-process adversary S that
fools all environments. There are four cases: ... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/1d52d1e1de07e4fd8cf3ea9e3f689583_lecture3_4.pdf |
ver, and send “cheat” on direct line.
– Get output (G,b’) from TP. If b’=0 then output the ouptut of A from the
run where decommitments failed. If b’=1 output the ouptut of A from the
run where all decommitments succeed.
If for both values of b some decommitments failed, give (G,-) to TP
as the prover, send “no ch... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/1d52d1e1de07e4fd8cf3ea9e3f689583_lecture3_4.pdf |
).
– Else output nothing (or alternatively output a default
value, say (x0,1) for some x0 for which a w0 is known.)
Analysis of the protocol
Let A be an adversary that interacts with the protocol in the Fwzk
R -hybrid
1.
2.
R and fools all environments. There are four cases:
model. Need to construct an ideal-pr... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/1d52d1e1de07e4fd8cf3ea9e3f689583_lecture3_4.pdf |
, and chose b=1. But this occurs
with probability 2-k.
Note:
1.
2.
The protocol and analysis are purely combinatorial (“information
theoretic”), no computational issues involved. All the “computational
issues” are pushed to the realization Fwzk
The same analysis works for a number of other ZK protocols with weak ... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/1d52d1e1de07e4fd8cf3ea9e3f689583_lecture3_4.pdf |
0 then c’ opens to a permutation of G.
i
This problem can be solved by using special commitments. But
the general use of commitments failed.
Parallel composition of Blum’s protocol
• Solution 2 [Brassard-Crepeau-Yung]:
Use “equivocable commitments” (given secret key, can open
commitments both ways):
VÆP: public c... | https://ocw.mit.edu/courses/6-897-selected-topics-in-cryptography-spring-2004/1d52d1e1de07e4fd8cf3ea9e3f689583_lecture3_4.pdf |
Lecture 9
8.321 Quantum Theory I, Fall 2017
48
Lecture 9 (Oct. 4, 2017)
9.1 Spin- 1
2 in an AC Field
Consider a spin- 1 system in a time-dependent magnetic field. The Hamiltonian is
2
H = −
ge
2
m
S
· B(t .
)
(9.1)
We will consider a particular class of time-dependent magnetic fields, which we can write in the
form
B(t) ... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
)
(cid:12)
(cid:12)
(cid:12)
geB
0
2m
(cid:12)
(cid:12)
(cid:12)
(cid:12)
,
H0 = ω0Sz
.
(9.4)
(9.5)
(9.6)
(9.7)
(9.8)
(Note that we are taking e < 0 so that the signs work out here.) The time-evolution operator due
to this part of the Hamiltonian is
(cid:126)
U0(t) = e−iH0t/ .
The equation of motion in the interaction ... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
the first line we have expanded the exponentials, using the fact that the Pauli matrices
square to the identity. In the second line, we have used the fact that σz anticommutes with both
σx and σy. Note that
σx + iσy =
(cid:18)0 1(cid:19)
1 0
(cid:19)
(cid:18)0 −i
i
0
i
+
=
(cid:18)
(cid:19)
0 2
0 0
.
(9.14)
This is why ... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
1 t. The frequency of
ωR =
(cid:12)
(cid:12)
(cid:12)
(cid:12)
geB
1
2m
(cid:12)
(cid:12)
(cid:12)
(cid:12)
,
(9.19)
Lecture 9
8.321 Quantum Theory I, Fall 2017
50
is called the Rabi frequency. Note that the time-evolution operator,
UI(t
) = e−iωRS t/(cid:126)
x
−
= e
(cid:16) ω tR
2
i
(cid:17) x
σ
,
does not oscillat... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
19)(cid:19)(cid:18)1
0
(cid:19)
(cid:33)(cid:18)1
0
=
=
=
(cid:18)
cos
(cid:18) ωRt
2
(cid:32) cos(cid:0) ωRt
2
−i sin(cid:0) ωRt
2
(cid:32) cos(cid:0) ωRt
(cid:1)
2
−i sin(cid:0) ωRt
2
(cid:33)
.
(cid:1)
Thus, after a time t = π
ωR
, we have
|ψI(π/ωR)(cid:105) →
(cid:18)
(cid:19)
0
−i
,
and after a time t = 2π , we ha... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
ff + B (t)⊥
· S ) .⊥
ω
γ
,
Beff := B0 +
γ :=
ge
2m
.
(9.27)
(9.28)
(9.29)
Now, let’s work in the interaction picture with these choices. Going to the interaction picture is
going to a rotating frame, that rotates with H0. Previously, we went to a frame that rotated about
the z-axis at frequency ω0; now we are going to a ... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
)a(cid:48)(cid:11) ,
ca(cid:48)(t)
(cid:12)
a(cid:48)
where the |a(cid:48)(cid:105) form an energy eigenbasis, and
ca(cid:48)(t) = e−iEa(cid:48) (t−t0)/(cid:126)ca(cid:48)(t0) .
We can consider these particles in position space, and define
ua(cid:48)(x) = (cid:10)x(cid:12)
(cid:12)a(cid:48)(cid:11)
(9.32)
(9.33)
(9.34)
... | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
MIT OpenCourseWare
https://ocw.mit.edu
8.321 Quantum Theory I
Fall 2017
For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms. | https://ocw.mit.edu/courses/8-321-quantum-theory-i-fall-2017/1d8cd3d97c8c26f16bea95051466574c_MIT8_321F17_lec9.pdf |
Engineering Risk Benefit Analysis
1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ESD.72
CBA 3.
Bases for Comparison of Alternatives
George E. Apostolakis
Massachusetts Institute of Technology
Spring 2007
CBA 3. Bases for Comparison of Alternatives
1
Overview
•(Net) Present Worth or Value [(N)PW or
(N)PV] ... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
be $500 per month for 3 years at a nominal interest rate
of 10%. Assuming monthly compounding, what is the
present price you are paying?
From CBA 2, Slide 14, we get
)n,i,A/P(
=
(1
+
i)
n
)i1(i
+
1
−
n
Here: A = $500/mo, i = 10/12 = 0.83%, n = 36 months
,5P
=
000
+
[500
=
,5
000
+
,15
505
=
,20$
.01(
+
0083
)
36
−
.... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
15,000
-400
-400
3,000
• The benefits from these alternatives are
identical. We must select one.
• Assume that i = 10%.
CBA 3. Bases for Comparison of Alternatives
8
Total Investment Comparisons (2)
10(PW
%)
3B
−=
,12
000
−
,1
200
2
1.1
1
−
2
1.1x1.0
+
,1
500
3
1.1
=
−=
,12
000
−
,1
200
736.1x
+
,1
.1
500
331
−=
,12... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
: F = 1,200(F/P, 9, 1) = 1,200x1.091 = $1,308
(cid:190) End of year 2: 1,200x1.092 = 1,426
End of Year
0
1
2
3
B3
-$12,000
-1,308
-1,426
1,943
B4
-$15,000
-436
-475
3,885
CBA 3. Bases for Comparison of Alternatives
11
Impact of Inflation (2)
• Recalculate the PWs.
10(PW
%)
3B
−=
,12
000
−
−=
,12$
908
−<
,12$
870
=
−... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
1.1
−=
$
485
<
0
• B3 should be accepted, just as in slide 9.
• PW- or AE-based results using total and
incremental investments are identical.
CBA 3. Bases for Comparison of Alternatives
14
Internal Rate of Return (IRR)
• It is the interest rate for which the equivalent receipts of a
cash flow equal the equivalent d... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
Flows with a Single IRR
•
The IRR is a useful concept when the shape of
PW(i) is like the one on Fig. 6.3 (slide 18).
Sufficient Conditions
1. F0 < 0 (The first nonzero cash flow is a disbursement)
2. The sequence F0, F1, F2, …, Fn, has one change in
sign only.
3. PW(0) > 0 (sum of all receipts > sum of all
disburse... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
alternative are all zero.
CBA 3. Bases for Comparison of Alternatives
22
IRR on Incremental Investment
1. Make sure the cash flows satisfy the conditions on
slide 19.
2. List alternatives in ascending order based on
initial cost.
3. The “current best” alternative can be the “Do
Nothing” one.
4. Determine the differ... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
26
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0
($2,000)
($4,000)
Example (4)
A1 A2 A2-A1
0.1987
0.2499
0.1
0.2
0.3
0.4
0.5
0.1056
CBA 3. Bases for Comparison of Alternatives
27
Example (5)
To compare A3 to A1, we must solve
0 = -5,000 + 1,100(P/A, x31, 10)
0
−=
,5
000
+
100,1
10
)x1(
1
+
−
31
10
)x1(x
+
31
31
i
... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
(2)
Similarly,
i*
A0 =
%15
i*
A1 =
%25
i*
A2 =
%9.19
i*
A3
=
%4.21
• The “best” alternative (i.e., the one having the
highest IRR) is A1, not A3 (slide 28).
CBA 3. Bases for Comparison of Alternatives
31
IRR on Total Investment (3)
A1 A2 A3
$16,000
$14,000
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
($2,000)
0
($4... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
400
=
,2
026
>
0
10
+
)15.01(
−
)15.01(15.0
+
1
10
=
• Therefore, A1 becomes the current best alternative.
CBA 3. Bases for Comparison of Alternatives
35
The Example Revisited (2)
Similarly, PW(15)A2-A1 = -3,000 + 500(P/A, 15, 10)
)15(PW
−=−
AA
2
1
,3
000
+
500
10
+
)15.01(
−
)15.01(15.0
+
1
10
=
−=
490
<
0
• Therefor... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
3. Bases for Comparison of Alternatives
39
Example (1)
Alternative
A
B
C
Initial Cost
$4,000
$16,000
$20,000
Annual Cost
$6,400
$1,400
$1,000
Lifetime
6 years
3 years
4 years
A, B, and C all fulfill the same objective, but for a
different number of years; select the least costly for i
= 7%
CBA 3. Bas... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
is (approximately) the same as the original
value of 7.48K.
• The AEs that we calculated in slide 41 represent the
following extended cash flows.
CBA 3. Bases for Comparison of Alternatives
43
t (years)
0
1
2
3
4
5
6
7
8
9
10
11
12
Extended Cash Flows
A
(in $000)
4
6.4
6.4
6.4
6.4
6.4
10.4
6.4... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
CBA 3. Bases for Comparison of Alternatives
45
Present Worth of Original Alternatives
• PW(A, 6 yrs) = 4 + 6.4(P/A, 7%, 6) = 4 +(6.4)(4.76) =
= $34.46K
• PW(B, 3 yrs) = 16 + 1.4 (P/A, 7%, 3) =
= 16 +(1.4)(2.62) = $19.68K
• PW(C, 4 yrs) = 20 + 1 (P/A, 7%, 4) = 20 + 1(3.4) =
= $23.4K
• These are the PWs of costs ove... | https://ocw.mit.edu/courses/esd-72-engineering-risk-benefit-analysis-spring-2007/1ddaa9c180aa7db04223045ffdc70817_cba3.pdf |
Big Picture
1
2.003J/1.053J Dynamics and Control I, Spring 2007
Professor Thomas Peacock
2/7/2007
Lecture 1
Newton’s Laws, Cartesian and Polar
Coordinates, Dynamics of a Single Particle
Big Picture
First Half of the Course → Momentum Principles (Force, Vectors) Newtonian
Dynamics
Second Half of the Course → Lagra... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1e1173e9515ba00437cf6685d160de3e_lec01.pdf |
resultant force moves in such a manner
that the time rate of change of its linear momentum is equal to the force.
�
F = ma for a single particle.
where F is the force, m is the mass, and a is the acceleration.
III. 3rd Law - Forces that result from interactions of particles and such forces be
tween two particles a... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1e1173e9515ba00437cf6685d160de3e_lec01.pdf |
and Polar
3
r is position, and t is time. The direction of v is in the direction of Δr as Δt → 0.
The acceleration:
Acceleration is the time rate of change of its velocity.
a =
dv
dt
=
d2 r
dt2
Two coordinate systems: Cartesian and Polar
Velocities and accelerations can be expressed using a variety of differe... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1e1173e9515ba00437cf6685d160de3e_lec01.pdf |
ˆθ + rθ ¨ eˆθ − rθ˙2eˆr
v =
a =
dv
dt
a = (¨r − rθ˙2) ˆer + (rθ ¨ + 2 ˙rθ˙) ˆeθ
d
dt
eˆθ = −θ˙eˆr
Proof that dt = θeˆθ:
deˆr
˙
Figure 3: Differentiation of unit vectors. Changes in the direction of unit vector
eˆr can be related to changes in θ. Figure by MIT OCW.
deˆr
dt
= lim
Δ ˆer
Δt→0 Δt
|eˆr|Δθ
=... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1e1173e9515ba00437cf6685d160de3e_lec01.pdf |
mentum Conservation
Using an inertial frame of reference, here is the expression of Newton II:
�
F = ma
.
Linear Momentum Principle
�
F = (mv) = p˙
d
dt
(p = mv = Linear Momentum)
If �
F = 0, p is constant. (Conservation of Linear Momentum)
Angular Momentum Principle
Define Angular Momentum about B in an ine... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1e1173e9515ba00437cf6685d160de3e_lec01.pdf |
× mv.
If τB = 0 and vB = 0 or vB � mv ⇒ h˙ B = 0 (Conservation of Angular
Momentum)
Cite as: Thomas Peacock and Nicolas Hadjiconstantinou, course materials for 2.003J/1.053J Dynamics and
Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month ... | https://ocw.mit.edu/courses/2-003j-dynamics-and-control-i-spring-2007/1e1173e9515ba00437cf6685d160de3e_lec01.pdf |
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
SLOAN SCHOOL OF MANAGEMENT
15.565 Integrating Information Systems:
Technology, Strategy, and Organizational Factors
15.578 Global Information Systems:
Communications & Connectivity Among Information Systems
Spring 2002
Lecture 4
INTER- AND INTRA-
ORGANIZATIONAL SYSTEMS
1
Diff... | https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/1e11f1d7504656e102fec6aa1f2283f7_lecture04.pdf |
SPAWNING ENTIRELY NEW BUSINESSES
EFFECTIVE STRATEGIES DO ALL THREE!
6
EXAMPLE
FIRM INFRASTRUCTURE
HUMAN RESOURCE MANAGEMENT
TECHNOLOGY DEVELOPMENT
MARGIN
PROCUREMENT
INBOUND
LOGISTICS
OPERATIONS
OUTBOUND
LOGISTICS
MARKETING
AND SALES
SERVICE
MARGIN
POTENTIAL NEW ENTRANT
FIRM INFRASTRUCTURE
HUMAN RESOU... | https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/1e11f1d7504656e102fec6aa1f2283f7_lecture04.pdf |
• “Kill or Cure” - Alternatives?
Mfg
Direct
60%
(rising)
(dropping)
Chain Drug Store
Distributors/
Wholesalers
40%
{ McKesson
20%
Independent
Drug Stores
9
RELATIONSHIP BETWEEN DRUGSTORE
AND WHOLESALER
• 3-5 Major Wholesalers, many small players
• “Good-Old-Boy” Relationship
• “Sales” calls to creat... | https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/1e11f1d7504656e102fec6aa1f2283f7_lecture04.pdf |
ICE AND WAREHOUSE PRODUCTIVITY INCREASED
• ROLE OF SALESPEOPLE CHANGED
• Reduced by 50%
• Sell “System”
13
LONG-TERM IMPACTS
• MARKET SHARE? (mid-1970s=20%)
< 30%
30-50%
>50%
• REVENUES? (mid-1970s=$720M)
< $10B
$10-20B
>$20B
14
IMPACT ON DRUG WHOLESALING
INDUSTRY STRUCTURE
• RAISED “TABLE STAKES”
• N... | https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/1e11f1d7504656e102fec6aa1f2283f7_lecture04.pdf |
• Support cost and differentiation strategies
• Alters industry structure
• Spawn entirely new businesses
• NOTE INTERDEPENDENCE OF
STRATEGY, TECHNOLOGY AND ORGANIZATION
18 | https://ocw.mit.edu/courses/15-565j-integrating-esystems-global-information-systems-spring-2002/1e11f1d7504656e102fec6aa1f2283f7_lecture04.pdf |
Simplest Car Following Tra(cid:14)c Flow Model.
Rodolfo R. Rosales
.
(cid:3)
MIT, Friday March 26, 1999.
Abstract
These notes describe in some detail the continuum limit behavior of a very simple car following
tra(cid:14)c (cid:13)ow model. The formation and behavior of shock waves is described. This model is the
one s... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
Measure distance ~x along the road in the same direction the cars move (so the car velocities ~u
are all
n
non-negative). Number the cars so that
~x
is an increasing sequence ( ~x
~x
) > car length > 0
n
n
n
+1
f
g
(cid:0)
(identify ~x
with the location of (say) the front end of the car).
n
Remark 1.1 We use tildes ove... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
1999 | Rosales.
notation
h
= (1= ~(cid:26)
) = ~x
~x
for the car separation. Typical shapes for the car velocity
U and
n
n
n
n
+1
~
~
the car (cid:13)ow
Q = ~(cid:26)
U (both functions of ~(cid:26)) are shown in (cid:12)gure 1.1.
~
~
(cid:0)
Then the model is given by the following set of coupled ODE’s
d ~x
n
~
d
t
= ~... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
)
and (cid:26)
=
;
(1.4)
n
n
n
dt
x
x
n
n
+1
(cid:0)
where (cid:15) = 1=(L(cid:26)
) is a small nondimensional number | with the values above and with L a large
J
fraction of a mile, we get (cid:15) = O(10
) . Note also that the nondimensional versions of the car
(cid:0)
2
velocity and car (cid:13)ow functions have the... | 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 mile). Thus our assumption
above (where we took L a large fraction of a mile) is quite reasonable. This, in addition to
(cid:15) = O(10
) , yields (in the nondimensionalization above in (1.3)) a time scale
in the
(cid:0)
2
L(cid:26)
J
q
m
order of a few minutes | 6 min for L a ful l mile and 3 min for half a mile.... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
limit we are taking. In practice (cid:15) is (cid:12)xed. However, since (cid:15) is
small, we expect the limit will give us useful information regarding the behavior of the model (1.4).
4
Think of how many points per wavelength are needed to have a reasonable drawing of a sine wave.
Simple Tra(cid:14)c Flow Model.
5
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
We expect (cid:26) to be reasonably nice and (generally) have O(1) partial derivatives
and
.
@(cid:26)
@(cid:26)
@ t
@x
(cid:26)
= (cid:26)(x
; t) :
(2.3)
n
n
We now rewrite the equations for the model (1.4) in terms of the densities rather than the car
positions. Thus we have
d
(cid:0)
1
2
d
u
u
n
n
+1
(cid:26)
=
(cid... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
that (cid:26) above in (2.3) must satisfy the PDE
5
For example: we used
=
in remark 1.2 (with
20) to determine
.
(cid:26)
(cid:26)
(cid:3)
m
N
L
(cid:25)
L
min
@(cid:26)
@ q
@(cid:26)
@(cid:26)
0 =
+
=
+ c
(2.5)
@ t
@x
@ t
@x
Simple Tra(cid:14)c Flow Model.
6
MIT, Friday March 26, 1999 | Rosales.
in the limit (... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
go beyond one, for as soon as (cid:26)
reaches one, the n
car will
n
th
stop, while the (n + 1)
car will be moving at a non-negative velocity. (iii) Thus, the condition
th
0 < (cid:26)
1 will be preserved. (iv) This is enough to guarantee a solution for all times, for a solution
n
(cid:20)
can cease to exist only if it... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
) behaves nicely, it does approximate quite well
the behavior of the solution of (1.4).
2. The solution of (2.5) exhibits breakdown with formation of in(cid:12)nities in the
derivatives in the regions where the density (cid:26) is increasing with x. In these
regions, the solution of (1.4) also shows progressive steepen... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
function across a discontinuity. This
condition is called the Rankine{Hugoniot jump condition.
The (so called) entropy condition must hold
across shocks the density increases.
(2.8)
In terms of the characteristic curves for equation (2.5), this means that the curves converge
into the shock | and terminate there. Thus t... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
a Taylor series centered at x
. That is u
= u
+ u
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... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
@(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 are bounded, the e(cid:11)ects of this
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
important for many reasons, some of which we will explain
later on. In particular: in any numerical calculation we must make sure that all times scales are
handled properly, even if they are not immediately apparent in the solution | the precise meaning
of this last rather strange statement will be clari(cid:12)ed belo... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
this is the same type of solution used in the von Neumann stability analysis of numerical schemes.
(cid:0)
f
(cid:0)
g
(cid:16)
(cid:17)
Simple Tra(cid:14)c Flow Model.
10
MIT, Friday March 26, 1999 | Rosales.
where
(cid:25)
k
(cid:25) (these solutions are periodic in the wavenumber k , since the exponential is
(cid:0... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
)
is precisely the time scale over
m
which rapid variations in the car separations are \wiped out" by the time evolution of
the model. This is the process il lustrated by the MatLab script randCFSM. After these variations
are eliminated, this time scale plays no role, except to the extent that it keeps eliminating any ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
this need not be so with a numerical scheme if one is not careful. Precisely because
the equations being approximated are so forceful about dissipating errors, naive numerical
approximations can easily over do the e(cid:11)ect and end up amplifying the pertur-
bations! A simple example of this is provided by the equati... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
in (3.3) have negative real parts, so al l
the scales decay. Thus, if we wait long enough, not just the short wavelength (a few car distances
long) variations wil l vanish, but the long ones as wel l. Although this conclusion is based on the
linearized analysis in (3.1 { 3.3) and thus is valid only for smal l perturbat... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
28)
. It is clear that
m
the model (1.4) does not al low accidents (car col lisions). These would require (at the very least)
that (cid:26)
> 1 somewhere, sometime. But we showed earlier (see the paragraph above the note 2.1)
n
that the equations wil l not let this happen. The time (cid:28)
is closely associated with t... | 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:15)
(cid:15)
(cid:15)
y
y
+
= x
x
=
=
(cid:14)
;
n
n
n
n
n
+1
+1
(cid:0)
(cid:0)
n
(cid:26)
(cid:26)
(cid:26)
(cid:0)
(cid:26)
(cid:3)
(cid:3)
(cid:3)
2
where we used (3.1) and neglected quadratic terms in the perturbations. Thus
2
(cid:26)
(cid:3)
(cid:14)
=
(y
y
) :
n
n
n
+1
(cid:0)
(cid:15)
(cid:0)
Since u
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
= 2 u
. These numbers are
m
J
m
max
m
1
2 q
m
2
(cid:26)
J
compatible with the typical values given earlier above equation (1.3), except that the maximum car
velocity seems a bit low (though not out of range). Then again, the typical values given are from
measurements in the NYC Lincoln tunnel in the 1950’s (where, per... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
J
~(cid:26)
!
(cid:0)
where (cid:26)
= ‘
. This yields
J
(cid:0)
1
u
= u
;
(cid:26)
=
and q
= (cid: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 altoget... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
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)
. Similarl... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
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 car given and constant
. The ini-
1
2
N
N
9
tial conditions are such that (see (cid:12)gure 5.1) x
(0) = 0, x
(0) <
(cid:25) and
N
1
(cid:0)
(cid:26)
(0) = (cid:26)
+ (1
(cid... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
MIT, Friday March 26, 1999 | Rosales.
This equation determines the value of (cid:15) in terms of the number of cars in the hump and the densities
given by (5.1). Note also the relationship
(cid:0)
N
1
(cid:15)(N
1) =
(cid:26)
(x
x
) :
h
n
n
n
+1
(cid:0)
(cid:0)
n
p
=
X
As the number of cars increases (continuum limit) ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
equation
@ c
@
1
2
0 =
+
(
c
) ; with c(x; 0) = c
C (x) ;
(5.3)
N
@ t
@x
2
(cid:0)
where
4 < c
= 4
8(cid:26)
< 4 and C = (4 + c
)r(x). Thus the initial pro(cid:12)le for c has a \dip"
N
N
N
(cid:0)
(cid:0)
instead of a \hump".
In terms of c the shock condition (2.7) states: the shock speed is the
average of the charact... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
Then the shock starts at
1
t
=
and x
= (cid:16)
+ (c
C ((cid:16)
))t
:
S
S
m
N
m
S
(cid:0)
m
S
(cid:0)
Note that (cid:16)
must correspond to a location on the back end of the initial hump.
m
Typical solution after shock forms.
r
r
S
r
N
Shock
x
S
c
t
N
Areas under shock and multiple valued curve are equal.
Ty... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
and terminate
there. The only part that remains is the very stretched out front. Because the stretching is linear
in (cid:26), this part becomes a straight line, joining the front edge of the shock with the position of the
leading characteristic starting at the front edge of the initial hump (i.e. x = c
t). Thus the wa... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
0
A =
C (x)dx = (4 + c
)A
8((cid:15)(N
1)
(cid:25)(cid:26)
) ;
N
r
h
N
(cid:0)
(cid:25)
Z
(cid:25)
(cid:0)
(cid:0)
where we have used (5.2) and the fact that 4 + c
= 8(1
(cid:26)
) to write the last (approximate)
N
N
(cid:0)
equality. The formula for x
follows because this area must be conserved. Speci(cid:12)cally, no... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
Thus, in order to do the graphical comparisons of the continuum limit with the actual solutions
of the (1.4), the script quadCFSM uses an improved approximation, which we describe next
(the idea is actually very simple). As stated earlier, after a while the details of the solution are
- p
x = x
L
Area = A
c » c
N
... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
the
(cid:25)
t
(cid:25) (cid:0)
x
front part of the sawtooth, by the solution that follows from initial conditions as in (5.6). Other
than this, we use the same ideas that lead to (5.5), to obtain the improved approximation:
1. There is a shock at
: : : : : : : : : : : : : : : : : : : : : : : : : x
= c
t
.
S
N
2A(1 + B... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
>
>
>
>
>
>
>
>
>
>
>
>
>
>
Just one issue remains now and it is how to best choose B . For a given target time around which one
;
desires the approximation to be good, one can use (5.5) to get an estimate of what is the range of
characteristics that are making up the front of the saw-tooth. That is, one can determine ... | https://ocw.mit.edu/courses/18-306-advanced-partial-differential-equations-with-applications-fall-2009/1e6a824d45c144cecd4c0154ea3006a0_MIT18_306f09_lec24_CF_Simple_Model.pdf |
X
MIT OpenCourseWare
http://ocw.mit.edu
18.306 Advanced Partial Differential Equations with Applications
Fall 2009
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Simple Tra(cid:14)c Flow Model.
21
MIT, Friday March 26, 1999 | Rosales.
Thus, we obtain
(cid:15)(N
... | 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 |
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
conduct the analysis and drive technology investment
7
Progressive Exploration Capabilities
Sustainable
Planetary
Surface
Capability
Accessible ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
InIn--space propulsion,
Isp>3000 sec, high thrust
Isp>3000 sec, high thrust
Sustainable power
•• Sustainable power
systems
systems
Intelligent systems, orbital
Intelligent systems, orbital
and planetary
and planetary
Crew countermeasures for
•• Crew countermeasures for
indefinite duration
indefinite duration... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
2.52.5
Exploration
Exploration
and
and
Expeditions
Expeditions
2.62.6
Space
Space
Transportation
Transportation
9
An Agency-Wide Approach
THREADS
THREADS
Enterprises...
Enterprises...
1.0
Systems Integration, Analysis,
Concepts, Modeling
2.0
Enabling Advanced Research
and Technology
3.0
Technology Flight
Demons... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
, EVA)
√ Regenerative Life Support
Systems
√ Surface Science & Mobility
(Human-Involved)
√ Materials and Structures
(Manufacturing Validation)
√ Advanced Habitation Systems
x Space Nuclear Power
x In Situ Resource Utilization
x In Situ Manufacturing
√ Cryogenic Propellant Depots
x Space Medicine and Health Care
x Fl... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
3
Min Energy
Tether / Chemical
SEP/
Chem
HPEP/NEP
VaSImR
Gas Core NT
Trip time is for the crew departing from HEO.
0.5
1.0
1.5
2.0
Round Trip Mission Duration (years)
2.5
3.0
3.5
12
Agency Investments
Prioritized In-Space Propulsion Technologies
Process
•Requirements/Goals
Established by NASA
Enterprises
•... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
.
Report Available - Space Radiation Cancer Risk Projections
14
Hurdles: Crew Health & Safety
Artificial Gravity NEP Vehicle System Concepts
• Objective
– Develop and assess integrated NEP and artificial gravity
(AG) vehicle systems concepts as a means to mitigate the
deleterious effects of zero gravity on humans
... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
) (45%)
Aerobraking (42%)
Consum-
ables
HW
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8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
Space Architect Team/New Vision for
Space Exploration
19
Architecture Studies
• Architectures are used to:
– Understand requirements for exploration in the context of ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
exploration spacecraft
Artificial-g
Mars Transfer
Vehicle
GEO SAR
22
Architecture Study #1
Exploration Metro Map
Sun, Mercury, Venus
Sun-Earth L1 , L2
High Earth Orbit
Earth-Moon L1, L2
Earth
Low Earth Orbit
Moon
d
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r
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b
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g
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h
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A
Mars
Outer ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
h
t
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a
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A
Mars
Outer Planets
and beyond
25
National Vision for Space Exploration
THE FUNDAMENTAL GOAL OF THIS VISION IS TO ADVANCE U.S.
SCIENTIFIC, SECURITY, AND ECONOMIC INTEREST THROUGH A ROBUST
SPACE EXPLORATION PROGRAM
Implement a sustained and afforda... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Mars
Scout
Mars Robotic Missions
Outer Moons
Cassini
Saturn
Arrival
Cassini
Titan
Landing
Jupiter
Icy Moons
Orbiter
Earth-Like Planets
and Life
Hubble Space
Telescope
Kepler
Mission
Webb Space
Telescope
Terrestrial Planet
Finder
Spitzer Space
Telescope
Space Interferometry
Mission
Optical Comm Demo
Nuclear Power / Pro... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
search for evidence of life, to
understand the history of the solar system, and to prepare for future human exploration.
(1.5) NASA shall conduct human expeditions to Mars to extend the search for life and to
expand the frontiers of human exploration after successfully demonstrating human
exploration mission to the ... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
liquid water as candidate site
for evidence of extant life/pre-biotic chemistry
Explore Global Evolution of Mars: Examine initial conditions and investigate
why terrestrial planets evolved differently, much more so than we had
thought, if no evidence of past or present liquid water has been found
30
Notional Archit... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
conjunction
opposition (See chart ? for details)
crew/cargo* separately
predeploy 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
M... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
O
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 Mission
Transfer to Moon
Chem/... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Develop Capabilities through infusion
of new technologies as they become
available consistent with flight
hardware schedule
Develop Capabilities through infusion of
breakthrough technologies when they
become available
Agency Programmatic Approach
Current Structure & new management
methods
Smaller NASA Infrastruct... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
unar Arrival
Lunar Ascent/Descent
Lunar Departure
Earth Arrival
Earth Surface Landing
Surface Landing Infrastructure
Mars Robotic Precursors
Lunar Robotic Precursors
Bioastronautics
Management Structure
Agency Infrastructure
Civil Service Role
International Partnerships
Acquisition Strategy
Budget/Cost Strategy
Capabil... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Robotic Science continues af
Human Departure
Robotic Science concluded at
departure
Mission Design Approach
Convenient Opportunities
Any Opportunity
SFL extant life (Hydrothermal deposits)
SFL Global Evolution
91-500 Days (Long)
(See Chart ? for inferred capabilities)
Sustained Outpost
(McMurdo model)
> 500 Days
Whe... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
LEO
28.5
HEO
Different LV
Existing LV
Other
Lunar Vicinity
Update existing infrastructure Build new NASA Infrastructure
Use new Industry infrastructure
Heliocentric Transfer to Mars
Crew Propulsive transit
Nuclear
(See chart ? for propulsion
metrics)
Advanced Chemical
Cargo Propulsive Transit
Nuclear
Advanced Chemical... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
ISS
Higher autonomy than ISS
Full autonomy
Operations Infrastructure for Moon
Navigation/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 Orbi... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
biter in 2008/Lander 2009
only
Orbiter 2008/Lander by 2012 on
(See Chart ? for lunar robotic optio
Precursors
Start in 2011 - multiple missions
(See Chart ? for Mars robotic options)
Start in 2016 or later
Multiple orbiters, landers & sample returnsMultiple orbiters and landers
Bioastronautics
Use ground research only... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Location for Assembly**
Orbit Location for final Crew
Rendezvous
Launch Infrastructure
Crew Propulsive transit
Cargo Propulsive Transit
Crew/Cargo
HLLV
51.6
LEO
New LV
LEO
28.5
HEO
Different LV
Existing LV
Other
Lunar Vicinity
HEO
Lunar Vicinity
Update existing infrastructure Build new NASA Infrastructure
Use new Indu... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Operations Infrastructure for Moon
Navigation/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
Earth Orbit Approach
Crew to Orbit approach
Orbit Location for... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
in 2016 or later
Orbiter in 2008/Lander 2009
only
Orbiter 2008/Lander by 2012 onlyMultiple orbiters, landers & sample returnsMultiple orbiters and landers
Use ground research only to
certify crews for deep space
Use ISS and ground research t
certify crews for deep space
Use ISS, ground research and Moon to
certify crew... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
Different LV
Existing LV
Other
Lunar Vicinity
Update existing infrastructure Build new NASA Infrastructure
Use new Industry infrastructure
Heliocentric Transfer to Mars (In-Space Transportation)
Crew Propulsive transit
Nuclear
(See chart ? for propulsion
metrics)
Advanced Chemical
Cargo Propulsive Transit
Nuclear
Adva... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
)
Campaign Different Site
Campaign same sites
Sustained presence with robotics
Mission Control
Same autonomy as ISS
Higher autonomy than ISS
Full autonomy
Operations Infrastructure for Moon
Navigation/Communication
Space Weather
Use existing US assets, no
additional investment
Use existing US assets, no
additional inv... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
2011 - 1 mission only
Lunar Robotic Precursors
Orbiter in 2008/Lander 2009
only
Orbiter 2008/Lander by 2012 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 l... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
ate
Separate
Lander
Lander
Crew Launch
EARTH
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
• Cl... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
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 Architecture
Exploration Research Testbeds
Exploration Research Needs
Integrated Mission Validation
Ground
ISS
Lunar
Mars
Robo... | https://ocw.mit.edu/courses/16-892j-space-system-architecture-and-design-fall-2004/1eb80d3e0594fe46d8a6cc8a1321d6dc_architecture_mit.pdf |
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