T
C
T
Correlations between two quantities, A and B are
measured via the correlation coecient
cAB =
AB
,
(A)(B)
(47)
where 2 (A) = A2 ens A 2 ( is the standard
ens
deviation), and A = A A ens . AB is t
CS345 Notes for Lecture 10/14cfw_16/96
Saraiya's Containment Test
Containment of CQ's is NPcomplete in general.
Sariaya's algorithm is a polynomialtime test
of Q1 Q2 for the common case that no pred
Then, absolute internal energy A can be calculated for any
with
U
A ( ) A ( 0 ) =
0
d.
(40)
The real potential function, for which we want to calculate
A is U0 .
So, constructed U interpolates betwee
CS345 Notes for Lecture 10/14cfw_16/96
Saraiya's Containment Test
Containment of CQ's is NPcomplete in general.
Sariaya's algorithm is a polynomialtime test
of Q1 Q2 for the common case that no pred
CS345 Notes for Lecture 10/21/96
Proof L/S Algorithm Works: OnlyIf
Suppose Q1 Q2. Let D be any of the canonical
DB's.
If Q1(D) contains the frozen head of Q1, then
since Q1 Q2, so does Q2(D).
Therefo
Allowing the cell shape to change is critical in the case of
some phase transitions.
In the original paper, the authors used this method to
model a fcchcp phase transition in Ni.
Notes
M
VT E
Within t
NosHoover method
[W. Hoower, Phys.Rev.A 31, 1695 (1985)]
The Hamiltonian is modied by adding a virtual degree of
freedom (timescale variable s) with its own Ks and Us .
This introduces a dimensionle
CS345 Notes for Lecture 10/21/96
Proof L/S Algorithm Works: OnlyIf
Suppose Q1 Q2. Let D be any of the canonical
DB's.
If Q1(D) contains the frozen head of Q1, then
since Q1 Q2, so does Q2(D).
Therefo
Solving for the T (t ) leads to
T
dT (t )
+ T = T0 , T (t ) = const . et /T + T0
dt
(22)
where the constant is Ti T0 , Ti is the initial temperature.
By scaling v v , the energy changes by
E = (2 1) 3
CS345 Notes for Lecture 10/16/96
Generalization to Unions of CQ's
P1 P2
Pk Q1 Q2
Qn i for
all Pi there is some one Qj such that Pi Qj .
Proof (If)
Obvious.
Proof (Only If)
Assume the containment holds
Pressure is less straightforward than the total energy or
temperature of the system, but still accessible during MD
calculations.
Now, we start with the generalized equipartition theorem
for the parti
CS345 Notes for Lecture 10/16/96
Generalization to Unions of CQ's
P1 P2
Pk Q1 Q2
Qn i for
all Pi there is some one Qj such that Pi Qj .
Proof (If)
Obvious.
Proof (Only If)
Assume the containment holds
C
E
(NVT )
In canonical ensemble the system is closed, but not
heatisolated.
Instead, it is immersed in a large heat bath.
Now the occupation probabilities follow the
Boltzmann distribution:
pi =
1 E
CS345 Notes for Lecture 10/14/96
Conjunctive Queries
= safe, datalog rules:
H : G1 &
&
G
n
Most common form of query; equivalent to
selectprojectjoin queries.
Useful for optimization of active elem
Molecular Dynamics simulations
Lecture 05:
Equilibrium Thermodynamics
Dr. Jani Kotakoski
University of Helsinki
Fall 2011
Notes
T
E
A macroscopic system in a certain environment can be
modeled by cons
CS345 Notes for Lecture 10/14/96
Conjunctive Queries
= safe, datalog rules:
H : G1 &
&
G
n
Most common form of query; equivalent to
selectprojectjoin queries.
Useful for optimization of active elem
R
P
Another part where we may need to replace the original
potential is at the shortest interatomic distances.
In most analytic potentials the repulsive part simply
allows having the potential minimum
TCP
CSE 6590
Winter 2012
February 14, 2012
1
TCP
Services
Flow control
Connection establishment and termination
Congestion control
2
TCP Services
Transmission Control Protocol (RFC 793)
connection ori
However, ab initio calculations give [Solid State Physics:
Advances in Research and Applications, 43 (1990) 1]:
Element
V
Nb
W
Ecoh (eV)
5.31
7.57
8.90
Ef (eV)
2.1 0.2
2.6 0.3
4.0 0.2
This comparison
TCP
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February 14, 2012
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TCP
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Flow control
Connection establishment and termination
Congestion control
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F
T
B
P
For a pair potential, Uij = Uji since the potential only
depends on rij = rij  = rji . This simplies the force
calculation.
In the case of a threebody potential, things are more
dicult,
Morse Potential
Pair potentials work reasonably for simple metals (e.g., Na,
Mg, Al and fcc/hcp metals). Another often used one is the
Morse potential [Phys. Rev. 34 (1930) 57].
Also used in the mdmor
As a model, lets consider two oscillators, which are
separated by distance R.
Each oscillator has charges of e with separations x1 and
x2 . The particles oscillate along the x axis.
+
x2

R
+
x1

Le
Winter 2006
COSC6490B: Issues in Information IntegrationGodfrey
Negation
Datalog with Negation
Okay. Let us add not to the Datalog language (Datalog).
E.g.,
cousin (X, Y) grandparent (P, X),
grandpar
D
I
P
Pair potentials:
U(r) =
Pair functionals:
U[F , r] =
Cluster potentials:
U(r) =
U0 +
i ,j
U2 (ri , rj ) +
U0 +
i ,j ,k
Cluster functionals:
U[F , r] =
i ,j
i
U2 (ri , rj )
i ,j
i
F
j
U2 (ri , rj
Winter 2006
COSC6490B: Issues in Information IntegrationGodfrey
Negation
Datalog with Negation
Okay. Let us add not to the Datalog language (Datalog).
E.g.,
cousin (X, Y) grandparent (P, X),
grandpar
D
I
P
Pair potentials:
U(r) =
Pair functionals:
U[F , r] =
Cluster potentials:
U(r) =
U0 +
i ,j
U2 (ri , rj ) +
U0 +
i ,j ,k
Cluster functionals:
U[F , r] =
i ,j
i
U2 (ri , rj )
i ,j
i
F
j
U2 (ri , rj
Multicasting
CSE 6590
Winter 2012
February 14, 2012
1
Internet Multicast Service Model
128.59.16.12
128.119.40.186
multicast
group
226.17.30.197
128.34.108.63
128.34.108.60
Multicast group concept: us