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 the covariance of
A and B.
Correlation coecient cAB is a
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 predicate appears more than twice among the subgoals of Q1.
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 between U0 and a harmonic
lattice
U(r, ) = U0 (r) +
A ( = 0
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 predicate appears more than twice among the subgoals of Q1.
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).
Therefore, the L/S test will be positive for all
canonical DB'
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 these methods, the stays constant while the
number of at
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 dimensionless friction factor with virtual
mass Q , which controls
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).
Therefore, the L/S test will be positive for all
canonical DB'
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 NkB T .
2
Using this and the rate equation in the deni
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.
Let D be the canonical (frozen) database from
CQ Pi .
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 particle positions qk :
qk
dH
dqk
= kB T .
(13)
In Cartesian
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.
Let D be the canonical (frozen) database from
CQ Pi .
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 Ei /(kB T )
e
= e(Ei A)/(kB T ) .
Q
Normalizing factor,
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 elements
(\triggers," constraints, instantiated views).
Use
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 constructing a smaller model system with
relevant constrain
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 elements
(\triggers," constraints, instantiated views).
Use
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 at correct place.
It also gives a proper description o
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 oriented, reliable communication
over reliable and unrelia
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 neglects the eect of relaxation, but in
simple metals i
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 oriented, reliable communication
over reliable and unrelia
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, since Uij = Uji .
When we have both twobody terms Uij
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 mdmorse code.
Functional form is
U(r) =
De2(rij r0 ) 2De(rij
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

Let p1 and p2 denote the
momenta.
The force constant is C
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),
grandparent (P, Y),
X = Y,
not sibling (X, Y).
We only allow us
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 )+
i ,j
U3 (ri , rj , rk )
U2 (ri , rj )+
F
j
g2 (ri ,
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),
grandparent (P, Y),
X = Y,
not sibling (X, Y).
We only allow us
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 )+
i ,j
U3 (ri , rj , rk )
U2 (ri , rj )+
F
j
g2 (ri ,
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: use of indirection
a host sends IP datagrams to multicas