the monte carlo method in condensed matter physics
Fundamentals of the monte carlo method for neutral and charged particle transport
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09/04/2014, 16:23
... provide intuition for the design of the
measurement. Monte Carlo methods are an adjunct to this process as well, serving in the
analysis of the experiment and verifying or invalidating the design.
... =sinθ cos φ = u
0
cos Θ + sin Θ(w
0
cos Φ cos φ
0
− sin Φ sin φ
0
)
v =sinθ sin φ = v
0
cos Θ + sin Θ(w
0
cos Φ sin φ
0
+sinΦcosφ
0
)
w =cosθ = w
0
cos Θ − sin Θ sin θ
0
cos Φ (7.13)
Returning ... Science
Practical results
intuition
intuition
analysis
verification
Figure 1.6: The role of Monte Carlo methods in applied science.
1.1 Why is Monte Carlo?
If Monte Carlo did not exist there would be strong...
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many-body quantum theory in condensed matter physics
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24/04/2014, 17:13
... useful starting point for calcu-
lations. For example in atomic physics, where electrons orbiting a point-like positively
Introduction to
Many-body quantum theory in
condensed matter physics
Henrik ... of the
lattice, V
el−latt
, and the vibrating part, i.e. the phonons, V
el−ph
. The latter term must
be there since a vibrating ion is giving rise to a vibrating electrical potential in uencing
the ... by
using the operator algebra Eq. (1.42) we show below that this operator in fact is the
Chapter 2
The electron gas
The study of the interacting electron gas moving in a charge compensating background...
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Simulation and the Monte Carlo Method Second Edition potx
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27/06/2014, 08:20
... at certain random times and are
served by a single server. Amving customers who find the server busy wait in the
queue. Customers are served in the order in which they arrive. The interarrival ... the Markov chain
is
transient, and they may not be
satisfied if the Markov chain is recurrent (namely when the states are null-recurrent). The
following theorem gives a method for obtaining ... that the number of arrivals in
an interval
(a,
6)
is
independent of the number of arrivals in interval
(c,
d)
when the two
intervals do not intersect. Such considerations lead to the...
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APPLICATIONS OF MONTE CARLO METHOD IN SCIENCE AND ENGINEERING_2 pot
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29/06/2014, 13:20
... via the exchange of the orientation of the lattice point A
by the orientation of some of neighboring points, e.g. by the orientation of the point B. Using
(2) we calculate the energy of the ... well. The algorithm of the pore
migration involves
-
the determination of the direction of the motion
-
the calculation of eventual change of the pore position in this direction.
Monte Carlo ... spins. The
magnetic dipole interaction works on all spins because it is due to magnetic field
interspersed in all space. Then the summation includes the interaction energy between i-th
spin...
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APPLICATIONS OF MONTE CARLO METHOD IN SCIENCAPPLICATIONS OF MONTE CARLO METHOD IN SCIENCE AND ENGINEERING_1E AND ENGINEERING_1 doc
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29/06/2014, 13:20
... photon
scattering in the image taken with the IDC detector can clearly be seen, the DIC image is quite
sharper. The resulting BSR values are shown in 2. In the DIC detector, the signal blurring
originates ... scattering in the detector volume. Since the scattering cross
section increases with photon energy, the BSR values also increase with the mean spectrum
energy. In the IDC detector, signal blurring ... defects. With the Monte- Carlo
simulation is it possible to simulate the scattering effects in the specimen and also the
distribution of the scattered radiation on the detector. If we know the intensity...
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SIMULATION AND THE MONTE CARLO METHOD Episode 2 pdf
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12/08/2014, 07:22
... substituting
into the Lagrangian the relations between the variables thus obtained.
EXAMPLE
1.18
Linear Programming Problem
Consider the following linear programming problem:
min
cTx
X ... at certain random times and are
served by a single server. Amving customers who find the server busy wait in the
queue. Customers are served in the order in which they arrive. The interarrival ...
PRELIMINARIES
1.15.1 Lagrangian
Method
The main components of the Lagrangian method are the Lagrange multipliers and the La-
grange function, The method was developed by Lagrange in 1797 for the...
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SIMULATION AND THE MONTE CARLO METHOD Episode 3 potx
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12/08/2014, 07:22
... reduced by using efficient search techniques (see
[2]).
In general, the inverse-transform method requires that the underlying cdf,
F,
exists
in a form for which the corresponding inverse function ...
where the initial value,
XO,
is called the seed and the
a,
c, and
m
(all positive integers) are
called the multiplier, the increment and the modulus, respectively. Note that applying the ...
X.
Otherwise, return to Step
1.
The theoretical basis of the acceptance-rejection method is provided by the following
theorem.
Theorem 2.3.1
The random variable generated according
to...
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A Guide to Monte Carlo Simulations in Statistical Physics, Second Edition potx
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22/03/2014, 09:20
... dependence of
the internal energy for the non-interacting Ising model, and this is also shown
in Fig. 2.1. Another important quantity, the entropy, measures the amount of
disorder in the system. The entropy ... and the phase boundary terminates at the critical temperature T
c
as
shown in Fig. 2.4. In this model it is easy to see, by invoking the symmetry
involving reversal of all the spins and the sign ... problems in statistical thermodynamics as applied to
condensed matter physics or materials science. There exist many other simu-
lational problems in physics (e.g. simulating the spectral intensity...
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