Discovering Nontrivial and Functional Behavior in Register Machines
ADHESIVE FORCES ON HELIUM IN NONTRIVIAL...
Transcript of ADHESIVE FORCES ON HELIUM IN NONTRIVIAL...
ADHESIVE FORCES ON HELIUM INNONTRIVIAL GEOMETRIES
E. S. H.
, A. Hernando
, R. Mayol
and M. Pi
University of Buenos Aires, Argentina
University of Barcelona, Spain
RPMBT14, July 2007 – p.1
Vapor particle + matter
RPMBT14, July 2007 – p.2
Vapor particle + matter
RPMBT14, July 2007 – p.2
Vapor particle + matter
RPMBT14, July 2007 – p.2
A popular choice
! "
RPMBT14, July 2007 – p.3
A popular choice
! "
$# %'& & ( # *) *+ ,
RPMBT14, July 2007 – p.3
A popular choice
! "
$# %'& & ( # *) *+ ,
# .- / # 01 2 2 / 3 2 2 - "
RPMBT14, July 2007 – p.3
Geometries with high symmetry
The LJ potential is analytically integrable (or quasiintegrable)
RPMBT14, July 2007 – p.4
FSM-16 hexagonal pores with six 3-9’s
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14d (Å)
-280-260-240-220-200-180-160-140-120-100
-80-60-40-20
02040
A, D
A, M
B, M
B, DA, D
B, M
B, D
Summation of six 3-9 potentials
(from M. Rossi, D. E. Galli and L. Reatto, JLTP 146, 98 (2006))
RPMBT14, July 2007 – p.5
Open questions
4
How legitimate is the continuum hypothesis?
How accurate is a LJ potential?
For metallic planar half-solids, an ab-initio is
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
Open questions
4
4 How legitimate is the continuum hypothesis?
How accurate is a LJ potential?
For metallic planar half-solids, an ab-initio is
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
Open questions
4
4 How legitimate is the continuum hypothesis?
4 How accurate is a LJ potential?
For metallic planar half-solids, an ab-initio is
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
Open questions
4
4 How legitimate is the continuum hypothesis?
4 How accurate is a LJ potential?
4 For metallic planar half-solids, an ab-initio
#
is
65 5 7 $# 8 :9;
(A. Chizmeshya, M. W. Cole, and E. Zaremba, J. Low Temp. Phys. 110, 677
(1998).)
RPMBT14, July 2007 – p.6
New question
Is the inverse problem solvable?, i.e., given < = $#
, can wefind sources
?
< = # & ( # *) *+
If so, then for almost any geometry,
RPMBT14, July 2007 – p.7
New question
Is the inverse problem solvable?, i.e., given < = $#
, can wefind sources
?
< = # & ( # *) *+
If so, then for almost any geometry,
RPMBT14, July 2007 – p.7
It is solvable!
For a half-solid with bulk density % & ,
# > ? ?@A B C 2 DFE GH 2
true for the LJ family
so that for other matter distributions
RPMBT14, July 2007 – p.8
It is solvable!
For a half-solid with bulk density % & ,
# > ? ?@A B C 2 DFE GH 2 true for the LJ family
. $I J ? ?LKNM O C D E GH
so that for other matter distributions
RPMBT14, July 2007 – p.8
It is solvable!
For a half-solid with bulk density % & ,
# > ? ?@A B C 2 DFE GH 2 true for the LJ family
. $I J ? ?LKNM O C D E GH
so that for other matter distributions
> ? ?@ A B CPRQ Q ? P D
E GH PRQ Q ? P
RPMBT14, July 2007 – p.8
A friendly unit cell
RPMBT14, July 2007 – p.9
Six half-solids make an hexagonal pore
RPMBT14, July 2007 – p.10
with strong overlap at the vertices
RPMBT14, July 2007 – p.11
so, we recommend SIX CUSPS INSTEAD
RPMBT14, July 2007 – p.12
with potential landscape
RPMBT14, July 2007 – p.13
The wedge
RPMBT14, July 2007 – p.14
The wedge was (ESH et al in PRB 73, 245406 (2006))
RPMBT14, July 2007 – p.15
while it may be
RPMBT14, July 2007 – p.16
with potential
RPMBT14, July 2007 – p.17
A striped substrate
RPMBT14, July 2007 – p.18
A sawtooth substrate
RPMBT14, July 2007 – p.19
FSM-16 hexagonal pores
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14d (Å)
-280-260-240-220-200-180-160-140-120-100
-80-60-40-20
02040
A, D
A, M
B, M
B, DA, D
B, M
B, D
Summation of six 3-9 potentials
RPMBT14, July 2007 – p.20
FSM-16 hexagonal pores
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14d (Å)
-280-260-240-220-200-180-160-140-120-100
-80-60-40-20
02040
A, D
A, M
B, M
B, DA, D
B, M
B, D
Summation of 3-9 potentialsvs. integration of the LJ field
RPMBT14, July 2007 – p.20
Metallic hexagonal pores
0 5 10d (Å)
-40
-20
0
20
40
Cs
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Metallic hexagonal pores
0 5 10d (Å)
-40
-20
0
20
40
CsK
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Metallic hexagonal pores
0 5 10d (Å)
-80
-60
-40
-20
0
20
40
CsKCs
Mg
Cs
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Metallic hexagonal pores
0 5 10d (Å)
-280
-240
-200
-160
-120
-80
-40
0
40
CsKMgFSM-16 Potential B
CsKMgFSM-16 Potential BFSM-16 Potential A
CsKMg
CsKMg
Integrated elementary vCCZ six planes with VCCZ
Potential along diagonal
RPMBT14, July 2007 – p.21
Standard DF theory at zero temperature
S T U V
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [ V W *) # % )ZY #
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [ V W *) # % )ZY #
\ S\ % ]
gives
RPMBT14, July 2007 – p.22
Standard DF theory at zero temperature
S T U V
T W *) # X % )ZY # [ V W *) # % )ZY #
\ S\ % ]
gives
^ !`_ a cb % b ed )ZY # " % )ZY # U % )ZY #
RPMBT14, July 2007 – p.22
Some density profiles obtained with DFT
-10 -5 0 5 10x (Å)
-10
-5
0
5
10
z (Å
)
4He in FSM-16 poreN/L = 0.8 Å-1
-10 -5 0 5 10x (Å)
-10
-5
0
5
10
z (Å
)
4He in Cs poreN/L = 2 Å-1
RPMBT14, July 2007 – p.23
Some EOS computed with DFT
-6
-4
-2
0
2
Ω /
N (
K)
Six planar V3-9 potentialsIntegrated VLJ
EOS for 4He in FSM-16 hexagonal porePotential B
0 0.2 0.4 0.6 0.8 1N / L (Å-1)
-150
-140
-130
-120
-110
E / N (K)µ (K)
RPMBT14, July 2007 – p.24
Some EOS computed with DFT
-4
-3
-2
-1
0Ω
/ N
(K
)Six VCCZ potentialsIntegrated vCCZ
EOS for 4He in Mg hexagonal poreCCZ potential
0 0.2 0.4 0.6 0.8 1N / L (Å-1)
-60-55-50-45-40-35
E / N (K)µ (K)
RPMBT14, July 2007 – p.24
Some energetics
f g fh i jh T lk m ln m opoLo qr qsq sopoLo
t f uv Y j
-178.36 -135.98 0.31t f u v Y g
-140.77 -105.36 0.34
w -51.04 -37.62 0.36Wx
-23.98 -17.22 0.39Vzy -16.35 -11.58 0.41m
-10.41 -7.24 0.44i
-9.45 -6.54 0.44|~ -9.01 -6.22 0.45RPMBT14, July 2007 – p.25
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
4
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
4
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
4 Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Why Cesium?
4 Planar Cs is heliophobic below 2 K,
4
BUT rounding, folding, roughening, etc, can makeheliophilic (i.e., cylinders and wedges;
4 Experimental evidence on hysterectic behavior andstrong dependence of the dynamics of the contact linein rough Cs surfaces,(J. Klier, P. Leiderer, D. Reinelt, and A. F. G. Wyatt, Phys. Rev. B 72, 245410
(2005))
4 the He–Cs system is an interesting laboratory forexperimenting on wetting physics.
RPMBT14, July 2007 – p.26
Some comparison among methods
-10 -5 0 5 10x (Å)
-10
-5
0
5
10
z (Å
)
He on Cs Hexagonal pore
0 5 10d (Å)
0
0.01
0.02
0.03
0.04
0.05
x-axis
integrationsummation
at N / L = 7 Å-1
z-axis
RPMBT14, July 2007 – p.27
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
if one knows the planar field .
The numerical algorithm is fast and precise.
No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
The numerical algorithm is fast and precise.
No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
4 No sound qualitative differences are to be found ineither calculation,
but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
4 No sound qualitative differences are to be found ineither calculation,
4 but substantial quantitative ones may show up.
Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28
Some summary
4 It is possible to fold, roll up, twist, squeeze, break,wrinkle... a planar solid and get the adsorptionpotential
felt by an atom in its vicinity
4 if one knows the planar field #
.
4 The numerical algorithm is fast and precise.
4 No sound qualitative differences are to be found ineither calculation,
4 but substantial quantitative ones may show up.
4 Nextcoming release (RPMBT15 and/or earliermeetings): Condensation of
He in polygonal andcurved pores in 2D and 3D at zero and finitetemperatures.
RPMBT14, July 2007 – p.28