formulasearchengine - User contributions [en]

Photon polarization

2013-12-20T17:12:44Z

129.63.129.196: Fixed an error in the first sentence.

{{Science with neutrons}}
'''Neutron spin echo''' spectroscopy is an [[inelastic neutron scattering]] technique invented by [[Ferenc Mezei]] in the 1970s, and developed in collaboration with John Hayter.<ref>
{{cite book |
booktitle = Neutron Spin Echo |
title = Neutron Spin Echo |
editor = Mezei, F. |
series = Lecture Notes in Physics Vol. 128 |
publisher = Springer |
address = Berlin, Heidelberg, New York |
year = 1980 |
issue = 128
}}
</ref>
In recognition of his work and in other areas, Mezei was awarded the first [http://neutron.neutron-eu.net/n_ensa/Prize Walter Haelg Prize] in 1999.

The [[spin echo]] spectrometer possesses an extremely high energy resolution (roughly one part in 100,000). Additionally, it measures the density-density correlation (or [[intermediate scattering function]]) F(Q,t) as a function of momentum transfer Q and time. Other neutron scattering techniques measure the dynamic structure factor S(Q,ω), which can be converted to F(Q,t) by a [[Fourier transform]], which may be difficult in practice. For weak inelastic features S(Q,ω) is better suited, however, for (slow) relaxations the natural representation
is given by F(Q,t). Because of its extraordinary high effective energy resolution compared to other neutron scattering techniques, NSE is an ideal method to observe<ref>{{cite journal |
author= [[Bela Farago|B. Farago]] |
journal=Physica B |
volume= 385-386 |
pages=688–691 |
year= 2006 |
title=Neutron spin echo study of well organized soft matter systems |
doi=10.1016/j.physb.2006.05.292|bibcode = 2006PhyB..385..688F }}</ref>
overdamped internal dynamic modes (relaxations) and other diffusive processes in materials such as a [[polymer blend]]s, [[alkane]] chains, or [[microemulsion]]s. The extraordinary power of NSE spectrometry was further demonstrated recently<ref name="pmid21081097">{{cite journal |author=[[Bela Farago|B. Farago]], Li J, Cornilescu G, [[David J E Callaway|Callaway DJE]], Bu Z |title=Activation of Nanoscale Allosteric Protein Domain Motion Revealed by Neutron Spin Echo Spectroscopy |journal=[[Biophysical Journal]] |volume=99 |issue=10 |pages=3473–3482 |date=November 2010 |pmid=21081097 |pmc=2980739 |doi=10.1016/j.bpj.2010.09.058 |url=http://linkinghub.elsevier.com/retrieve/pii/S0006-3495(10)01208-7|bibcode = 2010BpJ....99.3473F }}</ref><ref>{{cite journal |journal=[[Proceedings of the National Academy of Sciences|Proc Natl Acad Sci USA]] |volume=102 |issue=49 |pages=17646–17651 |year=2005 |author=Bu Z, Biehl R, Monkenbusch M, Richter D, [[David J E Callaway|Callaway DJE]] |title=Coupled protein domain motion in Taq polymerase revealed by neutron spin-echo spectroscopy |pmid=16306270 |doi=10.1073/pnas.0503388102 |pmc=1345721 |bibcode = 2005PNAS..10217646B }}</ref> by the direct observation of coupled internal [[protein dynamics]] in the [[protein]]s [[NHERF1]] and [[Taq polymerase]], allowing the direct visualization of protein [[molecular machine|nanomachinery]] in motion.

==How it works==
Basically Neutron spin echo is a [[Time of flight|time-of-flight]] technique. Concerning the neutron spins it has a strong analogy to the so-called [[Hahn echo]],<ref>
{{cite journal |
author=E.L. Hahn |
journal=Physical Review |
volume=80 |
page=580 |
year=1950 |
title=Spin Echoes|bibcode = 1950PhRv...80..580H |doi = 10.1103/PhysRev.80.580 }}</ref> well known in the
field of [[NMR]]. In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation,
that leads to a restituation of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of the
nuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam.
The [[Larmor precession]] of the neutron spin in a preparation zone with a magnetic field before the sample encodes
the individual velocities of neutrons in the beam into precession angles. Close to the sample the time reversal is effected by a so-called
flipper. A symmetric decoding zone follows such that at its end the precession angle accumulated in the preparation zone is exactly compensated
(provided the sample did not change the neutron velocity, i.e. elastic scattering), all spins rephase to form the "spin-echo". Ideally the full polarization is restored. This effect does not depend on the velocity/energy/wavelength of the incoming neutron.
If the scattering at the sample is not elastic but changes the neutron velocity, the rephasing will become incomplete and a loss of final
polarization results, which depends on the distribution of differences in the time, which the neutrons need to fly through the symmetric first (coding) and second (decoding)precession zones. The time differences occur due to a velocity change acquired by non-elastic scattering at the sample.
The distribution of these time differences is proportional (in the linearization approximation which is appropriate for quasi-elastic high resolution spectroscopy) to the spectral part of the [[scattering function]] S(Q,ω). The effect on the measured beam polarization is proportional
to the cos-Fourier transform of the spectral function, the [[intermediate scattering function]] F(Q,t). The time parameter depends on the neutron
wavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magnetic
field in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field. For some further explanations pertaining the NSE principle with animations see: [http://pathfinder.neutron-eu.net/idb/methods/spin-echo pathfinder.neutron-eu.net].

'''It is important to note: all the spin manipulations are just a means to detect velocity changes of the neutron''', which influence—for technical
reasons—in terms of a Fourier transform of the spectral function in the measured intensity. The velocity changes of the neutrons convey
the physical information which is available by using NSE, i.e.

<math> I(Q,t) \propto S(Q) + \int \cos (\omega t) \, S(Q,\omega)\, dt </math> where
<math> \omega \propto \Delta v </math> and <math> t \propto B \times \lambda^3 </math>.

B denotes the precession field strength, λ the
(average) neutron wavelength and Δv the neutron velocity change upon scattering at the sample.

The main reason for using NSE is that by the above means it can reach Fourier times of up to many 100ns, which corresponds to energy
resolutions in the neV range. The closest approach to this resolution by a spectroscopic neutron instrument type, namely the
[[backscattering spectrometer]] (BSS), is in the range of 0.5 to 1 μeV.
The spin-echo trick allows to use an intense beam of neutrons with a wavelength distribution of 10% or more and at the same time to be
sensitive to velocity changes in the range of less than 10−4.

Note: the above explanations assumes the generic NSE configuration—as first utilized by the IN11 instrument at the [[Institut Laue–Langevin]] (ILL)--. Other approaches
are possible like the [[resonance spin-echo]], [[NRSE]] with concentrated a DC field and a RF field in the flippers at the end of
preparation and decoding zones which then are without magnetic field (zero field). In principle these approaches are equivalent concerning
the connection of the final intensity signal with the intermediate scattering function. Due to technical difficulties until now they have not
reached the same level of performance than the generic (IN11) NSE types.

==What it can measure==
In [[soft matter]] research the structure of macromolecular objects is often investigated by [[small angle neutron scattering]], SANS.
The exchange of [[hydrogen]] with [[deuterium]] in some of the molecules creates scattering contrast between even equal chemical species. The SANS diffraction pattern—if interpreted in real space—corresponds to a snapshot picture of the molecular arrangement. Neutron spin echo instruments can analyze the inelastic broadening of the SANS intensity and thereby analyze the motion of the macromolecular objects.<ref>
{{ cite journal |
doi = 10.1016/j.crhy.2007.10.001 |
author = M. Monkenbusch and D. Richter |
title = High resolution neutron spectroscopy - a tool for the investigation of dynamics of polymers and soft matter |
journal = Comptes Rendus Physique |
volume = 8 |
pages = 845–864 |
year = 2007
|bibcode = 2007CRPhy...8..845M }}
</ref>
A coarse analogy would be a photo with a certain opening time instead of the SANS like snapshot. The opening time corresponds to the [[Fourier time]] which depends on the setting of the NSE spectrometer, it is proportional to the magnetic field (integral) and to the third power of the neutron wavelength. Values up to several hundreds of nanoseconds are available. Note that the spatial resolution of the scattering experiment is in the nanometer range, which means that a time range of e.g. 100 ns corresponds to effective molecular motion velocities of 1 nm/100 ns = 1 cm/s. This may be compared to the typical neutron velocity of 200..1000 m/s used in these type of experiments.

==NSE and spin-incoherent scattering (from protons)==
Many inelastic studies that use normal [[time-of-flight]] (TOF) or backscattering spectrometers rely on the huge incoherent neutron scattering
cross section of protons. The scattering signal is dominated by the corresponding contribution, which represents the (average) self-correlation
function (in time) of the protons.

For NSE spin [[incoherent scattering]] has the disadvantage that it flips the neutron spins during scattering with a probability of 2/3.
Thus converting 2/3 of the scattering intensity into "non-polarized" background and putting a factor of -1/3 in front of the cos-Fourier integral
contribution pertaining the incoherent intensity. This signal subtracts from the coherent echo signal. The result may be a complicated
combination which cannot be decomposed if only NSE is employed.
However, in pure cases, i.e. when there is an overwhelming intensity contribution due to protons, NSE can be used to measure their incoherent spectrum.

The intensity situation of NSE—for e.g. soft-matter samples—is the same as in small angle scattering ([[Small-angle neutron scattering|SANS]]). Which means that
molecular objects with coherent scattering contrast at low Q (momentum transfer) show a much larger intensity as the incoherent contribution
(which is the background level). But at larger Q usually somewhere around Q=0.3 A−1 the incoherent scattering becomes stronger
than the coherent part. At least for hydrogen containing systems contrast requires the presence of some protons and even pure deuterated
samples show spin-incoherent scattering from deuterons, however, 40 times weaker than the proton scattering.

Fully protonated samples allow successful measurements but at intensities of the order of the SANS background level.<ref>{{ cite journal |
author = A. Wischnewski and M. Monkenbusch and L. Willner and D. Richter and G. Kali |
title = Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts |
journal = Physical Review Letters |
volume = 90 |
page = 058302 |
year = 2003
|doi = 10.1103/PhysRevLett.90.058302 |bibcode = 2003PhRvL..90e8302W }}
</ref>
This requires correspondingly long counting times.

Note: This interference with the spin manipulation of the NSE technique occurs only with '''spin-incoherent''' scattering. Isotopic incoherent
scattering yields a "normal" NSE signal.

== Existing spectrometers ==
* [http://www.ill.eu/in11/ IN11] ([[Institut Laue-Langevin]],[http://www.ill.fr ILL], Grenoble, France)
* [http://www.ill.eu/in15/ IN15] ([[Institut Laue-Langevin]],[http://www.ill.fr ILL], Grenoble, France)
* J-NSE ([[Juelich Centre for Neutron Science]] [http://www.jcns.info JCNS], Juelich, Germany, hosted by [http://wwwnew.frm2.tum.de FRMII], Munich (Garching), Germany)
* NG5-NSE ([http://www.ncnr.nist.gov NIST CNRF], Gaithersburg, USA)
* NSE@SNS ([http://www.fz-juelich.de/jcns JCNS] [http://neutrons.ornl.gov/instruments/SNS/NSE/ SNS, Oak Ridge])
* RESEDA ([[FRM II Munich]] [http://wwwnew.frm2.tum.de FRMII], Munich, Germany
* V5/SPAN ([http://www.hmi.de Hahn-Meitner Institut], Berlin, Germany)
* C2-2 ([http://www.issp.u-tokyo.ac.jp ISSP], Tokai, Japan)

== See also ==
* [[Biological small-angle scattering]]
* [[Larmor precession]]
* [[Neutron resonance spin echo]]
* [[NMR]]
* [[Protein domain]]
* [[Soft matter]]
* [[Spin echo]]

==References==
{{reflist}}

[[Category:Neutron scattering]]

Photoacoustic Doppler effect

2013-11-21T19:22:58Z

129.63.253.67: /* Application */

{{Infobox scientist
| name = Leon Melvyn Simon
| image = Leon Simon.jpeg
| image_size =
| alt =
| caption = Leon Simon in 2005 (photo from [[MFO]]{{disambiguation needed|date=October 2013}})
| birth_date = {{Birth date|1945|07|06}}
| birth_place =
| death_date = 
| death_place =
| residence =
| citizenship =
| nationality =
| fields = [[Geometric measure theory]], [[harmonic map]]s, [[partial differential equation]]s
| workplaces = [[University of Adelaide]], [[Flinders University]], [[Australian National University]], [[University of Melbourne]], [[University of Minnesota]], [[ETH Zurich]], [[Stanford University]]
| alma_mater = [[University of Adelaide]]
| doctoral_advisor = [[James H. Michael]]
| academic_advisors =
| doctoral_students = [[Richard Schoen]], [[Neshan Wickramasekera]]
| notable_students =
| known_for = Regularity problem for [[codimension]]–1 <math>n</math>–dimensional [[minimal surface]]s
| influenced = [[Geometric measure theory]]
| awards = [[Australian Mathematical Society Medal]] 1983, [[List of Fellows of the Australian Academy of Science|Fellow of the Australian Academy of Science]] 1983, [[Bôcher Memorial Prize]] 1994, [[Fellow of the American Academy of Arts and Sciences]] 1994, [[Fellow of the Royal Society]] 2003
| signature = 
| signature_alt =
| footnotes =
| spouse =
}}

'''Leon Melvyn Simon''' is a [[Bôcher Memorial Prize|Bôcher Prize]]-winning<ref name="bprize">See {{harv|AMS|1994}}.</ref> [[mathematician]]. He is currently Professor in the Mathematics Department at [[Stanford University]].

==Biography==

===Academic career===
Leon Simon, born July 6, 1945, received his B.Sc from the [[University of Adelaide]] in 1967, and his Ph.D. in 1971 from the same institution, under the direction of [[James H. Michael]]. His doctoral thesis was titled ''Interior Gradient Bounds for Non-Uniformly Elliptic Equations''. He was employed from 1968 to 1971 as a Tutor in Mathematics by the University.

Simon has since held a variety of academic positions. He worked first at [[Flinders University]] as a lecturer, then at [[Australian National University]] as a professor, at the [[University of Melbourne]], the [[University of Minnesota]], at [[ETH Zurich]], and at Stanford. He first came to Stanford in 1973 as Visiting Assistant Professor and was awarded a full professorship in 1986.

===Honours===
In 1983 Simon was awarded the [[Australian Mathematical Society Medal]]. In the same year he was elected as a [[List of Fellows of the Australian Academy of Science|Fellow]] of the [[Australian Academy of Science]].
In 1994, he was awarded the [[Bôcher Memorial Prize]].<ref name="bprize"/><ref name="bbio">See his brief biography {{harv|Walker|2006}}.</ref><ref name="ebio">See his [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Simon.html extended biography] at the [[MacTutor History of Mathematics Archive]].</ref> The Bôcher Prize is awarded every five years to a groundbreaking author in [[mathematical analysis|analysis]]. In the same year he was also elected a [[fellow of the American Academy of Arts and Sciences]].<ref name="bbio"/><ref name="ebio"/> In May 2003 he was elected a [[fellow of the Royal Society]].<ref>See the list of {{cite web | url=http://royalsociety.org/about-us/fellowship/fellows/|title= Fellows|publisher= Royal Society |accessdate = 15 October 2010}} available at the [[Royal Society]] web site.</ref> In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-07-20.</ref>

==Work==

===Research activity===
He has an [[Erdős number]] of 3. He has authored several mathematics textbooks, including the ''Lectures on Geometric Measure Theory''<ref>This is basically a textbook describing many results in [[geometric measure theory]] and the mathematical tools used in this field: see {{harv|Simon|1984}}.</ref> and ''An Introduction to Multivariable Mathematics''. He published the [[monograph]] ''Theorems on regularity and singularity of energy minimizing maps'' in 1996, based in part on lectures he gave at [[Eidgenössische Technische Hochschule]] (ETH) in Zürich.

===Teaching activity===
Simon has more than 100 'mathematical descendants', according to the [[Mathematics Genealogy Project]].<ref>See the entry "''[http://genealogy.math.ndsu.nodak.edu/id.php?id=38879 Leon M. Simon]''" at the [[Mathematics Genealogy Project]].</ref> Among his doctoral students there is [[Richard Schoen]], a former winner of the Bôcher Memorial Prize.

==See also==
*[[Geometric measure theory]]
*[[Harmonic map]]
*[[Minimal surface]]

==References==
{{reflist|30em}}

==Bibliography==
*{{Citation
| last = AMS
| first =
| author-link = American Mathematical Society
| title = Leon Simon receives 1994 Bôcher Memorial Prize
| journal = [[Notices of the American Mathematical Society]]
| volume = 41
| issue = 2
| pages = 99–100
|date=February 1994
| language =
| url =
| jstor =
| archiveurl =
| archivedate =
| doi =
| id =
| mr = 1262536
| zbl =
}}.
*{{MacTutor|id=Simon|title=Leon Melvyn Simon|date=November 2006}}
*{{Citation
| last = Walker
| first = Rosanne
| contribution = Simon, Leon (1945 – )
| date = 25 May 2006
| origyear = 2001
| title = [[Encyclopedia of Australian Science]]
| place = Melbourne
| publisher = [[eScholarship Research Centre]]
| contribution-url = http://www.eoas.info/biogs/P003748b.htm
| id =
}}.

==References==
*{{Citation
| last = Simon
| first = Leon
| author-link =
| title = Lectures on Geometric Measure Theory
| place = [[Canberra]]
| publisher = [[Centre for Mathematics and its Applications|Centre for Mathematics and its Applications (CMA)]], [[Australian National University]]
| series = Proceedings of the Centre for Mathematical Analysis
| volume = 3
| year = 1984
| pages =VII+272 (loose errata)
| language =
| url = http://maths.anu.edu.au/research.publications/proceedings/003/
| doi =
| id =
| isbn = 0-86784-429-9
| mr = 0756417
| zbl = 0546.49019
}}.

==External links==
*{{MathGenealogy|id=38879|title=Leon M. Simon}}

{{Authority control|VIAF=108409773}}

{{Persondata 
| NAME =Simon, Leon
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Australian mathematician
| DATE OF BIRTH = 1945
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Simon, Leon}}
[[Category:1945 births]]
[[Category:Living people]]
[[Category:Australian mathematicians]]
[[Category:Fellows of the Royal Society]]
[[Category:Stanford University Department of Mathematics faculty]]
[[Category:Fellows of the Australian Academy of Science]]
[[Category:Fellows of the American Mathematical Society]]