1,447 research outputs found
Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field
The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution
Uniform Semiclassical Approximation for the Wigner Symbol in Terms of Rotation Matrices
A new uniform asymptotic approximation for the Wigner symbol is given in
terms of Wigner rotation matrices (-matrices). The approximation is uniform
in the sense that it applies for all values of the quantum numbers, even those
near caustics. The derivation of the new approximation is not given, but the
geometrical ideas supporting it are discussed and numerical tests are
presented, including comparisons with the exact -symbol and with the
Ponzano-Regge approximation.Comment: 44 pages plus 20 figure
Adiabatic Motion of a Quantum Particle in a Two-Dimensional Magnetic Field
The adiabatic motion of a charged, spinning, quantum particle in a two -
dimensional magnetic field is studied. A suitable set of operators generalizing
the cinematical momenta and the guiding center operators of a particle moving
in a homogeneous magnetic field is constructed. This allows us to separate the
two degrees of freedom of the system into a {\sl fast} and a {\sl slow} one, in
the classical limit, the rapid rotation of the particle around the guiding
center and the slow guiding center drift. In terms of these operators the
Hamiltonian of the system rewrites as a power series in the magnetic length
\lb=\sqrt{\hbar c\over eB} and the fast and slow dynamics separates. The
effective guiding center Hamiltonian is obtained to the second order in the
adiabatic parameter \lb and reproduces correctly the classical limit.Comment: 17 pages, LaTe
Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)
A quantal guiding center theory allowing to systematically study the
separation of the different time scale behaviours of a quantum charged spinning
particle moving in an external inhomogeneous magnetic filed is presented. A
suitable set of operators adapting to the canonical structure of the problem
and generalizing the kinematical momenta and guiding center operators of a
particle coupled to a homogenous magnetic filed is constructed. The Pauli
Hamiltonian rewrites in this way as a power series in the magnetic length making the problem amenable to a perturbative analysis. The
first two terms of the series are explicitly constructed. The effective
adiabatic dynamics turns to be in coupling with a gauge filed and a scalar
potential. The mechanism producing such magnetic-induced geometric-magnetism is
investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include
Studies relating to ground anchorage systems
This thesis comprises 28 papers which illustrate the nature and direction of development
work and associated research undertaken between 1965 and 1993 on soil and rock
anchorage systems. The research was performed in order to obtain a basic
understanding of the behaviour of newly developed anchorage systems in a variety of
ground types and conditions, in order to improve anchorage designs, construction
methods and testing procedures, and thereby encourage the safe and economic
application of ground anchorages worldwide.
Field development of anchorage construction methods in gravels, sand, clays, marls and
chalk using cement grout injection techniques is described together with equations
evolved to estimate the ultimate resistance to withdrawal for each ground type, based on
systematic testing of full scale anchorages.
A new design method for single and multi tied stiff retaining walls installed in any soil is
detailed and validated by large scale tests and closely monitored case histories. The
interactions between wall, anchorage and soil are illustrated, coupled with the refinement
of overall stability analyses in cohesionless soils using wedge and log spiral based
mechanisms of failure.
For the rapid installation of anchorages in granular soils, vibratory driving is investigated
in the laboratory and two distinct types of motion are found to exist. Theoretical
equations of motion are developed to define the penetration processes and facilitate the
design of vibrodrivers and vibrohammers.
World practice in relation to the design, construction, testing and behaviour of rock
anchorages is appraised, and field studies permit an improved understanding of uplift
capacity by general shear failure, load transfer mechanisms, bond at rock/grout and
grout/tendon interfaces, debonding, service performance and post-failure behaviour.
Acceptance criteria related to service behaviour are created for load relaxation and creep
displacement with time, which are independent of ground type and potentially of short
duration.
The extent and nature of steel tendon corrosion is described based on an international
study of the corrosion performance of post-tensioned anchorages. Guidance is provided
on class of protection, design principles and acceptable protective systems.
For rock tunnelling by drill and blast methods of excavation, a fundamental
understanding of rock bolt behaviour under static and dynamic loading is provided.
Field, laboratory and finite element studies are combined to investigate the character of
blast induced wave forms within a rock mass and the effect of these signatures on the
rock bolt system. Attenuation relationships for peak particle velocity and peak dynamic
bolt load are presented together with effect of bolt prestress, bolt length, and both single
and two speed resin systems. Observations confirm that resin bonded rock bolts have a
remarkable resilience to close proximity blasting, and the data provide a new
understanding of stress transfer in tensioned bolts under static and dynamic conditions.
A simple device to control rock bolt tensioning is developed and applied as a result of
observed variations in prestress during production bolting.
Ground anchorage technology is reviewed to highlight areas where further investigation
and study would enhance understanding of anchorage behaviour and improve standards
of practice.PUBLICATIONS INCLUDED IN THESIS:
#2. HSU, T.C.,
LITTLEJOHN, G.S. &
MARCHBANK, B.M.
(1965) "Elongation in the Tension Test as a Measure of
Ductility"
Proc. Amer. Soc. Test. Mat., 65, 874-98.
(Hsu wrote the paper and supervised the research of Littlejohn and Marchbank who
provided the data.)
#3. LITTLEJOHN, G.S. (1968) "Recent Developments in Ground Anchor
Construction"
Ground Engineering, 1(3), 32-36 & 46.
#4. HANNA, T.H. & (1969) "Retaining Wall Tie-Backs"
LITTLEJOHN, G.S. Consulting Engineer, May, 50-53, June, 49-52.
(Hanna and Littlejohn contributed equally to this paper.)
#6. LITTLEJOHN, G.S.
#8. LITTLEJOHN, G.S.,
JACK, B.J. &
SLIWINSKI, Z.J.
(1971) "Anchored Diaphragm Walls - Some Design and
Construction Considerations"
Journal of the Institution of Highway Engineers,
18 (4), 15-29.
(Littlejohn co-ordinated this paper and contributed half the data.)
#13. LITTLEJOHN, G.S. & (1974) "A Case History Study of Multi-Tied Diaphragm
MACFARLANE, I.M. Walls"
Proc. Conf. on Diaphragm Walls and Anchorages,
113-121, Institution of Civil Engineers, London.
(Littlejohn wrote the paper. Macfarlane provided technical data.)
#14. LITTLEJOHN, G.S. & (1974) "Ground Anchors at Devonport Nuclear Complex"
TRUMAN-DAVIES, C. Ground Engineering, 7 (6), 19-24.
(Littlejohn wrote the paper. Truman-Davies supervised the field work.)
#16. LITTLEJOHN, G.S. & (1975) "Rock Anchors - State-of-the-Art Part 1: Design"
BRUCE, D.A. Ground Engineering, 8 (3), 25-32, 8 (4), 41-48.
(Littlejohn wrote the paper and supervised Bruce's Ph.D. programme.)
#18. LITTLEJOHN, G.S. & (1975) "Rock Anchors - State-of-the-Art Part 2;
BRUCE, D.A. Construction"
Ground Engineering, 8 (5), 34-45, 8 (6), 36-45.
(Littlejohn wrote the paper and supervised Bruce's Ph.D. programme.)
#19. LITTLEJOHN, G.S. & (1976) "Rock Anchors - State-of-the-Art Part 3: Stressing
BRUCE, D.A. and Testing"
Ground Engineering, 9 (2), 20-29, 9 (3), 55-60, 9
(4), 33-44.
(Littlejohn wrote the paper and supervised Bruce's Ph.D. programme.)
#20. LITTLEJOHN, G.S., (1977) "A Study of Rock Slope Reinforcement at Westfield
NORTON, P.J. & Open Pit and the Effect of Blasting on Prestressed
TURNER, M.J. Anchors"
Proc. Conference on Rock Engineering, University
of Newcastle-upon-Tyne, England.
(Littlejohn wrote the paper. Norton and Turner provided technical data.)
#22. LITTLEJOHN, G.S., (1977) "Anchor Field Tests in Carboniferous Strata"
BRUCE, D.A. & Revue Francaise de Geotechnique No. 3,
DEPPNER, W. January 1978, 82-86.
(Littlejohn wrote the paper. Bruce and Deppner provided field data.)
#28. LITTLEJOHN, G.S. & (1979) "Long Term Performance of High Capacity Rock
BRUCE, D.A. Anchors at Devonport"
Ground Engineering, 12 (7), 25-33.
(Littlejohn and Bruce jointly wrote the paper. Bruce provided the field data under the
supervision of Littlejohn.)
#29. LITTLEJOHN, G.S.
#30. LITTLEJOHN, G.S.
#32. RODGER, A.A. & (1980) "A Study of Vibratory Driving in Granular Soils"
LITTLEJOHN, G.S. Geotechnique, 30 (3), 269-93.
(Rodger and Littlejohn jointly wrote the paper. Littlejohn supervised Rodger's Ph.D.
programme)
#34. LITTLEJOHN, G.S. (1981) "Acceptance Criteria for the Service Behaviour of
Ground Anchorages"
Ground Engineering, 14 (3), 26-29 & 36.
#36. LITTLEJOHN, G.S.
#50. LITTLEJOHN, G.S. (1987) "Ground Anchorages : Corrosion Performance"
Proc. Instn. Civ. Engrs., Part 1, 82, 645-662.
#51. LITTLEJOHN, G.S., (1987) "Monitoring the Influence of Blasting on the
RODGER, A.A., Performance of Rock Bolts at Penmaenbach
MOTHERSILLE, D.K.V. Tunnel"
& HOLLAND, D.C. Proc. Int. Conf. on Foundations and Tunnels,
University of London, 1,99-106.
(Littlejohn and Rodger jointly wrote the paper and supervised Mothersille's and
Holland's research work.)
#52. LITTLEJOHN, G.S. (1988) "Sprayed Concrete for Underground Support"
Proc. 3rd Int. Conf. on Underground Space and
Earth Sheltered Buildings, Shanghai, China.
#53. LITTLEJOHN, G.S. (1988) "Rock Anchorages for Underground Support"
Proc. 3rd Int. Conf. on Underground Space and
Earth Sheltered Buildings, Shanghai, China.
"Thermal Behaviour of Grouted Supports for
Pipelines"
Department of Energy - Offshore Technology Report
'Grouts and Grouting for Construction and Repair of
Offshore Structures', OTH 88289, 111-120.
(Littlejohn and Hughes jointly wrote the paper. Hughes provided the laboratory data
under Littlejohn's supervision.)
#56. RODGER, A.A., (1989) "Instrumentation Used to Monitor the
LITTLEJOHN, G.S., Influence of Blasting on the Performance of
HOLLAND, D.C. & Rock Bolts at Penmaenbach Tunnel"
MOTHERSILLE, D.K.V. Proc. Conf. on Instrumentation in
Geotechnical Engineering, University of
Nottingham, 267-279.
(Rodger and Littlejohn jointly wrote the paper and supervised Mothersille's and
Holland's research work.)
#58. LITTLEJOHN, G.S., (1989) "Dynamic Response of Rock Bolt Systems"
RODGER, A.A., Proc. Int. Conf. on Foundations and Tunnels,
MOTHERSILLE, D.K.V. University of London (Sept.), 2, 57-64.
& HOLLAND, D.C.
(Littlejohn and Rodger wrote the paper and supervised Mothersille's and Holland's
research work.)
#61. LITTLEJOHN, G.S.
#62. LITTLEJOHN, G.S.
#64. LITTLEJOHN, G.S.
#74. RODGER, A.A., (1993) "Dynamic Response of Rock Bolts at Pen y Clip
LITTLEJOHN, G.S., Tunnel in North Wales"
HOLLAND, D.C. & Proc. Int. Cong, on Options for Tunnelling, Int.
XU, H. Tunnelling Assoc., Amsterdam.
(Rodger and Littlejohn jointly wrote the paper and supervised Holland's and Xu's
research.)
#75. LITTLEJOHN, G.S. (1993) "A Simple Device to Control Rock Bolt Tensioning"
& CONWAY, J. Tunnels & Tunnelling, (in press).
(Littlejohn and Conway jointly wrote the paper. Littlejohn planned and supervised
the experimental work.
Diagonalization of multicomponent wave equations with a Born-Oppenheimer example
A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed
Symplectic and Semiclassical Aspects of the Schl\"afli Identity
The Schl\"afli identity, which is important in Regge calculus and loop
quantum gravity, is examined from a symplectic and semiclassical standpoint in
the special case of flat, 3-dimensional space. In this case a proof is given,
based on symplectic geometry. A series of symplectic and Lagrangian manifolds
related to the Schl\"afli identity, including several versions of a Lagrangian
manifold of tetrahedra, are discussed. Semiclassical interpretations of the
various steps are provided. Possible generalizations to 3-dimensional spaces of
constant (nonzero) curvature, involving Poisson-Lie groups and q-deformed spin
networks, are discussed.Comment: 40 pages, 8 figure
Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion
For a multicomponent wave field propagating into a multidimensional
conversion region, the rays are shown to be helical, in general. For a
ray-based quantity to have a fundamental physical meaning it must be invariant
under two groups of transformations: congruence transformations (which shuffle
components of the multi-component wave field) and canonical transformations
(which act on the ray phase space). It is shown that for conversion between two
waves there is a new invariant not previously discussed: the intrinsic helicity
of the ray
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