109 research outputs found
Compressional Mode Softening and Euler Buckling Patterns in Mesoscopic Beams
We describe a sequence of Euler buckling instabilities associated with the transverse modes of a mesoscopic beam subjected to compressional strain. As the strain is increased, successively higher normal mode frequencies are driven to zero; each zero signals an instability in the corresponding normal mode that can be realized if all lower instabilities are suppressed by constraints. When expressed in terms of the critical buckling modes, the potential energy functional takes the form of a multimode Ginzburg–Landau system that describes static equilibria in the presence of symmetry breaking forces. This model is used to analyse the complex equilibrium shapes that have been observed experimentally in strained mesoscopic beams. Theoretically predicted critical strain values agree with the appearances of higher order mode structures as the length-to-width aspect ratio increases. The theory also predicts upper bounds on the individual mode amplitudes that are consistent with the data. Based on insights from the theory, we suggest possible origins of the buckling patterns
Symmetries of the near horizon of a Black Hole by Group Theoretic methods
We use group theoretic methods to obtain the extended Lie point symmetries of
the quantum dynamics of a scalar particle probing the near horizon structure of
a black hole. Symmetries of the classical equations of motion for a charged
particle in the field of an inverse square potential and a monopole, in the
presence of certain model magnetic fields and potentials are also studied. Our
analysis gives the generators and Lie algebras generating the inherent
symmetries.Comment: To appear in Int. J. Mod. Phys.
Quantum Effects in the Mechanical Properties of Suspended Nanomechanical Systems
We explore the quantum aspects of an elastic bar supported at both ends and
subject to compression. If strain rather than stress is held fixed, the system
remains stable beyond the buckling instability, supporting two potential
minima. The classical equilibrium transverse displacement is analogous to a
Ginsburg-Landau order parameter, with strain playing the role of temperature.
We calculate the quantum fluctuations about the classical value as a function
of strain. Excitation energies and quantum fluctuation amplitudes are compared
for silicon beams and carbon nanotubes.Comment: RevTeX4. 5 pages, 3 eps figures. Submitted to Physical Review Letter
Implications of non-feasible transformations among icosahedral orbitals
The symmetric group that permutes the six five-fold axes of an
icosahedron is introduced to go beyond the simple rotations that constitute the
icosahedral group . Owing to the correspondence , the
calculation of the Coulomb energies for the icosahedral configurations
based on the sequence can be brought
to bear on Racah's classic theory for the atomic d shell based on . Among the elements of is the kaleidoscope
operator that rotates the weight space of SO(5) by . Its use
explains some puzzling degeneracies in d^3 involving the spectroscopic terms
^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5,
99. Revtex, 1 ps figur
Orbifold Models in M-Theory
Among orbifold compactifications of -theory, we examine
models containing the particle physics Standard Model in four-dimensional
spacetimes, which appear as fixed subspaces of the ten-dimensional spacetimes
at each end of the interval, , spanning the
dimension. Using the projection to break the gauge symmetry in each
of the four-planes and a limiting relation to corresponding heterotic string
compactifications, we discuss the restrictions on the possible resulting gauge
field and matter spectra. In particular, some of the states are non-local: they
connect two four-dimensional Worlds across the dimension.
We illustrate our programmable calculations of the matter field spectrum,
including the anomalous U(1) factor which satisfies a universal Green-Schwarz
relation, discuss a Dynkin diagram technique to showcase a model with
gauge symmetry, and discuss generalizations to
higher order orbifolds.Comment: 23 pages, 2 figures, 4 tables; LaTeX 3 time
Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries
It is proved that the potentials of the form (with being
integer) provide a ``bridge'' between the U(5) symmetry of the Bohr Hamiltonian
with a harmonic oscillator potential (occuring for ) and the E(5) model of
Iachello (Bohr Hamiltonian with an infinite well potential, materialized for
infinite ). Parameter-free (up to overall scale factors) predictions for
spectra and B(E2) transition rates are given for the potentials ,
, , corresponding to ratios of 2.093, 2.135,
2.157 respectively, compared to the ratios 2.000 of U(5) and 2.199 of
E(5). Hints about nuclei showing this behaviour, as well as about potentials
``bridging'' the E(5) symmetry with O(6) are briefly discussed. A note about
the appearance of Bessel functions in the framework of E(n) symmetries is given
as a by-product.Comment: LaTeX, 17 pages, 9 postscript figure
Lattice-dynamics of a Disordered solid-solid Interface
Generic properties of elastic phonon transport at a disordered interface are
studied. The results show that phonon transmittance is a strong function of
frequency and the disorder correlation length. At frequencies lower than the
van Hove singularity the transmittance at a given frequency increases as the
correlation length decreases. At low frequencies, this is reflected by
different power-laws for phonon conductance across correlated and uncorrelated
disordered interfaces which are in approximate agreement with perturbation
theory of an elastic continuum. These results can be understood in terms of
simple mosaic and two-colour models of the interface.Comment: 17 pages, 5 figures, submitted to PR
The Eliashberg Function of Amorphous Metals
A connection is proposed between the anomalous thermal transport properties
of amorphous solids and the low-frequency behavior of the Eliashberg function.
By means of a model calculation we show that the size and frequency dependence
of the phonon mean-free-path that has been extracted from measurements of the
thermal conductivity in amorphous solids leads to a sizeable linear region in
the Eliashberg function at small frequencies. Quantitative comparison with
recent experiments gives very good agreement.Comment: 4pp., REVTeX, 1 uuencoded ps fig. Original posting had a corrupted
raw ps fig appended. Published as PRB 51, 689 (1995
On the 3n+l Quantum Number in the Cluster Problem
It has recently been suggested that an exactly solvable problem characterized
by a new quantum number may underlie the electronic shell structure observed in
the mass spectra of medium-sized sodium clusters. We investigate whether the
conjectured quantum number 3n+l bears a similarity to the quantum numbers n+l
and 2n+l, which characterize the hydrogen problem and the isotropic harmonic
oscillator in three dimensions.Comment: 8 pages, revtex, 4 eps figures included, to be published in
Phys.Rev.A, additional material available at
http://radix2.mpi-stuttgart.mpg.de/koch/Diss
Glass-Like Heat Conduction in High-Mobility Crystalline Semiconductors
The thermal conductivity of polycrystalline semiconductors with type-I
clathrate hydrate crystal structure is reported. Ge clathrates (doped with Sr
and/or Eu) exhibit lattice thermal conductivities typical of amorphous
materials. Remarkably, this behavior occurs in spite of the well-defined
crystalline structure and relatively high electron mobility (). The dynamics of dopant ions and their interaction with the
polyhedral cages of the structure are a likely source of the strong phonon
scattering.Comment: 4 pages, 3 postscript figures, to be published, Phys. Rev. Let
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