1,412 research outputs found
Sparse random matrices and vibrational spectra of amorphous solids
A random matrix approach is used to analyze the vibrational properties of
amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative
eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n
independent non-zero elements in each row. The average values =0 and
dispersion =V^2 for all non-zero elements. The density of vibrational
states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle
law with radius independent of N. We argue that for n^2 << N this model can be
used to describe the interaction of atoms in amorphous solids. The level
statistics of matrix M is well described by the Wigner surmise and corresponds
to repulsion of eigenfrequencies. The participation ratio for the major part of
vibrational modes in three dimensional system is about 0.2 - 0.3 and
independent of N. Together with term repulsion it indicates clearly to the
delocalization of vibrational excitations. We show that these vibrations spread
in space by means of diffusion. In this respect they are similar to diffusons
introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous
silicon. Our results are in a qualitative and sometimes in a quantitative
agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure
Investigating solid N as a new source of ultra-cold neutrons
The dynamical structure factor of solid N in the phase
(K) is measured at the IN4 time-of-flight spectrometer at the Institut
Laue Langevin, and the potential performance of this substance as a UCN
converter is assessed. The cross-section to down-scatter neutrons to ultra-cold
neutron energies is determined as a function of incident energy, as well as the
up-scattering mean free path. The UCN production cross-section is found to be
approximately 20% of that of deuterium. However, UCN with energy 181 neV have
an up-scattering mean free path of 46 cm at K, which is times
larger than deuterium. Therefore, a large volume N source
may produce an improved UCN density if sufficient isotopic purity can be
achieved.Comment: 7 pages, 6 figure
Crystal-like high frequency phonons in the amorphous phases of solid water
The high frequency dynamics of low- (LDA) and high-density amorphous-ice
(HDA) and of cubic ice (I_c) has been measured by inelastic X-ray Scattering
(IXS) in the 1-15 nm^{-1} momentum transfer (Q) range. Sharp phonon-like
excitations are observed, and the longitudinal acoustic branch is identified up
to Q = 8nm^{-1} in LDA and I_c and up to 5nm^{-1} in HDA. The narrow width of
these excitations is in sharp contrast with the broad features observed in all
amorphous systems studied so far. The "crystal-like" behavior of amorphous
ices, therefore, implies a considerable reduction in the number of decay
channels available to sound-like excitations which is assimilated to low local
disorder.Comment: 4 pages, 3 figure
Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations
The approach of the elastic continuum limit in small amorphous bodies formed
by weakly polydisperse Lennard-Jones beads is investigated in a systematic
finite-size study. We show that classical continuum elasticity breaks down when
the wavelength of the sollicitation is smaller than a characteristic length of
approximately 30 molecular sizes. Due to this surprisingly large effect
ensembles containing up to N=40,000 particles have been required in two
dimensions to yield a convincing match with the classical continuum predictions
for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk
systems. The existence of an effective length scale \xi is confirmed by the
analysis of the (non-gaussian) noisy part of the low frequency vibrational
eigenmodes. Moreover, we relate it to the {\em non-affine} part of the
displacement fields under imposed elongation and shear. Similar correlations
(vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table
Irreversible reorganization in a supercooled liquid originates from localised soft modes
The transition of a fluid to a rigid glass upon cooling is a common route of
transformation from liquid to solid that embodies the most poorly understood
features of both phases1,2,3. From the liquid perspective, the puzzle is to
understand stress relaxation in the disordered state. From the perspective of
solids, the challenge is to extend our description of structure and its
mechanical consequences to materials without long range order. Using computer
simulations, we show that the localized low frequency normal modes of a
configuration in a supercooled liquid are causally correlated to the
irreversible structural reorganization of the particles within that
configuration. We also demonstrate that the spatial distribution of these soft
local modes can persist in spite of significant particle reorganization. The
consequence of these two results is that it is now feasible to construct a
theory of relaxation length scales in glass-forming liquids without recourse to
dynamics and to explicitly relate molecular properties to their collective
relaxation.Comment: Published online: 20 July 2008 | doi:10.1038/nphys1025 Available from
http://www.nature.com/nphys/journal/v4/n9/abs/nphys1025.htm
Numerical study of anharmonic vibrational decay in amorphous and paracrystalline silicon
The anharmonic decay rates of atomic vibrations in amorphous silicon (a-Si)
and paracrystalline silicon (p-Si), containing small crystalline grains
embedded in a disordered matrix, are calculated using realistic structural
models. The models are 1000-atom four-coordinated networks relaxed to a local
minimum of the Stillinger-Weber interatomic potential. The vibrational decay
rates are calculated numerically by perturbation theory, taking into account
cubic anharmonicity as the perturbation. The vibrational lifetimes for a-Si are
found to be on picosecond time scales, in agreement with the previous
perturbative and classical molecular dynamics calculations on a 216-atom model.
The calculated decay rates for p-Si are similar to those of a-Si. No modes in
p-Si reside entirely on the crystalline cluster, decoupled from the amorphous
matrix. The localized modes with the largest (up to 59%) weight on the cluster
decay primarily to two diffusons. The numerical results are discussed in
relation to a recent suggestion by van der Voort et al. [Phys. Rev. B {\bf 62},
8072 (2000)] that long vibrational relaxation inferred experimentally may be
due to possible crystalline nanostructures in some types of a-Si.Comment: 9 two-column pages, 13 figure
Detecting controlling nodes of boolean regulatory networks
Boolean models of regulatory networks are assumed to be tolerant to perturbations. That qualitatively implies that each function can only depend on a few nodes. Biologically motivated constraints further show that functions found in Boolean regulatory networks belong to certain classes of functions, for example, the unate functions. It turns out that these classes have specific properties in the Fourier domain. That motivates us to study the problem of detecting controlling nodes in classes of Boolean networks using spectral techniques. We consider networks with unbalanced functions and functions of an average sensitivity less than 23k, where k is the number of controlling variables for a function. Further, we consider the class of 1-low networks which include unate networks, linear threshold networks, and networks with nested canalyzing functions. We show that the application of spectral learning algorithms leads to both better time and sample complexity for the detection of controlling nodes compared with algorithms based on exhaustive search. For a particular algorithm, we state analytical upper bounds on the number of samples needed to find the controlling nodes of the Boolean functions. Further, improved algorithms for detecting controlling nodes in large-scale unate networks are given and numerically studied
Anharmonicity, vibrational instability and Boson peak in glasses
We show that a {\em vibrational instability} of the spectrum of weakly
interacting quasi-local harmonic modes creates the maximum in the inelastic
scattering intensity in glasses, the Boson peak. The instability, limited by
anharmonicity, causes a complete reconstruction of the vibrational density of
states (DOS) below some frequency , proportional to the strength of
interaction. The DOS of the new {\em harmonic modes} is independent of the
actual value of the anharmonicity. It is a universal function of frequency
depending on a single parameter -- the Boson peak frequency, which
is a function of interaction strength. The excess of the DOS over the Debye
value is at low frequencies and linear in in the
interval . Our results are in an excellent
agreement with recent experimental studies.Comment: LaTeX, 8 pages, 6 figure
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