276 research outputs found
Roughness of tensile crack fronts in heterogenous materials
The dynamics of planar crack fronts in heterogeneous media is studied using a
recently proposed stochastic equation of motion that takes into account
nonlinear effects. The analysis is carried for a moving front in the
quasi-static regime using the Self Consistent Expansion. A continuous dynamical
phase transition between a flat phase and a dynamically rough phase, with a
roughness exponent , is found. The rough phase becomes possible due
to the destabilization of the linear modes by the nonlinear terms. Taking into
account the irreversibility of the crack propagation, we infer that the
roughness exponent found in experiments might become history-dependent, and so
our result gives a lower bound for .Comment: 7 page
Roughness of moving elastic lines - crack and wetting fronts
We investigate propagating fronts in disordered media that belong to the
universality class of wetting contact lines and planar tensile crack fronts. We
derive from first principles their nonlinear equations of motion, using the
generalized Griffith criterion for crack fronts and three standard mobility
laws for contact lines. Then we study their roughness using the self-consistent
expansion. When neglecting the irreversibility of fracture and wetting
processes, we find a possible dynamic rough phase with a roughness exponent of
and a dynamic exponent of z=2. When including the irreversibility,
we conclude that the front propagation can become history dependent, and thus
we consider the value as a lower bound for the roughness exponent.
Interestingly, for propagating contact line in wetting, where irreversibility
is weaker than in fracture, the experimental results are close to 0.5, while
for fracture the reported values of 0.55--0.65 are higher.Comment: 15 pages, 6 figure
A comparative study of crumpling and folding of thin sheets
Crumpling and folding of paper are at rst sight very di erent ways of con
ning thin sheets in a small volume: the former one is random and stochastic
whereas the latest one is regular and deterministic. Nevertheless, certain
similarities exist. Crumpling is surprisingly ine cient: a typical crumpled
paper ball in a waste-bin consists of as much as 80% air. Similarly, if one
folds a sheet of paper repeatedly in two, the necessary force becomes so large
that it is impossible to fold it more than 6 or 7 times. Here we show that the
sti ness that builds up in the two processes is of the same nature, and
therefore simple folding models allow to capture also the main features of
crumpling. An original geometrical approach shows that crumpling is
hierarchical, just as the repeated folding. For both processes the number of
layers increases with the degree of compaction. We nd that for both processes
the crumpling force increases as a power law with the number of folded layers,
and that the dimensionality of the compaction process (crumpling or folding)
controls the exponent of the scaling law between the force and the compaction
ratio.Comment: 5 page
VAV1 (vav 1 oncogene)
Review on VAV1 (vav 1 oncogene), with data on DNA, on the protein encoded, and where the gene is implicated
Solution of the Percus-Yevick equation for hard discs
We solve the Percus-Yevick equation in two dimensions by reducing it to a set
of simple integral equations. We numerically obtain both the pair correlation
function and the equation of state for a hard disc fluid and find good
agreement with available Monte-Carlo calculations. The present method of
resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure
Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity
We report some new observation concerning the statistics of Longest
Increasing Subsequences (LIS). We show that the expectation of LIS, its
variance, and apparently the full distribution function appears in statistical
analysis of some simple nonlinear stochastic partial differential equation
(SPDE) in the limit of very low noise intensity.Comment: 6 pages, 4 figures, reference adde
The spectrum of large powers of the Laplacian in bounded domains
We present exact results for the spectrum of the Nth power of the Laplacian
in a bounded domain. We begin with the one dimensional case and show that the
whole spectrum can be obtained in the limit of large N. We also show that it is
a useful numerical approach valid for any N. Finally, we discuss implications
of this work and present its possible extensions for non integer N and for 3D
Laplacian problems.Comment: 13 pages, 2 figure
Self Consistent Expansion for the Molecular Beam Epitaxy Equation
Motivated by a controversy over the correct results derived from the dynamic
renormalization group (DRG) analysis of the non linear molecular beam epitaxy
(MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory
is considered. The scaling exponents are obtained for spatially correlated
noise of the general form . I find a lower critical dimension , above, which the linear MBE solution appears. Below the
lower critical dimension a r-dependent strong-coupling solution is found. These
results help to resolve the controversy over the correct exponents that
describe non linear MBE, using a reliable method that proved itself in the past
by predicting reasonable results for the Kardar-Parisi-Zhang (KPZ) system,
where DRG failed to do so.Comment: 16 page
The future of climate modeling
Recently a number of scientists have proposed substantial changes to the practice of
climate modeling, though they disagree over what those changes should be. We provide an
overview and critical examination of three leading proposals: the unified approach, the
hierarchy approach and the pluralist approach. The unified approach calls for an accelerated
development of high-resolution models within a seamless prediction framework. The hierarchy
approach calls for more attention to the development and systematic study of hierarchies of
related models, with the aim of advancing understanding. The pluralist approach calls for
greater diversity in modeling efforts, including, on some of its variants, more attention to
empirical modeling. After identifying some of the scientific and institutional challenges faced
by these proposals, we consider their expected gains and costs, relative to a business-as-usual
modeling scenario.We find the proposals to be complementary, having valuable synergies. But
since resource limitations make it unlikely that all three will be pursued, we offer some
reflections on more limited changes in climate modeling that seem well within reach and that
can be expected to yield substantial benefits
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