1,555 research outputs found
Self-Affinity in the Gradient Percolation Problem
We study the scaling properties of the solid-on-solid front of the infinite
cluster in two-dimensional gradient percolation. We show that such an object is
self affine with a Hurst exponent equal to 2/3 up to a cutoff-length
proportional to the gradient to the power (-4/7). Beyond this length scale, the
front position has the character of uncorrelated noise. Importantly, the
self-affine behavior is robust even after removing local jumps of the front.
The previously observed multi affinity, is due to the dominance of overhangs at
small distances in the structure function. This is a crossover effect.Comment: 4 pages, 4 figure
Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion
We study a non-linear convective-diffusive equation, local in space and time,
which has its background in the dynamics of the thickness of a wetting film.
The presence of a non-linear diffusion predicts the existence of fronts as well
as shock fronts. Despite the absence of memory effects, solutions in the case
of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to
a balance between non-linear diffusion and convection we, in particular, show
that solitary waves appear. For large times they merge into a single solitary
wave exhibiting a topological stability. Even though our results concern a
specific equation, numerical simulations supports the view that anomalous
diffusion and the solitary waves disclosed will be general features in such
non-linear convective-diffusive dynamics.Comment: Corrected typos, added 3 references and 2 figure
Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone
We suggest that the observed large-scale universal roughness of brittle
fracture surfaces is due to the fracture process being a correlated percolation
process in a self-generated quadratic damage gradient. We use the quasi-static
two-dimensional fuse model as a paradigm of a fracture model. We measure for
this model, that exhibits a correlated percolation process, the correlation
length exponent nu approximately equal to 1.35 and conjecture it to be equal to
that of uncorrelated percolation, 4/3. We then show that the roughness exponent
in the fuse model is zeta = 2 nu/(1+2 nu)= 8/11. This is in accordance with the
numerical value zeta=0.75. As for three-dimensional brittle fractures, a
mean-field theory gives nu=2, leading to zeta=4/5 in full accordance with the
universally observed value zeta =0.80.Comment: 4 pages RevTeX
Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone
We show that the roughness exponent zeta of an in-plane crack front slowly
propagating along a heterogeneous interface embeded in a elastic body, is in
full agreement with a correlated percolation problem in a linear gradient. We
obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We
develop an elastic brittle model based on both the 3D Green function in an
elastic half-space and a discrete interface of brittle fibers and find
numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We
also obtain by direct numerical simulations zeta=0.6 in excellent agreement
with our prediction. This modelling is for the first time in close agreement
with experimental observations.Comment: 4 pages RevTeX
Band Formation during Gaseous Diffusion in Aerogels
We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides
of and react in silica aerogel rods with porosity of 92 % and average pore size
of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin
sheet-like structures. We present a numerical study of the phenomenon. Due to
the difference in boundary conditions between this system and those usually
studied, we find the sheet-like structures in the aerogel to differ
significantly from older studies. The influence of random nucleation centers
and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on
request from author
Failure Processes in Elastic Fiber Bundles
The fiber bundle model describes a collection of elastic fibers under load.
the fibers fail successively and for each failure, the load distribution among
the surviving fibers change. Even though very simple, the model captures the
essentials of failure processes in a large number of materials and settings. We
present here a review of fiber bundle model with different load redistribution
mechanism from the point of view of statistics and statistical physics rather
than materials science, with a focus on concepts such as criticality,
universality and fluctuations. We discuss the fiber bundle model as a tool for
understanding phenomena such as creep, and fatigue, how it is used to describe
the behavior of fiber reinforced composites as well as modelling e.g. network
failure, traffic jams and earthquake dynamics.Comment: This article has been Editorially approved for publication in Reviews
of Modern Physic
Viscous stabilization of 2D drainage displacements with trapping
We investigate the stabilization mechanisms due to viscous forces in the
invasion front during drainage displacement in two-dimensional porous media
using a network simulator. We find that in horizontal displacement the
capillary pressure difference between two different points along the front
varies almost linearly as function of height separation in the direction of the
displacement. The numerical result supports arguments taking into account the
loopless displacement pattern where nonwetting fluid flow in separate strands
(paths). As a consequence, we show that existing theories developed for viscous
stabilization, are not compatible with drainage when loopless strands dominate
the displacement process.Comment: The manuscript has been substantially revised. Accepted in Phys. Rev.
Let
UBC-Nepal expedition: The use of oral antioxidants does not alter cerebrovascular function at sea-level or high-altitude
Hypoxia is associated with an increased systemic and cerebral formation of free radicals and associated reactants that may be linked to impaired cerebral vascular function a neurological sequela. To what extent oral antioxidants prophylaxis impacts cerebrovascular function in humans throughout the course of acclimatization to the hypoxia of terrestrial high-altitude has not been examined. Thus, the purpose of the current study was to examine the influence of orally ingested antioxidants at clinically relevant doses (vitamin C, E, and alpha-lipoic acid) on cerebrovascular regulation at sea-level (344 m; n = 12; female n = 2 participants), and at high altitude (5050 m; n = 9; female n = 2), in a randomized, placebo-controlled, and double-blinded crossover design. Hypercapnic and hypoxic cerebrovascular reactivity tests of the internal carotid (ICA)] were conducted at sea-level, while global and regional cerebral blood flow [i.e. ICA and vertebral artery (VA)] were assessed after 10–12 days following arrival at 5050 m. At sea-level, acute administration of antioxidants did not alter cerebral hypoxic cerebrovascular reactivity (pre vs. post: 1.5 ± 0.7 vs. 1.2 ± 0.8 %∆CBF/-%∆SpO2; P = 0.96), or cerebral hypercapnic cerebrovascular reactivity (pre vs. post: 5.7 ± 2.0 vs. 5.8 ± 1.9 %∆CBF/∆mmHg; P = 0.33). Furthermore, global cerebral blood flow (P = 0.43), as well as cerebral vascular conductance (ICA P = 0.08; VA P = 0.32), were unaltered at 5050 m following antioxidant administration. In conclusion, these data show that an oral antioxidant cocktail known to attenuate systemic oxidative stress failed to alter cerebrovascular function at sea-level and cerebral blood flow during acclimatization to high-altitude
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