1,275 research outputs found
Mapping functions and critical behavior of percolation on rectangular domains
The existence probability and the percolation probability of the
bond percolation on rectangular domains with different aspect ratios are
studied via the mapping functions between systems with different aspect ratios.
The superscaling behavior of and for such systems with exponents
and , respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev.
Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order
approximation of the mapping functions and for and ,
respectively; the exponents and can be obtained from numerically
determined mapping functions and , respectively.Comment: 17 pages with 6 figure
Comparison of the biomechanical tensile and compressive properties of decellularised and natural porcine meniscus
Meniscal repair is widely used as a treatment for meniscus injury. However, where meniscal damage has progressed such that repair is not possible, approaches for partial meniscus replacement are now being developed which have the potential to restore the functional role of the meniscus, in stabilising the knee joint, absorbing and distributing stress during loading, and prevent early degenerative joint disease. One attractive potential solution to the current lack of meniscal replacements is the use of decellularised natural biological scaffolds, derived from xenogeneic tissues, which are produced by treating the native tissue to remove the immunogenic cells. The current study investigated the effect of decellularisation on the biomechanical tensile and compressive (indentation and unconfined) properties of the porcine medial meniscus through an experimental-computational approach. The results showed that decellularised medial porcine meniscus maintained the tensile biomechanical properties of the native meniscus, but had lower tensile initial elastic modulus. In compression, decellularised medial porcine meniscus generally showed lower elastic modulus and higher permeability compared to that of the native meniscus. These changes in the biomechanical properties, which ranged from less than 1% to 40%, may be due to the reduction of glycosaminoglycans (GAG) content during the decellularisation process. The predicted biomechanical properties for the decellularised medial porcine meniscus were within the reported range for the human meniscus, making it an appropriate biological scaffold for consideration as a partial meniscus replacement
Critical adsorption at chemically structured substrates
We consider binary liquid mixtures near their critical consolute points and
exposed to geometrically flat but chemically structured substrates. The
chemical contrast between the various substrate structures amounts to opposite
local preferences for the two species of the binary liquid mixtures. Order
parameters profiles are calculated for a chemical step, for a single chemical
stripe, and for a periodic stripe pattern. The order parameter distributions
exhibit frustration across the chemical steps which heals upon approaching the
bulk. The corresponding spatial variation of the order parameter and its
dependence on temperature are governed by universal scaling functions which we
calculate within mean field theory. These scaling functions also determine the
universal behavior of the excess adsorption relative to suitably chosen
reference systems
Geometric Frustration and Dimensional Reduction at a Quantum Critical Point
We show that the spatial dimensionality of the quantum critical point
associated with Bose--Einstein condensation at T=0 is reduced when the
underlying lattice comprises a set of layers coupled by a frustrating
interaction. Our theoretical predictions for the critical temperature as a
function of the chemical potential correspond very well with recent
measurements in BaCuSiO [S. E. Sebastian \textit{et al}, Nature
\textbf{411}, 617 (2006)].Comment: 5 pages, 2 figure
On the finite-size behavior of systems with asymptotically large critical shift
Exact results of the finite-size behavior of the susceptibility in
three-dimensional mean spherical model films under Dirichlet-Dirichlet,
Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The
corresponding scaling functions are explicitly derived and their asymptotics
close to, above and below the bulk critical temperature are obtained. The
results can be incorporated in the framework of the finite-size scaling theory
where the exponent characterizing the shift of the finite-size
critical temperature with respect to is smaller than , with
being the critical exponent of the bulk correlation length.Comment: 24 pages, late
Canonical Solution of Classical Magnetic Models with Long-Range Couplings
We study the canonical solution of a family of classical spin
models on a generic -dimensional lattice; the couplings between two spins
decay as the inverse of their distance raised to the power , with
. The control of the thermodynamic limit requires the introduction of
a rescaling factor in the potential energy, which makes the model extensive but
not additive. A detailed analysis of the asymptotic spectral properties of the
matrix of couplings was necessary to justify the saddle point method applied to
the integration of functions depending on a diverging number of variables. The
properties of a class of functions related to the modified Bessel functions had
to be investigated. For given , and for any , and lattice
geometry, the solution is equivalent to that of the model, where the
dimensionality and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on
dynamic functions, as two times correlations . We show, under general
conditions, that must obey the following scaling behavior , where the scaling variable is
and , two
undetermined functions. The presence of a non constant exponent
signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure
Dimensional Crossover in the Large N Limit
We consider dimensional crossover for an Landau-Ginzburg-Wilson model
on a -dimensional film geometry of thickness in the large -limit. We
calculate the full universal crossover scaling forms for the free energy and
the equation of state. We compare the results obtained using ``environmentally
friendly'' renormalization with those found using a direct, non-renormalization
group approach. A set of effective critical exponents are calculated and
scaling laws for these exponents are shown to hold exactly, thereby yielding
non-trivial relations between the various thermodynamic scaling functions.Comment: 25 pages of PlainTe
Fractals at T=Tc due to instanton-like configurations
We investigate the geometry of the critical fluctuations for a general system
undergoing a thermal second order phase transition. Adopting a generalized
effective action for the local description of the fluctuations of the order
parameter at the critical point () we show that instanton-like
configurations, corresponding to the minima of the effective action functional,
build up clusters with fractal geometry characterizing locally the critical
fluctuations. The connection between the corresponding (local) fractal
dimension and the critical exponents is derived. Possible extension of the
local geometry of the system to a global picture is also discussed.Comment: To appear in Physical Review Letter
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