4,209 research outputs found
Limitation of finite element analysis of poroelastic behavior of biological tissues undergoing rapid loading
The finite element method is used in biomechanics to provide numerical solutions to simulations of structures having complex geometry and spatially differing material properties. Time-varying load deformation behaviors can result from solid viscoelasticity as well as viscous fluid flow through porous materials. Finite element poroelastic analysis of rapidly loaded slow-draining materials may be ill-conditioned, but this problem is not widely known in the biomechanics field. It appears as instabilities in the calculation of interstitial fluid pressures, especially near boundaries and between different materials. Accurate solutions can require impractical compromises between mesh size and time steps. This article investigates the constraints imposed by this problem on tissues representative of the intervertebral disc, subjected to moderate physiological rates of deformation. Two test cylindrical structures were found to require over 10(4) linear displacement-constant pressure elements to avoid serious oscillations in calculated fluid pressure. Fewer TaylorâHood (quadratic displacementâlinear pressure elements) were required, but with complementary increases in computational costs. The VermeerâVerruijt criterion for 1D mesh size provided guidelines for 3D mesh sizes for given time steps. Pressure instabilities may impose limitations on the use of the finite element method for simulating fluid transport behaviors of biological soft tissues at moderately rapid physiological loading rates
A symmetry group of a Thue-Morse quasicrystal
We present a method of coding general self-similar structures. In particular,
we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal,
i.e., of a nonperiodic ground state of a certain translation-invariant,
exponentially decaying interaction.Comment: 6 pages, Late
Accurate structure factors from pseudopotential methods
Highly accurate experimental structure factors of silicon are available in
the literature, and these provide the ideal test for any \emph{ab initio}
method for the construction of the all-electron charge density. In a recent
paper [J. R. Trail and D. M. Bird, Phys. Rev. B {\bf 60}, 7863 (1999)] a method
has been developed for obtaining an accurate all-electron charge density from a
first principles pseudopotential calculation by reconstructing the core region
of an atom of choice. Here this method is applied to bulk silicon, and
structure factors are derived and compared with experimental and Full-potential
Linear Augmented Plane Wave results (FLAPW). We also compare with the result of
assuming the core region is spherically symmetric, and with the result of
constructing a charge density from the pseudo-valence density + frozen core
electrons. Neither of these approximations provide accurate charge densities.
The aspherical reconstruction is found to be as accurate as FLAPW results, and
reproduces the residual error between the FLAPW and experimental results.Comment: 6 Pages, 3 figure
Geometry of jet spaces and integrable systems
An overview of some recent results on the geometry of partial differential
equations in application to integrable systems is given. Lagrangian and
Hamiltonian formalism both in the free case (on the space of infinite jets) and
with constraints (on a PDE) are discussed. Analogs of tangent and cotangent
bundles to a differential equation are introduced and the variational Schouten
bracket is defined. General theoretical constructions are illustrated by a
series of examples.Comment: 54 pages; v2-v6 : minor correction
Cooperative secretions facilitate host range expansion in bacteria
The majority of emergent human pathogens are zoonotic in origin, that is, they can transmit to humans from other animals. Understanding the factors underlying the evolution of pathogen host range is therefore of critical importance in protecting human health. There are two main evolutionary routes to generalism: organisms can tolerate multiple environments or they can modify their environments to forms to which they are adapted. Here we use a combination of theory and a phylogenetic comparative analysis of 191 pathogenic bacterial species to show that bacteria use cooperative secretions that modify their environment to extend their host range and infect multiple host species. Our results suggest that cooperative secretions are key determinants of host range in bacteria, and that monitoring for the acquisition of secreted proteins by horizontal gene transfer can help predict emerging zoonoses
Dissolution dominating calcification process in polar pteropods close to the point of aragonite undersaturation
Thecosome pteropods are abundant upper-ocean zooplankton that build aragonite shells. Ocean acidification results in the lowering of aragonite saturation levels in the surface layers, and several incubation studies have shown that rates of calcification in these organisms decrease as a result. This study provides a weight-specific net calcification rate function for thecosome pteropods that includes both rates of dissolution and calcification over a range of plausible future aragonite saturation states (Omega_Ar). We measured gross dissolution in the pteropod Limacina helicina antarctica in the Scotia Sea (Southern Ocean) by incubating living specimens across a range of aragonite saturation states for a maximum of 14 days. Specimens started dissolving almost immediately upon exposure to undersaturated conditions (Omega_Ar,0.8), losing 1.4% of shell mass per day. The observed rate of gross dissolution was different from that predicted by rate law kinetics of aragonite dissolution, in being higher at Var levels slightly above 1 and lower at Omega_Ar levels of between 1 and 0.8. This indicates that shell mass is affected by even transitional levels of saturation, but there is, nevertheless, some partial means of protection for shells when in undersaturated conditions. A function for gross dissolution against Var derived from the present observations was compared to a function for gross calcification derived by a different study, and showed that dissolution became the dominating process even at Omega_Ar levels close to 1, with net shell growth ceasing at an Omega_Ar of 1.03. Gross dissolution increasingly dominated net change in shell mass as saturation levels decreased below 1. As well as influencing their viability, such dissolution of pteropod shells in the surface layers will result in slower sinking velocities and decreased carbon and carbonate fluxes to the deep ocean
Sub-critical and Super-critical Regimes in Epidemic Models of Earthquake Aftershocks
We present an analytical solution and numerical tests of the epidemic-type
aftershock (ETAS) model for aftershocks, which describes foreshocks,
aftershocks and mainshocks on the same footing. The occurrence rate of
aftershocks triggered by a single mainshock decreases with the time from the
mainshock according to the modified Omori law K/(t+c)^p with p=1+theta. A
mainshock at time t=0 triggers aftershocks according to the local Omori law,
that in turn trigger their own aftershocks and so on. The effective branching
parameter n, defined as the mean aftershock number triggered per event,
controls the transition between a sub-critical regime n<1 to a super-critical
regime n>1. In the sub-critical regime, we recover and document the crossover
from an Omori exponent 1-theta for t<t* to 1+theta for t<t* found previously in
[Sornette and Sornette, 1999a] for a special case of the ETAS model. In the
super-critical regime n>1 and theta>0, we find a novel transition from an Omori
decay law with exponent 1-theta fot t<t* to an explosive exponential increase
of the seismicity rate fot t>t*. The case theta<0 yields an infinite n-value.
In this case, we find another characteristic time tau controlling the crossover
from an Omori law with exponent 1-theta for t<tau, similar to the local law, to
an exponential increase at large times. These results can rationalize many of
the stylized facts reported for aftershock and foreshock sequences, such as (i)
the suggestion that a small p-value may be a precursor of a large earthquake,
(ii) the relative seismic quiescence sometimes observed before large
aftershocks, (iii) the positive correlation between b and p-values, (iv) the
observation that great earthquakes are sometimes preceded by a decrease of
b-value and (v) the acceleration of the seismicity preceding great earthquakes.Comment: Latex document of 41 pages + 6 eps figures + 1 tabl
Eigenvalue Problem in Two Dimension for An Irregular Boundary
An analytical perturbative method is suggested for solving the Helmholtz
equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where
{\psi} vanishes on an irregular closed curve. We can thus find the energy
levels of a quantum mechanical particle confined in an infinitely deep
potential well in two dimensions having an irregular boundary or the vibration
frequencies of a membrane whose edge is an irregular closed curve. The method
is tested by calculating the energy levels for an elliptical and a
supercircular boundary and comparing with the results obtained numerically.
Further, the phenomenon of level crossing due to shape variation is also
discussed.Comment: 16 pages, 4 figures, v2 matches the journal versio
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